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http://mathhelpforum.com/calculus/132113-inequality.html	# Math Help - An Inequality? 1. ## An Inequality? (A Challenging One: Prove or disprove) Prove or disproe: For any positive integer n and $x \in [0,\pi], \quad \sum_{k=1}^n \frac{1}{k} \sin kx \geq 0$ 2. Originally Posted by elim Prove or disproe: For any positive integer n and $x \in [0,\pi], \quad \sum_{k=1}^n \frac{1}{k} \sin kx \geq 0$ Dear elim, You could show that this statement is correct using mathamatical induction. Can you give it a try? If you need more help please don't hesitate to reply back. 3. ## Some how I just could not see this clearly before Say n (>1) is the smallest integer such that for some minimal point $x_0 \in (0,\pi)$, $\sum_{k=1}^n \frac{1}{k} \sin kx_0 \leq 0$, then $\sin nx_0 < 0$ On the other hand the critical points for the function $f_n(x) = \sum_{k=1}^n \frac{1}{k}\sin kx$ are $x = \frac{(2m+1)\pi}{n+1}, \quad m=0,\cdots,\left[\frac{n-1}{2}\right]$ They are the points in $(0,\pi)$ such that $\sum_{k=1}^n \cos kx = \frac{\cos \frac{(n+1)x}{2} \sin \frac{nx}{2}}{\sin \frac{x}{2}} = 0$ (note that $\sin \frac{nx_0}{2} \neq 0$ by our finding above) But $\sin \frac{n(2m+1)\pi}{n+1} = \sin \left( 2m\pi+\frac{n-2m}{n+1}\right) = \sin \frac{n-2m}{n+1} > 0$ Thus we get a contradiction and we actually proved that $\forall n \in \mathbf{N}^+, \forall x\in (0,\pi) \left( \sum_{k=1}^n \frac{1}{k}\sin kx > 0\right)$ This is a bit stronger statement. Thanks Sudharaka for the direction. I thought this problem needs more advanced tech to solve. 4. Originally Posted by elim It seems that I still not be able to figure out the way of using induction. say n (>1) is the smallest integer such that for some $x_0 \in (0,\pi)$, we have $\sum_{k=1}^n \frac{1}{k} \sin kx \leq 0$, then what? I did get the critical points for the function $f_n(x) = \sum_{k=1}^n \frac{1}{k}\sin kx$. They are $x = \frac{(2m+1)\pi}{n+1}, \quad m=0,\cdots,\left[\frac{n-1}{2}\right]$ They are the points in $(0,\pi)$ such that $\sum_{k=1}^n \cos kx = \frac{\cos \frac{(n+1)x}{2} \sin \frac{nx}{2}}{\sin \frac{x}{2}} = 0$ Dear elim, We have to show that for any positive integer n and $ x \in [0,\pi], \quad \sum_{k=1}^n \frac{1}{k} \sin kx \geq 0$ When n=1, $\sum_{k=1}^1 \frac{1}{k} \sin kx =sinx\geq{0}~Since,~x \in [0,\pi]$ Therefore the expression is true for n=1 Suppose the expression is true for n=p where $p\in{Z^{+}}$ Then, $\sum_{k=1}^p \frac{1}{k} \sin kx\geq0$ Now, $\frac{1}{(p+1)} \sin (p+1)x\geq{0}~Since,~p+1>0~and~x\in[0,\pi]$ Therefore, $\sum_{k=1}^p \frac{1}{k} \sin kx+\frac{1}{(p+1)} \sin (p+1)x\geq{0}$ Hence, $\sum_{k=1}^{p+1} \frac{1}{k} \sin kx\geq0$ Therefore our the expression is true for $n=p+1~where~p\in{Z^+}$ Hence by mathamatical induction the expression is true for all $n\in{Z^+}$ Now, $\frac{1}{(p+1)} \sin (p+1)x\geq{0}~Since,~p+1>0~and~x\in[0,\pi]$ On the other hand, actually I did used math induction to prove the inequality is true for all positive integer n and all $x \in [0,\pi]$ by showing that no such an integer n>1 and $x_0 \in (0,\pi)$ to let $\sum_{k=1}^n \frac{1}{k} \sin kx_0 \leq 0$ happen assuming (**) $\sum_{k=1}^m \frac{1}{k} \sin kx_0 > 0$ for $1 \leq m < n, \quad x \in (0,\pi)$ which is true for m=1	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 33, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8913304805755615, "perplexity": 524.1795508573471}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438044271733.81/warc/CC-MAIN-20150728004431-00253-ip-10-236-191-2.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/41257/find-remaining-vertices-of-a-square-given-2	# Find remaining vertices of a square, given 2 I need a hint for this problem. Let the vertices of a square ABCD represent on the Argand diagram the complex numbers a,b,c, and d respectively. A,B,C,D are taken anti-clockwise in the order named. If $$a = 3 + i, b = 4 - 2i$$, find c and d. For a different problem, where square was at the origin, I used the idea that $$i(z_1)$$ is an anti-clockwise rotation and since it's a square etc. But here it's not at the orgin. Any help is much appreciated. Thanks. - You can make a translation so that one of the vertices goes to the origin, then make the inverse translation. - Got it, I did a translation of (3+i) and (4-2i) to get 2 points and then moved them back after rotation to get, C = (7-i) and D = 6 + 2i, which checks out. Thanks! – mathguy80 May 25 '11 at 13:43 Hint: $b$ to $c$ is a rotation through $\pi/2$ of $a$ to $b$. - Hint: You can find the side of the square from $\|b-a\|$. If you think of walking around the square anti-clockwise, at each corner you make a left turn of $\frac{\pi}{2}$ and go the same distance. - Haven't studied polar form of complex numbers yet, this and @Ben Bosisel idea seems more elegant one I have studied that! Until then that translation solution worked fine. Thanks. – mathguy80 May 25 '11 at 13:45 You don't need polar form, all you need to know is that when you multiply a complex number by $i$ you rotate it by 90 degrees, counterclockwise. – Gerry Myerson May 26 '11 at 0:29 A rotation in the complex plane around point $b$ with angle $\theta$ has the expression $z \mapsto b+(z-b)\cdot e^{i\theta}$, where $e^{i\theta}=\cos \theta+i\sin \theta$. - Thanks, need to study the trignometry form of complex numbers first! – mathguy80 May 25 '11 at 13:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8933342099189758, "perplexity": 432.1517840028877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860122501.61/warc/CC-MAIN-20160428161522-00049-ip-10-239-7-51.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/how-to-find-equipotential-surface-for-given-case.851041/	# How to find equipotential surface for given case? 1. Jan 6, 2016 ### Dexter Neutron Q:- Describe equipotential surface due to a uniform grid consisting of long equally spaced parallel charged wires in a plane. The answer given in my textbook is - Equipotential surface have shape which changes periodically. At far off distances it becomes parallel to the plane. Why the equipotential surface changes periodically here?Please Explain. Any help would be appreciated. 2. Jan 6, 2016 ### nuclear_chris I can answer the second question. At far off distances the grid should look like a uniformly charged plane. This results in the potential being equivalent to that of a uniformly charged plane. 3. Jan 6, 2016 ### DrStupid Because the charge distribution changes periodical (wire - no wire - wire - no wire - ...). Similar Discussions: How to find equipotential surface for given case?	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8693698644638062, "perplexity": 1862.8193581415849}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105086.81/warc/CC-MAIN-20170818175604-20170818195604-00426.warc.gz"}
http://medicalimaging.wikia.com/wiki/Image_reconstruction_in_diffuse_optical_imaging	# Image reconstruction in diffuse optical imaging 27pages on this wiki ## Linear image reconstructionEdit The forward problem, discussed above, involves calculating simulated data y (which may be CW, time-domain or frequency-domain data), given a forward operator F and knowledge of the sources q and internal optical properties x (which may include µa and µ's). The forward problem may therefore be formulated as: $y=F(x)$. (3) To reconstruct an image, it is necessary to solve the inverse problem, which is to calculate the internal optical properties x, given data y and sources q (Arridge 1999): $x=F^{-1}(y)$. (4) This is a non-linear problem but it can be linearised if the actual optical properties x are close to an initial estimate x0 and the measured data y is close to the simulated measurements y0. This is typically the case in difference imaging where measurements are taken before and after a small change in the optical properties. Then we can expand (3) about x0 in a Taylor series: $y=y_0 + F'(x_0)(x-x_0)+F''(x_0(x-x_0)^2+...$. (5) where and are the first and second-order Fréchet derivatives of F, respectively. The Fréchet derivative is a linear integral operator mapping functions in the image space to functions in the data space. In some cases, such as in section 3.3.1, the kernel of the integral operator is known in terms of the Green's functions. This approach was taken by Boas et al. (1994). More generally, the forward problem can be solved by a numeric technique by representing the Fréchet derivatives and by matrices J (the Jacobian) and H (the Hessian), respectively. Equation 5 can then be linearised by neglecting higher order terms and considering changes in the optical properties and data to give the linear problem (6): $\Delta y = \mathbf{J} \Delta x$. (6) Linearising the change in intensity in this way gives rise to the Born approximation; linearising the change in log intensity instead is the Rytov approximation and may lead to improved images by reducing the dynamic range of y. Either way, image reconstruction consists of the problem of inverting the matrix J, or some form of normalised J. This may be large, underdetermined and ill-posed but standard matrix inversion methods can be used. These techniques differ in the way in which the matrix inversion is regularised to suppress the effect of measurement noise and modelling errors. Perhaps the most common techniques are truncated singular value decomposition, Tikhonov regularisation, and the algebraic reconstruction technique (ART) (Gaudette et al. 2000). The Moore-Penrose inverse J-1=JT(J JT)-1 offers a more efficient inversion if J is underdetermined and leads naturally to a Tikhonov-type formulation (7) where I is the identity matrix and λ is a regularisation parameter. J itself is calculated from the forward model, most efficiently using the adjoint method of Arridge and Schweiger (1995). The linear inverse problem can then be expressed as: $\Delta x = \mathbf{J}^T (\mathbf{J J}^T + \lambda \mathbf{I})^{-1} \Delta y$. (7) ## Non-linear image reconstructionEdit If the inverse problem cannot be assumed to be that of reconstructing the difference between two similar states, but is instead a reconstruction from a single acquisition to obtain absolute values of the optical properties, the linear approximation cannot be justified and the full non-linear problem must be solved. This is commonly the case in breast imaging (Dehghani et al. 2003), and in static imaging of the brain (Bluestone et al. 2001, Hintz et al. 2001, Hebden et al. 2002). To solve the non-linear problem, we define an objective function ψ, which represents the difference between the measured data y and data which is simulated using the forward model F(x). If $\hat x$ is the distribution of optical parameters which minimises ψ, then it is also the model which best fits the data, and is therefore taken to be the image. However, because the problem is ill-posed, it must be regularised, and can be expressed as: $\psi = \left \Vert y - f(x)\right \Vert ^2 + \alpha \left \Vert \Pi \right \Vert ^2$, (8) where α is a regularisation parameter, and Π represents prior information. This may be very simple, for example Π = I, in which case (8) becomes an iterative solution of (7). However, it is increasingly common for Π to include anatomical and other information, see section 3.4.3. $\left \Vert . \right \Vert ^2$ represents the L2-norm and gives the least squares solution. Equation 8 can be extended to include the covariance of the data CP and the covariance of the image CQ as follows: $\psi = (y-f(x))^T C_P (y-f(x)) + \alpha (\Pi ^T C_Q \Pi)$. (9) This approach gives a weighted least squares solution which reduces the influence of noise and cross-talk both in the data and in the image. Measuring CP and CQ may not be straightforward. Equation 9 is a non-linear minimisation problem which is generally solved either by a Newton method such as the Levenberg-Marqardt algorithm, or by a gradient method such as conjugate gradients (Arridge 1999). ## UniquenessEdit No general uniqueness results exist for optical imaging, because of the range of different unknowns (µa, µ's, refractive index, coupling coefficients, anisotropy, geometry, etc.) and the range of different measurables (time-domain or frequency-domain measurements or CW measurements of intensity alone). Some useful results do exist, however, to illustrate situations which may not yield unique solutions (Isakov 1993). The first important uniqueness result directly relevant to the diffusion equation was derived by Arridge and Lionheart (1998) and developed further by Arridge (1999). They demonstrated that measurements of intensity alone cannot separate the effects of absorption and scatter. Furthermore, if the refractive index is also unknown, even frequency-domain or time-domain measurements are not sufficient for uniqueness, although Matcher (1999) showed that uniqueness may be restored if the underlying model is taken to be the P1 approximation. The specific case of optical mammography using a slab geometry was analysed by Romanov and He (2000), who showed that if full time-domain data are available then reflection measurements (where the sources and detectors are on the same side of the slab) can uniquely determine a piecewise continuous distribution of either µa or µ's if the other parameter is given, but transmission measurements can distinguish µa and µ's if both are unknown. In an interesting application of uniqueness theory, Corlu et al. (2003) used a uniqueness argument to determine which wavelengths gave the optimal separation between different chromophores in spectroscopic imaging, and to reconstruct directly for chromophore concentration. Arridge and Lionheart (1998) illustrated their uniqueness result with an example of two distributions of µa and µ's which gave indistinguishable intensity data on the boundary, and Hoenders (1997) described a whole class of solutions which could not be distinguished from one another. More specifically, Schweiger and Arridge (1999a) plotted the objective function of the inverse problem against µa and µ's for a range of different datatypes extracted from the TPSF and showed that, where certain combinations of datatypes gave a well-behaved minimum, measurements of intensity alone gave an objective function with an extended minimum at approximately µa µ's = constant, suggesting that µa and µ's could not be separated. However, as Hoenders (1997) points out, the existence of a solution to an inverse problem depends on more than just the uniqueness. It also depends on other issues including the quality of the data and the statistical behaviour of the problem. In particular, even if a problem is non-unique, it may be possible to distinguish between two identical data sets if appropriate prior information is available, whether it is used implicitly in the form of regularisation or normalisation of the Jacobian (Pei et al. 2001, Xu et al. 2002), or explicitly. This may enable the theoretical results outlined above to be reconciled with experimental work by Schmitz et al. (2002) and Pei et al. (2001), and by Jiang et al. (2002) and Xu et al. (2002) who have reconstructed images showing some separation between µa and µ's from intensity data alone. It remains to be seen how non-uniqueness affects reconstruction of clinical images, where the potential for a reconstruction to converge to an incorrect solution may be unacceptable. ## Use of prior informationEdit Advances in modelling and reconstruction techniques cannot overcome the fact that diffuse optical imaging is a non-unique, ill-posed, underdetermined problem and that this puts a limit on the image quality, particularly the spatial resolution, which can be achieved. One way to improve the quality of the image reconstruction is to make maximum use of prior information, which can be obtained from anatomical imaging techniques or by considering the physics and the physiology of the problem. This reduces the effect of the ill-posedness by improving the accuracy of the model, and makes the problem better determined by allowing the small number of measurements which are obtained to be used in a more effective way. For example, Ntziachristos et al. (2000) used an MR image of a breast to provide the location of a tumour a priori. Using this approach, the spatial resolution of the optical image effectively becomes that of the MR image. The reduction in quantitative accuracy due to the partial volume effect seen in optical images reconstructed without prior information does not occur, and truly quantitative images of the haemodynamic properties of the tumour can be obtained. The most straightforward way to include prior information into the image reconstruction is to use an anatomically realistic forward model (section 3.3.3). This increases the accuracy of the forward model so that it can represent the measurements more precisely, thereby improving the image reconstruction. Further improvements can be made by including information about the covariance of the data CP, and of the image CQ, as in (9). The diagonal of CP is simply the variance of each measurement, and gives an indication of the reliability of that measurement. Off-diagonal elements are the covariance between each pair of measurements and give an indication of the interdependence between measurements. Introducing CP into (9) transforms the fit between the data and the model into a basis where all measurements are independent. CQ contains information about the predicted smoothness of the image. Prior knowledge of the anatomy can also be incorporated into the inverse problem. In the example of a breast tumour given above, the change in optical properties is assumed to come from either a region of interest defined from anatomy (Ntziachristos et al. 2002) or be heavily biased towards that region (Brooksby et al. 2003, Li et al. 2003). The degradation in image quality due to uncertainties in the anatomical prior, and the best way to minimise this degradation, are as yet uncertain (Schweiger and Arridge 1999b). Including prior anatomical information has advantages for both linear and non-linear reconstruction (Boas et al. 2004a) Another approach is to express (8) as a statistical inverse problem in a Bayesian framework. Bayes theorem can be written as p(x\|y)p(y\|x)p(x) where p(x\|y) is the posterior probability of obtaining the image x given the data y, p(y\|x) is the likelihood of obtaining y given x (which is obtained by solving the forward problem), and p(x) is the prior density, which in these terms is simply an estimate, made before carrying out the experiment, of the most likely image. If we assume that the distribution of errors is Gaussian, then Bayes theorem takes the form $p(x\|y) \propto exp(-\left \Vert y - f(x)) \right \Vert ^2) exp(-\left \Vert \Pi \right \Vert^2)$. (10) where the likelihood $p(y\|x) \propto exp(- \left \Vert y - f(x) \right \Vert ^2)$ and the prior $p(y\|x) \propto exp(- \left \Vert \Pi \right \Vert ^2)$. The value of x which maximises (10) is the maximum a posteriori (MAP) estimate. Maximising (10) is equivalent to minimising its negative logarithm, which is (8), but can offer further approaches which deal with prior information and covariance estimates in a direct and intuitive manner (Kwee 1999, Kohlemainen 2001, Mosegaard and Sambridge 2002, Evans and Stark 2002, Oh et al. 2002). Recently, efforts have been made to incorporate Monte Carlo techniques into the inverse problem. Standard Monte Carlo techniques are too slow to be used for practical image reconstruction, although faster methods are available. One example is the Metropolis-Hastings algorithm which is an example of a Markov Chain Monte Carlo (MCMC) technique, in which individual photon steps are drawn from a biased random walk which is chosen to minimise the number of discarded photons (Mosegaard and Sambridge 2002). These techniques have been used as the basis of image reconstruction algorithms in EIT (Kaipio et al. 2000, West et al. 2004), partly because the Monte Carlo simulations form a probability density which can be interpreted as the Bayesian maximum a posteriori estimate, leading very naturally to a statistical expression of the inverse problem (Evans and Stark 2002). The approaches discussed above assume that the prior information, whether in terms of the data covariance or the image statistics, is governed by Gaussian statistics. This is not necessarily the case: a Poisson model for the data may be more appropriate if photon counting errors are significant, and assuming that the pixel values are distributed as Gaussian random variables forces the image to be homogeneously and isotropically smooth. The latter issue has been identified as a significant weakness and has been addressed in two ways. First, Kaipio et al. (1999) introduced an inhomogeneous, anisotropic image covariance term which allowed, for example, a change in optical properties in the brain to be correlated more closely with neighbouring pixels in the brain than with those in the skull. A second approach is to minimise the total variation, defined as the integral of the absolute gradient of the image, rather than the L2-norm (Borsic 2002). The L2-norm forces the image to be smooth, and is optimal if the optical properties are distributed as a Gaussian random field. If the distribution of optical properties is known to be piecewise constant, the L2-norm will smooth the image, whereas minimising total variation will reduce oscillations in the image but still allow boundaries to be sharp. Other non-Gaussian priors may be considered. ## Methods that exploit symmetryEdit Some improvements to speed and robustness of the inverse problem can be obtained for systems that possess symmetry. Examples are rotational symmetry in a cylinder or sphere, or translational symmetry in a slab. It is easiest to develop this idea for the analytical version of the linear inversion kernels based on Green's functions. Green's functions are the kernels of the inverse solver for a PDE, and when the domain possesses symmetry, the PDE may often be solved by a separation of variables technique, which implies that the inversion kernels can be expressed as the product of functions in the separated variables. In the work of Markel and Schotland (2001), the slab geometry gives rise to a product of transverse plane waves and one-dimensional integral equations in the perpendicular direction. It is this decoupling of transverse propagating waves, and perpendicular scalar waves that allows faster inversion of a set of one dimensional integral equations, rather than one coupled 3D integral equation. The solution of these linear equations builds up a solution in the basis of the transverse component, which can then be transformed into image space by a fast transform method. Similar methods apply in the cylindrical and spherical geometries where the transverse components are Fourier and spherical harmonic waves respectively. Furthermore the case where only part of the data is sampled can be included by convolution with a masking function. Finally Markel et al. (2003) considered extension to the nonlinear case by applying an iterative method, linearised around the symmetric case. As well as the analytical case, a discrete implementation such as FEM can also be developed. This approach was developed by Metherall et al. (1996) for EIT, and applied to optical tomography by Hampel and Freyer (1998). ## Solving for coupling coefficientsEdit The measured data in optical tomography depends not only on the properties of the object under examination, but also on the characteristics of the source and detector fibres, instabilities in the source power and detector efficiency, and on the efficiency with which light is coupled into and out of the medium. A well-designed calibration procedure can minimise the effects of the optical fibres and the instrumentation (Hillman et al. 2000, McBride et al. 2001) but characterising the coupling between the fibres and the tissue can be more difficult. One approach which has been successfully adopted, particularly with regard to optical topography, is difference imaging, in which images are reconstructed using the difference between measurements recorded at two states in such a way that coupling effects cancel (Section 4.1). Alternatively, images can be reconstructed using temporal data only (Hebden et al. 2002), although this may reduce the ability to separate the absorption and scattering properties. These approaches are not always appropriate, however, and so techniques have been developed to correct for coupling effects during image reconstruction. Schmitz et al. (2000) and Boas et al. (2001) introduced a method for solving for the unknown coupling coefficients as part of the image reconstruction problem. Each source and detector was associated with a complex coupling term. A measurement Mij between source i and detector j was modelled as Mij = SiDjmij where Si and Dj are the source and detector scaling factors and mij is the ideal measurement, depending only on the internal optical properties of the object. The reconstruction problem is then posed in terms of minimising the difference between the measured data and SiDjmij, where Si and Dj are solved for in the inverse problem. Images could be reconstructed successfully if up to 80% uncertainty in amplitude was added to simulated data (Boas et al. 2001). The technique has since been extended to allow small errors in optode position to be corrected (Culver et al. 2003, Stott et al. 2003) and has been used for dynamic breast imaging (Intes et al. 2003). Vilhunen et al. (2004) have implemented a related method which can be used when the sources and detectors have rotational symmetry. Oh et al. (2002) used a Bayesian formulation to reconstruct 3D images non-linearly by treating the unknown source-detector coupling coefficients as unwanted nuisance parameters. ## Use of dynamic informationEdit Image reconstruction is generally applied to the spatial domain but additional information can be obtained by examining the temporal evolution of the signal. Physiological signals from the heart rate, ventilation and blood vessels are time-dependent. If the image acquisition time is short compared to the physiological fluctuations, an image time series can be obtained, which can then be processed to give dynamic images showing parameters such as the covariance or the amplitude and phase at a particular frequency of physiological interest (Barbour et al. 2001, Graber et al. 2002). A different situation occurs when the image acquisition rate is not short compared to the physiological changes. In this case, the optical properties change during the acquisition of each image and so a straightforward static image reconstruction would not be valid. The Kalman filter technique has been used to model the image space as a state whose properties evolve with time in a known manner, the details of which are supplied as prior information. It may be expressed as: $x_{t+1} = \mathbf{K} x_t + n_t$, (11) where xt is the image x at time t, K is the state transition matrix and nt is additive noise at time t. In the simplest case, K is the identity matrix, in which case the update is a random walk. This approach helps to condition the inverse problem by using the current state, and knowledge of how it evolves, to constrain the possible solutions for the next state. It can be used to image events which occur on a shorter timescale than the image acquisition by calculating an updated image using the Kalman filter when only a limited subset of data has been acquired. This is ideally suited for systems which acquire data from sources sequentially but the detectors simultaneously, in which case an updated state can be estimated when each source is activated. This approach has been successfully applied to both simulated data (Kohlemainen et al. 2003) and real data (Prince et al. 2003) in optical tomography. Eppstein et al. (2001, 2002) have developed an image reconstruction technique for fluorescence tomography which uses the Kalman filter to update each iteration of a static non-linear reconstruction procedure. ## Recovery of object shapeEdit Another approach to optimising the use of data in optical tomography is not to reconstruct for a large number of image pixels, which leads to a highly underdetermined problem, but instead to reconstruct for the boundaries and properties of internal regions which can be assumed to have piecewise constant optical properties. One method to solve for the boundaries of internal regions is to formulate a minimisation problem where the image parameters are the Fourier coefficients of the smooth region boundaries. This was first solved assuming the optical properties of the regions are known a priori (Kohlemainen et al. 1999), and later extended to solve simultaneously for both the region boundaries and the optical properties (Kohlemainen et al. 2000a). A further refinement was to use an initial static image reconstruction to identify the number of regions and their approximate locations before finally solving for the boundaries and optical properties of the regions (Kohlemainen et al. 2000b). In 3D, it may be more appropriate to assume that regions of interest are ellipsoidal and to solve for the parameters of the ellipse rather than Fourier components (Kilmer et al. 2003). A promising technique for the inverse shape estimation problem is provided by representing internal regions using a level set function. This is a function which is 1 inside the regions and 0 elsewhere. This method assumes that the optical properties of the background and regions of interest are known, but does not place constraints on the number of regions or their shapes. 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Opt. 41(25) 5427-5437.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8051351308822632, "perplexity": 1877.1437964108575}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188773.10/warc/CC-MAIN-20170322212948-00073-ip-10-233-31-227.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/1631414/confirmation-of-interest-and-financial-mathematics-problem	# Confirmation of Interest and financial mathematics problem I'm having trouble with two questions 1. A fund earns a nominal rate of interest of 6% compounded every two years. Calculate the amount that must be contributed now to have 1000 at the end of six years. My thoughts: Since it is compounded every two years, then the interest is divided by $.5$, so I get: $Present Value = 10001/(1+20.06)^3$ = $711.78$ Is that correct? • Is this an actuarial science (exam FM) question? – Clarinetist Jan 29 '16 at 2:22 • @Clarinetist No, a textbook question I'm trying to figure out – user270494 Jan 29 '16 at 2:25 • Could you give more context? What textbook is this? Is this in a finance class, math class, or actuarial science class? – Clarinetist Jan 29 '16 at 2:26 • Mathematical Finance class – user270494 Jan 29 '16 at 2:28 This answer assumes that you know actuarial notation. Judging by your previous questions, you do. We have $$i^{(1/2)} = 0.06$$ (why?), and thus the effective rate is $$\dfrac{i^{(1/2)}}{1/2} = 0.12\text{.}$$ This is the two-year effective rate. Six years is equivalent to three two-year periods. The equivalent discount factor is $$v = \dfrac{1}{1.12}$$ so the present value of $1000$ from three two-year periods is $$1000v^{3} = \dfrac{1000}{(1.12)^3}$$ which matches your answer.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8004144430160522, "perplexity": 437.4335753183475}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347415315.43/warc/CC-MAIN-20200601071242-20200601101242-00373.warc.gz"}
https://www.astro.gla.ac.uk/users/eduard/cesra/?paged=20	### Source regions of the type II radio burst observed during a CME–CME interaction on 2013 May 22 by P. Mäkelä et al.* 2016-12-06 Occasionally the Sun ejects a pair of magnetized plasma clouds, called coronal mass ejections (CMEs), roughly into the same propagation direction in closely timed sequence. If the second CME is faster than the first one, the CMEs could either just slip through each other or they could collide and interact, when the following CME catches up the preceding one. The possibility of the CME-CME interaction was first suggested by Gopalswamy […] ### Simultaneous Submillimeter and Hard X-Ray Intermittent Processes during Flares by Guillermo Giménez de Castro et al.* 2016-11-29 Intermittency is a disruptive characteristic of a process, which can be associated, in many cases, with a sudden energy release. Intermittency is a key characteristic of flares that should become evident in the flux time evolution at many different wavelengths. We investigate the similarities and differences of the intermittency during a solar flare in bremsstrahlung hard X-rays and synchrotron+free-free submillimeter emission. For this we chose a particular event that presents […] ### Energetic electrons generated during solar flares by Gottfried Mann 2016-11-22 The Sun is an active star. It manifests not only in everybody’s well-known Sun spots with the related 11-year cycle. This activity manifests not only as the well-known sun spot phenomenon with a related 11-year cycle, but also in flares, coronal mass ejections (CMEs), and solar energetic particle (SEP) events. Thus, the Sun is a giant particle accelerator. Basically, a flare occurs as a local enhancement of the Sun’s emission of […] ### Solar Type III Radio Bursts: Directivity Characteristics by G. Thejappa and R. J. MacDowall 2016-11-15 Type III radio bursts are a group of fast drifting radio emissions associated with solar flares [see also previous CESRA highlights on type III bursts here and here]. These radio emissions are believed to be excited at the fundamental and second harmonic of the electron plasma frequency, by the electron beam excited Langmuir waves through a mechanism called the plasma mechanism. This mechanism attributes the dipole and quadrupole beam patterns for the fundamental and harmonic emissions. […] ### Multiwavelength study of 20 jets that emanate from the periphery of active regions by Sargam M. Mulay et al.* 2016-11-01 Solar jets are transient phenomena observed in the solar atmosphere. They appear as sharp-edged, impulsive, and collimated flows of plasma that move outwards with a bright spot at the footpoint, which forms an ‘inverted-Y’ topology of magnetic field lines. They are observed throughout the atmosphere i.e. in the photosphere (Hα, Ca II K surges), chromosphere (UV), transition region (EUV) and corona (X-ray). Jets can occur in different environments such as coronal holes (CHs; Young & […] ### Decameter type III bursts with changing frequency drift-rate signs by V. Melnik et al.* 2016-10-18 We discuss properties of type III bursts that change the sign of their drift rate from negative to positive and vice versa. Moreover, these bursts may change the sign of their drift rates more than once. These particular type III bursts were observed simultaneously by the radio telescopes UTR-2, URAN-2, and NDA in the frequency range 8-41 MHz. The negative drift rates of these bursts are similar to those of […] ### Propagation of Coronal Mass Ejections: Aerodynamic Drag by Nishtha Sachdeva and Prasad Subramanian 2016-10-04 Coronal Mass Ejections (CMEs) are hot, massive blobs of plasma and magnetic fields that erupt from the Sun, and are sometimes Earth-directed. Depending on their speed and mass these transients can strongly effect the space weather, causing geomagnetic storms and damage to space bound technologies. It is therefore imperative to understand the CME kinematics and propagation dynamics. Close to the Sun, CMEs are governed by Lorentz Forces, while they are […] ### Diagnostics of the acceleration modulation process based on quasi-periodic variations of flare emission by Kupriyanova et al.* 2016-09-27 Quasi-periodic pulsations (QPPs) with the characteristic time scales from a few seconds up to tens of minutes are frequently seen in the time profiles of solar and stellar flare emission (Nakariakov et al., 2016 ). Among all the possibilities of QPPs explanation, two reasons are discussed more actively: magnetohydrodynamic (MHD) oscillations in plasma waveguides and periodic reconnection. 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https://www.arxiv-vanity.com/papers/1712.08821/	# On the moduli space of nonnegatively curved metrics on Milnor spheres Anand Dessai The author acknowledges support by SNF grant 200021E-172469 and the DFG priority program SPP 2026. ###### Abstract Let be a Milnor sphere or, more generally, the total space of a linear -bundle over with . We show that the moduli space of metrics of nonnegative sectional curvature on has infinitely many path components. The same holds true for the moduli space of metrics of positive Ricci curvature on . ## 1 Introduction For a closed smooth manifold , let be the set of Riemannian metrics on , equipped with the -topology, and let denote the subspace of metrics of nonnegative sectional curvature. The diffeomorphism group acts on by pulling back metrics. The moduli space is the quotient space, equipped with the quotient topology. Corresponding notations will be used for other curvature bounds. In this note we consider total spaces of linear -bundles over . These manifolds are very interesting, both from a topological and a geometric point of view. Milnor showed that among them there are manifolds which are homeomorphic to but not diffeomorphic to with its standard smooth structure [Mi56]. Following modern terminology a homotopy sphere which is the total space of a linear -bundle over will be called Milnor sphere. Grove and Ziller showed that every Milnor sphere admits a metric of nonnegative sectional curvature and asked whether its moduli space has infinitely many components (see [GZ00], Thm. A and Problem 5.6]). In this note we show that this question has an affirmative answer. ###### Main Theorem. For every Milnor sphere the moduli space of nonnegatively curved metrics has infinitely many path components. The main ingredients of the proof are the construction of metrics of nonnegative sectional curvature on certain cohomogeneity one manifolds due to Grove and Ziller, the diffeomorphism classification of Milnor spheres and an idea of Gromov and Lawson for distinguishing components of metrics of positive scalar curvature on compact spin manifolds. The proof is in a sense rather simple as it does not use more involved techniques like the APS-index theorem or the Kreck-Stolz invariant (which could also be used to give slightly different proofs for the results of this paper). At the end of this note we explain how the proof can be adjusted to show the analogous statement for the total space of every linear -bundle over with . Prior to the work of Grove and Ziller only one exotic -dimensional sphere was known to admit a metric of nonnegative sectional curvature, the so-called Gromoll-Meyer sphere [GM74]. Among the exotic -dimensional spheres can be described as Milnor spheres (see [Mi59, EK62]) and, hence, each of these carries metrics of nonnegative sectional curvature by [GZ00]. Recently, Goette, Kerin and Shankar [GKS17] have put out a preprint in which the authors give a construction of metrics of nonnegative sectional curvature on exotic -dimensional spheres including the remaining four cases. We don’t know whether the Main Theorem extends to the latter ones. The proof of the Main Theorem also shows that for every Milnor sphere the moduli space of metrics of positive Ricci curvature has infinitely many connected components. This was known before. In fact, Wraith [Wr11] has shown by different methods that for every homotopy sphere of dimension , , which bounds a parallelizable manifold the moduli space of metrics of positive Ricci curvature has infinitely many connected components (the corresponding statement for positive scalar curvature is classical, see [GL83], pp. 131–132). The study of the space of metrics under curvature bounds and its moduli space (or its observer moduli space) has been an active research area in the last years. In this note our focus is on Milnor spheres and on total spaces of linear -bundles over . For a survey of some of the many other recent developments and references we refer to [TW15]. This note is structured as follows. In the next section we review the Grove-Ziller construction [GZ00] of nonnegatively curved metrics on principal -bundles, principal -bundles and associated sphere bundles over . This leads to infinitely many metrics on every Milnor sphere which are simultaneously of nonnegative sectional and positive scalar curvature and which can be extended to nonnegatively curved metrics on the associated disk bundles. The section also contains a review of the classification of Milnor spheres up to orientation preserving diffeomorphism via the -invariant of Eells and Kuiper. In the following section we use an idea of Gromov and Lawson [GL83] to show that these metrics belong to pairwise distinct path components of the moduli space . The argument also shows that these metrics evolve under the Ricci flow to metrics which belong to pairwise distinct components of . In the last section we discuss the modifications needed to extend the result to the total space of a linear -bundle over with . Acknowledgement. Some of the results of this note were obtained and announced during the Mini-Workshop Spaces and Moduli Spaces of Riemannian Metrics at the Mathematical Research Institute of Oberwolfach in January 2017 (see [De17], p. 15). It is my pleasure to thank the institute, the organizers and the participants for the stimulating working environment. I also like to thank David González-Álvaro and Michael Wiemeler for helpful comments on an earlier version of this note. ## 2 Nonnegative curvature on Milnor spheres Let be a closed connected smooth manifold with finite fundamental group on which a compact Lie group acts smoothly with cohomogeneity one. Then the quotient space is an interval and can be described as the union of disk bundles over the two nonprincipal orbits glued together along their boundaries. In the case where the nonprincipal orbits are of codimension two Grove and Ziller constructed an invariant metric of nonnegative sectional curvature on each disk bundle such that the metric is a product metric near the boundary and the restriction to the boundary is isometric to the normal homogeneous space (with respect to a fixed bi-invariant metric on ). Here denotes the principal isotropy subgroup of the -action. By gluing the two disk bundles isometrically and equivariantly along the boundary the cohomogeneity one manifold inherits a -invariant metric of nonnegative sectional curvature (see [GZ00] for details on the construction of these metrics and for basic facts about cohomogeneity one manifolds). The construction involves various choices. In particular, it involves a rotationally symmetric nonnegatively curved metric on the -disk which is of product form on a neighborhood of the boundary (see [GZ00], Remark 2.7) and which can be chosen to be of positive curvature on its complement. In the same paper Grove and Ziller showed (among many other things) that the total space of any principal -bundle admits a cohomogeneity one action by with finite principal isotropy subgroup, one dimensional nonprincipal isotropy subgroups and singular orbits of codimension two. Here acts freely on the fibers via the principal action and covers the well-known cohomogeneity one action of on induced from the action of by conjugation on the space of symmetric real -matrices with vanishing trace (see [GZ00], §3, for details). We fix an invariant Grove-Ziller metric of nonnegative sectional curvature on . Note that acts freely and isometrically on and that the quotient is the total space of the associated principal -bundle over . Let denote the 7-dimensional manifold obtained from the Riemannian product of and the round sphere of radius one by dividing out the diagonal action of (where the latter acts via the standard 4-dimensional -representation on ). The submersion metric on has nonnegative sectional curvature by the Gray-O’Neill formula [ON66, Gr67]. It follows from the Grove-Ziller construction that every horizontal space of the Riemannian submersion contains a plane of positive sectional curvature. Hence, again by the Gray-O’Neill formula the submersion metric on has positive scalar curvature everywhere. Note that can also be described in terms of the principal -bundle as the sphere bundle of the associated oriented -dimensional vector bundle . Sphere bundles of this kind will be called linear -bundles over . The isomorphism classes of principal -bundles over or, equivalently, of oriented -dimensional vector bundles are classified by . Up to isomorphism is determined by its Euler class and its first Pontrjagin class and any pair with can occur. If is a generator of then the total space of the sphere bundle of is a homotopy sphere and is, in fact, homeomorphic to as first shown by Milnor using Morse theory [Mi56]. We fix a generator of and denote by the principal -bundle with Euler class equal to and first Pontrjagin class equal to , an odd integer. Let be the associated vector bundle and let and be the total space of the associated unit sphere and disk bundle, respectively. Recall that the Milnor sphere comes with a Grove-Ziller metric of nonnegative sectional curvature. We equip the closed -dimensional disk with a rotationally symmetric metric of nonnegative sectional curvature which is of product form near the boundary and which extends the round metric on the unit sphere. Now can be identified with the quotient and, hence, inherits a submersion metric of nonnegative sectional curvature by the Gray-O’Neill formula [ON66, Gr67]. For further reference we summarize the discussion in the following (see [GZ00]) ###### Theorem 2.1. Every Milnor sphere admits a metric which is simultaneously of nonnegative sectional curvature and positive scalar curvature and which extends to a metric of nonnegative sectional curvature on the disk bundle which is of product form near the boundary. Next we review the classification of Milnor spheres up to orientation preserving diffeomorphism via the -invariant of Eells and Kuiper. We fix an orientation of by requiring that the square of a generator of evaluated on the fundamental class is positive and orient accordingly. Note that is not parallelizable since its signature is equal to one. Note also that and have unique spin structures and that is the spin boundary of . Milnor showed that among the -dimensional manifolds , odd, some are not diffeomorphic to the standard sphere, thereby exhibiting the first examples of exotic 7-dimensional spheres [Mi56]. To distinguish from the standard sphere Milnor first used an invariant which is based on Hirzebruch’s signature theorem and later introduced an invariant defined in terms of a parallelizable manifold with boundary [Mi59]. Subsequently, Eells and Kuiper modified this approach and defined an invariant using spin manifolds, the signature and the -genus. All these invariants depend only on the oriented diffeomorphism type of , are additive with respect to connected sum operation and change sign if one changes the orientation. By the work of Milnor [Mi59] and the -cobordism theorem of Smale [Sm62] the set of diffeomorphism classes of oriented closed smooth manifolds homeomorphic to form a cyclic group of order with respect to connected sum operation. Moreover, the elements of this group are determined by their -invariant as well as by their -invariant. In the following we will consider the Eells-Kuiper invariant computed in terms of . Let and be oriented as before. For odd the invariant can be computed from to be (see [EK62], Eq. (11)) μ(Mk)≡(p21[Wk]−4⋅sign(Wk))/(27⋅7)≡~h/28modZ, where . Here is defined by first taking a preimage of under and then evaluating on the fundamental class of . The set of -invariants of , odd, can be computed to be equal to {r/28∈Q/Z∣r=0,1,3,6,7,8,10,13,14,15,17,20,21,22,24,27}. Note that any of these elements in can be obtained from infinitely many distinct odd integers . For further reference we summarize the discussion in the following (see [EK62]) ###### Theorem 2.2. The distinct closed oriented smooth manifolds homeomorphic to can be distinguished by their -invariant. Among them are diffeomorphic to a Milnor sphere and any Milnor sphere is orientation preserving diffeomorphic to for infinitely many odd integers . If with then is congruent to for some . Therefore the -invariants of the Milnor spheres (up to orientation) belong to {±r/28∈Q/Z∣r=0,1,3,4,6,7,8,10,11,13,14}. Hence, ignoring orientation, of the distinct closed smooth manifolds homeomorphic to are diffeomorphic to a Milnor sphere. We fix a Milnor sphere for some and choose an infinite family of Milnor spheres , such that each is orientation preserving diffeomorphic to and such that all are . For example one can choose the family , (since in the Milnor spheres and are orientation preserving diffeomorphic for all ). Let be the Grove-Ziller metric on considered before (see Thm. 2.1) and let denote the corresponding element in the moduli space obtained by pulling back via a diffeomorphism . Note that does not depend on the choice of the diffeomorphism and that we may choose the diffeomorphism to be orientation preserving. Also note that can be represented by a metric on which is simultaneously of nonnegative sectional and positive scalar curvature. In the next section we will show that the elements , , belong to different path components of . ## 3 Proof of the Main Theorem We fix a Milnor sphere and consider the elements , , from the last section. We will show below that these elements belong to pairwise distinct path components of . The proof is by contradiction, the idea may be summarized as follows: Consider and , . In the first step we show that a path in connecting and can be lifted and deformed to a path in the space of metrics of positive scalar curvature such that represents , represents and such that is constant near the end points. An elegant way to obtain the deformation from nonnegative sectional curvature to positive scalar curvature (and even positive Ricci curvature) uses work of Böhm and Wilking on the Ricci flow [BW07]. After stretching the interval we may assume that the metric on , , defined by the metrics , , has positive scalar curvature. In the second step we use a variant of the following elementary version of the relative index of Gromov and Lawson for compact spin manifolds (see [GL83]): Suppose and are two metrics of positive scalar curvature on a closed spin manifold of dimension . Suppose in addition that extends to a metric of nonnegative scalar curvature on a spin manifold with spin boundary and that is of product form near the boundary. Then the -genus of the closed -dimensional spin manifold vanishes if and belong to the same component of . We apply this to our Milnor manifold and to the disk bundles considered in Theorem 2.1. In the last step we compute the -genus of the corresponding closed -dimensional spin manifold to be non-zero, thereby arriving at the desired contradiction. Here are the details. ###### Theorem 3.1 (Main Theorem). For , , the classes and belong to different path components of . Proof: Let us assume to the contrary that and belong to the same path component. We fix orientation preserving diffeomorphisms for . Recall from the end of the last section that the element is represented by the metric . Now consider a path connecting and in . By Ebin’s slice theorem [Eb70] the path can be lifted to a path , , in which starts in . Hence, the Riemannian manifolds and are isometric by the orientation preserving diffeomorphism . The metric lies in the same -orbit of . If is obtained as the pullback of by an orientation reversing diffeomorphism of we will replace by its pullback under an orientation reversing diffeomorphism of . So in the following we can assume that and are isometric by an orientation preserving diffeomorphism for . As shown by Böhm and Wilking [BW07] the metric for fixed evolves under the Ricci flow instantly to a metric on of positive Ricci curvature. Hence, the path , , evolves under this flow immediately to a path in the space of metrics of positive Ricci curvature. Concatenation of the evolved path and the trajectories of the end points of then yields a path connecting the end points and . Note that is a path in the space of metrics of positive scalar curvature, , since the metric has positive scalar curvature at the end points of the interval and positive Ricci curvature for points in the interior. After reparametrization and a small perturbation leaving the endpoints fixed we may assume that is a smooth path which is constant close to the end points and . The metrics , , define a metric on which is fiberwise of positive scalar curvature. After stretching the interval sufficiently (i.e. after increasing the distance between different fibers sufficiently) one obtains a metric on , , which has positive scalar curvature (see [GL80], Lemma 3). Let denote the corresponding path in . Next we will use the elementary relative index invariant of Gromov and Lawson for compact spin manfolds (see [GL83], pp. 130–131) to derive a contradiction. We fix orientation preserving isometries for . Recall from Theorem 2.1 that extends to a metric, say , of nonnegative sectional curvature on which is of product form near the boundary. By gluing , and via and together we obtain a closed -dimensional Riemannian spin manifold X=Wk0∪φ0(M×[0,a])∪φ1(−Wk1) which is of nonnegative scalar curvature and has positive scalar curvature somewhere. By Lichnerowicz’ theorem [Li63] the Dirac operator of is invertible and its index vanishes. Note that is diffeomorphic to and glued together via an orientation preserving diffeomorphism. Now the signature of , , does not depend on the choice of the gluing map and is equal to the sum of the signatures of and (see for example [Mi56, Mi59], [EK62], p. 98). Hence, sign(X)=sign(Wk0)−sign(Wk1)=1−1=0. The vanishing of the -genus and the signature of forces the Pontrjagin number to vanish as well (here denotes the fundamental class of ). The Pontrjagin number can be computed in terms of the disk bundles . More precisely, one has ⟨p1(X)2,[X]⟩=p21[Wk0]−p21[Wk1], where, as before, is defined by first taking a preimage of under and then evaluating its square on the fundamental class of , (see [EK62]). The tangent bundle of the disk bundle is stably isomorphic to , where denotes the projection . Hence, , where is the fixed generator. This gives a contradiction since is non-zero. ###### Remark 3.2. The proof shows that the metrics obtained by applying the Ricci flow to lifts of , , represent pairwise distinct components of the moduli space of metrics of positive Ricci curvature (and as well). Hence, for any Milnor sphere the moduli space has infinitely many connected components (cp. [Wr11]). ###### Remark 3.3. In the recent preprint [GKS17] Goette, Kerin and Shankar give a construction of metrics of nonnegative sectional curvature on exotic -dimensional spheres including the non-Milnor spheres. The latter can be described as -orbi-bundles but do not come with any obvious null-cobordism with nice geometric properties. This makes it difficult to treat their moduli spaces with the methods above. ## 4 Moduli spaces for linear S3-bundles over S4 In this section we discuss the modifications needed to extend the Main Theorem to the total space of a linear -bundle over with . The latter condition is fulfilled precisely when the Euler class of the underlying -dimensional vector bundle is non-trivial. In the case where the Euler class is trivial the first Pontrjagin class of takes values in and determines the vector bundle up to isomorphism. So the argument for the Milnor spheres does not apply to this situation. However, in the case where the Euler class is non-trivial the proof of the Main Theorem does extend with minor modifications. ###### Theorem 4.1. Let be the total space of a linear -bundle over with . Then the moduli space of metrics of nonnegative sectional curvature on has infinitely many path components. The same holds true for the moduli space of metrics of positive Ricci curvature on . Proof: Recall that the isomorphism classes of principal -bundles over , or, equivalently, the isomorphism classes of oriented -dimensional real vector bundles are determined by the Euler class and the first Pontrjagin class and any pair with can occur. We restrict to bundles with non-trivial Euler class since . Let be a fixed generator. Then the Euler class of can be written as for some integer . Note that changes sign if we change the orientation of the bundle. Since the moduli space of the associated sphere bundle does not depend on the orientation we may assume from now on that . For , , let denote the oriented -dimensional real vector bundle over with (and ). Let and denote the associated sphere and disk bundles, respectively. The integral cohomology of is concentrated in degree , with and . As before we orient and such that . Now the manifold in the theorem is diffeomorphic to for some and some with . So our aim is to show that and have infinitely many path components. As in the proof of the Main Theorem we want to find for infinitely many of nonnegative sectional curvature such that each is diffeomorphic to as an oriented manifold and such that the induced metrics on represent pairwise distinct path components of the moduli space. The classification of total spaces of linear -bundles over up to homeomorphism was considered by Tamura already shortly after Milnor exhibited the first examples of exotic -dimensional spheres. In particular, it is shown in [Ta58], Thm. 3.1, that and are homeomorphic if . From smoothing theory one knows that the obstructions for being -homeomorphic or diffeomorphic belong to finite sets since is an Eilenberg-MacLane space (see [KS77]) and is -connected with cyclic of order (see [Mi59, Sm62, KM63, Ce68, Wa70, Br72, HM74]). This implies that the family contains an infinite subfamily of pairwise diffeomorphic manifolds. In order to obtain more precise information we will use the classification of total spaces of linear -bundles over with vanishing rational cohomology in degree . These spaces (and other two-connected -manifolds) have been classified to a large extent by Wilkens who applied handlebody theory building on techniques of Wall. Crowley and Escher completed the classification using the topological Eells-Kuiper invariant of Kreck and Stolz (see [CE03] and references therein). From this classification one knows that and are diffeomorphic as oriented manifolds if (see [CE03], Cor. 1.6, where corresponds to in our notation). Now the proof follows the line of argument for the Main Theorem: For , fixed, one considers the family , . Each is diffeomorphic to by an orientation preserving diffeomorphism and comes with a Grove-Ziller metric of nonnegative sectional curvature with the properties described in Theorem 2.1. By computing the relative index invariant one finds that the metrics induce elements in the moduli space which belong to pairwise distinct path components. Moreover, the corresponding metrics on evolve under the Ricci flow to metrics which represent pairwise distinct components of .	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9793575406074524, "perplexity": 333.4641114299344}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662552994.41/warc/CC-MAIN-20220523011006-20220523041006-00176.warc.gz"}
https://brilliant.org/problems/do-you-know-matrices/	# Do you Know Matrices ? Algebra Level pending $$\displaystyle A$$ is the $$\displaystyle n \times n$$ matrix whose elements are all $$\displaystyle '1'$$ and$$\displaystyle B$$ is the $$\displaystyle n \times n$$ matrix whose diagonal elements are all $$\displaystyle 'n'$$ and other elements are $$\displaystyle 'n-r'$$ . Then $$\displaystyle A^{2}$$ is a scalar multiple of A and hence , $$\displaystyle ( B-rI)[B - (n^{2}-nr+R)I]$$ is ? Here $$\displaystyle I$$ is the Identity matrix. ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8459809422492981, "perplexity": 124.46140671887038}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423320.19/warc/CC-MAIN-20170720181829-20170720201829-00586.warc.gz"}
https://edurev.in/course/quiz/attempt/-1_Chemistry-Test-2-Equilibrium-I-And-II--Thermodynam/0bd54ab0-38ea-46c0-97b1-8289ad68ae45	Courses # Chemistry Test 2 - Equilibrium I And II, Thermodynamics, Hydrogen, Hydrocarbons, Redox, States Of Matter, P-Block ## 45 Questions MCQ Test NEET Mock Test Series & Past Year Papers \| Chemistry Test 2 - Equilibrium I And II, Thermodynamics, Hydrogen, Hydrocarbons, Redox, States Of Matter, P-Block Description This mock test of Chemistry Test 2 - Equilibrium I And II, Thermodynamics, Hydrogen, Hydrocarbons, Redox, States Of Matter, P-Block for NEET helps you for every NEET entrance exam. This contains 45 Multiple Choice Questions for NEET Chemistry Test 2 - Equilibrium I And II, Thermodynamics, Hydrogen, Hydrocarbons, Redox, States Of Matter, P-Block (mcq) to study with solutions a complete question bank. The solved questions answers in this Chemistry Test 2 - Equilibrium I And II, Thermodynamics, Hydrogen, Hydrocarbons, Redox, States Of Matter, P-Block quiz give you a good mix of easy questions and tough questions. NEET students definitely take this Chemistry Test 2 - Equilibrium I And II, Thermodynamics, Hydrogen, Hydrocarbons, Redox, States Of Matter, P-Block exercise for a better result in the exam. You can find other Chemistry Test 2 - Equilibrium I And II, Thermodynamics, Hydrogen, Hydrocarbons, Redox, States Of Matter, P-Block extra questions, long questions & short questions for NEET on EduRev as well by searching above. QUESTION: 1 ### Which of the following alkenes will react fastest with under catalytic hydrogenation conditions? Solution: The reactivity order towards H2 is cis > iso > trans i.e in option A the alkene is cis. QUESTION: 2 ### The heat of hydrogenation of 1-hexene is 126 . When a second double bond is introduced in the molecule, the heat of hydrogenation of the resulting compound is 230 . The resulting compound (diene) is Solution: 1,3 -hexadiene is a conjugated diene, hence it is more stable than the first compound. The heat of hydrogenation decreases as the stability of the molecule increases. The stability of 13 hexadiene is more than that of a compound which contain two double bonds. QUESTION: 3 ### Heat of hydrogenation of benzene is 51 kcal/mol and its resonance energy is 36 kcal/mol. Then the heats of hydrogenation of cyclohexadiene and cyclohexene per mole respectively are Solution: Total energy to break 3 bond in benzene is 87 [51+36]. So to break one bond i.e. in cyclohexaene is 87/3= 29kcal/mol. And to break 2 bond i.e.in cyclohexadiene is 292= 58 kcal/mole. QUESTION: 4 gas is liberated at cathode and anode both by electrolysis of the following aq. solution except in : Solution: At the cathode (C), water is reduced to hydroxide and hydrogen gas. The net process is the electrolysis of an aqueous solution of NaCl into industrially Electrolysis of aqueous sodium chloride yields hydrogen and chlorine, with aqueous sodium. Chlorine gas bubbles out of the melt above the anode. QUESTION: 5 “10 volume” means : Solution: H2O2 is the special concentration terms.10 volume of H2Omeans that 1ml of H2O2 gives 10 ml of O2. For example, if it was mentioned 30 volume of H2O2, then its means that 1ml of H2O2 gives 30ml of O2. QUESTION: 6 (heavy water) and differ in following except Solution: Chemical properties won't change in case of isotopes. Therefore answer is D. QUESTION: 7 When 0.532 g of benzene (B.P. C) is burnt in a constant volume system with an excess of oxygen, 22.3 KJ of heat is given out. for the combustion process is given by : Solution: QUESTION: 8 The work done by the system in a cyclic process involving one mole of an ideal monoatomic gas is 50 KJ/cycle, The heat absorbed by the system per cycle is Solution: According to the first law of thermodynamics, ∆Q=∆U+∆W and for a cyclic process, change in internal energy(∆U) is zero. Hence ∆Q=∆W where ∆Q is the heat absorbed and ∆W is the work done. Therefore heat absorbed is 50 kJ QUESTION: 9 Which of the following is not correct ? Solution: It should be equal to T, not (-T) QUESTION: 10 The heat released when & HCl neutralise is : Solution: QUESTION: 11 The heat of formation of is 380 kcals/mole and that of is 195 kcals/mole. The heat (in kcals/mole) of the thermite reaction is Solution: QUESTION: 12 Enthalpy of Rhombic sulphur of C is Solution: Rhombic sulphur is the standard state of sulphur or in its pure state.And in standard state it is taken as zero. QUESTION: 13 Which of the following is not a state function ? Solution: A state function is the property of the system whose value depends only on the initial and final state of the system and is independent of the path.Heat (q) and work (W) are not state functions being path dependent. QUESTION: 14 Which of the following reaction is favored by increase of temperature ? Solution: In options a,c and d, we can say that energy is also a part of the products which is indicated by the + sign between the product and the energy but in case of reaction B, you can see that with the products energy is taken inside that is it is a negative sign so when we transfer that part of the equation to the product side, we can see that in the product there is a sign of plus along with energy which means that energy is given along with the products to obtain the reactants .you can conclude that option B is the correct answer because it is an endothermic reaction QUESTION: 15 The for the decomposition of (if its degree of dissociation under one atomic pressure is 90%) is Solution: QUESTION: 16 The pH of 10-7 M HCl is Solution: Without calculation one can also say that the answer is a because acid has a ph value less than 7. QUESTION: 17 1c.c. of 0.1N HCl is added to 99 c.c. aqueous solution of sodium chloride.The pH of the resulting solution will be Solution: Normality volume = (0.1) (0.001) Normality volume = 0.0001 L Volume of solution = Volume of NaCl + Volume of HCL Volume of solution = 1 + 0.001 Volume of solution = 1.001 L Since NaCl is a salt and is neutral so it does not effect pH of a solution. Now, Normality of HCL in a resulting solution = 0.0001 / 1.001 Normality of HCL in a resulting solution = 0.0001 N So, pH = - log [H⁺] pH = - log (0.0001) pH = 4 which shows that the pH of the resulting solution is 4 QUESTION: 18 0.2 molar aqueous solution of is found to be 90% ionized at 298 K.The pH of the solution is Solution: Lets calculate the pOH first, Since 1 mol Ba(OH)2 gives 2 moles of OH- 0.2 moles will give 0.4 mol OH- However its 90% ionised and hence [OH-] = 0.36 M So pOH = -log [0.36] = 0.443 pH = 14-0.443 = 13.55 QUESTION: 19 If the maximum concentration of in water is 0.01M at 298K, its maximum concentration in 0.1M NaCl will be Solution: Concentrations of the ions: The dissociation reaction for PbCl2 in water is write as, PbCl2→Pb2+(aq)+2Cl−(aq) The maximum concentration of PbCl2 in water is 0.01 M We can find concentration of the ions using the stoichiometry from the above reaction. The concentration of Pb²⁺ ion is 0.01 M and concentration of Cl⁻ ion is 2×0.01=0.02M. Solubility product: The solubility product of PbCl2 can be written as, KSP=[Pb2+][Cl]−2 Let us insert in the concentrations of Pb and Cl. KSP=(0.01)(0.02) Ksp =4.0×10−6 Concentration of Pb2+ using common ion effect: WhenPbCl2 is dissolved in 1MNaCl, there is a common ion Cl−. This decreases the solubility of PbCl2 due to the common ion effect. The concentration of Cl− in 0.1MNaCl is 0.1. Let us plug in this value to find the new concentration of Pb2+ ion. Ksp=[Pb2+][Cl]2 4×10−6=[Pb2+](0.1)2 [Pb2+]=0.014×10−6 [Pb2+]=0.0004M=4×10−4 M QUESTION: 20 When equal volumes of the following solution are mixed, precipitation of AgCl will occur only with Solution: AgCl is precipitated only when [Ag+][Cl-] > Ksp On mixing equal volumes of two solutions, concentration becomes halved. QUESTION: 21 Ammonium hydrogen sulphide is contained in a closed vessel at 313 K when total pressure at equilibrium is found to be 0.8 atm. The value of for the reaction Solution: Ammonium hydrogen sulphide is contained in a closed vessel at 313K when total pressure at equilibrium is found to be 0.8 atm. NH4HS(s)⇌NH3(g)+H2S(g) PNH3=PH2S=P Total pressure PNH3+PH2S=P+P=2P But total pressure is 0.8 atm. 2P=0.8 P=0.4 atm PNH3=PH2S=P=0.4 atm The value of the equilibrium constant for the reaction,is Kp=PNH3×PH2S Kp=0.4×0.4 Kp=0.16 QUESTION: 22 Which of the following hydrocarbons has the highest melting point? Solution: Melting point order is para > ortho > meta on basis of symmetry . So option b is correct. QUESTION: 23 Propylene is passed through conc. and the prodcut thus obtained on hydrolysis with boiling water gives Solution: QUESTION: 24 Reaction of ethene with in gives Solution: When alkenes react with Br2 in presence of CCl4 it gives vicinnyl dibromides (1 2 dibromide ) QUESTION: 25 The major product obtained when isobutane is treated with chlorine in the presence of light is Solution: The major product is tert butyl chloride as firstly isobutylchloride is formed but then hydride shift takes place due to which chlorine shift to more stable tertiary carbocation and hence the product is tert butyl chloride. QUESTION: 26 acts as Solution: SO2 can act as both oxidizing as well as reducing agent since it has +4 oxidation state which is exactly between its highest oxidation state +6 and lowest oxidation state +2 , Thus it can change its oxidation number either from +4 to-2(reduction) and +4 to+6 (oxidation) QUESTION: 27 Which one of the following leads to a redox reaction Solution: Redox reactions are characterized by the transfer of electrons between chemical species, most often with one species undergoing oxidation while another species undergoes reduction. 2KI+Cl2⟶2KCl +I2 It is an example of a redox reaction. Hence, option C is correct. QUESTION: 28 The compound contains atoms X,Y,Z. The oxidation number of X is 2, Y is 5 and Z is –2, a possible formula of the compound is Solution: The net charge on the compound should be zero. Or the sum of oxidation states = 0. Given: oxidation number of X is +2, Y is +5 and Z is -2. In XYZ2: 2+5+2×(−2)=+3 In Y2(XZ3)2: 2×5+2×(2+3×(−2))=+2 In X3(YZ4)2: 3×2+2×(5+4×(−2))=0 In X3(YZ4)2: 3×2+2×(5+4×(−2))=0 In X3(Y4Z)2: 3×2+2×(4×5−2)=42 A compound contains atoms X, Y and Z . The oxidation number of X is +2 , Y is +5 and Z is -2. The possible formula of the compound is X3(YZ4)2. QUESTION: 29 Which of the following statements is correct regarding the structures of the molecules Solution: QUESTION: 30 How many allotropic forms of carbon are there ? Solution: Carbon has three well known allotropes which are graphite, daimond and buck minster fullerene. QUESTION: 31 Graphite has a layered structure. The distance between the layers is Solution: Since the layers are only weakly attracted to each other, they can easily slide past one another. This is why graphite is used in pencil lead. The distance between layers is 335 pm. Carbon atoms in diamond are covalently bonded and are arranged in a three-dimensional tetrahedral structure. QUESTION: 32 Coal gas is a mixture of Solution: Coal gas contains a variety of calorific gases including hydrogen, carbon monoxide, methane, ethylene and volatile hydrocarbons together with small quantities of non-calorific gases such as carbon dioxide and nitrogen. QUESTION: 33 Formic acid (HCOOH) on heating with concentrated gives Solution: H2SO4 + HCOOH → CO + H2SO4•H2O. Sulfuric acid react with formic acid to produce carbon monoxide and hydrate sulfuric acid. QUESTION: 34 Which of the following gases is used for the purification of nickel ? Solution: CO is the gas used for purification of nickel and this process is called Mond process. QUESTION: 35 The most stable oxidation state of boron is Solution: The elments of the boron family adopts oxidation states +3 or +1. The +3 oxidation states are favorable except for the heavier elements, such as Tl, which prefer the +1 oxidation state due to its stability; this is known as the inert pair effect. QUESTION: 36 Which of the following products are formed when boron is fused with NaOH ? Solution: Boron reacts with fused sodium hydroxide to form sodium borate and hydrogen. B + 6NaOH →→ 2Na3BO3 + 3H2 QUESTION: 37 When borax is dissolved in water, Solution: QUESTION: 38 reacts with to produce Solution: B2H6 + 6Cl2 → 2BCl3 + 6HCl Diborane react with chlorine to produce boron(III) chloride and hydrogen chloride... QUESTION: 39 In the Serepeck process, the bauxite ore is treated with Solution: Serpeck process is a method of purification of Bauxite ore containing silica (SiO2) as the main impurity. The reaction involved are- Al2O3.2H2O+3C+N2⟶2AlN+3CO+2H2O 2AlN+6H2O⟶2NH3+Al(OH)3 QUESTION: 40 Anhydrous produces fumes in the air because of Solution: Anhydrous aluminium chloride is hydrolised partly with the moisture in the atmosphere to give HCl gas. This HCl gets combine to moisture in air giving white fumes. So white fumes appear by hydrolysis. QUESTION: 41 Alzeimer’s diseases is caused by the depostion of Solution: QUESTION: 42 A real gas obeying van der Waals equation will resemble an ideal gas if Solution: According to van der Waals equation for 1 mole of a real gas (P+(a/V2))(V−b)=RT If a and b are small, a/V2 and b can be neglected as compared to P and V and the equation reduces to PV=RT. Hence, a real gas will resemble an ideal gas when constants a and b are small. QUESTION: 43 In which of the following pairs do the molecules (gaseous) have the same root-mean-square speed Solution: RMS speed = √(3RT/M) where, T is temperature, R is universal gas constant and M is molecular mass of gas Here molecular mass is same for N2 (14x2=28) and CO (12+16=28) so rms speed will also b same for them as rest all is constant QUESTION: 44 According to the kinetic theory of gases, between two successive collisions, an ideal-gas molecule travels Solution: According to kinetic theory the gas molecules are in a state of constant rapid motion in all possible directions colloiding in a random manner with one another and with the walls of the container and between two successive collisions molecules travel in a straight line path but show haphazard motion due to collisions. QUESTION: 45 The pressure at the base of a column of liquid of length l and held at an angle to the vertical is Solution: Pressure at the base of a liquid column =hdg Here h=height of the column d=density of liquid g=acceleration due to gravity since the column is inclined at an angle θ the vertical height=l cosθ Pressure=lcosθd*g =ldgcosθ Here P=d=density so option (d) is correct =pgl cosθ	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8512499928474426, "perplexity": 3171.1826610899416}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107894175.55/warc/CC-MAIN-20201027111346-20201027141346-00007.warc.gz"}
http://tex.stackexchange.com/questions/87893/half-of-a-document-in-pdflatex-half-in-xelatex/87896	# Half of a document in pdfLaTeX, half in XeLaTeX As far as I know, I cannot use `microtype` in XeLaTeX, and cannot use `fontspec` in pdfLaTeX. I am rendering Chinese symbols only on one page, and I need this line: `\newfontfamily{\J}[Scale=0.85]{Osaka}` to render the symbols properly. I want to use `microtype` and `fontspec` at the same time; is it possible to tell latex to switch into "pdfLaTeX" mode to render the first half of the document, and then switch back into XeLaTeX to render the other half? - Have you tried LuaLaTeX? `fontspec` and parts of `microtype` work with it. – doncherry Dec 21 '12 at 17:51 I haven't tried LuaLaTeX. I'll give it a shot now. Is there a fundamental syntax change between pdflatex and LuaLaTeX? – alexy13 Dec 21 '12 at 18:03 Or use `pdfpages` to insert the second half (pre-generated with `xelatex`) into the main document generated with `pdflatex`. – JLDiaz Dec 21 '12 at 18:19 @alexy13 See my answer. Basically: No, the syntax is the same; the packages typically loaded are a mixture of pdfLaTeX and XeLaTeX packages. – doncherry Dec 21 '12 at 19:10 If the Chinese part is restricted to one page it would probably be best to compile it with XeTeX and include it using `pdfpages`. – Alan Munn Dec 21 '12 at 20:04 I recommend LuaLaTeX, since it supports `fontspec` and parts of `microtype`: protrusion and expansion; whereas kerning, spacing, and tracking are not (yet?) supported, cf. the `microtype` documentation. For a little background on LuaLaTeX, see: On your actual question: If you need to switch compilers mid-page, I’m not sure there’s any option other than manually puzzling the pieces together, e.g. with `pdfpages`, as JLDiaz suggested. Also note that there is a beta version of `microtype` that supports XeLaTeX, but I don’t know which features; see e.g. neic.dk - XeLaTeX with microtype on TeX-Live 2012. - Yes, I have experiment with LuaLaTeX and recommend too. It is relative simple to port pdfLaTeX (if you code your doc in UTF-8) and XeLaTeX to LuaTeX. – lazyboy Dec 21 '12 at 19:48 This is one of the cases where LuaTeX and XeTeX are not equivalent. The standard package for dealing with Asian languages `xecjk` makes extensive use of XeTeX-specific functionality, especially `xetexinterchartoks`, which doesn't exist in LuaTeX. See Is there a LuaTeX analogue to xetexinterchartoks. – Alan Munn Dec 21 '12 at 20:03 @AlanMunn: Thanks, good to know! I've only ever used Latin (and a wee bit of Greek) script with either compiler. – doncherry Dec 21 '12 at 20:17 You can't change the engine midway through a document. Although much of the time LuaTeX can be used as a drop-in alternative to XeTeX, in the case of Chinese it's not usually true. If you are using `xecjk` to compile the Chinese portion of the text, then it will not work to compile the document with LuaTeX, since `xecjk` makes extensive use of functionality that is specific to XeTeX, specifically `xeinterchartoks`. See: for more details on this. In this situation it would be best to compile the Chinese portion of the document separately using XeTeX and then include the page(s) into the main document using the `pdfpages` package. For some more useful information about mixed script documents involving `xecjk` see especially Leo Liu's answer to: -	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9284981489181519, "perplexity": 2700.8414339578135}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246659483.51/warc/CC-MAIN-20150417045739-00130-ip-10-235-10-82.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/227246-how-solve-differential-equation-initial-conditions.html	Thread: How to solve a a differential equation with initial conditions? 1. How to solve a a differential equation with initial conditions? I'm having trouble with this: Is my answer right? If not, which one works? :/ 2. Re: How to solve a a differential equation with initial conditions? This is correct. How did you solve it? All you need to do is integrate the original expression once. Solve for the constant using the initial condition of $y'$ Then integrate again and solve for the constant using the initial condition of $y$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9949265718460083, "perplexity": 290.1218787965773}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189031.88/warc/CC-MAIN-20170322212949-00141-ip-10-233-31-227.ec2.internal.warc.gz"}
https://www.zora.uzh.ch/id/eprint/140512/	# Context-based retrieval of functional modules in protein-protein interaction networks Dobay, Maria Pamela; Stertz, Silke; Delorenzi, Mauro (2018). Context-based retrieval of functional modules in protein-protein interaction networks. Briefings in Bioinformatics, 19(5):995-1007. ## Abstract Various techniques have been developed for identifying the most probable interactants of a protein under a given biological context. In this article, we dissect the effects of the choice of the protein–protein interaction network (PPI) and the manipulation of PPI settings on the network neighborhood of the influenza A virus (IAV) network, as well as hits in genome-wide small interfering RNA screen results for IAV host factors. We investigate the potential of context filtering, which uses text mining evidence linked to PPI edges, as a complement to the edge confidence scores typically provided in PPIs for filtering, for obtaining more biologically relevant network neighborhoods. Here, we estimate the maximum performance of context filtering to isolate a Kyoto Encyclopedia of Genes and Genomes (KEGG) network Ki from a union of KEGG networks and its network neighborhood. The work gives insights on the use of human PPIs in network neighborhood approaches for functional inference. ## Abstract Various techniques have been developed for identifying the most probable interactants of a protein under a given biological context. In this article, we dissect the effects of the choice of the protein–protein interaction network (PPI) and the manipulation of PPI settings on the network neighborhood of the influenza A virus (IAV) network, as well as hits in genome-wide small interfering RNA screen results for IAV host factors. We investigate the potential of context filtering, which uses text mining evidence linked to PPI edges, as a complement to the edge confidence scores typically provided in PPIs for filtering, for obtaining more biologically relevant network neighborhoods. Here, we estimate the maximum performance of context filtering to isolate a Kyoto Encyclopedia of Genes and Genomes (KEGG) network Ki from a union of KEGG networks and its network neighborhood. The work gives insights on the use of human PPIs in network neighborhood approaches for functional inference. ## Statistics ### Citations Dimensions.ai Metrics 3 citations in Web of Science® 2 citations in Scopus®	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8135569095611572, "perplexity": 3957.7517860357434}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370515113.54/warc/CC-MAIN-20200403154746-20200403184746-00039.warc.gz"}
https://www.rdocumentation.org/packages/utils/versions/3.5.1/topics/file.edit	# file.edit 0th Percentile ##### Edit One or More Files Edit one or more files in a text editor. Keywords utilities ##### Usage file.edit(…, title = file, editor = getOption("editor"), fileEncoding = "") ##### Arguments one or more character vectors containing the names of the files to be displayed. These will be tilde-expanded: see path.expand. title the title to use in the editor; defaults to the filename. editor the text editor to be used. See ‘Details’. fileEncoding the encoding to assume for the file: the default is to assume the native encoding. See the ‘Encoding’ section of the help for file. ##### Details The behaviour of this function is very system dependent. Currently files can be opened only one at a time on Unix; on Windows, the internal editor allows multiple files to be opened, but has a limit of 50 simultaneous edit windows. The title argument is used for the window caption in Windows, and is currently ignored on other platforms. Any error in re-encoding the files to the native encoding will cause the function to fail. The default for editor is system-dependent. On Windows it defaults to "internal", the script editor, and in the macOS GUI the document editor is used whatever the value of editor. On Unix the default is set from the environment variables EDITOR or VISUAL if either is set, otherwise vi is used. UTF-8-encoded paths not valid in the current locale can be used. files, file.show, edit, fix, library(utils) # NOT RUN { # open two R scripts for editing file.edit("script1.R", "script2.R") # }	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9150789380073547, "perplexity": 4390.163841515371}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823320.11/warc/CC-MAIN-20181210080704-20181210102204-00417.warc.gz"}
http://eprints.pascal-network.org/archive/00002048/	Learnability of Probabilistic Automata via Oracles Omri Guttman, S V N Vishwanathan and Bob Williamson In: Algorithmic Learning Theory, 2005, 08 - 11 Oct 2005, Singapore. ## Abstract Efficient learnability using the state merging algorithm is known for a subclass of probabilistic automata termed $\mu$-distinguishable. In this paper, we prove that state merging algorithms can be extended to efficiently learn a larger class of automata. In particular, we show learnability of a subclass which we call $\mu_{2}$-distinguishable. Using an analog of the Myhill-Nerode theorem for probabilistic automata, we analyze $\mu$-distinguishability and generalize it to $\mu_{p}$-distinguishability. By combining new results from property testing with the state merging algorithm we obtain KL-PAC learnability of the new automata class. PDF - Requires Adobe Acrobat Reader or other PDF viewer. EPrint Type: Conference or Workshop Item (Oral) Project Keyword UNSPECIFIED Computational, Information-Theoretic Learning with StatisticsLearning/Statistics & OptimisationTheory & Algorithms 2048 S V N Vishwanathan 16 January 2006	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.860744059085846, "perplexity": 3446.094019100106}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131299054.80/warc/CC-MAIN-20150323172139-00044-ip-10-168-14-71.ec2.internal.warc.gz"}
https://mathtuition88.com/2016/07/12/excision-property-in-measure-theory/	# Excision property of measurable sets (Proof) If $A$ is a measurable set of finite outer measure that is contained in $B$, then $\displaystyle m^(B\setminus A)=m^(B)-m^(A).$ Proof: By the measurability of $A$, \begin{aligned} m^(B)&=m^(B\cap A)+m^(B\cap A^c)\\ &=m^(A)+m^(B\setminus A). \end{aligned} Since $m^*(A)<\infty$, we have the result.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 6, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9940465688705444, "perplexity": 1415.6614843140603}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257731.70/warc/CC-MAIN-20190524184553-20190524210553-00214.warc.gz"}
https://en.m.wikibooks.org/wiki/Practical_Electronics/Series_RL	# Practical Electronics/Series RL ## Series RCEdit Electric circuit of two components R and L connected in series ## Circuit analysisEdit ### Circuit's ImpedanceEdit In Rectangular coordinate • ${\displaystyle Z=Z_{R}+Z_{L}}$ ${\displaystyle Z=R+\omega L={\frac {1}{R}}(1+j\omega T)}$ ${\displaystyle T={\frac {L}{R}}}$ In Polar coordinate • ${\displaystyle Z=Z_{R}+Z_{L}}$ ${\displaystyle Z=R\angle 0+\omega L\angle 90=\|Z\|\angle \theta ={\sqrt {R^{2}+(\omega L)^{2}}}\angle Tan^{-}1\omega {\frac {L}{R}}}$ ${\displaystyle Tan\theta =\omega {\frac {L}{R}}=2\pi f{\frac {L}{R}}={\frac {t}{2\pi {\frac {L}{R}}}}}$ The value of ${\displaystyle \theta ,\omega ,f}$ depend on the value of R and L . Therefore when the value of R or L changed the value of Phase angle difference between Current and Voltage , Frequency , and Angular of Frequency also change ${\displaystyle \omega ={\frac {R}{L}}Tan\theta }$ ${\displaystyle f={\frac {1}{2\pi }}{\frac {R}{L}}Tan\theta }$ ${\displaystyle t=2\pi {\frac {L}{R}}{\frac {1}{Tan\theta }}}$ ### Circuit's ResponseEdit Natural Response of the cicuit can be obtained by setting the differential equation of the circuit to zero ${\displaystyle C{\frac {dV}{dt}}+{\frac {V}{R}}=0}$ ${\displaystyle {\frac {dV}{dt}}=-{\frac {1}{RC}}V}$ ${\displaystyle \int {\frac {dV}{V}}=-{\frac {1}{RC}}\int dt}$ ${\displaystyle LnV=-({\frac {1}{RC}})t+e^{c}}$ ${\displaystyle V=Ae^{-}({\frac {1}{RC}})t}$ ${\displaystyle V=Ae^{-}({\frac {t}{T}})}$ ${\displaystyle V=e^{c}=IR}$ ${\displaystyle T={\frac {L}{R}}}$ The natural reponse of the circuit is an exponential decrease ## SummaryEdit Circuit Series RL Configuration Impedance ${\displaystyle Z=Z_{R}+Z_{L}=R+j\omega L={\frac {1}{R}}(1+j\omega T)}$ ${\displaystyle T={\frac {L}{R}}}$ Diferenial Equation ${\displaystyle C{\frac {dV}{dt}}+{\frac {V}{R}}=0}$ Root of the equation ${\displaystyle V=Ae^{(}-{\frac {t}{T}})}$ ${\displaystyle Z\angle \theta }$ ${\displaystyle {\sqrt {R^{2}+(\omega L)^{2}}}\angle Tan^{-}1\omega {\frac {L}{C}}}$ Phase Angle Difference between Voltage and Current ${\displaystyle Tan\theta =\omega {\frac {L}{R}}}$ ${\displaystyle \omega }$ ${\displaystyle \omega ={\frac {1}{Tan\theta }}{\frac {L}{R}}}$ ${\displaystyle f}$ ${\displaystyle \omega ={\frac {Tan\theta }{2\pi }}{\frac {L}{R}}}$ ${\displaystyle t}$ ${\displaystyle t={\frac {2\pi }{Tan\theta }}{\frac {R}{L}}}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 31, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9210867881774902, "perplexity": 2616.601659631122}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464054915149.6/warc/CC-MAIN-20160524015515-00148-ip-10-185-217-139.ec2.internal.warc.gz"}
https://tohoku.pure.elsevier.com/en/publications/a-semidefinite-programming-approach-to-a-cross-intersection-probl	# A semidefinite programming approach to a cross-intersection problem with measures Sho Suda, Hajime Tanaka, Norihide Tokushige Research output: Contribution to journalArticlepeer-review 2 Citations (Scopus) ## Abstract We present a semidefinite programming approach to bound the measures of cross-independent pairs in a bipartite graph. This can be viewed as a far-reaching extension of Hoffman’s ratio bound on the independence number of a graph. As an application, we solve a problem on the maximum measures of cross-intersecting families of subsets with two different product measures, which is a generalized measure version of the Erdős–Ko–Rado theorem for cross-intersecting families with different uniformities. Original language English 113-130 18 Mathematical Programming 166 1-2 https://doi.org/10.1007/s10107-016-1106-3 Published - 2017 Nov 1 ## Keywords • Cross-intersecting families • Intersection theorem • Measure • Semidefinite programming	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8901844024658203, "perplexity": 2834.7662712527226}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988753.97/warc/CC-MAIN-20210506114045-20210506144045-00335.warc.gz"}
http://mathoverflow.net/questions/46044/information-criteria-for-ridge-regression/46053	Information criteria for ridge regression Hi -- is there any analogue or adjustment of, say, Schwartz Bayesian (or other) information criterion that would be applicable to model selection in ridge regression with a given ridge parameter $\eta$, i.e. $\hat{\beta}_\eta = (X'X+\eta I)^{-1}X'Y$? Thanks!! - The ridge estimator corresponds to the posterior mean under a Normal linear regression model with a conjugate Normal-inverse-gamma prior on the regression coefficients: $\beta \mid \sigma^2, \lambda \sim \mbox{N}(0, \lambda^{-1}\sigma^2 \mbox{I})$ and $\sigma^2 \sim \mbox{IG}(a,b)$ for known hyperparameters $a$ and $b$. One may additionally put a prior distribution over $\lambda$. If you consider a discrete number of possible values for $\lambda$ then one may compute posterior probabilities for each of these values or compute Bayes factors to compare different values. Thanks! Do I understand it right that in your notation $\lambda$ is the ridge parameter ($\eta$ in the question)? I am a bit confused as to how to use these priors to construct some analogue of AIC or BIC, I am actually concerned with selecting a subset of $X$'s to use. It does look like cross-validation is the way to go, as you suggest. – laxxy Nov 15 2010 at 2:25 OK, I misread the question -- I thought you were asking about using BIC or AIC to select the value of the ridge parameter. For doing subset selection of the predictors I'd look into the lasso estimator rather than ridge regression. There is a whole ton of literature on penalized regression, of which ridge is one flavor and lasso is another. The Elements of Statistical Learning is probably the classical text for these things. – R Hahn Nov 15 2010 at 3:01 Thanks for the references! The situation is this: there is a model that generates data (Y and X). Under some parameter values, some X's may happen to be very close, plus some small noise, likely due to simulation error. Full-sample OLS tries to use this noise, and produces crazy estimates. However, it is almost always the best model in cross-validation. Setting the ridge parameter first and then doing cross-val. to pick components of X seems to work better, but I am not sure if there is a good way to do that. Have to look closer at lasso, first impression so far is that it overfits somewhat. – laxxy Nov 16 2010 at 14:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8981029391288757, "perplexity": 282.98983330225695}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696384213/warc/CC-MAIN-20130516092624-00049-ip-10-60-113-184.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/12944/what-is-product-of-delta-function-with-itself/12988	# what is product of delta function with itself? what is the product of delta function with itself ? what is the dot product with itself ? - In the standard setup, neither of these is defined. See en.wikipedia.org/wiki/Distribution_(mathematics) . – Qiaochu Yuan Dec 3 '10 at 20:56 product with itself / square mathoverflow.net/questions/48067/… – Pratik Deoghare Dec 3 '10 at 21:03 @crasic: Why doesn't it seem believable? Convolution with $\delta(x-x_1)$ is translation by $x_1$. Now for any function $f(x)$, compare $(f(x)\delta(x-x_1))\delta(x-x_2)$ with $f(x)(\delta(x-x_1)\delta(x-x_2))$. – Rahul Dec 3 '10 at 21:23 @J. M.: To me special functions is something completely different - but I can not put my finger on exactly what special functions is. – AD. Dec 4 '10 at 7:49 @Rajesh D: Could you give more context? I have made an edit to explain that you cannot define $\delta^2$ meaningfully. – Jonas Teuwen Dec 4 '10 at 15:46 A distribution is actually a linear functional on the space of compactly supported infinitely differentiable functions (the so called "test functions"). A function $f$ is compactly supported if $\overline{\{x : f(x) \neq 0\}}$ is compact (the overline denotes the closure). The $\delta$-distribution is a linear functional such that for all $\phi \in C_c^\infty(\mathbb{R}^n)$ we have that $\langle \delta, \phi \rangle = \phi(0)$. When you want to compute the product of distributions the problem is that you don't have a property which you would really like to have, that is associativity. So for distributions $\alpha$, $\beta$ and $\gamma$ we usually have that $(\alpha \cdot \beta) \cdot \gamma \neq \alpha \cdot (\beta \cdot \gamma)$. Wikipedia gives an example. However this does not really turn out to be a problem in applications. What we do have is convolution. When we want to do convolution we prefer a smaller class of distributions (for example because on the smaller class the Fourier transform of a distribution in this class is again a distribution in this class). This actually has a rougher class of test-functions, as test functions here we take the Schwartz functions, that are the smooth functions of which the function itself and all its derivatives are rapidly decreasing. $f$ is said to be rapidly decreasing if there are constants $M_n$ such that $\|f(x)\| \leq M_N \|x\|^{-N}$ as $x \to \infty$ for $N = 1,2,3,\ldots$. To begin defining the convolution we first define what the convolution of Schwartz-function is with a tempered distribution. Let $f$ be our tempered distribution, then we can show that the following definition actually makes sense: $$\langle \phi * f, \psi \rangle := \langle f, \tilde{\phi} * \psi \rangle$$ where $\tilde{\phi}(x) = \phi(-x)$. Note that the RHS is well-defined. Convolution is a nice thing, we can see that if we start with a tempered distribution and convolute it with a test function, the result will be smooth. Now, $L_1 * L_2$ is the unique distribution $L$ with the property that $L * \phi = L_1 * (L_2 * \phi)$. We can show that this is commutative. Fine, now note that $\delta * \phi(x) = \phi(x - y)\|_{y = 0} = \phi(x)$. So we see that $\delta * \delta = \delta$. If you want me to comment on the dot product of distributions, you first would have to explain what you mean with that. So far for this short digression on distributions. EDIT: Okay, you want to compute $\delta^2$. Let $\phi_n$ be an approximation to the identity and let it converge to $\delta$ in the sense of distributions, but $\phi_n^2$ does not converge at all since the integral against a test function that does not vanish at the origin blows up as $n \to \infty$. - Here it is stated that: $\int_{-\infty}^\infty \delta (\xi-x) \delta(x-\eta) \, dx = \delta(\xi-\eta).$ Does the integral make the difference? Or the arguments of the two $\delta$s? – draks ... May 7 '12 at 21:54 @draks It is some kind of tensor product right? – Jonas Teuwen May 7 '12 at 22:13 What makes you think that? To me it looks like a "standard" multiplication... – draks ... May 8 '12 at 6:47 You don't multiply them in the same point. – Jonas Teuwen May 8 '12 at 8:20 OK, can I square $\sqrt{\delta(x)}$? Or better $\lim_{a \to 0} \sqrt{\delta_a}$, e.g. $\sqrt{\delta_a(x)}=\exp(-x^2/\color{red}{2}a^2)$ – draks ... May 8 '12 at 8:35 Here is a heuristic to suggest that it will be difficult to define the square of the delta function. The Fourier transform has the property that it takes the convolution of two functions to the product of their Fourier transforms, and vice versa, ie, it takes the product of two functions to their convolution. Remember that the Fourier transform of the delta function is the constant function($=1$). Now suppose that $\delta^2$ exists. Then its Fourier transform would be the convolution of two constant functions. Such a convolution would shoot to infinity at every point. Even the theory of distributions can't handle such kind of stuff. So how would you imagine the inverse Fourier transform of this? How would it make sense? - This answer is primarily to expand on this comment. From that comment and the following, it seems to me draks thinks of the delta as a function, and from the title, it seems the OP also does. Or at least, this was true at the time of posting the comment and the question respectively. Eradicate this misconception from your minds at once, if it is there. The delta is not a function, although it is sometimes called "Delta function". Let me give you a bit of background, a little timeline of my relationship with the Delta. 1. I first heard of it from my father, a Physics professor and physicist, who introduced it to me as a function equalling 0 outside 0 and infinity in 0. Such a function seemed abstruse to me, but I had other worries up my mind so I didn't bother investigating. This is how Dirac originally thought of the Delta when introducing it, but, as we shall see, this definition is useless because it doesn't yield the one most used identity involving this "function"; 2. Then I had Measure theory, and voilà a Dirac Delta again, this time a measure, which gives a set measure 0 if 0 is not in it, and 1 if 0 is in. More precisely, $\delta_0$ is a measure on $\mathbb{R}$, and if $A\subseteq\mathbb{R}$, then $\delta_0(A)=0$ if $0\not\in A$, and 1 otherwise. Actually, I was introduced to uncountably many Deltas, one for each $x\in\mathbb{R}$. $\delta_x$, for $x\in\mathbb{R}$, was a measure on the real line, giving measure 0 to a set $A\subseteq\mathbb{R}$ with $x\not\in A$, and 1 to a set containing $x$; 3. Then I had Physics 2 and Quantum Mechanics, and this Delta popped up as a function, and I was like, WTF! It's a measure, not a function! Both courses did say it was a distribution, and not a function, so I was like, what in the world is a distribution? But both courses, when using it, always treated it like a function; 4. Then I had Mathematical Physics, including a part of Distribution theory, and I finally was like, oh OK, that is what a distribution is! The measure and the distribution are close relatives, since the distribution is nothing but the integral with respect to the measure of the function this distribution is given as an argument. In both settings, it is a priori meaningless to multiply two deltas. Well, one could make a product measure, but that would just be another delta on a Cartesian product, no need for special attention. In the distribution setting, we have what this answer says, which gives us an answer as to what the product might be defined as, and what problems we might run into. So what is the product of deltas? And what is the comment's statement all about? The answer to the first question is: there is no product of deltas. Or rather, to multiply distributions you need convolutions, and those need some restrictions to be associative. The second question can be answered as follows. That statement is a formal abbreviations. You will typically use that inside a double integral like: $$\int_{\mathbb{R}}f(\xi)\int_{\mathbb{R}}\delta(\xi-x)\delta(x-\eta)dxd\xi,$$ which with the formal statement reduces to $f(\eta)$. I have seen such integrals in Quantum Mechanics, IIRC. I remember some kind of spectral theorem for some kind of operators where there was a part of the spectrum, the discrete spectrum, which yielded an orthonormal system of eigenvectors, and the continuous spectrum somehow yielded deltas, but I will come back here to clarify after searching what I have of those lessons for details. Edit: $\newcommand{\braket}[1]{\left\|#1\right\rangle} \newcommand{\xbraket}[1]{\|#1\rangle}$ I have sifted a bit, and found the following: Spectral theorem Given a self-adjoint operator $A$, the set of eigenvectors $\braket{n}$ of $A$ can be completed with a family of distributions $\braket{a}$, indicised by a continuous parameter $a$, which satisfy: \begin{align} A\braket{n}={}&a_n\braket{n} && \braket{n}\in H, \\ A\braket{a}={}&a\braket{a} && \braket{a}\text{ distribution}, \end{align} in such a way as to form a "generalized" basis of $H$, in the sense that all the vectors of $H$ can be written as an infinite linear combination: $$\braket{\psi}=\sum c_n\braket{n}+\int da\,c(a)\braket{a}.$$ The set of eigenvalues (proper and generalized) of $A$ is called the spectrum of $A$ and is a subset of $\mathbb{R}$. What happens to the Parseval identity? Naturally: $$\langle\psi,\psi\rangle=\sum\|c_n\|^2+\int da\,\|c(a)\|^2.$$ So this "basis" is orthonormal in the sense that the eigenvectors are, the distributions have as product a family of deltas, or: $$\langle a,a'\rangle=\delta(a-a'),$$ and multiplying the eigenvectors by the distributions also yields a nice big 0. The famous identity I mentioned in the timeline above and then forgot to expand upon is actually what defines the delta, or at least what the QM teacher used to define it: $$\int_{\mathbb{R}}f(x)\delta(x-x_0)=f(x_0),$$ for any function $f:\mathbb{R}\to\mathbb{R}$ and $x_0\in\mathbb{R}$. If the $\delta$ were a function, it would have to be zero outside 0, but I'm sure you know all too well that altering the value of a function in a single point doesn't alter the integral, and the integral in the identity above would be an integral of a function that is 0 save for a point, so it would be 0, and if $f(x_0)\neq0$ the identity wouldn't hold. Notice how this formal statement is much like an analogous statement for Kronecker deltas: $$\sum_n\delta_{nm}\delta_{nl}=\delta_{ml}.$$ Imagine taking this to the continuum: the sums become integrals, and what can $\delta_{nm}$ become if not $\delta(n-m)$? So the statement is just a formal analog of the true statement with Kronecker Deltas when going into the continuum. Of course, distributionally it makes no sense, nor in terms of measure. I have no idea how integrals with two deltas may be useful, and I have found none in my sifting. I will sift more, and perhaps Google, and if I find anything interesting, I'll be back. Update: $\newcommand{\lbar}{\overline} \newcommand{\pa}[1]{\left(#1\right)}$ I decided I'd just stop the sifting and concentrate on my exams. I googled though, and found this. Another argument I thought up myself in favor of the statement is the following. Let $\phi$ be a functions. It is pretty natural to say: $$\phi=\int_{\mathbb{R}}\phi(a)\delta(x-a)da,$$ since for any $x$ this yields $\phi(x)$. Now what happens to the $L^2$-norm? $$N:=\\|\phi\\|_{L^2}^2=\int_{\mathbb{R}}\lbar{\phi(x)}\phi(x)dx=\int_{\mathbb{R}}\lbar{\int_{\mathbb{R}}\phi(a')\delta(x-a')da'}\cdot\pa{\int_{\mathbb{R}}\phi(a)\delta(x-a)da}dx.$$ The complex conjugation can be brought inside the first integral. Now to a physicist integrals that don't swap are evil, and we surely don't want any evil around, so we assume we can reorder the three integrals the way we want, and get: $$N=\int_{\mathbb{R}}da\,\phi(a)\cdot\pa{\int_{\mathbb{R}}da'\,\lbar{\phi(a')}\cdot\pa{\int_{\mathbb{R}}dx\,\delta(x-a)\delta(x-a')}}.$$ Suppose the formal statement holds. Then the innermost integral yields $\delta(a-a')$, and the second innermost one yields $\lbar{\phi(a)}$, which then combines with $\phi(a)$ outside it to form $\|\phi(a)\|^2$, which integrated gives the $L^2$ norm of $\phi$, squared. If the statement doesn't hold, it seems unreasonable to think we can still get the squared norm out of that mess. So the statement must hold, otherwise the integrals won't swap. - I think the answer provided by Jonas is correct, but Jonas assumed "product" meant convolution as this is normally the only binary operation that usually make sense with the Dirac delta function. So if by product you mean convolution then: δ∗δ=δ If by "product" you meant point-wise multiplication, then the answer is: Undefined. The usual approach is to treat δ as the limit of some nascent delta function. See Delta Function for examples of these nascent delta functions. So if you multiply two nascent δ functions and then take the limit, the result will vary depending on the particular pair of nascent δ functions selected. In most cases the integral of the point-wise product of two nascent δ functions is zero as the limit is taken, in some cases the integral is 1, in other cases the value of the integral tends to infinity as the limit of nascent δ is taken. For example If you multiply the rectangle nascent δ with the nascent δ that is a triangle pulse, then integral of the resulting cubic tends to zero as the interval tends to 0. If you multiply the sinc version of the nascent δ with itself, then the integral is equal to the frequency of the sinc function. In this case the integral tends to infinity as the frequency of the sinc function tends to infinity. Because of this, the original answer given (The question makes no sense) is the best because the term "product" in its common meaning (e.g. point-wise multiplication of two functions) leads to contradictory results for the limit process. Using the term "product" when you mean convolution (the only operation that produces meaningful results) is at best confusing. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9702511429786682, "perplexity": 279.86959459944245}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783397428.37/warc/CC-MAIN-20160624154957-00146-ip-10-164-35-72.ec2.internal.warc.gz"}
https://byjus.com/rate-of-decay-formula/	Rate Of Decay Formula Rate of Decay Formula The decay of a particular nucleus cannot be predicted and is not affected by physical influences like temperature, unlike chemical reactions. The rate of isotope decay depends on two factors. The total number of undecayed nuclei present in the system on doubling the average and undecayed nuclei must double the rate of decay. The stability of the isotope since some isotope decay rapidly. The rate of decay gives the number of nuclei that decay per second. Rate of Decay Formula is given as $\dpi{120}&space;\large&space;\frac{-d[A]}{dt}=k[A]$ On integrating above equation, we have $\dpi{120}&space;\large&space;ln\frac{[A_{0}]}{[A]}=kt$ The half life (t1/2) is given by $\dpi{120}&space;\large&space;t_{1/2}=\frac{0.693}{k}$ Example 1 The half-life of a 226-radium is 1622 years. Determine the time it will take for a sample of 226-radium to decay to 10% of its original radioactivity. Solution Use t1/2 equation to find the rate constant. k = 0.693 / 1622 = 4.27 × 10-4 year $\dpi{120}&space;\large&space;ln\frac{[A_{0}]}{[A]}=kt$ Insert the value for k into the integrated form of the rate equation 4.27 × 10−4 × t = ln(100/10) t = 5392 years Example 2 A piece of wood is found to give 10 counts per minute per gram of carbon when subjected to 14C analysis. New wood counts of 15 cpmg-1. The half-life of 14C is 5570 years. Determine the age of the old wood. Solution Use t1/2 equation to find the rate constant k = 0.693 / 5570 = 1.24 × 10-4 years Substitute the value of k into the integrated form of the rate equation. 1.24 × 10-4 × t = ln(14C content in new wood / content in old wood) = ln(15/10) = ln1.5 t = 3270 years old Practise This Question A pizza is cut into 6 equal pieces. After having a slice of pizza, the pizza left on the plate is shown below: Which graphical method resembles this?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9183393716812134, "perplexity": 1860.8374973082489}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203021.14/warc/CC-MAIN-20190323201804-20190323223804-00224.warc.gz"}
http://www.chegg.com/homework-help/questions-and-answers/speed-bicycle-rider-combined-mass-100-kg-momentum-1500-kgcar-traveling-answer-m-s-q208862	## need help fast At what speed do a bicycle and its rider,with a combined mass of 100 kg, have the same momentum as a 1500 kgcar traveling at Answer in m/s.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8768183588981628, "perplexity": 2443.6853218013753}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706009988/warc/CC-MAIN-20130516120649-00060-ip-10-60-113-184.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/480003/finding-the-limit-lim-limits-x-to-infty-frac1e1-frac1xxx	# finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$ Can someone show me how to calculate the limit: $$\lim_{x \to \infty }\left(\frac{1}{e}\left(1+\frac{1}{x}\right)^x\right)^x$$ I tried to use taylor series but failed. Thanks - Take the logarithm, \begin{align} \log \left(\frac{1}{e}\left(1+\frac{1}{x}\right)^x\right)^x &= x\left(\log \left(1+\frac1x\right)^x - 1\right)\\ &= x\left(x\log\left(1+\frac1x\right)-1\right)\\ &= x\left(-\frac{1}{2x} + O\left(\frac{1}{x^2}\right)\right). \end{align} - Assume the limit exists and has value $L$ Then $$\log{L} = \lim_{x\to\infty} x \log{\left [ \frac{1}{e} \left ( 1+\frac{1}{x}\right)^x\right]} =\lim_{x\to\infty} x \left [ -1 + x \log{\left ( 1+\frac{1}{x}\right)}\right]$$ Taylor expand the log term for large $x$: $$\log{L} = \lim_{x\to\infty} x \left [-1 + x \left (\frac{1}{x} - \frac{1}{2 x^2} + \cdots\right)\right]= -\frac12$$ Therefore $L=e^{-1/2}$. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000094175338745, "perplexity": 2036.921721229093}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049270527.3/warc/CC-MAIN-20160524002110-00096-ip-10-185-217-139.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/3321119/a-question-about-derivation-of-fourier-coefficients/3321160	# A question about derivation of Fourier coefficients [duplicate] As the textbook said: Trigonometrical polynomials \begin{align} f(x)=\frac{a_0}{2} + \sum_{v=1}^{n}(a_v\cos{vx}+b_v\sin{vx}) \tag{1} \end{align} The Fourier coefficients can be expressed simply by the following formulas: $$a_u=\frac{1}{\pi}\int_{-\pi}^{\pi}f(x)\cos{ux}\,dx, {\ } b_u=\frac{1}{\pi}\int_{-\pi}^{\pi}f(x)\sin{ux}\,dx. \tag{2}$$ The proof follows if we multiply Eq. (1) by $$\cos{ux}$$ or $$\sin{ux}$$ and then integrate. /////////////////////////////////////////////////////////////////////// My derivation: \begin{align} \cos{ux}\,f(x) & = \frac{a_0}{2} \cos{ux} + \sum_{v=1}^{n}(a_v\cos{vx} \cos{ux} +b_v\sin{vx} \cos{ux}) \\ \int_{-\pi}^{\pi}\cos{ux}\,f(x)\,dx & = \frac{a_0}{2} \int_{-\pi}^{\pi} \cos{ux}\,dx \\ & \phantom{={}} + \sum_{v=1}^{n}\left(a_v \int_{-\pi}^{\pi}\cos{vx} \cos{ux}\,dx +b_v \int_{-\pi}^{\pi}\sin{vx} \cos{ux}\,dx\right) \end{align} According to the orthogonality relations of the trigonometric functions, we get: \begin{align} & \int_{-\pi}^{\pi} \cos{ux}\,dx =0, \\ & \int_{-\pi}^{\pi}\cos{vx} \cos{ux}\,dx = \pi, \quad \text{if } u=v, \\ & \int_{-\pi}^{\pi}\sin{vx} \cos{ux}\,dx =0. \end{align} So, if $$u=v$$ \begin{align} \int_{-\pi}^{\pi}\cos{ux}\,f(x)\,dx & = \sum_{v=1}^{n} a_v \int_{-\pi}^{\pi}\cos{vx} \cos{ux}\,dx = \sum_{v=1}^{n} a_v \pi \end{align} I can’t get the Eq. (2), where’s the mistake? Thanks. my question's unique part is, derivate this equation: \begin{align} \sum_{v=1}^{n} a_v \int_{-\pi}^{\pi}\cos{vx} \cos{ux}\,dx = a_v \pi \end{align} and it was solved by @Ak19. • Except at $v=u$, the sum is $0$ . So on the RHS you'll simply have $a_v\pi=a_u\pi$ – Ak. Aug 12 '19 at 15:16 • As I mentioned in the comment, $$\sum_{v=1}^na_v\int_{-\pi}^{\pi}\cos vx \cos ux \ dx = a_1\int_{-\pi}^{\pi}\cos x \cos ux \ dx+a_v\int_{-\pi}^{\pi}\cos 2x \cos ux \ dx+\cdots +\\a_u\int_{-\pi}^{\pi}\cos ux \cos ux \ dx+\cdots+ a_n\int_{-\pi}^{\pi}\cos nx \cos ux \ dx\\=a_1\cdot0 +a_2\cdot0+\cdots a_u\cdot\pi+\cdots a_n\cdot0 = a_u\pi$$ So, $$a_u\pi = \int_{-\pi}^{\pi}f(x)\cos(ux)dx \implies a_u =\frac1\pi\int_{-\pi}^{\pi}f(x)\cos(ux)dx$$ – Ak. Aug 12 '19 at 15:29 • @Ak19 I got it, thank you very much. – mathisbeauty Aug 12 '19 at 16:14 • @Shogun no, my question is just for my “cancel-out” step, it’s specific. – mathisbeauty Aug 12 '19 at 16:54 To generalize, the derivation is easier if you prove it for a complex variable; i.e: $$c_n = \frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)e^{-inx}dx:n\in\mathbb{Z}$$ where the Fourier expansion is of the form $$f(x)=\sum_{n\in\mathbb{Z}}c_n e^{inx}$$. for $$f:\mathbb{R}\rightarrow\mathbb{C}$$; simply consider $$\mathbb{R}$$ as a subset of $$\mathbb{C}$$ and you can use this method for $$f:\mathbb{R}\rightarrow\mathbb{R}$$. Proof: Fix $$m\in\mathbb{Z}$$. Consider the integral: $$\int_{-\pi}^{\pi}f(x)e^{-imx}dx=\int_{-\pi}^{\pi}\sum_{n\in\mathbb{Z}}c_n e^{inx}e^{-imx}dx$$ $$=\sum_{n\in\mathbb{Z}}\int_{-\pi}^{\pi}c_n e^{inx}e^{-imx}dx.$$ Clearly if there is any residual exponential term, integrating that term from $$-\pi$$ to $$\pi$$ will yield $$0$$, regardless of the magnitude of the coefficient of that term, as any exponential term refers simply to a rotation, which will be the same at $$-\pi$$ and $$\pi$$. We have: $$=\cdots+0+\int_{-\pi}^{\pi}c_n dx + 0 + \cdots$$ $$=2\pi c_n,$$ divide by $$2\pi$$ to find $$c_n$$. This proof comes with a nice visualization with epicycles: see here. There's no mistake in your proof; you just need the last 'canceling-out' step. • Thank you very much. – mathisbeauty Aug 12 '19 at 16:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 27, "wp-katex-eq": 0, "align": 5, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9997418522834778, "perplexity": 1468.0777850142283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038085599.55/warc/CC-MAIN-20210415125840-20210415155840-00341.warc.gz"}
http://eprints.nottingham.ac.uk/13545/	## A reaction-diffusion model for inter-species competition and intra-species cooperation Rasheed, Shaker M. (2013) A reaction-diffusion model for inter-species competition and intra-species cooperation. PhD thesis, University of Nottingham. Preview PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader This thesis deals with a two component reaction-diffusion system (RDS) for competing and cooperating species. We have analyse in detail the stability and bifurcation structure of equilibrium solutions of this system, a natural extension of the Lotka-Volterra system. We find seven topologically different regions separated by bifurcation boundaries depending on the number and stability of equilibrium solutions, with four regions in which the solutions are similar to those in the Lotka-Volterra system. We study RDS in the small parameter of the range $0< \lambda \ll 1$ (fast diffusion and slow reaction), and in a few cases we assume $\lambda=O(1)$. We consider three types of initial conditions, and we find three types of travelling wave solutions using numerical and asymptotic methods. However, neither numerical nor asymptotic methods were able to find a particular travelling wave solution which connects a coexistence state say, $(u_0,w_0)$ to an extinction state $(0,0)$ when $0< \lambda \ll 1$. This type can be found when the reaction-diffusion system satisfy the symmetry property and $\lambda=1$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9006307721138, "perplexity": 672.3227532093597}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542002.53/warc/CC-MAIN-20161202170902-00207-ip-10-31-129-80.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/passing-limits-through-integrals.303705/	# Passing limits through integrals 1. Mar 30, 2009 ### rsq_a This seems to be an elementary question, but I rarely have to deal with rigor these days, so excuse me if there's a simple answer. I'm looking for a theorem that will allow me to state, $$F(z) = \int_0^b \frac{f(\tau)}{\tau - z} d\tau \sim \int_0^b \frac{f(\tau)}{\tau} d\tau$$ as $z \to 0$ and $f(\tau): \mathbb{C} \to \mathbb{C}$, but it's real along the path of integration. I believe $f(\tau)[/tex] satisfies these properties: • [itex]f(0) = 0$ and $f(b) = 0$ • $f(\tau)$ is Holder continuous along the path of integration Note that F(z) is well-defined and Holder continuous along the line because of the values of f at the endpoints. An example would be, $$\int_0^1 \frac{\sqrt{\tau}}{\tau - z} d\tau$$ 2. Mar 30, 2009 ### CompuChip What is it that you are looking for. Do you want a theorem that will tell you that the integral you wrote down is a primitive of f(z), or do you want a theorem that will tell you that you can replace t - z by t if z goes to zero. Because the latter simply follows from continuity of F(z) at z = 0. 3. Mar 30, 2009 ### rsq_a Huh. I guess it's that simple. Sorry, tripped over myself there. 4. Mar 30, 2009 ### CompuChip Would it make you feel less stupid to know that I usually look such things up, like when I really need to know the conditions of passing limits through integrals? Otherwise I usually write something like: "I don't know the exact theorem, but f is continuously differentiable which is - although overkill - definitely a sufficient condition." 5. Apr 2, 2009	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8671847581863403, "perplexity": 578.6180407348992}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589752.56/warc/CC-MAIN-20180717144908-20180717164908-00369.warc.gz"}
http://math.stackexchange.com/questions/103897/why-is-an-angle-dimensionless	# Why is an angle dimensionless? [duplicate] I was trying out Dimensional Analysis on a few equations and realized that angles have no dimension. Otherwise equations such as $s=r\theta$ are not dimensionally consistent. Further, why don't trigonometric ratios have any dimension? PS: I couldn't find any appropriate tag for this question. Could someone re tag as appropriate? Thanks. - ## marked as duplicate by Zev Chonoles, Amzoti, Andrey Rekalo, Danny Cheuk, Alex WertheimJul 12 '13 at 18:56 The answer to both your questions is the same - trig ratios and radian measure are both dimensionless because they are defined as the ratio of two lengths, which have the same units so they cancel. – Ragib Zaman Jan 30 '12 at 9:57 @RagibZaman In that case does it mean that Dimensional Analysis cannot be applied to equations which involve ratios of 2 quantities with the same unit? – Green Noob Jan 30 '12 at 10:03 Further, how can we extend this logic for angles in degrees? I don't think it is defined as a ratio of two lengths. – Green Noob Jan 30 '12 at 10:08 @GreenNoob: No it does not mean Dimensional Analysis cannot be applied, it just means such ratios have an empty dimension. If they are equated or compared to an expression with a non-empty dimension, then there is an error, but if they are equated or compared to another such ratio or an explicit number, then no error is detected. – Marc van Leeuwen Jan 30 '12 at 10:09 When doing dimensional analysis on a problem which has an angle as a parameter, you generally find that the solution can involve an arbitrary function of the angle, as in e.g. the problem of how far a ball travels under a gravitational field $g$ if thrown with velocity $v$ at angle $\theta$ (the dimensional analysis solution is $x\propto v^2/g \times f(\theta)$ – Chris Taylor Jan 30 '12 at 10:34 Compare to a ratio of weights, it is weights that you compare. You get no units for the ratio, right ? I mean the result is independent of choice of units. But with angles your ratio is with lengths ! not angles ! so don't be surprized that you get "units". Any partition of an angle is named with "units" The funny thing is that unit transformation with angles obeys the same laws as with any other unit. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.915841817855835, "perplexity": 564.2725720335167}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398461529.84/warc/CC-MAIN-20151124205421-00148-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.bloombergprep.com/gmat/practice-question/1/402/verbal-section-reading-comprehension-reading-comprehension-structure-questions/	We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests. ## Up to 90+ points GMAT score improvement guarantee ### The best guarantee you’ll find Our Premium and Ultimate plans guarantee up to 90+ points score increase or your money back. ## Master each section of the test ### Comprehensive GMAT prep We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests. ## Schedule-free studying ### Learn on the go Study whenever and wherever you want with our iOS and Android mobile apps. ## The most effective way to study ### Personalized GMAT prep, just for you! The third paragraph performs which of the following functions in the passage? Incorrect. [[snippet]] It is true that the third paragraph elaborates on modern discoveries in the field discussed by the passage. However, this new information does not support the second paragraph, it contradicts it. Incorrect. [[snippet]] The third paragraph does not present a conclusion, least of all the final conclusion of the passage. Moreover, we can eliminate this answer choice by looking at the first sentence, even the first word, of the last paragraph: Still. This structure word indicates that the last paragraph has something different to add to what was previously discussed. Incorrect. [[snippet]] The third paragraph does not cite an example, and even if it did, it would not necessarily mean that this is its function, it's purpose. Do not confuse content with structure Furthermore, the information in the third paragraph does not support the second paragraph, as this answer choice suggests, but actually presents a different, more up-to-date view of the topic at hand. Great! [[snippet]] The second, third, and fourth paragraph describe steps (phases) in the progression of scientific views over time (chronologically) on the question of water on Mars. Incorrect. [[snippet]] The third paragraph indeed presents information. However, this information does not undermine the last paragraph in any way. The last paragraph discusses an ongoing debate and the information given in the third paragraph is simply one step in this debate. It supports the previous paragraph by elaborating on modern discoveries in the discussed scientific field. It presents the final conclusion regarding the question discussed in this passage. It cites an example which proves the point of the second paragraph. It describes one of several phases in a chronological review of a scientific debate. It presents information which undermines the conclusion made in the last paragraph.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8567572236061096, "perplexity": 1294.600930476578}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107900860.51/warc/CC-MAIN-20201028191655-20201028221655-00530.warc.gz"}
http://math.stackexchange.com/questions/533/classifying-quasi-coherent-sheaves-on-projective-schemes	# Classifying Quasi-coherent Sheaves on Projective Schemes I know some references where I can find this, but they seem tedious(Both Hartshorne and Ueno cover this). I am wondering if there is an elegant way to describe these. If this task is too difficult in general, how about just $\mathbb{P}^n$? Thanks! - ## 1 Answer Quasi-coherent sheaves on affine schemes (say $Spec(A)$) are obtained by taking an $A$-module $M$ and the associated sheaf (by localizing $M$). This gives an equivalence of categories between $A$-modules and q-c sheaves on $Spec(A)$. Let $R$ be a graded ring, $R = R_0 + R_1 + \dots$ (direct sum). Then we can, given a graded $R$-module $M$, consider its associated sheaf $\tilde{M}$. The stalk of this at a homogeneous prime ideal $P$ is defined to be the localization $M_{(P)}$, which is defined as generated by quotients $m/s$ for $s$ homogeneous of the same degree as $m$ and not in $P$. In short, we get sheaves of modules on the affine scheme just as we get the normal sheaves of rings. We get sheaves of modules on the projective scheme in the same homogeneous localization way as we get the sheaf of rings. However, it's no longer an equivalence of categories. Why? Say you had a graded module $M= M_0 + M_1 + \dots$ (in general, we allow negative gradings as well). Then it is easy to check that the sheaves associated to $M$ and $M' = M_1 + M_2 + \dots$ are exactly the same. Nevertheless, it is possible to get every sheaf on $Proj(R)$ for $R$ a graded ring in this way. See Proposition II.5.15 in Hartshorne. - Sorry I didn't respond sooner, nice answer so far, but one more request. Can you tie the last fact(about losing eq of cat to the fact that M and M' have the same sheaves) back to the geometry of Proj. I am thinking it comes from the fact that Proj is isomorphic to shifted proj(I just mean overthe same ring with the grading scaled by some factor.) thanks! – BBischof Jul 25 '10 at 5:27 Yes, $Proj R$ is isomorphic to $Proj R^{(d)}$ where $R^{(d)} = \bigoplus_{n} R_{nd}$; this is a version of the $d$-uple embedding of projective space. Now, $M', M$ agree in sufficiently large dimensions. This means that if you scale the grading by some large $d$, we have $M'^{(d)}, M^{(d)}$ isomorphic as $R^{(d)}$-modules. In particular, their associated sheaves on $Proj(R^{(d)}$ are the same. Pulling back to $Proj(R)$ gives isomorphic sheaves. – Akhil Mathew Jul 25 '10 at 5:39 [Of course, this relies on the fact that pulling back the sheaf associated to $M^{(d)}$ from the $d$-uple embedding gives you the sheaf associated to $M$, which I'm not sure really explains things well.] Maybe one way to think of it is on projective space over a field. Say you have some section of the sheaf associated to $M'$. Then on the $i$th hyperplane multiply by $x_i$ to a high power to get something of $M$. Then divide by $x_i$ to the same power, since it is nonzero on this hyperplane. – Akhil Mathew Jul 25 '10 at 5:43 Alright, I am glad that my intuition was correct there. So, we are safe in Proj to think about R-mod instead of QCsheaves, we should just keep in mind that some of them will yield the same sheaves. And sorry for taking so long to respond, these two comments didn't show up, so I didn't notice you responded. :/ – BBischof Jul 25 '10 at 19:06 Also, I have accepted this answer. I think that seeing them simply as R-mods is simple enough. :D – BBischof Jul 25 '10 at 19:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9712750315666199, "perplexity": 217.8647612251585}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657131238.51/warc/CC-MAIN-20140914011211-00255-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}
https://asmedigitalcollection.asme.org/IJTC/proceedings-abstract/TRIB2003/37068/39/300167	This paper presents a study of the stick-slip frictional phenomenon when large contact areas subjected to uneven contact loads are involved. The objective of the investigation is to gain better understanding of the phenomenon from experimental observations and to develop a mathematical representation that can be used for modeling, simulation and design purposes. A dynamic integral-model has been proposed and simulations have been carried out. The effects of various system parameters on the behavior of the system have been studied experimentally and analytically. The simulation results using the proposed integral-model are in good agreement with the experimental results. The latter also show that stick-slip vibrations can be influenced by the loading conditions. This content is only available via PDF.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8723037242889404, "perplexity": 322.2864700377197}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500628.77/warc/CC-MAIN-20230207170138-20230207200138-00637.warc.gz"}
https://www.physicsforums.com/threads/expansion-and-conservation-of-energy.407620/	# Expansion and conservation of energy 1. Jun 3, 2010 ### TrickyDicky According to quantum field theory there is an intrinsic energy of the vacuum or zero point energy (which is being related to cosmological constant by some cosmologists, i.e.:http://philsci-archive.pitt.edu/archive/00000398/00/cosconstant.pdf [Broken] ), so if space stretches with expansion, is the energy of this space vacuum being created all the time? if so, is this in conflict with the energy conservation law? Last edited by a moderator: May 4, 2017 2. Jun 3, 2010 ### nicksauce In GR, energy is only (necessarily) conserved locally. This means that the stress tensor satisfies $$\nabla^{\mu}T_{\mu\nu} = 0$$. The stress tensor that can be used to represent vacuum energy $$T_{\mu\nu} = Cg_{\mu\nu}$$ (for some constant C) certainly satisfies this. Alternatively, if you want a Newtonian viewpoint, vacuum energy has a negative pressure, and the field does "negative work" to expand the universe. This "negative works" allows for extra energy in the field taking up more volume. It is the exact opposite situation as with photons, where photons have positive pressure and thus do work in expanding the universe, which exactly compensates for the energy loss (redshift) in the photons). 3. Jun 3, 2010 ### TrickyDicky So you are saying GR doesn't have to follow the first law of thermodynamics? Still expansion is an observed fact not directly derived from GR which is a theory of gravitation. Maybe someone has a more direct answer to my question? 4. Jun 3, 2010 ### nicksauce Global energy conservation (or the first law of thermodynamics) comes from the time invariance of the Lagrangian, as a consequence of Noether's theorem. In an expanding universe, the Lagrangian is time dependent. There are other problems with energy in GR: One can't identify the energy of the gravitational field properly because all neighbourhoods look locally flat. However, you can still derive all the basic equations of cosmology just by using Netwon's law of gravity, and basic thermodynamics. If we believe that the universe is isotropic and homogenous on large scales, and that it is governed by GR on large scales, then it is necessarily true that it will be expanding or contracting. The static solution is unstable, meaning that any small perturbations will cause it to start expanding or contracting. Einstein's failure to realize this is why his cosmological constant was called his "greatest mistake." 5. Jun 3, 2010 ### TrickyDicky That's correct. Am I to conclude that the expansion of the universe is somewhat in conflict with global energy conservation ,but that it is a fact assumed by the scientific stablishment and either is not seen as a real problem or simply ignored, or seen as small problem and there is people already figuring it out? Or none of the above? 6. Jun 3, 2010 ### Ich There is no such thing as global energy conservation in explicitly time-dependent situations. So how could expansion be in conflict with something that does not exist? That said, the issue of energy is tricky in GR. There are physical descriptions that restore global energy conservation (google "pseudotensor"). If you have a problem with non-conservation, find comfort in these. 7. Jun 3, 2010 ### TrickyDicky Ok, so there is no conflict because the first law of thermodynamics doesn't apply to time-dependent situations such as expansion, is that it? I guess what bugs me a little is that most of physics seems to be time-invariant and yet expansion scapes this rule. 8. Jun 4, 2010 ### Chalnoth One way of thinking of it is that energy is only one component of the stress-energy tensor, which is the object upon which gravity acts. Individual components of the stress-energy tensor are not conserved: the quantity as a whole is. And conservation of the totality of the stress-energy tensor (which includes things like momentum, pressure, and shear as well as energy) forces the non-conservation of individual components of the tensor, under the right conditions. In general, you only get conservation of individual components like energy in a flat space-time. Now, any small enough region of space-time can be described as being flat (which is why it is possible to say that energy is conserved locally, but only if you use coordinates in which the space-time is flat in that local region). But in general you can't describe space-times as being globally flat in this way, so energy conservation is forced to fail due to stress-energy conservation. 9. Jun 4, 2010 ### yenchin 10. Jun 4, 2010	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.917333722114563, "perplexity": 616.1123066174373}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267861456.51/warc/CC-MAIN-20180618222556-20180619002556-00170.warc.gz"}
http://physics.stackexchange.com/questions/65368/what-really-is-the-magnetic-force-on-a-wire	# What really is the Magnetic Force on a wire? I have a doubt regarding the significance of a force on a wire. Well, first of all, I know that if I have a particle and if there are several forces acting over it, then we can compute one total force $F$ that gives the same effect as the combination of the several forces, and this force is just the vector sum. Well, this is pretty good: a vector depends on the point it's being applied (since it's an element of the tangent space at the point), so that since all the forces are on the same point (the same tangent space) we can take their sum and get another thing acting on the same point. This is pretty clear and simple to understand. My doubt is when we have a wire for example. For a wire normally we use the relationship: $$F=\int_\gamma i \ \gamma'(t)\times B(\gamma(t)) \ dt$$ In other words, we parametrize the wire with some curve $\gamma$, and we integrate $i \gamma' \times B$ over the wire to get the "force on the wire". But now this is confusing me, we are summing vectors at different points, and getting a vector that I don't know where's located. What I mean is: while when working with particles it makes sense to add the forces and use the total force on the same particle, with a wire this is kind of confusing, because it has length, so what should really mean "a force on a wire" since it's not just a point? Thanks in advance for the help. - The integral is analogous to a sum. You are summing all the forces acting upon the wire. So $F$ is the net force on the wire as a whole, i.e. considering the wire as an extended body. Think in this way: imagine that the charges are confined inside the wire, so every charge exerts a force on the wire, so the net force that the wire "feels" is the sum of every force that exert every charge. – Anuar May 21 '13 at 14:20 The force law you show gives us the total force on the wire. This force comes from the sum total of forces on all the electrons moving through the wire. So imagine that your wire is supported at either end, and the magnetic field is strictly between the two supports, so the total force on the wire is – in some sense – between the two supports. Then, if you want to keep the wire in place, the supports have to exert a total force that is equal and opposite to the electromagnetic force. This answer might make you happy, but it's important to note that I've just swept your question under the rug a little. We usually don't think of forces as being "located" at a precise spot. The reason for this is pretty basic. To simplify physics, we group particles together into collective objects, and frequently just assume that there are forces (that we ignore) within those objects to make sure that they don't get destroyed by the forces we're analyzing. This allows us to just look at the sum of forces. For example, we frequently deal with rigid bodies, in which all the particles are described completely by a single position (the position of the center of mass, for example) and the orientation of the body. You might say that we ignore the fact that a rigid body is made up of smaller particles, and just treat it as one big particle. Or, when talking about a rope, we might talk about the tension in that rope being transmitted between different sections of the rope. So, in the case of the wire and its supports, those supports are extended objects, and the forces they exert are not located at a precise spot. But we treat them as rigid bodies, and look at the sum of the forces exerted by each infinitesimal part of them. We don't need to keep track of all those infinitesimal parts because we assume that the supports stay together, and maintain their shape. Same thing with your wire. We assume that the wire is continuous and doesn't break, so we can just treat it as a single object, and sum up all the forces. - The "magnetic force on the wire" means the magnetic force on the center of mass of the wire, which moves according to Euler's first law: $\vec F = M\frac d{dt}\vec v_{cm}$ where the terms are the total force, total mass and velocity vector of the center of mass. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9145724177360535, "perplexity": 146.39950767261868}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507443883.29/warc/CC-MAIN-20141017005723-00344-ip-10-16-133-185.ec2.internal.warc.gz"}
http://www.impan.pl/cgi-bin/dict?discuss	## discuss In this section we discuss in some detail the relationship ...... This is discussed more fully in [5]. These Banach algebras have been much discussed recently. We put off discussing this problem to Section 5. Rather than discuss this in full generality, let us look at a particular situation of this kind. the problem discussed [Not: “the discussed problem”] Go to the list of words starting with: a b c d e f g h i j k l m n o p q r s t u v w y z	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8930788636207581, "perplexity": 288.73321654002206}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737864605.51/warc/CC-MAIN-20151001221744-00047-ip-10-137-6-227.ec2.internal.warc.gz"}
http://logic.pdmi.ras.ru/~hirsch/abstracts/00random.html	Hirsch, E. A., Worst-case time bounds for MAX-K-SAT w.r.t. the number of variables using local search. Proceedings of RANDOM 2000, ICALP Workshops 2000, Proceedings in Informatics 8: 69-76. Carleton Scientific, 2000. Abstract. During the past three years there was an explosion of algorithms solving MAX-SAT and MAX-2-SAT in worst-case time of the order cK, where c<2 is a constant, and K is the number of clauses in the input formula. Such bounds w.r.t. the number of variables instead of the number of clauses are not known. Also, it was proved that approximate solutions for these problems (even beyond inapproximability ratios) can be obtained faster than exact solutions. However, the corresponding exponents still depended on the number of clauses in the input formula. In this paper we give a randomized (1-\epsilon)-approximation algorithm for MAX-k-SAT. This algorithm runs in time of the order ck,\epsilonN, where N is the number of variables, and ck,\epsilon<2 is a constant depending on k and \epsilon. Back to the list of papers	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8950338363647461, "perplexity": 643.0404262522652}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218186891.75/warc/CC-MAIN-20170322212946-00141-ip-10-233-31-227.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/moment-of-inertia-of-a-set-of-spinning-disks.904239/	# Moment of inertia of a set of spinning disks • #1 25 1 ## Homework Statement The shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.0000 m and (total) mass M = 100.0 mg. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point O. (a) What is the rotational inertia of the arrangement about that axis? (b) If we approximated the arrangement as being a uniform rod of mass M and length L, what percentage error would we make in calculating the rotational inertia? M = 100.0 mg = 1×10-4 kg L = 1.0000 m # of disks = 15 ## Homework Equations Inertia of a disk about a central diameter I = (MR2)/2 Inertia of set of particles I = ∑miri2 ## The Attempt at a Solution Itotal = (MR2)/4 + ∑miri2 Itotal = ML2 / 4⋅302 + (2M/15)(1 + 4 + 9 + 16 + 25 + 36 + 49)(L/15) Itotal = 8.298 kg - m2 Did I have the right solution? Last edited by a moderator: Related Introductory Physics Homework Help News on Phys.org • #2 BvU Homework Helper 2019 Award 13,690 3,335 Depends. They want you to compare it with ##I## for a rod with the same M and L. What did that give you ? Oh, sorry, that's part b. Still: a nice check... and for part a) I would check my dimensions if I were you. And the problem statement: are the disks really that light ? • #3 Simon Bridge Homework Helper 17,857 1,654 Hint: parallel axis theorem. • #4 BvU Homework Helper 2019 Award 13,690 3,335 Hi Simon ! I think the parallel axis theorem is there, but the work is a bit sloppy. M and m , numerator squared, denominator not, etc. • #5 25 1 Hi Simon ! I think the parallel axis theorem is there, but the work is a bit sloppy. M and m , numerator squared, denominator not, etc. I tried to separate the rotational inertia of the center disk and the remaining fourteen disks. Is that how it is done? I'm still having trouble finding the rotational inertia of the arrangement. • #6 BvU Homework Helper 2019 Award 13,690 3,335 Ah, yes. So SImon was right. Do you know about the parallel axis theorem ? You'll need it here. • #7 25 1 Ah, yes. So SImon was right. Do you know about the parallel axis theorem ? You'll need it here. Yeah, I do know about it. So I should just find the moment of a single disk then add it to its md2 for each disk? Is that correct? Making the solution for a as: 0.5mdiskrdisk2 + 0.5mdiskrdisk2(22 + 42 + 62 + 82 + 102 + 122 + 142) • #8 BvU Homework Helper 2019 Award 13,690 3,335 Go slower. There are terms missing your last line. the moment of a single disk then add it to its md2 for each disk? Is that correct? yes, if by ##d## you mean the distance from the axis to the center of mass. "moment of a single disk" for each disk is what I'm missing ... • #9 25 1 Go slower. There are terms missing your last line. yes, if by ##d## you mean the distance from the axis to the center of mass. "moment of a single disk" for each disk is what I'm missing ... Yeah, what I'm referring to d is the distance of one disk to the axis of rotation O. What I mean about moment of a single disk is its moment when spun at its center. So for example, the outermost disk has a distance of 14r from its center, then can I consider its moment to be 1/2 mr^2 + m(14r)^2. Then next to that disk is a disk 12r from the axis of rotation, then can I use 1/2 mr^2 + m(12r)^2. and so on... adding those all together in the end. • #10 BvU Homework Helper 2019 Award 13,690 3,335 Agreed. But I don't see the ##I## for each disk around its own center, except for the disk in the middle. • #11 25 1 Agreed. But I don't see the ##I## for each disk around its own center, except for the disk in the middle. This is what I'm referring to... The first term is for the center disk while the remaining is for the next ones, times two because there are rods from the left and right of the axis. This is letting m be the mass of each disk and r be the radius of each disk too. • #12 BvU Homework Helper 2019 Award 13,690 3,335 is the same as 0.5mdiskrdisk2 + 0.5mdiskrdisk2(22 + 42 + 62 + 82 + 102 + 122 + 142) ??? • #13 25 1 is the same as 0.5mdiskrdisk2 + 0.5mdiskrdisk2(22 + 42 + 62 + 82 + 102 + 122 + 142) ??? Sorry, I was confused at first... nevermind the former equation: 0.5mdiskrdisk2 + 0.5mdiskrdisk2(22 + 42 + 62 + 82 + 102 + 122 + 142) Is the other equation, the one in the image, the correct one I should use? Is that how parallel axis theorem applied in this problem? • #14 BvU Homework Helper 2019 Award 13,690 3,335 Seems to me the picture comes from the solution manual and we can't argue with that, can we ? So I should just find the moment of a single disk then add it to its md2 for each disk? Is that correct? answered with "yes" ! So the thing to do -- now that spoiler is in existence -- is check that your plan and the picture are in agreement. (And hopefully also see why I kept asking for the ##I## of the off-center disks around their own center ) • #15 25 1 Seems to me the picture comes from the solution manual and we can't argue with that, can we ? answered with "yes" ! So the thing to do -- now that spoiler is in existence -- is check that your plan and the picture are in agreement. (And hopefully also see why I kept asking for the ##I## of the off-center disks around their own center ) Found the inertia using that equation to be 8.35210^-6 kg-m^2 When it is considered as a thin rod of length 1 m, the inertia becomes 8.33310^-6 kg-m^2 The percent error becomes: 0.2217% (pretty low) BTW, I didn't get the image from a manual =( I used a math editor 'cause I don't know how to use LATEX here. Last edited: • #16 BvU Homework Helper 2019 Award 13,690 3,335 BTW, I didn't get the image from a manual =( I used a math editor 'cause I don't know how to use LATEX here So much the better ! You sure these disks are so light ? And then you still find a total ##I## of 8.35210^6 kg-m^2 for such a small rod ? • #17 25 1 So much the better ! You sure these disks are so light ? And then you still find a total ##I## of 8.35210^6 kg-m^2 for such a small rod ? Oh, sorry, the exponent are raised to a negative power • #18 BvU Homework Helper 2019 Award 13,690 3,335 ##\LaTeX## is easy ! Much faster than [ SUB] [ /SUB] etc.: $## ##$ {1\over 2} mr^2 + 2 \; {1\over 2} mr^2 \left ( 1 + 2^2 \right ) + ... $## ##$ yields$${1\over 2} mr^2 + 2 \; {1\over 2} mr^2 \left ( 1 + 2^2 \right ) + ...$$ Learn by right-clicking over a formula and Pick Show math as ..##\TeX## commands • #19 30 1 a rod of mass M and length L has moment of inertia,I=ML2/12 but it is only for a thin rod here the rod is a line passing through centers of disks,it's M.I constitute only small part of total M.I of the arrangement here,the moment of inertia the arrangement is comparable to the M.I of a rod of length L and mass M and width=2r=L/15 • #20 25 1 a rod of mass M and length L has moment of inertia,I=ML2/12 but it is only for a thin rod here the rod is a line passing through centers of disks,it's M.I constitute only small part of total M.I of the arrangement here,the moment of inertia the arrangement is comparable to the M.I of a rod of length L and mass M and width=2r=L/15 So I should still consider the radius when calculating the moment of the rod? Why so? • #21 30 1 the actual M.I is not like that it must calculated by calculating M.I of each disks about o it may be near to the M.I of the rod with width L/15 given above ,(answer to 2nd question) while the rod has no gaps that seen in the arrangement b/w disks you have to calculate M.I by I=Σmiri and parallel axis theorem.ie by calculating M.I of each disk about o that what you are still doing. • #22 25 1 the actual M.I is not like that it must calculated by calculating M.I of each disks about o it may be near to the M.I of the rod with width L/15 given above ,(answer to 2nd question) while the rod has no gaps that seen in the arrangement b/w disks you have to calculate M.I by I=Σmiri and parallel axis theorem.ie by calculating M.I of each disk about o that what you are still doing. Isn't that what I've done? Using the parallel axis theorem, I calculate each flat disk's rotational inertia. Thereafter, I've added each of their inertia to find the real moment of inertia of the arrangement. Thus, the inertia of the whole arrangement equals to the rotational inertia of the central disk plus the rotational inertia of the remaining fourteen disks which are place beside it. I didn't use the summation of mi times ri2 because it was not a set of particles, instead it was a set of disks which has a certain rotational inertia of (M*R2)/2 • #23 BvU Homework Helper 2019 Award 13,690 3,335 Hi, I think you have. Not clear to me either what akshay is referring to . • #24 25 1 Hi, I think you have. Not clear to me either what akshay is referring to . Yeah, I was pretty confused too. Just a follow-up question; what if the arrangement is not in a straight line. For example, the central disk has 7 adjacent disks to its left and 7 adjacent disks on top of it, making the arrangement form a 90 degree angle? Will the arrangement's rotational inertia be the same? • #25 TSny Homework Helper Gold Member 12,852 3,203 Just a follow-up question; what if the arrangement is not in a straight line. For example, the central disk has 7 adjacent disks to its left and 7 adjacent disks on top of it, making the arrangement form a 90 degree angle? Will the arrangement's rotational inertia be the same? Yes, you should be able to see that the rotational inertia will be the same for 90 degrees (or any other angle). • Last Post Replies 1 Views 660 • Last Post Replies 3 Views 2K • Last Post Replies 2 Views 7K • Last Post Replies 10 Views 3K • Last Post Replies 1 Views 2K • Last Post Replies 1 Views 12K • Last Post Replies 2 Views 3K • Last Post Replies 2 Views 2K • Last Post Replies 7 Views 3K • Last Post Replies 2 Views 913	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8247591257095337, "perplexity": 1184.07239529191}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141204453.65/warc/CC-MAIN-20201130004748-20201130034748-00618.warc.gz"}
https://physics.stackexchange.com/questions/415791/higgs-mechanism-and-wave-particle-duality	# Higgs Mechanism and Wave-Particle Duality According to Higgs Mechanism a particle acquires mass when it couples to the higgs field. Now consider Wave-Particle Duality. Suppose I am doing a Young's Double Slit Experiment using electrons. When they pass through the slits they behave like waves and quantum waves have no mass, there is just momentum given by de-Broglie relation. Now when they "impinge" upon a screen their behaviour is like that of a particle. So they must have mass. When did the electrons interact with the Higgs field to acquire mass when they did not have any mass while "passing" through the slits? Does this imply that Higgs field is decoupling and coupling with the electron field? Also, I could make the distance between the slits and the screen arbitrarily small, doesn't that imply that the coupling "speed" (for lack of a better word on my part) of Higgs field is infinite? • Why are the de-Brogile relations $E=\hbar\omega$ and $\vec p=\hbar \vec k$ inconsistent with mass? Mass means the dispersion relation is $E=\sqrt{(pc)^2+(mc^2)^2}$. – JEB Jul 9, 2018 at 13:45 • The de-Broglie relation is $\lambda = \frac{h}{mv}$ with $h$ as Planck's constant, $v$ velocity and $m$ the mass of the particle. If the $m$ were zero, the wavelaength $\lambda$ would be infinite which makes no sense. Jul 9, 2018 at 15:22 is a fundamental misconception about QM. The probability amplitude wavepacket desribing the motion of the electron fully accounts for the movement of its mass (and charge, and...) because this wavepacket, moving freely is restricted by the dispersive equation of Schroedinger, here in one dimension w.l.o.g., $$\left (i\hbar\partial_t + \frac{\hbar^2}{2m} \partial_x^2\right ) \psi =0,$$ which is manifestly "aware" of its mass. The relevant solution is essentially a spreading wavepacket $\psi (x,t)$, yielding a probability $$\Large \rho(x,t)=\|\psi\|^2=\frac{1}{\sqrt{1+4(t\hbar/m)^2}} e^{\frac{-2(x-vt)^2}{1+4(t\hbar/m)^2}} ,$$ in natural wavepacket length units, where v is the group velocity of the wavepacket. The relevant probability flow current to the right can be seen to be ~ $v \rho$, and so the rate of transport of mass to the right is $mv \rho$, as you should confirm.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9684738516807556, "perplexity": 465.03067624066085}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103329963.19/warc/CC-MAIN-20220627073417-20220627103417-00428.warc.gz"}
https://brilliant.org/problems/logical-log-1/	# Logical Log... #1 Algebra Level 4 Suppose that $$a, b, c \in \mathbb {R^{+}}$$ , such that $$a^{\log_3 7} = 27$$ , $$b^{\log_7 11} = 49$$ , and $$c^{\log_{11}25} = \sqrt{11}$$ . Find $a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_{11} 25)^2}.$ ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9862382411956787, "perplexity": 971.9655478881602}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719286.6/warc/CC-MAIN-20161020183839-00494-ip-10-171-6-4.ec2.internal.warc.gz"}
http://www.oa-roma.inaf.it/index.php/event/seminar-by-lars-mattsson/	• Questo evento è passato. # Drag and drift – decoupling of the dust and gas phases in astrophysical flows ## marzo 14 @ 11:45 - 12:45 Simulating the dynamics of gas and dust in various astrophysical contexts is a topic of intense research. It includes simulations of the turbulent interstellar medium (ISM), active galactic nuclei (AGN), proto-planetary discs, and dusty stellar winds. I will focus on the ISM and dust-driven stellar winds, however, and only briefly mention a few other examples. Using high-resolution (1024^3) simulations of homogeneous isothermal hydrodynamic turbulence, including a multi-disperse population of 10^7 dust grains imbedded in the gas, one may assess the efficiency of condensation, destruction and coagulation in molecular clouds. Due to hydrodynamic drag, large grains will decouple from a turbulent gas flow, while small grains will tend to follow the motions of the gas. Dust grains of various sizes will also cluster and increase the rate of grain-grain interaction. This may in turn lead to turbulence-driven coagulation and fragmentation. In a stellar-wind context the decoupling between gas and dust is often called “drift”, which is referring to the fact that the two phases may develop different mean-flow velocities. In a spherically-symmetric setting, a mean-flow model of drift is fairly simple. But there are significant 3D effects, as well as instabilities, which we must take into account. For instance, dust grains of various sizes will cluster and increase the rate of grain-grain interaction. Moreover, due to spatial separation of dust and gas, condensation is likely less effective than in a velocity-coupled case. There are several implications for dust-driven stellar winds which arise from this. One is that the momentum-transfer efficiency (from dust to gas) of large grains may be low as they cluster where the gas is not; another is that the sublimation rate increases as grains are more exposed to the radiation field. ### Dettagli Data: marzo 14 Ora: 11:45 - 12:45 Categoria Evento: ### Oratore Lars Mattsson (Uppsala University)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9120974540710449, "perplexity": 2355.3715621711217}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945624.76/warc/CC-MAIN-20180422154522-20180422174522-00621.warc.gz"}
https://worldwidescience.org/topicpages/a/angle-resolved+electron+energy.html	#### Sample records for angle-resolved electron energy 1. Mapping unoccupied electronic states of freestanding graphene by angle-resolved low-energy electron transmission OpenAIRE Wicki Flavio; Longchamp Jean-Nicolas; Latychevskaia Tatiana; Escher Conrad; Fink Hans-Werner 2016-01-01 We report angle-resolved electron transmission measurements through freestanding graphene sheets in the energy range of 18 to 30 eV above the Fermi level. The measurements are carried out in a low-energy electron point source microscope, which allows simultaneously probing the transmission for a large angular range. The characteristics of low-energy electron transmission through graphene depend on its electronic structure above the vacuum level. The experimental technique described here allow... 2. Angle-resolved photoelectron spectrometry: new electron optics and detection system International Nuclear Information System (INIS) Hoof, H.A. van. 1980-01-01 A new spectrometer system is described, designed to measure angle-resolved energy distributions of photoemitted electrons efficiently. Some results are presented of measurements on a Si(001) surface. (Auth.) 3. Photoemission Electron Spectroscopy IV: Angle-resolved photoemission spectroscopy OpenAIRE Lee, J. D.; Nagatomi, T. (Translator); Mizutani, G. (Translator); Endo, K. (Translation Supervisor) 2010-01-01 The angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental tool to probe themomentum-resolved electronic structure, i.e., the electronic band dispersion ε(k), of solids and their surfaces. ARPES is also an ideal tool to address the question concerning the electron correlation effect on quasiparticle excitations in the low-dimensional (one- or two-dimensional) correlated electron systems. In this issue, we briefly introduce representative studies of ARPES and their fruitf... 4. Electronic structure of Sr2RuO4 studied by angle-resolved photoemission spectroscopy International Nuclear Information System (INIS) Iwasawa, H.; Aiura, Y.; Saitoh, T.; Yoshida, Y.; Hase, I.; Ikeda, S.I.; Bando, H.; Kubota, M.; Ono, K. 2007-01-01 Electronic structure of the monolayer strontium ruthenate Sr 2 RuO 4 was investigated by high-resolution angle-resolved photoemission spectroscopy. We present photon-energy (hν) dependence of the electronic structure near the Fermi level along the ΓM line. The hν dependence has shown a strong spectral weight modulation of the Ru 4d xy and 4d zx bands 5. Determination of electronic states in crystalline semiconductors and metals by angle-resolved photoemission International Nuclear Information System (INIS) Mills, K.A. 1979-08-01 An important part of the theoretical description of the solid state is band structure, which relies on the existence of dispersion relations connecting the electronic energy and wavevector in materials with translational symmetry. These relations determine the electronic behavior of such materials. The elaboration of accurate band structures, therefore, is of considerable fundamental and practical importance. Angle-resolved photoemission (ARP) spectroscopy provides the only presently available method for the detailed experimental investigation of band structures. This work is concerned with its application to both semiconducting and metallic single crystals 6. Electronic structure of superconducting Bi2212 crystal by angle resolved ultra violet photoemission International Nuclear Information System (INIS) Saini, N.L.; Shrivastava, P.; Garg, K.B. 1993-01-01 The electronic structure of a high quality superconducting Bi 2 Sr 2 CaCu 2 Osub(8+δ) (Bi2212) single crystal is studied by angle resolved ultra violet photoemission (ARUPS) using He I (21.2 eV). Our results appear to show two bands crossing the Fermi level in ΓX direction of the Brillouin zone as reported by Takahashi et al. The bands at higher binding energy do not show any appreciable dispersion. The nature of the states near the Fermi level is discussed and the observed band structure is compared with the band structure calculations. (author) 7. A high performance angle-resolving electron spectrometer CERN Document Server Rossnagel, K; Skibowski, M; Harm, S 2001-01-01 We report on our new versatile photoelectron spectrometer Angular Spectrometer for Photoelectrons with High Energy REsolution (ASPHERE) which is part of beamline W3.2 (photon energies from 5 to 40 eV) but also compatible with beamline BW3 (40-1500 eV) at the Hamburger Synchrotronstrahlungslabor (HASYLAB). ASPHERE is a 180 deg. spherical analyzer (r sub 0 =100 mm) with a four-element input lens and is mounted on a two-axes goniometer with computer-controlled stepper motors which enables sequential angle-scanned measurements. The input lens is equipped with an iris aperture so that the angular resolution can be continuously adjusted from 0.2 deg. to 5 deg. sign . The fringe field of the condenser has been corrected for by tilting the angle of the input lens against the base plane of the hemispheres resulting in an overall energy resolution of 10 meV. To improve the speed of data acquisition three standard channeltron detectors are installed in the image plane of the analyzer which will be replaced by a multidet... 8. Electronic structure studies of BaFe2As2 by angle-resolved photoemission spectroscopy NARCIS (Netherlands) Fink, J.; Thirupathaiah, R.; Ovsyannikov, R.; Dürr, H.A.; Follath, R.; Huang, Y.; de Jong, S.; Golden, M.S.; Zhang, Y.Z.; Jeschke, H.O.; Valentí, R.; Felser, C.; Dastjani Farahani, S.; Rotter, M.; Johrendt, D. 2009-01-01 We report high resolution angle-resolved photoemission spectroscopy (ARPES) studies of the electronic structure of BaFe2As2, which is one of the parent compounds of the Fe-pnictide superconductors. ARPES measurements have been performed at 20 and 300 K, corresponding to the orthorhombic 9. Angle-Resolved Photoemission Spectroscopy on Electronic Structure and Electron-Phonon Coupling in Cuprate Superconductors Energy Technology Data Exchange (ETDEWEB) Zhou, X.J. 2010-04-30 In addition to the record high superconducting transition temperature (T{sub c}), high temperature cuprate superconductors are characterized by their unusual superconducting properties below T{sub c}, and anomalous normal state properties above T{sub c}. In the superconducting state, although it has long been realized that superconductivity still involves Cooper pairs, as in the traditional BCS theory, the experimentally determined d-wave pairing is different from the usual s-wave pairing found in conventional superconductors. The identification of the pairing mechanism in cuprate superconductors remains an outstanding issue. The normal state properties, particularly in the underdoped region, have been found to be at odd with conventional metals which is usually described by Fermi liquid theory; instead, the normal state at optimal doping fits better with the marginal Fermi liquid phenomenology. Most notable is the observation of the pseudogap state in the underdoped region above T{sub c}. As in other strongly correlated electrons systems, these unusual properties stem from the interplay between electronic, magnetic, lattice and orbital degrees of freedom. Understanding the microscopic process involved in these materials and the interaction of electrons with other entities is essential to understand the mechanism of high temperature superconductivity. Since the discovery of high-T{sub c} superconductivity in cuprates, angle-resolved photoemission spectroscopy (ARPES) has provided key experimental insights in revealing the electronic structure of high temperature superconductors. These include, among others, the earliest identification of dispersion and a large Fermi surface, an anisotropic superconducting gap suggestive of a d-wave order parameter, and an observation of the pseudogap in underdoped samples. In the mean time, this technique itself has experienced a dramatic improvement in its energy and momentum resolutions, leading to a series of new discoveries not 10. Intra- and intercycle interference of angle-resolved electron emission in laser-assisted XUV atomic ionization Science.gov (United States) Gramajo, A. A.; Della Picca, R.; López, S. D.; Arbó, D. G. 2018-03-01 A theoretical study of ionization of the hydrogen atom due to an XUV pulse in the presence of an infrared (IR) laser is presented. Well-established theories are usually used to describe the laser-assisted photoelectron effect: the well-known soft-photon approximation firstly posed by Maquet et al (2007 J. Mod. Opt. 54 1847) and Kazansky’s theory in (2010 Phys. Rev. A 82, 033420). However, these theories completely fail to predict the electron emission perpendicularly to the polarization direction. Making use of a semiclassical model (SCM), we study the angle-resolved energy distribution of PEs for the case that both fields are linearly polarized in the same direction. We thoroughly analyze and characterize two different emission regions in the angle-energy domain: (i) the parallel-like region with contribution of two classical trajectories per optical cycle and (ii) the perpendicular-like region with contribution of four classical trajectories per optical cycle. We show that our SCM is able to assess the interference patterns of the angle-resolved PE spectrum in the two different mentioned regions. Electron trajectories stemming from different optical laser cycles give rise to angle-independent intercycle interferences known as sidebands. These sidebands are modulated by an angle-dependent coarse-grained structure coming from the intracycle interference of the electron trajectories born during the same optical cycle. We show the accuracy of our SCM as a function of the time delay between the IR and the XUV pulses and also as a function of the laser intensity by comparing the semiclassical predictions of the angle-resolved PE spectrum with the continuum-distorted wave strong field approximation and the ab initio solution of the time-dependent Schrödinger equation. 11. Energy and angle resolved ion scattering spectroscopy: new possibilities for surface analysis International Nuclear Information System (INIS) Hellings, G.J.A. 1986-01-01 In this thesis the design and development of a novel, very sensitive and high-resolving spectrometer for surface analysis is described. This spectrometer is designed for Energy and Angle Resolved Ion Scattering Spectroscopy (EARISS). There are only a few techniques that are sensitive enough to study the outermost atomic layer of surfaces. One of these techniques, Low-Energy Ion Scattering (LEIS), is discussed in chapter 2. Since LEIS is destructive, it is important to make a very efficient use of the scattered ions. This makes it attractive to simultaneously carry out energy and angle dependent measurements (EARISS). (Auth.) 12. Setup for angle-resolved electron spectrometry using monochromatised synchrotron radiation International Nuclear Information System (INIS) Derenbach, H.; Franke, C.; Malutzki, R.; Wachter, A.; Schmidt, V. 1987-01-01 An apparatus is described which is well suited for angle-resolved electron spectrometry of free atoms and molecules using monochromatised synchrotron radiation. Two variations are presented, one for room temperature gaseous species, the other for metallic vapours. The analyser is of the cylindrical mirror type, designed, however, so as to accept with one sector the entire source volume independently of the photon beam diameter. It can be equipped with a positon-sensitive detector instead of a channeltron, which extends its potentiality. The system consists of up to three cylindrical mirror sector analysers (CMAs) where a double-sector CMA can be rotated around the photon beam direction, allowing angular distribution measurements, and another sector CMA is mounted in a fixed position providing a signal for reference purposes. A detailed description and experimental tests are given for the performance of the CMA, i.e. its imaging properties, resolution and transmissions, as well as for possible instrumental asymmetries affecting angle-resolved experiments. (orig.) 13. A brief update of angle-resolved photoemission spectroscopy on a correlated electron system. Science.gov (United States) Lee, W S; Vishik, I M; Lu, D H; Shen, Z-X 2009-04-22 In this paper, we briefly summarize the capabilities of state-of-the-art angle-resolved photoemission spectroscopy (ARPES) in the field of experimental condensed matter physics. Due to the advancement of the detector technology and the high flux light sources, ARPES has become a powerful tool to study the low energy excitations of solids, especially those novel quantum materials in which many-body physics are at play. To benchmark today's state-of-the-art ARPES technique, we demonstrate that the precision of today's ARPES has advanced to a regime comparable to the bulk-sensitive de Haas-van Alphen (dHvA) measurements. Finally, as an example of new discoveries driven by the advancement of the ARPES technique, we summarize some of our recent ARPES measurements on underdoped high-T(c) superconducting cuprates, which have provided further insight into the complex pseudogap problem. 14. A tunable low-energy photon source for high-resolution angle-resolved photoemission spectroscopy International Nuclear Information System (INIS) Harter, John W.; Monkman, Eric J.; Shai, Daniel E.; Nie Yuefeng; Uchida, Masaki; Burganov, Bulat; Chatterjee, Shouvik; King, Philip D. C.; Shen, Kyle M. 2012-01-01 We describe a tunable low-energy photon source consisting of a laser-driven xenon plasma lamp coupled to a Czerny-Turner monochromator. The combined tunability, brightness, and narrow spectral bandwidth make this light source useful in laboratory-based high-resolution photoemission spectroscopy experiments. The source supplies photons with energies up to ∼7 eV, delivering under typical conditions >10 12 ph/s within a 10 meV spectral bandwidth, which is comparable to helium plasma lamps and many synchrotron beamlines. We first describe the lamp and monochromator system and then characterize its output, with attention to those parameters which are of interest for photoemission experiments. Finally, we present angle-resolved photoemission spectroscopy data using the light source and compare its performance to a conventional helium plasma lamp. 15. Electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES) Energy Technology Data Exchange (ETDEWEB) Wu, Yun [Iowa State Univ., Ames, IA (United States) 2016-12-17 The discovery of quantum Hall e ect has motivated the use of topology instead of broken symmetry to classify the states of matter. Quantum spin Hall e ect has been proposed to have a separation of spin currents as an analogue of the charge currents separation in quantum Hall e ect, leading us to the era of topological insulators. Three-dimensional analogue of the Dirac state in graphene has brought us the three-dimensional Dirac states. Materials with three-dimensional Dirac states could potentially be the parent compounds for Weyl semimetals and topological insulators when time-reversal or space inversion symmetry is broken. In addition to the single Dirac point linking the two dispersion cones in the Dirac/Weyl semimetals, Dirac points can form a line in the momentum space, resulting in a topological node line semimetal. These fascinating novel topological quantum materials could provide us platforms for studying the relativistic physics in condensed matter systems and potentially lead to design of new electronic devices that run faster and consume less power than traditional, silicon based transistors. In this thesis, we present the electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES). 16. The use of angle resolved electron and photon stimulated desorption for the determination of molecular structure at surfaces International Nuclear Information System (INIS) 1983-01-01 A brief review of recent data related to the use of angle-resolved electron stimulated desorption and photon stimulated desorption in determining the structures of molecules at surfaces is made. Examples include a variety of structural assignments based on ESIAD (electron stimulated desorption ion angular distributions), the observation of short-range local ordering effects induced in adsorbed molecules by surface impurities, and the application of photon stimulated desorption to both ionic and covalent adsorbate systems. (Author) [pt 17. Electronic band structure of epitaxial PbTe (111) thin films observed by angle-resolved photoemission spectroscopy Science.gov (United States) Ye, Zhenyu; Cui, Shengtao; Shu, Tianyu; Ma, Songsong; Liu, Yang; Sun, Zhe; Luo, Jun-Wei; Wu, Huizhen 2017-04-01 Using angle-resolved photoemission spectroscopy (ARPES), we studied bulk and surface electronic band structures of narrow-gap semiconductor lead telluride (PbTe) thin films grown by molecular beam epitaxy both perpendicular and parallel to the Γ -L direction. The comparison of ARPES data with the first-principles calculation reveals the details of band structures, orbital characters, spin-orbit splitting energies, and surface states. The photon-energy-dependent spectra show the bulk character. Both the L and Σ valence bands are observed and their energy difference is determined. The spin-orbit splitting energies at L and Γ points are 0.62 eV and 0.88 eV, respectively. The surface states below and close to the valence band maximum are identified. The valence bands are composed of a mixture of Pb 6 s and Te 5 pz orbitals with dominant in-plane even parity, which is attributed to the layered distortion in the vicinity of the PbTe (111) surface. These findings provide insights into PbTe fundamental properties and shall benefit relevant thermoelectric and optoelectronic applications. 18. Electronic structure of R Sb (R =Y , Ce, Gd, Dy, Ho, Tm, Lu) studied by angle-resolved photoemission spectroscopy Science.gov (United States) Wu, Yun; Lee, Yongbin; Kong, Tai; Mou, Daixiang; Jiang, Rui; Huang, Lunan; Bud'ko, S. L.; Canfield, P. C.; Kaminski, Adam 2017-07-01 We use high-resolution angle-resolved photoemission spectroscopy (ARPES) and electronic structure calculations to study the electronic properties of rare-earth monoantimonides RSb (R = Y, Ce, Gd, Dy, Ho, Tm, Lu). The experimentally measured Fermi surface (FS) of RSb consists of at least two concentric hole pockets at the Γ point and two intersecting electron pockets at the X point. These data agree relatively well with the electronic structure calculations. Detailed photon energy dependence measurements using both synchrotron and laser ARPES systems indicate that there is at least one Fermi surface sheet with strong three-dimensionality centered at the Γ point. Due to the "lanthanide contraction", the unit cell of different rare-earth monoantimonides shrinks when changing the rare-earth ion from CeSb to LuSb. This results in the differences in the chemical potentials in these compounds, which are demonstrated by both ARPES measurements and electronic structure calculations. Interestingly, in CeSb, the intersecting electron pockets at the X point seem to be touching the valence bands, forming a fourfold-degenerate Dirac-like feature. On the other hand, the remaining rare-earth monoantimonides show significant gaps between the upper and lower bands at the X point. Furthermore, similar to the previously reported results of LaBi, a Dirac-like structure was observed at the Γ point in YSb, CeSb, and GdSb, compounds showing relatively high magnetoresistance. This Dirac-like structure may contribute to the unusually large magnetoresistance in these compounds. 19. Direct angle resolved photoemission spectroscopy and ... Since 1997 we systematically perform direct angle resolved photoemission spectroscopy (ARPES) on in-situ grown thin (< 30 nm) cuprate films. Specifically, we probe low-energy electronic structure and properties of high-c superconductors (HTSC) under different degrees of epitaxial (compressive vs. tensile) strain. 20. Electronic states localized at surface defects on Cu(755) studied by angle-resolved ultraviolet photoelectron spectroscopy using synchrotron radiation CERN Document Server Ogawa, K; Namba, H 2003-01-01 'Regularly stepped' and 'defective' surfaces of Cu(755) were prepared by low- and high-temperature annealing, respectively, of a clean specimen. Electronic states on both surfaces were studied by angle-resolved ultraviolet photoelectron spectroscopy using synchrotron radiation. On the defective Cu(755), we found a new photoelectron peak due to surface defects just below the Fermi level. The dispersion profile of the defect state is derived to be almost flat, which demonstrates the localized nature of the defects. High activity to oxygen adsorption of the defect state was revealed. (author) 1. Electronic anisotropies revealed by detwinned angle-resolved photo-emission spectroscopy measurements of FeSe Science.gov (United States) Watson, Matthew D.; Haghighirad, Amir A.; Rhodes, Luke C.; Hoesch, Moritz; Kim, Timur K. 2017-10-01 We report high resolution angle-resolved photo-emission spectroscopy (ARPES) measurements of detwinned FeSe single crystals. The application of a mechanical strain is used to promote the volume fraction of one of the orthorhombic domains in the sample, which we estimate to be 80 % detwinned. While the full structure of the electron pockets consisting of two crossed ellipses may be observed in the tetragonal phase at temperatures above 90 K, we find that remarkably, only one peanut-shaped electron pocket oriented along the longer a axis contributes to the ARPES measurement at low temperatures in the nematic phase, with the expected pocket along b being not observed. Thus the low temperature Fermi surface of FeSe as experimentally determined by ARPES consists of one elliptical hole pocket and one orthogonally-oriented peanut-shaped electron pocket. Our measurements clarify the long-standing controversies over the interpretation of ARPES measurements of FeSe. 2. Assessment of waveguiding properties of gallium oxide nanostructures by angle resolved cathodoluminescence in a scanning electron microscope International Nuclear Information System (INIS) Nogales, Emilio; Mendez, Bianchi; Piqueras, Javier 2011-01-01 Cathodoluminescence (CL) of Ga 2 O 3 nanowires and planar microstructures has been studied in a scanning electron microscope, as a function of the orientation angle of the structures relative to the position of the light detection system in the microscope chamber. CL contrast shows a marked dependence on the detection angle due to the waveguiding behaviour of the structures. The angle resolved cathodoluminescence (ARCL) measurements enable to evaluate the optical losses of guided blue-ultraviolet light in nanowires with diameters in the sub-wavelength range, deposited on graphite tape or silicon. In planar, branched feather-like microstructures, ARCL images demonstrate the directional-dependant light guiding behaviour of the nano-branches. -- Highlights: → Waveguiding behaviour of gallium oxide nanowires is studied using angle resolved CL. → Quantitative analysis of optical losses in sub-wavelength nanowires is carried out. → There is a strong dependence of the optical losses on the substrate. → Directional-dependant light guiding is observed in branched planar microstructures. 3. Electronic structure studies of ferro-pnictide superconductors and their parent compounds using angle-resolved photoemission spectroscopy (ARPES) Energy Technology Data Exchange (ETDEWEB) Setti, Thirupathaiah 2011-07-14 The discovery of high temperature superconductivity in the iron pnictide compound LaO{sub 1-x}F{sub x}FeAs with T{sub c} = 26 K as created enormous interest in the high-T{sub c} superconductor community. So far, four prototypes of crystal structures have been found in the Fe-pnictide family. All four show a structural deformation followed or accompanied by a magnetic transition from a high temperature paramagnetic conductor to a low temperature antiferromagnetic metal whose transition temperature T{sub N} varies between the compounds. Charge carrier doping, isovalent substitution of the As atoms or the application of pressure suppresses the antiferromagnetic spin density wave (SDW) order and leads to a superconducting phase. More recently high Tc superconductivity has been also detected in iron chalchogenides with similar normal state properties. Since superconductivity is instability of the normal state, the study of normal state electronic structure in comparison with superconducting state could reveal important information on the pairing mechanism. Therefore, it is most important to study the electronic structure of these new superconductors, i.e., to determine Fermi surfaces and band dispersions near the Fermi level at the high symmetry points in order to obtain a microscopic understanding of the superconducting properties. Using the technique angle-resolved photoemission spectroscopy (ARPES) one measures the electrons ejected from a sample when photons impinge on it. In this way one can map the Fermi surface which provides useful information regarding the physics behind the Fermi surface topology of high T{sub c} superconductors. Furthermore, this technique provides information on the band dispersion, the orbital character of the bands, the effective mass, the coupling to bosonic excitations, and the superconducting gap. This emphasizes the importance of studying the electronic structure of the newly discovered Fe-pnictides using ARPES. In this work we have 4. Method to map one-dimensional electronic wave function by using multiple Brillouin zone angle resolved photoemission Directory of Open Access Journals (Sweden) Dong-Wook Lee 2010-10-01 Full Text Available Angle resolved photoemission spectroscopy (ARPES is a powerful tool to investigate electronic structures in solids and has been widely used in studying various materials. The electronic structure information by ARPES is obtained in the momentum space. However, in the case of one-dimensional system, we here show that we extract the real space information from ARPES data taken over multiple Brillouin zones (BZs. Intensities in the multiple BZs are proportional to the photoemission matrix element which contains information on the coefficient of the Bloch wave function. It is shown that the Bloch wave function coefficients can be extracted from ARPES data, which allows us to construct the real space wave function. As a test, we use ARPES data from proto-typical one-dimensional system SrCuO2 and construct the real space wave function. 5. Electronic structure of K0.5CoO2 studied by angle-resolved photoemission spectroscopy International Nuclear Information System (INIS) Usui, H.; Iwasawa, H.; Hirose, M.; Maeda, Y.; Saitoh, T.; Osada, H.; Kyomen, T.; Hanaya, M.; Aiura, Y.; Kotani, Y.; Kubota, M.; Ono, K. 2010-01-01 We have investigated the electronic structure of K 0.5 CoO 2 in the metallic phase by high-resolution angle-resolved photoemission spectroscopy at a low temperature. An observed Fermi surface of K 0.5 CoO 2 was a large hexagonal one around the Γ point only, with no hole pockets on the Γ-K lines which was typically predicted by band-structure calculations with local-density approximation (LDA). We also found that a modulation of the Fermi velocity, which was the largest at K point and the smallest at M point, was again opposite to the prediction by LDA band-theory. In spite of this conflicting with LDA band-theory, our results are both in agreement with what was observed in Na x CoO 2 . 6. Electrostatic mass spectrometer for concurrent mass-, energy- and angle-resolved measurements International Nuclear Information System (INIS) Golikov, Yu.K.; Krasnova, N.K. 1999-01-01 A new electron-optical scheme is considered. An energy- and mass-analyser with angular resolution are combined in one device, in which a time-of-flight principle of mass separation is used. The tool is created on the basis of electrostatic field of quasi-conical systems possessing the high-energy dispersion and high-angular resolution. A regime of simultaneous angular and energy resolution is found. If there is an ion-pulsed source then the ion groups of equal mass will be registered at the same time at a position-sensitive detector located at the edge of the field. Real parameters of the suggested scheme are calculated 7. Direct angle resolved photoemission spectroscopy and ... Keywords. Condensed matter physics; high-c superconductivity; electronic properties; photoemission spectroscopy; angle resolved photoemission spectroscopy; cuprates; films; strain; pulsed laser deposition. 8. Electronic structure of ion arsenic high temperature superconductors studied by angle resolved photoemission spectroscopy Energy Technology Data Exchange (ETDEWEB) Liu, Chang [Iowa State Univ., Ames, IA (United States) 2011-01-01 The main purpose of the present thesis is to present our ARPES results on the iron arsenic superconductors. As revealed by a series of ARPES measurements on both the AEFe2As2 and the RFeAs(O,F) families (parent compound and carrier-doped systems), the electronic structures of the pnictides are complicated, three dimensional, and closely linked to their superconducting behavior (13; 14; 15; 16; 17; 18; 19). Parent compounds of these materials exhibit the basic hole-electron pocket dual plus an apparent Fermi surface reconstruction caused by long range antiferromagnetism (13; 15). When carriers are introduced, the chemical potential shifts in accordance with the Luttinger theorem and the rigid band shifting picture (13). Importantly, both the appearance and disappearance of the superconducting dome at low and high doping levels have intimate relation with topological changes at the Fermi surfaces, resulting in a specific Fermi topology being favored by superconductivity (15; 16). On the low doping side, superconductivity emerges in the phase diagram once the antiferromagnetic reconstruction disappears below the Fermi level, returning the Fermi surface to its paramagnetic-like appearance. On the high doping side, superconductivity disappears around a doping level at which the central hole pocket vanishes due to increasing electron concentration. Such phenomena are evidence for the governing role the electronic structure plays in their superconducting behavior. 9. Anisotropic electronic band structure of intrinsic Si(110) studied by angle-resolved photoemission spectroscopy and first-principles calculations Science.gov (United States) Matsushita, Stephane Yu; Takayama, Akari; Kawamoto, Erina; Hu, Chunping; Hagiwara, Satoshi; Watanabe, Kazuyuki; Takahashi, Takashi; Suto, Shozo 2017-09-01 We have studied the electronic band structure of the hydrogen-terminated Si(110)-(1 ×1 ) [H:Si(110)-(1 ×1 )] surface using angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations in the framework of density functional theory with local density approximation (LDA). The bulk-truncated H:Si(110)-(1 ×1 ) surface is a good template to investigate the electronic band structure of the intrinsic Si(110). In the ARPES spectra, seven bulk states and one surface state due to the H-H interaction are observed clearly. The four bulk states consisting of Si 3 px y orbitals exhibit anisotropic band dispersions along the high symmetric direction of Γ ¯-X ¯ and Γ ¯-X¯' directions, where one state shows one-dimensional character. The calculated band structures show a good agreement with the experimental results except the surface state. We discuss the exact nature of electronic band structures and the applicability of LDA. We have estimated the anisotropic effective masses of electrons and holes of Si(110) for device application. 10. Dissimilarities between the electronic structure of chemically doped and chemically pressurized iron pnictides from an angle-resolved photoemission spectroscopy study NARCIS (Netherlands) Thirupathaiah, S.; Rienks, E.D.L.; Jeevan, H.S.; Ovsyannikov, R.; Slooten, E.; Kaas, J.; van Heumen, E.; de Jong, S.; Duerr, H.A.; Siemensmeyer, K.; Follath, R.; Gegenwart, P.; Golden, M.S.; Fink, J. 2011-01-01 We have studied the electronic structure of EuFe2As2-xPx using high-resolution angle-resolved photoemission spectroscopy. Upon substituting As with the isovalent P, which leads to chemical pressure and to superconductivity, we observe a nonrigid-band-like change of the electronic structure along the 11. Dissimilarities between the electronic structure of chemically doped and chemically pressurized iron pnictides from an angle-resolved photoemission spectroscopy study NARCIS (Netherlands) Thirupathaiah, S.; Rienks, E.D.L.; Jeevan, H.S.; Ovsyannikov, R.; Slooten, E.; Kaas, J.; van Heumen, E.; de Jong, S.; Dürr, H.A.; Siemensmeyer, K.; Follath, R.; Gegenwart, P.; Golden, M.S.; Fink, J. 2010-01-01 We have studied the electronic structure of EuFe2As2-xPx using high resolution angle-resolved photoemission spectroscopy. Upon substituting As with the isovalent P, which leads to a chemical pressure and to superconductivity, we observe a non-rigid-band like change of the electronic structure along 12. Angle-resolved energy distributions of laser ablated silver ions in vacuum DEFF Research Database (Denmark) Hansen, T.N.; Schou, Jørgen; Lunney, J.G. 1998-01-01 The energy distributions of ions ablated from silver in vacuum have been measured in situ for pulsed laser irradiation at 355 nm. We have determined the energy spectra for directions ranging from 5 degrees to 75 degrees with respect to the normal in the intensity range from 100 to 400 MW/cm(2... 13. Momentum-resolved electronic structure at a buried interface from soft X-ray standing-wave angle-resolved photoemission NARCIS (Netherlands) Gray, A.X.; Minar, J.; Plucinski, L.; Huijben, Mark; Bostwick, A.; Rotenberg, E.; Yang, S.-H.; Braun, J.; Winkelmann, A.; Conti, G.; Eiteneer, D.; Rattanachata, A.; Greer, A.A.; Ciston, J.; Ophus, C.; Rijnders, Augustinus J.H.M.; Blank, David H.A.; Doennig, D.; Pentcheva, R.; Kortright, J.B.; Schneider, C.M.; Ebert, H.; Fadley, C.S. 2013-01-01 Angle-resolved photoemission spectroscopy (ARPES) is a powerful technique for the study of electronic structure, but it lacks a direct ability to study buried interfaces between two materials. We address this limitation by combining ARPES with soft X-ray standing-wave (SW) excitation (SWARPES), in 14. Probing long-range structural order in SnPc/Ag(111) by umklapp process assisted low-energy angle-resolved photoelectron spectroscopy Science.gov (United States) Jauernik, Stephan; Hein, Petra; Gurgel, Max; Falke, Julian; Bauer, Michael 2018-03-01 Laser-based angle-resolved photoelectron spectroscopy is performed on tin-phthalocyanine (SnPc) adsorbed on silver Ag(111). Upon adsorption of SnPc, strongly dispersing bands are observed which are identified as secondary Mahan cones formed by surface umklapp processes acting on photoelectrons from the silver substrate as they transit through the ordered adsorbate layer. We show that the photoemission data carry quantitative structural information on the adsorbate layer similar to what can be obtained from a conventional low-energy electron diffraction (LEED) study. More specifically, we compare photoemission data and LEED data probing an incommensurate-to-commensurate structural phase transition of the adsorbate layer. Based on our results we propose that Mahan-cone spectroscopy operated in a pump-probe configuration can be used in the future to probe structural dynamics at surfaces with a temporal resolution in the sub-100-fs regime. 15. Evidence for Anionic Excess Electrons in a Quasi-Two-Dimensional Ca2N Electride by Angle-Resolved Photoemission Spectroscopy. Science.gov (United States) Oh, Ji Seop; Kang, Chang-Jong; Kim, Ye Ji; Sinn, Soobin; Han, Moonsup; Chang, Young Jun; Park, Byeong-Gyu; Kim, Sung Wng; Min, Byung Il; Kim, Hyeong-Do; Noh, Tae Won 2016-03-02 Angle-resolved photoemission spectroscopy (ARPES) study of a layered electride Ca2N was carried out to reveal its quasi-two-dimensional electronic structure. The band dispersions and the Fermi-surface map are consistent with the density functional theory results except for a chemical potential shift that may originate from the high reactivity of surface excess electrons. Thus, the existence of anionic excess electrons in the interlayer region of Ca2N is strongly supported by ARPES. 16. Electronic Structure of Epitaxial Thin Films of the Transparent Conducting Oxide La:BaSnO3 Measured By In-Situ Angle-Resolved Photoemission Spectroscopy Science.gov (United States) Lochocki, Edward; Paik, Hanjong; Uchida, Masaki; Schlom, Darrell; Shen, Kyle Lanthanum-doped barium stannate (La:BaSnO3) is a transparent conducting oxide where single crystals have exhibited unusually high mobility and oxygen stability. Here we present in-situ angle-resolved photoemission (ARPES) measurements of La:BaSnO3 epitaxial films that were co-deposited onto lattice-matched rare-earth scandate substrates by molecular-beam epitaxy (MBE). Density functional theory (DFT) calculations agree well with the observed valence bands and predict a parabolic conduction band. However, the features observed near the Fermi energy (EF) are non-dispersive yet localized in momentum space. This unusual appearance may be the result of quasi-localized charge carriers or out-of-plane momentum broadening. Over long measurement periods, we also observe changes to the valence band and near-EF feature that bear a strong resemblance to the beam-induced two-dimensional electron gases previously reported in SrTiO3 and KTaO3. The origin of these unexpected phenomena and their relationship to the structural and transport properties of these films will be discussed. 17. Angle-resolved electron and ion spectroscopy apparatus on the soft X-ray photochemistry beamline BL27SU at SPring-8 CERN Document Server Ueda, K; Senba, Y; Okada, K; Shimizu, Y; Chiba, H; Ohashi, H; Tamenori, Y; Okumura, H; Saitô, N; Nagaoka, S; Hiraya, A; Ishiguro, E; Ibuki, T; Suzuki, I H; Koyano, I 2001-01-01 We have designed and constructed the apparatus for the angular distribution measurements of photoejected electrons and ions from free molecules, as a part of the endstation of the c-branch of the beamline BL27SU, a soft X-ray photochemistry beamline at SPring-8. The experimental procedures are described in combination with the use of a capability to switch the horizontal and vertical directions of the linear polarization of the light produced by the figure-8 undulator. As a typical example of the experimental results, we present angle-resolved energetic ion yield spectra in the O 1s excitation region of CO sub 2. 18. Electronic structure of single crystal UPd{sub 3}, UGe{sub 2}, and USb{sub 2} from hard X-ray and angle-resolved photoelectron spectroscopy Energy Technology Data Exchange (ETDEWEB) Beaux, M.F., E-mail: [email protected] [MPA Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Durakiewicz, T. [MPA Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Moreschini, L.; Grioni, M. [IPN, Ecole Polytechnique Federale (EPFL), CH-1015 Lausanne (Switzerland); Offi, F. [CNISM and Dipartimento de Fisica, Universita Roma Tre, Via della Vasca Navale 84, 1-00146 Rome (Italy); Monaco, G. [European Synchrotron Radiation Facility, B.P. 220, F-38042 Grenoble (France); Panaccione, G. [Istituto Officina dei Materiali CNR, Laboratorio TASC, Area Science Park, Basovizza S.S. 14 Km 163.5, I-34012 Trieste, 9 (Italy); Joyce, J.J.; Bauer, E.D.; Sarrao, J.L. [MPA Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Butterfield, M.T. [KLA-Tencor, 1 Technology Drive, Milpitas, CA (United States); Guziewicz, E. [Institute of Physics, Polish Academy of Sciences, Warsaw (Poland) 2011-11-15 Highlights: {yields} Electronic structure of single crystal UPd{sub 3}, UGe{sub 2}, and USb{sub 2} was measured by hard X-ray and angle-resolved photoemission spectroscopy. {yields} Angle resolved photoemission results demonstrate hybridization between U 5f and Pd 4d electrons within UPd{sub 3}. {yields} HAXPES probing of bulk features within of UPd{sub 3}, UGe{sub 2}, and USb{sub 2} samples with native oxide contamination demonstrated. {yields} Two distinct spectral features identified for Sb I and Sb II sites within USb{sub 2} HAXPES spectrum. {yields} Line shape analysis reveals correlations between Doniach-Sunjic asymmetry coefficients and 5f localization. - Abstract: Electronic structure of single crystal UPd{sub 3}, UGe{sub 2}, and USb{sub 2} has been measured from hard X-ray photoelectron spectroscopy (HAXPES) with 7.6 keV photons at the European Synchrotron Radiation Facility (ESRF). Lower photon energy angle-resolved photoelectron spectroscopy (ARPES) was also performed at the Synchrotron Radiation Center (SRC). Herein the following results are presented: (i) ARPES results demonstrate hybridization between the U 5f and Pd 4d electrons within UPd{sub 3}. (ii) The greatly reduced surface sensitivity of HAXPES enabled observation of the bulk core levels in spite of surface oxidation. Photoelectron mean-free-path versus oxide layer thickness considerations were used to model the effectiveness of HAXPES for probing bulk features of in-air cleaved samples. (iii) Two distinct features separated by 800 meV were observed for the Sb 3d core level. These two features are attributed to manifestations of two distinct Sb sites within the USb{sub 2} single crystal as supported by consideration of interatomic distances and enthalpy-of-formation. (iv) Doniach-Sunjic line shape analysis of core level spectral features revealed correlations between asymmetry coefficients and 5f localization. 19. Review of the theoretical description of time-resolved angle-resolved photoemission spectroscopy in electron-phonon mediated superconductors Energy Technology Data Exchange (ETDEWEB) Kemper, A.F. [Department of Physics, North Carolina State University, Raleigh, NC (United States); Sentef, M.A. [Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Hamburg (Germany); Moritz, B. [Stanford Institute for Materials and Energy Sciences (SIMES), SLAC National Accelerator Laboratory, Menlo Park, CA (United States); Devereaux, T.P. [Stanford Institute for Materials and Energy Sciences (SIMES), SLAC National Accelerator Laboratory, Menlo Park, CA (United States); Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA (United States); Freericks, J.K. [Department of Physics, Georgetown University, Washington, DC (United States) 2017-09-15 We review recent work on the theory for pump/probe photoemission spectroscopy of electron-phonon mediated superconductors in both the normal and the superconducting states. We describe the formal developments that allow one to solve the Migdal-Eliashberg theory in nonequilibrium for an ultrashort laser pumping field, and explore the solutions which illustrate the relaxation as energy is transferred from electrons to phonons. We focus on exact results emanating from sum rules and approximate numerical results which describe rules of thumb for relaxation processes. In addition, in the superconducting state, we describe how Anderson-Higgs oscillations can be excited due to the nonlinear coupling with the electric field and describe mechanisms where pumping the system enhances superconductivity. (copyright 2017 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) 20. Bulk electronic structure of superconducting LaRu2P2 single crystals measured by soft-X-ray angle-resolved photoemission spectroscopy. Science.gov (United States) Razzoli, E; Kobayashi, M; Strocov, V N; Delley, B; Bukowski, Z; Karpinski, J; Plumb, N C; Radovic, M; Chang, J; Schmitt, T; Patthey, L; Mesot, J; Shi, M 2012-06-22 We present a soft x-ray angle-resolved photoemission spectroscopy (SX-ARPES) study of the stoichiometric pnictide superconductor LaRu(2)P(2). The observed electronic structure is in good agreement with density functional theory (DFT) calculations. However, it is significantly different from its counterpart in high-temperature superconducting Fe pnictides. In particular, the bandwidth renormalization present in the Fe pnictides (~2-3) is negligible in LaRu(2)P(2) even though the mass enhancement is similar in both systems. Our results suggest that the superconductivity in LaRu(2) P(2) has a different origin with respect to the iron pnictides. Finally, we demonstrate that the increased probing depth of SX-ARPES, compared to the widely used ultraviolet ARPES, is essential in determining the bulk electronic structure in the experiment. 1. Exploring electronic structure of one-atom thick polycrystalline graphene films: A nano angle resolved photoemission study Science.gov (United States) Avila, José; Razado, Ivy; Lorcy, Stéphane; Fleurier, Romain; Pichonat, Emmanuelle; Vignaud, Dominique; Wallart, Xavier; Asensio, María C. 2013-01-01 The ability to produce large, continuous and defect free films of graphene is presently a major challenge for multiple applications. Even though the scalability of graphene films is closely associated to a manifest polycrystalline character, only a few numbers of experiments have explored so far the electronic structure down to single graphene grains. Here we report a high resolution angle and lateral resolved photoelectron spectroscopy (nano-ARPES) study of one-atom thick graphene films on thin copper foils synthesized by chemical vapor deposition. Our results show the robustness of the Dirac relativistic-like electronic spectrum as a function of the size, shape and orientation of the single-crystal pristine grains in the graphene films investigated. Moreover, by mapping grain by grain the electronic dynamics of this unique Dirac system, we show that the single-grain gap-size is 80% smaller than the multi-grain gap recently reported by classical ARPES. PMID:23942471 2. Angle-resolved photoemission spectroscopy with 9-eV photon-energy pulses generated in a gas-filled hollow-core photonic crystal fiber Energy Technology Data Exchange (ETDEWEB) Bromberger, H., E-mail: [email protected]; Liu, H.; Chávez-Cervantes, M.; Gierz, I. [Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg (Germany); Ermolov, A.; Belli, F.; Abdolvand, A.; Russell, P. St. J.; Travers, J. C. [Max Planck Institute for the Science of Light, Günther-Scharowsky-Str. 1, 91058 Erlangen (Germany); Calegari, F. [Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg (Germany); Institute for Photonics and Nanotechnologies, IFN-CNR, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); Li, M. T.; Lin, C. T. [Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart (Germany); Cavalleri, A. [Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg (Germany); Clarendon Laboratory, Department of Physics, University of Oxford, Parks Rd. Oxford OX1 3PU (United Kingdom) 2015-08-31 A recently developed source of ultraviolet radiation, based on optical soliton propagation in a gas-filled hollow-core photonic crystal fiber, is applied here to angle-resolved photoemission spectroscopy (ARPES). Near-infrared femtosecond pulses of only few μJ energy generate vacuum ultraviolet radiation between 5.5 and 9 eV inside the gas-filled fiber. These pulses are used to measure the band structure of the topological insulator Bi{sub 2}Se{sub 3} with a signal to noise ratio comparable to that obtained with high order harmonics from a gas jet. The two-order-of-magnitude gain in efficiency promises time-resolved ARPES measurements at repetition rates of hundreds of kHz or even MHz, with photon energies that cover the first Brillouin zone of most materials. 3. The electronic structure of clean and adsorbate-covered Bi2Se3: an angle-resolved photoemission study DEFF Research Database (Denmark) Bianchi, Marco; Hatch, Richard; Guan, Dandan 2012-01-01 , the Dirac point moves to higher binding energies, indicating an increasingly strong downward bending of the bands near the surface. This time-dependent band bending is related to a contamination of the surface and can be accelerated by intentionally exposing the surface to carbon monoxide and other species... 4. Identification of Ni2C electronic states in graphene-Ni(111) growth through resonant and dichroic angle-resolved photoemission at the C K -edge Science.gov (United States) Drera, G.; Cepek, C.; Patera, L. L.; Bondino, F.; Magnano, E.; Nappini, S.; Africh, C.; Lodi-Rizzini, A.; Joshi, N.; Ghosh, P.; Barla, A.; Mahatha, S. K.; Pagliara, S.; Giampietri, A.; Pintossi, C.; Sangaletti, L. 2017-10-01 The graphene-Ni(111) (GrNi) growth via chemical vapor deposition has been explored by resonant, angle-resolved, and dichroic photoemission spectroscopy (soft x-ray Res-ARPES) in order to identify the possible contributions to the electronic structure deriving from different phases that can coexist in this complex system. We provide evidences of electronic states so far unexplored at the Γ ¯ point of GrNi, appearing at the C K -edge resonance. These states show both circular dichroism (CD) and k dependence, suggesting a long-range orbital ordering, as well as a coherent matching with the underlying lattice. Through a comparison of core-level photoemission, valence band resonances, and constant initial-state spectroscopy, we demonstrate that these states are actually induced by a low residual component of nickel carbide (Ni2C ). These results also show that caution must be exercised while interpreting x-ray magnetic circular dichroism collected on C K -edge with Auger partial yield method, due to the presence of CD in photoelectron spectra unrelated to magnetic effects. 5. Orbital character and electron correlation effects on two- and three-dimensional Fermi surfaces in KFe2As2 revealed by angle-resolved photoemission spectroscopy Directory of Open Access Journals (Sweden) Teppei eYoshida 2014-04-01 Full Text Available We have investigated orbital character and electron correlation effects on Fermi surfaces in the hole-overdoped iron pnictide superconductor KFe2As2, which shows a low Tc of ~4 K, by angle-resolved photoemission spectroscopy. From the polarization-dependence of the ARPES spectra, we have determined the orbital character of each Fermi surface. Electron mass renormalization of each band is quantitatively consistent with de Haas-van Alphen results. The outer beta and middle zeta Fermi surfaces show large renormalization factor of m/mb ~6-7, while the inner Fermi surface has a smaller factor m/mb ~2. Middle hole Fermi surface zeta has strong three-dimensionality compared to other Fermi surfaces, indicating the d3z2-r2 orbital character, which may be related to the octet-line nodes recently observed by laser ARPES. The observed orbital-dependent mass renormalization would give constraints on the pairing mechanism with line nodes of this system. 6. Electronic structure and polar catastrophe at the surface of LixCoO2 studied by angle-resolved photoemission spectroscopy Science.gov (United States) Okamoto, Y.; Matsumoto, R.; Yagihara, T.; Iwai, C.; Miyoshi, K.; Takeuchi, J.; Horiba, K.; Kobayashi, M.; Ono, K.; Kumigashira, H.; Saini, N. L.; Mizokawa, T. 2017-09-01 We report an angle-resolved photoemission spectroscopy (ARPES) study of LixCoO2 single crystals which have a hole-doped CoO2 triangular lattice. Similar to NaxCoO2 , the Co 3 d a1 g band crosses the Fermi level with strongly renormalized band dispersion while the Co 3 d eg' bands are fully occupied in LixCoO2 (x =0.46 and 0.71). At x =0.46 , the Fermi surface area is consistent with the bulk hole concentration indicating that the ARPES result represents the bulk electronic structure. On the other hand, at x =0.71 , the Fermi surface area is larger than the expectation which can be associated with the inhomogeneous distribution of Li reported in the previous scanning tunneling microscopy study by Iwaya et al. [Phys. Rev. Lett. 111, 126104 (2013), 10.1103/PhysRevLett.111.126104]. However, the Co 3 d peak is systematically shifted towards the Fermi level with hole doping excluding phase separation between hole rich and hole poor regions in the bulk. Therefore, the deviation of the Fermi surface area at x =0.71 can be attributed to hole redistribution at the surface avoiding polar catastrophe. The bulk Fermi surface of Co 3 d a1 g is very robust around x =0.5 even in the topmost CoO2 layer due to the absence of the polar catastrophe. 7. Angle-resolving time-of-flight electron spectrometer for near-threshold precision measurements of differential cross sections of electron-impact excitation of atoms and molecules International Nuclear Information System (INIS) Lange, M.; Matsumoto, J.; Setiawan, A.; Panajotovic, R.; Harrison, J.; Lower, J. C. A.; Newman, D. S.; Mondal, S.; Buckman, S. J. 2008-01-01 This article presents a new type of low-energy crossed-beam electron spectrometer for measuring angular differential cross sections of electron-impact excitation of atomic and molecular targets. Designed for investigations at energies close to excitation thresholds, the spectrometer combines a pulsed electron beam with the time-of-flight technique to distinguish between scattering channels. A large-area, position-sensitive detector is used to offset the low average scattering rate resulting from the pulsing duty cycle, without sacrificing angular resolution. A total energy resolution better than 150 meV (full width at half maximum) at scattered energies of 0.5-3 eV is achieved by monochromating the electron beam prior to pulsing it. The results of a precision measurement of the differential cross section for electron-impact excitation of helium, at an energy of 22 eV, are used to assess the sensitivity and resolution of the spectrometer 8. Electronic structure of ThRu2Si2 studied by angle-resolved photoelectron spectroscopy: Elucidating the contribution of U 5 f states in URu2Si2 Science.gov (United States) Fujimori, Shin-ichi; Kobata, Masaaki; Takeda, Yukiharu; Okane, Tetsuo; Saitoh, Yuji; Fujimori, Atsushi; Yamagami, Hiroshi; Matsumoto, Yuji; Yamamoto, Etsuji; Tateiwa, Naoyuki; Haga, Yoshinori 2017-09-01 The electronic structure of ThRu2Si2 was studied using angle-resolved photoelectron spectroscopy (ARPES) with incident photon energies of h ν =655 -745 eV. Detailed band structure and the three-dimensional shapes of Fermi surfaces were derived experimentally, and their characteristic features were mostly explained by means of band-structure calculations based on density-functional theory. Comparison of the experimental ARPES spectra of ThRu2Si2 with those of URu2Si2 shows that they have considerably different spectral profiles, particularly in the energy range of 1 eV from the Fermi level, suggesting that U 5 f states are substantially hybridized in these bands. The relationship between the ARPES spectra of URu2Si2 and ThRu2Si2 is very different from the one between the ARPES spectra of CeRu2Si2 and LaRu2Si2 , where the intrinsic difference in their spectra is limited only in the very vicinity of the Fermi energy. The present result suggests that the U 5 f electrons in URu2Si2 have strong hybridization with ligand states and have an essentially itinerant character. 9. Angle-resolved photoemission extended fine structure International Nuclear Information System (INIS) Barton, J.J. 1985-03-01 Measurements of the Angle-Resolved Photoemission Extended Fine Structure (ARPEFS) from the S(1s) core level of a c(2 x 2)S/Ni(001) are analyzed to determine the spacing between the S overlayer and the first and second Ni layers. ARPEFS is a type of photoelectron diffraction measurement in which the photoelectron kinetic energy is swept typically from 100 to 600 eV. By using this wide range of intermediate energies we add high precision and theoretical simplification to the advantages of the photoelectron diffraction technique for determining surface structures. We report developments in the theory of photoelectron scattering in the intermediate energy range, measurement of the experimental photoemission spectra, their reduction to ARPEFS, and the surface structure determination from the ARPEFS by combined Fourier and multiple-scattering analyses. 202 refs., 67 figs., 2 tabs 10. Size effects in van der Waals clusters studied by spin and angle-resolved electron spectroscopy and multi-coincidence ion imaging International Nuclear Information System (INIS) Rolles, D; Pesic, Z D; Zhang, H; Bilodeau, R C; Bozek, J D; Berrah, N 2007-01-01 We have studied the valence and inner-shell photoionization of free rare-gas clusters by means of angle and spin resolved photoelectron spectroscopy and momentum resolving electron-multi-ion coincidence spectroscopy. The electron measurements probe the evolution of the photoelectron angular distribution and spin polarization parameters as a function of photon energy and cluster size, and reveal a strong cluster size dependence of the photoelectron angular distributions in certain photon energy regions. In contrast, the spin polarization parameter of the cluster photoelectrons is found to be very close to the atomic value for all covered photon energies and cluster sizes. The ion imaging measurements, which probe the fragmentation dynamics of multiply charged van der Waals clusters, also exhibit a pronounced cluster size dependence 11. Study of High Temperature Superconductors with Angle-Resolved Photoemission Spectroscopy Energy Technology Data Exchange (ETDEWEB) Dunn, Lisa 2003-05-13 The Angle Resolved Photoemission Spectroscopy (ARPES) recently emerged as a powerful tool for the study of highly correlated materials. This thesis describes the new generation of ARPES experiment, based on the third generation synchrotron radiation source and utilizing very high resolution electron energy and momentum analyzer. This new setup is used to study the physics of high temperature superconductors. New results on the Fermi surfaces, dispersions, scattering rate and superconducting gap in high temperature superconductors are presented. 12. Angle-resolved photoelectron spectroscopy studies of the many-body effects in the electronic structure of high-T{sub c} cuprates Energy Technology Data Exchange (ETDEWEB) Inosov, Dmytro S. 2008-06-18 In the present work some steps are done towards understanding the anomalous effects observed in the single-particle excitation spectra of cuprates. First, the electronic properties of BSCCO are considered. The main result of this part of the work is a model of the Green's function that is later used for calculating the two-particle excitation spectrum. Then, the matrix element effects in the photoemission spectra of cuprates are discussed. After a general introduction to the problem, the thesis focuses on the recently discovered anomalous behavior of the ARPES spectra that partially originates from the momentum-dependent photoemission matrix element. The momentum- and excitation energy dependence of the anomalous high-energy dispersion, termed ''waterfalls'', is covered in full detail. Understanding the role of the matrix element effects in this phenomenon proves crucial, as they obstruct the view of the underlying excitation spectrum that is of indisputable interest. For the optimally doped bilayer Bi-based cuprate, the renormalized two-particle correlation function in the superconducting state is calculated from ARPES data within an itinerant model based on the random phase approximation (RPA). (orig.) 13. Photoelectron spectroscopy at a free-electron laser. Investigation of space-charge effects in angle-resolved and core-level spectroscopy and realizaton of a time-resolved core-level photoemission experiment International Nuclear Information System (INIS) Marczynski-Buehlow, Martin 2012-01-01 The free-electron laser (FEL) in Hamburg (FLASH) is a very interesting light source with which to perform photoelectron spectroscopy (PES) experiments. Its special characteristics include highly intense photon pulses (up to 100 J/pulse), a photon energy range of 30 eV to 1500 eV, transverse coherence as well as pulse durations of some ten femtoseconds. Especially in terms of time-resolved PES (TRPES), the deeper lying core levels can be reached with photon energies up to 1500 eV with acceptable intensity now and, therefore, element-specific, time-resolved core-level PES (XPS) is feasible at FLASH. During the work of this thesis various experimental setups were constructed in order to realize angle-resolved (ARPES), core-level (XPS) as well as time-resolved PES experiments at the plane grating monochromator beamline PG2 at FLASH. Existing as well as newly developed systems for online monitoring of FEL pulse intensities and generating spatial and temporal overlap of FEL and optical laser pulses for time-resolved experiments are successfully integrated into the experimental setup for PES. In order to understand space-charge effects (SCEs) in PES and, therefore, being able to handle those effects in future experiments using highly intense and pulsed photon sources, the origin of energetic broadenings and shifts in photoelectron spectra are studied by means of a molecular dynamic N-body simulation using a modified Treecode Algorithm for sufficiently fast and accurate calculations. It turned out that the most influencing parameter is the ''linear electron density'' - the ratio of the number of photoelectrons to the diameter of the illuminated spot on the sample. Furthermore, the simulations could reproduce the observations described in the literature fairly well. Some rules of thumb for XPS and ARPES measurements could be deduced from the simulations. Experimentally, SCEs are investigated by means of ARPES as well as XPS measurements as a function of FEL pulse 14. Photoelectron spectroscopy at a free-electron laser. Investigation of space-charge effects in angle-resolved and core-level spectroscopy and realizaton of a time-resolved core-level photoemission experiment Energy Technology Data Exchange (ETDEWEB) Marczynski-Buehlow, Martin 2012-01-30 The free-electron laser (FEL) in Hamburg (FLASH) is a very interesting light source with which to perform photoelectron spectroscopy (PES) experiments. Its special characteristics include highly intense photon pulses (up to 100 J/pulse), a photon energy range of 30 eV to 1500 eV, transverse coherence as well as pulse durations of some ten femtoseconds. Especially in terms of time-resolved PES (TRPES), the deeper lying core levels can be reached with photon energies up to 1500 eV with acceptable intensity now and, therefore, element-specific, time-resolved core-level PES (XPS) is feasible at FLASH. During the work of this thesis various experimental setups were constructed in order to realize angle-resolved (ARPES), core-level (XPS) as well as time-resolved PES experiments at the plane grating monochromator beamline PG2 at FLASH. Existing as well as newly developed systems for online monitoring of FEL pulse intensities and generating spatial and temporal overlap of FEL and optical laser pulses for time-resolved experiments are successfully integrated into the experimental setup for PES. In order to understand space-charge effects (SCEs) in PES and, therefore, being able to handle those effects in future experiments using highly intense and pulsed photon sources, the origin of energetic broadenings and shifts in photoelectron spectra are studied by means of a molecular dynamic N-body simulation using a modified Treecode Algorithm for sufficiently fast and accurate calculations. It turned out that the most influencing parameter is the ''linear electron density'' - the ratio of the number of photoelectrons to the diameter of the illuminated spot on the sample. Furthermore, the simulations could reproduce the observations described in the literature fairly well. Some rules of thumb for XPS and ARPES measurements could be deduced from the simulations. Experimentally, SCEs are investigated by means of ARPES as well as XPS measurements as a function of 15. Tuning the electronic structure of bulk FeSe with chemical pressure using quantum oscillations and angle resolved photoemission spectroscopy (ARPES) Science.gov (United States) Coldea, Amalia FeSe is a unique and intriguing superconductor which can be tuned into a high temperature superconducting state using applied pressure, chemical intercalation and surface doping. In the absence of magnetism, the structural transition in FeSe is believed to be electronically driven, with the orbital degrees of freedom playing an important part. This scenario supports the stabilization of a nematic state in FeSe, which manifests as a Fermi surface deformation in the presence of strong interactions, as detected by ARPES. Another manifestation of the nematicity is the enhanced nematic susceptibility determined from elastoresistance measurements under applied strain. Isovalent Sulphur substitution onto the Selenium site constitutes a chemical pressure, which subtly modifies the electronic structure of FeSe, suppressing the structural transition without inducing high temperature superconductivity. I will present the evolution of the electronic structure with chemical pressure in FeSe, as determined from quantum oscillations and ARPES studies and I will discuss the suppression of the nematic electronic state and the role of electronic correlations. Experiments were performed at high magnetic field facilities in Tallahassee, Nijmegen and Toulouse and Diamond Light Source, UK. This work is mainly supported by EPSRC, UK (EP/I004475/1, EP/I017836/1) and I acknowledge my collaborators from Refs. . 16. Exploring the Electronic Structure and Chemical Homogeneity of Individual Bi2Te3 Nanowires by Nano-Angle-Resolved Photoemission Spectroscopy. Science.gov (United States) Krieg, Janina; Chen, Chaoyu; Avila, José; Zhang, Zeying; Sigle, Wilfried; Zhang, Hongbin; Trautmann, Christina; Asensio, Maria Carmen; Toimil-Molares, Maria Eugenia 2016-07-13 Due to their high surface-to-volume ratio, cylindrical Bi2Te3 nanowires are employed as model systems to investigate the chemistry and the unique conductive surface states of topological insulator nanomaterials. We report on nanoangle-resolved photoemission spectroscopy (nano-ARPES) characterization of individual cylindrical Bi2Te3 nanowires with a diameter of 100 nm. The nanowires are synthesized by electrochemical deposition inside channels of ion-track etched polymer membranes. Core level spectra recorded with submicron resolution indicate a homogeneous chemical composition along individual nanowires, while nano-ARPES intensity maps reveal the valence band structure at the single nanowire level. First-principles electronic structure calculations for chosen crystallographic orientations are in good agreement with those revealed by nano-ARPES. The successful application of nano-ARPES on single one-dimensional nanostructures constitutes a new avenue to achieve a better understanding of the electronic structure of topological insulator nanomaterials. 17. Angle-resolved photoemission spectra of graphene from first-principles calculations. Science.gov (United States) Park, Cheol-Hwan; Giustino, Feliciano; Spataru, Catalin D; Cohen, Marvin L; Louie, Steven G 2009-12-01 Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental technique for directly probing electron dynamics in solids. The energy versus momentum dispersion relations and the associated spectral broadenings measured by ARPES provide a wealth of information on quantum many-body interaction effects. In particular, ARPES allows studies of the Coulomb interaction among electrons (electron-electron interactions) and the interaction between electrons and lattice vibrations (electron-phonon interactions). Here, we report ab initio simulations of the ARPES spectra of graphene including both electron-electron and electron-phonon interactions on the same footing. Our calculations reproduce some of the key experimental observations related to many-body effects, including the indication of a mismatch between the upper and lower halves of the Dirac cone. 18. High Resolution Angle Resolved Photoemission Studies on Quasi-Particle Dynamics in Graphite Energy Technology Data Exchange (ETDEWEB) Leem, C.S. 2010-06-02 We obtained the spectral function of the graphite H point using high resolution angle resolved photoelectron spectroscopy (ARPES). The extracted width of the spectral function (inverse of the photo-hole lifetime) near the H point is approximately proportional to the energy as expected from the linearly increasing density of states (DOS) near the Fermi energy. This is well accounted by our electron-phonon coupling theory considering the peculiar electronic DOS near the Fermi level. And we also investigated the temperature dependence of the peak widths both experimentally and theoretically. The upper bound for the electron-phonon coupling parameter is 0.23, nearly the same value as previously reported at the K point. Our analysis of temperature dependent ARPES data at K shows that the energy of phonon mode of graphite has much higher energy scale than 125K which is dominant in electron-phonon coupling. 19. Dimensional Crossover in a Charge Density Wave Material Probed by Angle-Resolved Photoemission Spectroscopy Science.gov (United States) Nicholson, C. W.; Berthod, C.; Puppin, M.; Berger, H.; Wolf, M.; Hoesch, M.; Monney, C. 2017-05-01 High-resolution angle-resolved photoemission spectroscopy data reveal evidence of a crossover from one-dimensional (1D) to three-dimensional (3D) behavior in the prototypical charge density wave (CDW) material NbSe3 . In the low-temperature 3D regime, gaps in the electronic structure are observed due to two incommensurate CDWs, in agreement with x-ray diffraction and electronic-structure calculations. At higher temperatures we observe a spectral weight depletion that approaches the power-law behavior expected in one dimension. From the warping of the quasi-1D Fermi surface at low temperatures, we extract the energy scale of the dimensional crossover. This is corroborated by a detailed analysis of the density of states, which reveals a change in dimensional behavior dependent on binding energy. Our results offer an important insight into the dimensionality of excitations in quasi-1D materials. 20. Strong electron correlations in the normal state of the iron-based FeSe0.42Te0.58 superconductor observed by angle-resolved photoemission spectroscopy. Science.gov (United States) Tamai, A; Ganin, A Y; Rozbicki, E; Bacsa, J; Meevasana, W; King, P D C; Caffio, M; Schaub, R; Margadonna, S; Prassides, K; Rosseinsky, M J; Baumberger, F 2010-03-05 We investigate the normal state of the "11" iron-based superconductor FeSe0.42Te0.58 by angle-resolved photoemission. Our data reveal a highly renormalized quasiparticle dispersion characteristic of a strongly correlated metal. We find sheet dependent effective carrier masses between approximately 3 and 16m{e} corresponding to a mass enhancement over band structure values of m{}/m{band} approximately 6-20. This is nearly an order of magnitude higher than the renormalization reported previously for iron-arsenide superconductors of the "1111" and "122" families but fully consistent with the bulk specific heat. 1. Integrated experimental setup for angle resolved photoemission spectroscopy of transuranic materials. Science.gov (United States) Graham, Kevin S; Joyce, John J; Durakiewicz, Tomasz 2013-09-01 We have developed the Angle Resolved Photoemission Spectroscopy (ARPES) system for transuranic materials. The ARPES transuranic system is an endstation upgrade to the Laser Plasma Light Source (LPLS) at Los Alamos National Laboratory. The LPLS is a tunable light source for photoemission with a photon energy range covering the vacuum ultraviolet (VUV) and soft x-ray regions (27-140 eV). The LPLS was designed and developed for transuranic materials. Transuranic photoemission is currently not permitted at the public synchrotrons worldwide in the VUV energy range due to sample encapsulation requirements. With the addition of the ARPES capability to the LPLS system there is an excellent opportunity to explore new details centered on the electronic structure of actinide and transuranic materials. 2. Indoor Measurement of Angle Resolved Light Absorption by Black Silicon DEFF Research Database (Denmark) Amdemeskel, Mekbib Wubishet; Iandolo, Beniamino; Davidsen, Rasmus Schmidt 2017-01-01 Angle resolved optical spectroscopy of photovoltaic (PV) samples gives crucial information on PV panels under realistic working conditions. Here, we introduce measurements of angle resolved light absorption by PV cells, performed indoors using a collimated high radiance broadband light source. Our...... indoor method offers a significant simplification as compared to measurements by solar trackers. As a proof-of-concept demonstration, we show characterization of black silicon solar cells. The experimental results showed stable and reliable optical responses that makes our setup suitable for indoor......, angle resolved characterization of solar cells.... 3. Angle-resolved photoelectron cross section of CF4 International Nuclear Information System (INIS) Carlson, T.A.; Fahlman, A.; Svensson, W.A.; Krause, M.O.; Whitley, T.A.; Grimm, F.A.; Piancastelli, M.N.; Taylor, J.W. 1984-01-01 Partial photoelectron cross sections sigma and angular distribution parameters β were obtained for the first five valence orbitals in CF 4 : 1t 1 , 4t 2 , 1e, 3t 2 , and 4a 1 , as a function of photon energy from 17 to 70 eV. These data were taken with the aid of angle-resolved photoelectron spectroscopy and synchrotron radiation. The results were compared with earlier data on CCl 4 . Substantial differences were found. These are explained partly in terms of the absence of a Cooper minimum with a fluorine compound as opposed to the presence of a Cooper minimum with chlorine compounds and partly in terms of the position of shape resonances. Data on CF 4 were also compared with recent calculations of Stephens et al., who used the multiple-scattering Xα method. Structure in the photoelectron spectrum of CF 4 lying on the low energy side of the third band was identified as due to autoionization and evidence is given as to its specific nature 4. Precision angle-resolved autoionization resonances in Ar and Ne Energy Technology Data Exchange (ETDEWEB) Berrah, N.; Langer, B.; Gorczyca, T.W. [Western Michigan Univ., Kalamazoo, MI (United States)] [and others 1997-04-01 Theoretical work has shown that the electron angular distribution and the shape of the autoionization resonances are crucial to the understanding of certain types of electron-electron correlation. Autoionization resonances in Ne (Ar) result from the decay of the excited discrete state Ne{sup } 2s2p{sup 6} np (Ar{sup } 3s3p{sup 6} np) into the continuum state Ne{sup +} 2s{sup 2}2p{sup 5} + e{sup {minus}} (ks,kd) (Ar{sup +} 3s{sup 2}3p{sup 5} + e{sup {minus}} (ks,kd)). Since the continuum can also be reached by direct photoionization, both paths add coherently, giving rise to interferences that produce the characteristic Beutler-Fano line shape. In this work, the authors report on quantitative angle-resolved electron spectrometry studies of (a) the Ne 2s{sup 2}2p{sup 6} {r_arrow} 2s2p{sup 6} np (n=3-5) autoionizing resonances and the 2s{sup 2}2p{sup 6} {r_arrow} 2p{sup 4}3s3p doubly excited resonance, (b) the Ar 3s{sup 2}3p{sup 6} {r_arrow} 3s3p{sup 6} np (n=4-9) autoionization resonances and extended R-matrix calculations of the angular-distribution parameters for both Ne and Ar measurements. Their results are compared with previous theoretical work by Taylor. 5. Angle-resolved photoemission spectroscopy of rare earth LaSb{sub 2} Energy Technology Data Exchange (ETDEWEB) Michiardi, Matteo; Arnold, Fabian; Faerch Fisher, Karl Frederik; Svane, Axel; Bianchi, Marco; Brummerstedt Iversen, Bo; Hofmann, Philip [Aarhus University (Denmark); Shwetha, G.; Kanchana, V. [IIT-Hyderabad (India); Ganapathy, Vaitheeswaran [University of Hyderabad (India) 2016-07-01 Several rare earth diantimonides have been found to exhibit intriguing electronic properties such as anisotropic linear and non-saturating magnetoresistance. Among these materials, LaSb{sub 2} is not only considered for application in magnetoresistive devices but it is also found to be superconducting at low temperatures and it is investigated as candidate material to host charge density wave phases. Despite the several studies on its transport properties, the electronic structure of LaSb{sub 2} is still largely unknown. Here we present an angle-resolved photoemission spectroscopy and ab-initio calculation study of LaSb{sub 2}(001). The observed band structure is found to be in good agreement with theoretical predictions. Our results reveal that LaSb{sub 2} is a semimetal with a strongly nested two-dimensional Fermi surface. The low energy spectrum is characterized by four massive hole pockets and by four shallow, strongly directional, electron pockets that exhibit Dirac-like dispersion. We speculate on the possibility that this peculiar electronic structure drives the magnetoresistance to its quantum limit, explaining its unconventional behavior. 6. The ALOISA end station at Elettra: a novel multicoincidence spectrometer for angle resolved APECS CERN Document Server Gotter, R; Morgante, A; Cvetko, D; Floreano, L; Tommasini, F; Stefani, G 2001-01-01 Coincidence measurements have been extensively performed in atomic and molecular physics since early 1970s. To apply this methodology to solids and surfaces has been a major target since early days, but the long average time needed to complete a coincidence experiment has hampered its attainment. In particular the coincidence technique has not been yet applied in an angle resolved way such for studying the momentum correlation in the ejection of electron pairs from solid surfaces. The experimental chamber at the ALOISA beamline at Elettra, by means of a set of seven homemade electron analyzers, is the first apparatus able to perform Angle Resolved - Auger Photoelectron Coincidence Spectroscopy (AR-APECS) from solid surfaces. In the typical setup ten different pairs of coincident electrons can be measured simultaneously, so reducing the acquisition time by one order of magnitude. 7. Invited Article: High resolution angle resolved photoemission with tabletop 11 eV laser. Science.gov (United States) He, Yu; Vishik, Inna M; Yi, Ming; Yang, Shuolong; Liu, Zhongkai; Lee, James J; Chen, Sudi; Rebec, Slavko N; Leuenberger, Dominik; Zong, Alfred; Jefferson, C Michael; Moore, Robert G; Kirchmann, Patrick S; Merriam, Andrew J; Shen, Zhi-Xun 2016-01-01 We developed a table-top vacuum ultraviolet (VUV) laser with 113.778 nm wavelength (10.897 eV) and demonstrated its viability as a photon source for high resolution angle-resolved photoemission spectroscopy (ARPES). This sub-nanosecond pulsed VUV laser operates at a repetition rate of 10 MHz, provides a flux of 2 × 10(12) photons/s, and enables photoemission with energy and momentum resolutions better than 2 meV and 0.012 Å(-1), respectively. Space-charge induced energy shifts and spectral broadenings can be reduced below 2 meV. The setup reaches electron momenta up to 1.2 Å(-1), granting full access to the first Brillouin zone of most materials. Control over the linear polarization, repetition rate, and photon flux of the VUV source facilitates ARPES investigations of a broad range of quantum materials, bridging the application gap between contemporary low energy laser-based ARPES and synchrotron-based ARPES. We describe the principles and operational characteristics of this source and showcase its performance for rare earth metal tritellurides, high temperature cuprate superconductors, and iron-based superconductors. 8. Angle-resolved ion TOF spectrometer with a position sensitive detector Energy Technology Data Exchange (ETDEWEB) Saito, Norio [Electrotechnical Lab., Tsukuba, Ibaraki (Japan); Heiser, F.; Wieliczec, K.; Becker, U. 1996-07-01 A angle-resolved ion time-of-flight mass spectrometer with a position sensitive anode has been investigated. Performance of this spectrometer has been demonstrated by measuring an angular distribution of a fragment ion pair, C{sup +} + O{sup +}, from CO at the photon energy of 287.4 eV. The obtained angular distribution is very close to the theoretically expected one. (author) 9. Band structures of 4f and 5f materials studied by angle-resolved photoelectron spectroscopy. Science.gov (United States) Fujimori, Shin-ichi 2016-04-20 Recent remarkable progress in angle-resolved photoelectron spectroscopy (ARPES) has enabled the direct observation of the band structures of 4f and 5f materials. In particular, ARPES with various light sources such as lasers (hν ~ 7 eV) or high-energy synchrotron radiations (hν >/~ 400 eV) has shed light on the bulk band structures of strongly correlated materials with energy scales of a few millielectronvolts to several electronvolts. The purpose of this paper is to summarize the behaviors of 4f and 5f band structures of various rare-earth and actinide materials observed by modern ARPES techniques, and understand how they can be described using various theoretical frameworks. For 4f-electron materials, ARPES studies of CeMIn5(M = Rh, Ir, and Co) and YbRh2Si2 with various incident photon energies are summarized. We demonstrate that their 4f electronic structures are essentially described within the framework of the periodic Anderson model, and that the band-structure calculation based on the local density approximation cannot explain their low-energy electronic structures. Meanwhile, electronic structures of 5f materials exhibit wide varieties ranging from itinerant to localized states. For itinerant U5f compounds such as UFeGa5, their electronic structures can be well-described by the band-structure calculation assuming that all U5f electrons are itinerant. In contrast, the band structures of localized U5f compounds such as UPd3 and UO2 are essentially explained by the localized model that treats U5f electrons as localized core states. In regards to heavy fermion U-based compounds such as the hidden-order compound URu2Si2, their electronic structures exhibit complex behaviors. Their overall band structures are generally well-explained by the band-structure calculation, whereas the states in the vicinity of EF show some deviations due to electron correlation effects. Furthermore, the electronic structures of URu2Si2 in the paramagnetic and hidden-order phases are 10. Dynamics of Molecular Orientation Observed Using Angle Resolved Photoemission Spectroscopy during Deposition of Pentacene on Graphite. Science.gov (United States) Park, Sang Han; Kwon, Soonnam 2016-04-19 A real-time method to observe both the structural and the electronic configuration of an organic molecule during deposition is reported for the model system of pentacene on graphite. Structural phase transition of the thin films as a function of coverage is monitored by using in situ angle resolved photoemission spectroscopy (ARPES) results to observe the change of the electronic configuration at the same time. A photoemission theory that uses independent atomic center approximations is introduced to identify the molecular orientation from the ARPES technique. This study provides a practical insight into interpreting ARPES data regarding dynamic changes of molecular orientation during initial growth of molecules on a well-defined surface. 11. An experimentalist's guide to the matrix element in angle resolved photoemission International Nuclear Information System (INIS) Moser, Simon 2017-01-01 Highlights: • An introduction to the art of angle resolved photoemission is presented. • Matrix element effects are described by a nearly free electron final state model. • ARPES spectral weight of a Bloch band can be calculated from the Fourier transform of its Wannier orbital. • Experimental handedness and improper polarization introduce dichroism. • Instructive showcases from modern ARPES are discussed in detail. - Abstract: Angle resolved photoemission spectroscopy (ARPES) is commonly known as a powerful probe of the one-electron removal spectral function in ordered solid state. With increasing efficiency of light sources and spectrometers, experiments over a wide range of emission angles become more and more common. Consequently, the angular variation of ARPES spectral weight – often times termed “matrix element effect” – enters as an additional source of information. In this tutorial, we develop a simple but instructive free electron final state approach based on the three-step model to describe the intensity distribution in ARPES. We find a compact expression showing that the ARPES spectral weight of a given Bloch band is essentially determined by the momentum distribution (the Fourier transform) of its associated Wannier orbital – times a polarization dependent pre-factor. While the former is giving direct information on the symmetry and shape of the electronic wave function, the latter can give rise to surprising geometric effects. We discuss a variety of modern and instructive experimental showcases for which this simplistic formalism works astonishingly well and discuss the limits of this approach. 12. Angle-resolved photoluminescence spectrum of a uniform phosphor layer Science.gov (United States) Fujieda, Ichiro; Ohta, Masamichi 2017-10-01 A photoluminescence spectrum depends on an emission angle due to self-absorption in a phosphor material. Assuming isotropic initial emission and Lambert-Beer's law, we have derived simple expressions for the angle-resolved spectra emerging from the top and bottom surfaces of a uniform phosphor layer. The transmittance of an excitation light through the phosphor layer can be regarded as a design parameter. For a strongly-absorbing phosphor layer, the forward flux is less intense and more red-shifted than the backward flux. The red-shift is enhanced as the emission direction deviates away from the plane normal. When we increase the transmittance, the backward flux decreases monotonically. The forward flux peaks at a certain transmittance value. The two fluxes become similar to each other for a weakly-absorbing phosphor layer. We have observed these behaviors in experiment. In a practical application, self-absorption decreases the efficiency of conversion and results in angle-dependent variations in chromaticity coordinates. A patterned phosphor layer with a secondary optical element such as a remote reflector alleviates these problems. 13. Angle-resolved photoluminescence spectrum of a uniform phosphor layer Directory of Open Access Journals (Sweden) Ichiro Fujieda 2017-10-01 Full Text Available A photoluminescence spectrum depends on an emission angle due to self-absorption in a phosphor material. Assuming isotropic initial emission and Lambert-Beer’s law, we have derived simple expressions for the angle-resolved spectra emerging from the top and bottom surfaces of a uniform phosphor layer. The transmittance of an excitation light through the phosphor layer can be regarded as a design parameter. For a strongly-absorbing phosphor layer, the forward flux is less intense and more red-shifted than the backward flux. The red-shift is enhanced as the emission direction deviates away from the plane normal. When we increase the transmittance, the backward flux decreases monotonically. The forward flux peaks at a certain transmittance value. The two fluxes become similar to each other for a weakly-absorbing phosphor layer. We have observed these behaviors in experiment. In a practical application, self-absorption decreases the efficiency of conversion and results in angle-dependent variations in chromaticity coordinates. A patterned phosphor layer with a secondary optical element such as a remote reflector alleviates these problems. 14. Constant Matrix Element Approximation to Time-Resolved Angle-Resolved Photoemission Spectroscopy Directory of Open Access Journals (Sweden) James K. Freericks 2016-11-01 Full Text Available We discuss several issues associated with employing a constant matrix element approximation for the coupling of light to multiband electrons in the context of time-resolved angle-resolved photoemission spectroscopy (TR-ARPES. In particular, we demonstrate that the “constant matrix element approximation” —even when reasonable—only holds for specific choices of the one-electron basis, and changing to other bases, requires including nonconstant corrections to the matrix element. We also discuss some simplifying approximations, where a constant matrix element is employed in multiple bases, and the consequences of this further approximation (especially with respect to the calculated TR-ARPES signal becoming negative. We also discuss issues related to gauge invariance of the final spectra. 15. Modeling angle-resolved photoemission of graphene and black phosphorus nano structures. Science.gov (United States) Park, Sang Han; Kwon, Soonnam 2016-05-10 Angle-resolved photoemission spectroscopy (ARPES) data on electronic structure are difficult to interpret, because various factors such as atomic structure and experimental setup influence the quantum mechanical effects during the measurement. Therefore, we simulated ARPES of nano-sized molecules to corroborate the interpretation of experimental results. Applying the independent atomic-center approximation, we used density functional theory calculations and custom-made simulation code to compute photoelectron intensity in given experimental setups for every atomic orbital in poly-aromatic hydrocarbons of various size, and in a molecule of black phosphorus. The simulation results were validated by comparing them to experimental ARPES for highly-oriented pyrolytic graphite. This database provides the calculation method and every file used during the work flow. 16. Tuning across the BCS-BEC crossover in the multiband superconductor Fe1+ySe x Te1-x: An angle-resolved photoemission study. Science.gov (United States) Rinott, Shahar; Chashka, K B; Ribak, Amit; Rienks, Emile D L; Taleb-Ibrahimi, Amina; Le Fevre, Patrick; Bertran, François; Randeria, Mohit; Kanigel, Amit 2017-04-01 The crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation (BEC) is difficult to realize in quantum materials because, unlike in ultracold atoms, one cannot tune the pairing interaction. We realize the BCS-BEC crossover in a nearly compensated semimetal, Fe 1+ y Se x Te 1- x , by tuning the Fermi energy ε F via chemical doping, which permits us to systematically change Δ/ε F from 0.16 to 0.50, where Δ is the superconducting (SC) gap. We use angle-resolved photoemission spectroscopy to measure the Fermi energy, the SC gap, and characteristic changes in the SC state electronic dispersion as the system evolves from a BCS to a BEC regime. Our results raise important questions about the crossover in multiband superconductors, which go beyond those addressed in the context of cold atoms. 17. New Light Source Setup for Angle Resolved Light Absorption measurement of PV samples DEFF Research Database (Denmark) Amdemeskel, Mekbib Wubishet; Poulsen, Peter Behrensdorff; Thorsteinsson, Sune Here, we introduce measurements of angle resolved light absorption by PV cells, using broadband laser driven white light source with a bright, stable, broad spectral range and well collimated light.......Here, we introduce measurements of angle resolved light absorption by PV cells, using broadband laser driven white light source with a bright, stable, broad spectral range and well collimated light.... 18. New Light Source Setup for Angle Resolved Light Absorption measurement of PV sample DEFF Research Database (Denmark) Amdemeskel, Mekbib Wubishet; Poulsen, Peter Behrensdorff; Thorsteinsson, Sune Here, we introduce measurements of angle resolved light absorption by PV cells, using broadband laser driven white light source with a bright, stable, broad spectral range and well collimated light.......Here, we introduce measurements of angle resolved light absorption by PV cells, using broadband laser driven white light source with a bright, stable, broad spectral range and well collimated light.... 19. Angle-resolved photoemission spectroscopy (ARPES) studies of cuprate superconductors Energy Technology Data Exchange (ETDEWEB) Palczewski, Ari Deibert [Iowa State Univ., Ames, IA (United States) 2010-01-01 This dissertation is comprised of three different angle-resolved photoemission spectroscopy (ARPES) studies on cuprate superconductors. The first study compares the band structure from two different single layer cuprates Tl2Ba2CuO6+δ (Tl2201) Tc,max ~95 K and (Bi1.35Pb0.85)(Sr1.47La0.38)CuO6+δ (Bi2201) Tc,max 35 K. The aim of the study was to provide some insight into the reasons why single layer cuprate's maximum transition temperatures are so different. The study found two major di erences in the band structure. First, the Fermi surface segments close to ( π,0) are more parallel in Tl2201 than in Bi2201. Second, the shadow band usually related to crystal structure is only present in Bi2201, but absent in higher Tc Tl2201. The second study looks at the different ways of doping Bi2Sr2CaCu2O8+δ (Bi2212) in-situ by only changing the post bake-out vacuum conditions and temperature. The aim of the study is to systematically look into the generally overlooked experimental conditions that change the doping of a cleaved sample in ultra high vacuum (UHV) experiments. The study found two major experimental facts. First, in inadequate UHV conditions the carrier concentration of Bi2212 increases with time, due to the absorption of oxygen from CO2/CO molecules, prime contaminants present in UHV systems. Second, in a very clean UHV system at elevated temperatures (above about 200 K), the carrier concentration decreases due to the loss of oxygen atoms from the Bi-O layer. The final study probed the particle-hole symmetry of the pseudogap phase in high temperature superconducting cuprates by looking at the thermally excited bands above the Fermi level. The data showed a particle-hole symmetric pseudogap which symmetrically closes away from the nested FS before the node. The data is consistent with 20. Angle-resolved photoemission spectroscopy (ARPES) studies of cuprate superconductors Energy Technology Data Exchange (ETDEWEB) Palczewski, Ari Deibert [Iowa State Univ., Ames, IA (United States) 2010-01-01 This dissertation is comprised of three different angle-resolved photoemission spectroscopy (ARPES) studies on cuprate superconductors. The first study compares the band structure from two different single layer cuprates Tl2Ba2CuO6+δ (Tl2201) Tc, max ≈ 95 K and (Bi 1.35Pb0.85)(Sr1.47La0.38)CuO6+δ (Bi2201) Tc, max ≈ 35 K. The aim of the study was to provide some insight into the reasons why single layer cuprate's maximum transition temperatures are so different. The study found two major differences in the band structure. First, the Fermi surface segments close to (π,0) are more parallel in Tl2201 than in Bi2201. Second, the shadow band usually related to crystal structure is only present in Bi2201, but absent in higher Tc Tl2201. The second study looks at the different ways of doping Bi2Sr2CaCu2O8+δ (Bi2212) in-situ by only changing the post bake-out vacuum conditions and temperature. The aim of the study is to systematically look into the generally overlooked experimental conditions that change the doping of a cleaved sample in ultra high vacuum (UHV) experiments. The study found two major experimental facts. First, in inadequate UHV conditions the carrier concentration of Bi2212 increases with time, due to the absorption of oxygen from CO2/CO molecules, prime contaminants present in UHV systems. Second, in a very clean UHV system at elevated temperatures (above about 200 K), the carrier concentration decreases due to the loss of oxygen atoms from the Bi-O layer. The final study probed the particle-hole symmetry of the pseudogap phase in high temperature superconducting cuprates by looking at the thermally excited bands above the Fermi level. The data showed a particle-hole symmetric pseudogap which symmetrically closes away from the nested FS before the node. The data is 1. Soft X-ray angle-resolved photoemission with micro-positioning techniques for metallic V2O3 Science.gov (United States) Fujiwara, Hidenori; Kiss, Takayuki; Wakabayashi, Yuki K.; Nishitani, Yoshito; Mori, Takeo; Nakata, Yuki; Kitayama, Satoshi; Fukushima, Kazuaki; Ikeda, Shinji; Fuchimoto, Hiroto; Minowa, Yosuke; Mo, Sung-Kwan; Denlinger, Jonathan D.; Allen, James W.; Metcalf, Patricia; Imai, Masaki; Yoshimura, Kazuyoshi; Suga, Shigemasa; Muro, Takayuki; Sekiyama, Akira 2015-01-01 Soft X-ray angle-resolved photoemission has been performed for metallic V2O3. By combining a microfocus beam (40 µm × 65 µm) and micro-positioning techniques with a long-working-distance microscope, it has been possible to observe band dispersions from tiny cleavage surfaces with a typical size of several tens of µm. The photoemission spectra show a clear position dependence, reflecting the morphology of the cleaved sample surface. By selecting high-quality flat regions on the sample surface, it has been possible to perform band mapping using both photon-energy and polar-angle dependences, opening the door to three-dimensional angle-resolved photoemission spectroscopy for typical three-dimensional correlated materials where large cleavage planes are rarely obtained. PMID:25931096 2. Angle-resolved photoemission studies of the superconducting gap symmetry in Fe-based superconductors Directory of Open Access Journals (Sweden) Y.-B. Huang 2012-12-01 Full Text Available The superconducting gap is the fundamental parameter that characterizes the superconducting state, and its symmetry is a direct consequence of the mechanism responsible for Cooper pairing. Here we discuss about angle-resolved photoemission spectroscopy measurements of the superconducting gap in the Fe-based high-temperature superconductors. We show that the superconducting gap is Fermi surface dependent and nodeless with small anisotropy, or more precisely, a function of the momentum location in the Brillouin zone. We show that while this observation seems inconsistent with weak coupling approaches for superconductivity in these materials, it is well supported by strong coupling models and global superconducting gaps. We also suggest that a smaller lifetime of the superconducting Cooper pairs induced by the momentum dependent interband scattering inherent to these materials could affect the residual density of states at low energies, which is critical for a proper evaluation of the superconducting gap. 3. Tunable vacuum ultraviolet laser based spectrometer for angle resolved photoemission spectroscopy Energy Technology Data Exchange (ETDEWEB) Jiang, Rui; Mou, Daixiang; Wu, Yun; Huang, Lunan; Kaminski, Adam [Division of Materials Science and Engineering, Ames Laboratory, Ames, Iowa 50011 (United States); Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States); McMillen, Colin D.; Kolis, Joseph [Department of Chemistry, Clemson University, Clemson, South Carolina 29634 (United States); Giesber, Henry G.; Egan, John J. [Advanced Photonic Crystals LLC, Fort Mill, South Carolina 29708 (United States) 2014-03-15 We have developed an angle-resolved photoemission spectrometer with tunable vacuum ultraviolet laser as a photon source. The photon source is based on the fourth harmonic generation of a near IR beam from a Ti:sapphire laser pumped by a CW green laser and tunable between 5.3 eV and 7 eV. The most important part of the set-up is a compact, vacuum enclosed fourth harmonic generator based on potassium beryllium fluoroborate crystals, grown hydrothermally in the US. This source can deliver a photon flux of over 10{sup 14} photon/s. We demonstrate that this energy range is sufficient to measure the k{sub z} dispersion in an iron arsenic high temperature superconductor, which was previously only possible at synchrotron facilities. 4. Periodicity-Free Unfolding Method of Electronic Energy Spectra Science.gov (United States) Kosugi, Taichi; Nishi, Hirofumi; Kato, Yasuyuki; Matsushita, Yu-ichiro 2017-12-01 We propose a novel periodicity-free unfolding method of electronic energy spectra. Our new method solves the serious problem that a calculated electronic band structure strongly depends on the choice of the simulation cell, i.e., primitive cell or supercell. The present method projects the electronic states onto the free-electron states, giving rise to plane-wave unfolded spectra. Using the method, the energy spectra can be calculated as a quantity independent of the choice of the simulation cell. We examine the unfolded energy spectra in detail for the following three models and clarify the validity of our method: a one-dimensional two-chain model, monolayer graphene, and twisted bilayer graphene. We also discuss the relation between our present method and the spectra observed in angle-resolved photoemission spectroscopy (ARPES) experiments. 5. Angle-resolved photoemission spectroscopy with quantum gas microscopes Science.gov (United States) Bohrdt, A.; Greif, D.; Demler, E.; Knap, M.; Grusdt, F. 2018-03-01 Quantum gas microscopes are a promising tool to study interacting quantum many-body systems and bridge the gap between theoretical models and real materials. So far, they were limited to measurements of instantaneous correlation functions of the form 〈O ̂(t ) 〉 , even though extensions to frequency-resolved response functions 〈O ̂(t ) O ̂(0 ) 〉 would provide important information about the elementary excitations in a many-body system. For example, single-particle spectral functions, which are usually measured using photoemission experiments in electron systems, contain direct information about fractionalization and the quasiparticle excitation spectrum. Here, we propose a measurement scheme to experimentally access the momentum and energy-resolved spectral function in a quantum gas microscope with currently available techniques. As an example for possible applications, we numerically calculate the spectrum of a single hole excitation in one-dimensional t -J models with isotropic and anisotropic antiferromagnetic couplings. A sharp asymmetry in the distribution of spectral weight appears when a hole is created in an isotropic Heisenberg spin chain. This effect slowly vanishes for anisotropic spin interactions and disappears completely in the case of pure Ising interactions. The asymmetry strongly depends on the total magnetization of the spin chain, which can be tuned in experiments with quantum gas microscopes. An intuitive picture for the observed behavior is provided by a slave-fermion mean-field theory. The key properties of the spectra are visible at currently accessible temperatures. 6. Angle resolved x-ray photoelectron spectroscopy (ARXPS) analysis of lanthanum oxide for micro-flexography printing Science.gov (United States) Hassan, S.; Yusof, M. S.; Embong, Z.; Maksud, M. I. 2016-01-01 Micro-flexography printing was developed in patterning technique from micron to nano scale range to be used for graphic, electronic and bio-medical device on variable substrates. In this work, lanthanum oxide (La2O3) has been used as a rare earth metal candidate as depositing agent. This metal deposit was embedded on Carbon (C) and Silica (Si) wafer substrate using Magnetron Sputtering technique. The choose of Lanthanum as a target is due to its wide application in producing electronic devices such as thin film battery and printed circuit board. The La2O3 deposited on the surface of Si wafer substrate was then analyzed using Angle Resolve X-Ray Photoelectron Spectroscopy (ARXPS). The position for each synthetic component in the narrow scan of Lanthanum (La) 3d and O 1s are referred to the electron binding energy (eV). The La 3d narrow scan revealed that the oxide species of this particular metal is mainly contributed by La2O3 and La(OH)3. The information of oxygen species, O2- component from O 1s narrow scan indicated that there are four types of species which are contributed from the bulk (O2-), two chemisorb component (La2O3) and La(OH)3 and physisorp component (OH). Here, it is proposed that from the adhesive and surface chemical properties of La, it is suitable as an alternative medium for micro-flexography printing technique in printing multiple fine solid lines at nano scale. Hence, this paper will describe the capability of this particular metal as rare earth metal for use in of micro-flexography printing practice. The review of other parameters contributing to print fine lines will also be described later. 7. Angle resolved x-ray photoelectron spectroscopy (ARXPS) analysis of lanthanum oxide for micro-flexography printing Energy Technology Data Exchange (ETDEWEB) Hassan, S., E-mail: [email protected]; Yusof, M. S., E-mail: [email protected]; Maksud, M. I., E-mail: [email protected] [Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Johor (Malaysia); Embong, Z., E-mail: [email protected] [Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Johor (Malaysia) 2016-01-22 Micro-flexography printing was developed in patterning technique from micron to nano scale range to be used for graphic, electronic and bio-medical device on variable substrates. In this work, lanthanum oxide (La{sub 2}O{sub 3}) has been used as a rare earth metal candidate as depositing agent. This metal deposit was embedded on Carbon (C) and Silica (Si) wafer substrate using Magnetron Sputtering technique. The choose of Lanthanum as a target is due to its wide application in producing electronic devices such as thin film battery and printed circuit board. The La{sub 2}O{sub 3} deposited on the surface of Si wafer substrate was then analyzed using Angle Resolve X-Ray Photoelectron Spectroscopy (ARXPS). The position for each synthetic component in the narrow scan of Lanthanum (La) 3d and O 1s are referred to the electron binding energy (eV). The La 3d narrow scan revealed that the oxide species of this particular metal is mainly contributed by La{sub 2}O{sub 3} and La(OH){sub 3}. The information of oxygen species, O{sup 2-} component from O 1s narrow scan indicated that there are four types of species which are contributed from the bulk (O{sup 2−}), two chemisorb component (La{sub 2}O{sub 3}) and La(OH){sub 3} and physisorp component (OH). Here, it is proposed that from the adhesive and surface chemical properties of La, it is suitable as an alternative medium for micro-flexography printing technique in printing multiple fine solid lines at nano scale. Hence, this paper will describe the capability of this particular metal as rare earth metal for use in of micro-flexography printing practice. The review of other parameters contributing to print fine lines will also be described later. 8. Insights from angle-resolved photoemission spectroscopy on the metallic states of YbB6(001): E(k) dispersion, temporal changes, and spatial variation NARCIS (Netherlands) Frantzeskakis, E.; de Jong, N.; Zhang, J.X.; Zhang, X.; Li, Z.; Liang, C.L.; Wang, Y.; Varykhalov, A.; Huang, Y.K.; Golden, M.S. 2014-01-01 We report high-resolution angle-resolved photoelectron spectroscopy (ARPES) results on the (001) cleavage surface of YbB6, a rare-earth compound that has been recently predicted to host surface electronic states with topological character. We observe two types of well-resolved metallic states, whose 9. Valence-band structure of cubic CdS as determined by angle-resolved photoemission Science.gov (United States) Stampfl, A. P. J.; Hofmann, Ph.; Schaff, O.; Bradshaw, A. M. 1997-04-01 The valence-band structure of cubic CdS along the Γ-Σ-X direction and at all high-symmetry points has been experimentally determined using angle-resolved photoemission and compared to two local density approximation (LDA) calculations as well as to a recent quasiparticle calculation. The Cd 4d level was found to be semibandlike with an energy dispersion of up to 1 eV. The energy difference between the experimental and our calculated linear-muffin-tin orbital (LMTO) LDA energies falls, as expected, along a line of positive gradient. The quasiparticle calculation by Pollmann and co-workers fits the experimental values somewhat better than the LMTO calculation, although a difference of ~1.0 eV was still found to occur for the Cd 4d band. The self-interaction and relaxation-corrected pseudopotential LDA results by the same group give the best fit to within ~+/-0.5 eV for nearly all critical energies measured. Comparison with previously reported photoemission results on the wurtzite structure shows that energies at equivalent symmetry points agree within experimental error. 10. Angle-resolved photoemission spectroscopy studies of metallic surface and interface states of oxide insulators Science.gov (United States) 2017-11-01 Over the last decade, conducting states embedded in insulating transition metal oxides (TMOs) have served as gateways to discovering and probing surprising phenomena that can emerge in complex oxides, while also opening opportunities for engineering advanced devices. These states are commonly realized at thin film interfaces, such as the well-known case of LaAlO3 (LAO) grown on SrTiO3 (STO). In recent years, the use of angle-resolved photoemission spectroscopy (ARPES) to investigate the k-space electronic structure of such materials led to the discovery that metallic states can also be formed on the bare surfaces of certain TMOs. In this topical review, we report on recent studies of low-dimensional metallic states confined at insulating oxide surfaces and interfaces as seen from the perspective of ARPES, which provides a direct view of the occupied band structure. While offering a fairly broad survey of progress in the field, we draw particular attention to STO, whose surface is so far the best-studied, and whose electronic structure is probably of the most immediate interest, given the ubiquitous use of STO substrates as the basis for conducting oxide interfaces. The ARPES studies provide crucial insights into the electronic band structure, orbital character, dimensionality/confinement, spin structure, and collective excitations in STO surfaces and related oxide surface/interface systems. The obtained knowledge increases our understanding of these complex materials and gives new perspectives on how to manipulate their properties. 11. High-resolution angle-resolved photoemission investigation of potassium and phosphate tungsten bronzes International Nuclear Information System (INIS) Paul, Sanhita; Kumari, Spriha; Raj, Satyabrata 2016-01-01 Highlights: • Electronic structure of potassium and phosphate tungsten bronzes. • Origin of transport anomalies in bronzes. • Flat segments of Fermi surfaces are connected by a nesting vector, q. • Nesting driven charge-density wave is responsible for the anomalies. - Abstract: We have performed high-resolution angle-resolved photoemission spectroscopy (ARPES) and density functional ab initio theoretical calculation to study the electronic structure of potassium (K 0.25 WO 3 ) and phosphate (P 4 W 12 O 44 ) tungsten bronzes. We have experimentally determined the band dispersions and Fermi surface topology of these bronzes and compared with our theoretical calculations and a fair agreement has been seen between them. Our experimental as well as theoretical investigation elucidates the origin of transport anomalies in these bronzes. The Fermi surfaces of these bronzes consist of flat patches, which can be connected with each other by a constant nesting wave vector, q. The scattering wave vectors found from diffraction measurements match with these nesting vectors and the anomalies in the transport properties of these bronzes can be well explained by the evolution of charge-density wave with a partial nesting between the flat segments of the Fermi surfaces. 12. Angle Resolved Performance Measurements on PV Glass and Modules DEFF Research Database (Denmark) Juutilainen, Line Tollund; Thorsteinsson, Sune; Poulsen, Peter Behrensdorff 2016-01-01 The angular response of PV-modules has significant impact on the energy production. This is especially pronounced in BIPV where installation angles often are far from optimal. Nevertheless, a gain in energy yield may be obtained by choosing a proper glass as superstrate. In this work we present t... 13. A flexible setup for angle-resolved X-ray fluorescence spectrometry with laboratory sources Energy Technology Data Exchange (ETDEWEB) Spanier, M., E-mail: [email protected]; Herzog, C.; Grötzsch, D.; Kramer, F.; Mantouvalou, I.; Malzer, W.; Kanngießer, B. [Institute for Optics and Atomic Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin (Germany); Lubeck, J.; Weser, J.; Streeck, C.; Beckhoff, B. [Physikalisch-Technische Bundesanstalt, Abbestraße 2-12, 10587 Berlin (Germany) 2016-03-15 X-ray fluorescence (XRF) analysis is one of the standard tools for the analysis of stratified materials and is widely applied for the investigation of electronics and coatings. The composition and thickness of the layers can be determined quantitatively and non-destructively. Recent work showed that these capabilities can be extended towards retrieving stratigraphic information like concentration depth profiles using angle-resolved XRF (ARXRF). This paper introduces an experimental sample chamber which was developed as a multi-purpose tool enabling different measurement geometries suited for transmission measurements, conventional XRF, ARXRF, etc. The chamber was specifically designed for attaching all kinds of laboratory X-ray sources for the soft and hard X-ray ranges as well as various detection systems. In detail, a setup for ARXRF using an X-ray tube with a polycapillary X-ray lens as source is presented. For such a type of setup, both the spectral and lateral characterizations of the radiation field are crucial for quantitative ARXRF measurements. The characterization is validated with the help of a stratified validation sample. 14. Field-angle-resolved anisotropy in superconducting CeCoIn5 using realistic Fermi surfaces Science.gov (United States) Das, Tanmoy; Vorontsov, A. B.; Vekhter, I.; Graf, Matthias J. 2013-05-01 We compute the field-angle-resolved specific heat and thermal conductivity using realistic model band structures for the heavy-fermion superconductor CeCoIn5 to identify the gap structure and location of nodes. We use a two-band tight-binding parametrization of the band dispersion as input for the self-consistent calculations in the quasiclassical formulation of the superconductivity. Systematic analysis shows that modest in-plane anisotropy in the density of states and Fermi velocity in tetragonal crystals significantly affects the fourfold oscillations in thermal quantities, when the magnetic field is rotated in the basal plane. The Fermi-surface anisotropy substantially shifts the location of the lines in the H-T plane, where the oscillations change sign compared to quasicylindrical model calculations. In particular, at high fields, the anisotropy and sign reversal are found even for isotropic gaps. Our findings imply that a simultaneous analysis of the specific heat and thermal conductivity, with an emphasis on the low-energy sector, is needed to restrict potential pairing scenarios in multiband superconductors. We discuss the impact of our results on recent measurements of the Ce-115 family, namely, CeTIn5 with T= Co, Rh, Ir. 15. Beamline for angle-resolved photoemission spectroscopy at low-temperature constructed at NTT Atsugi R and D Center International Nuclear Information System (INIS) Suzuki, Satoru; Yamamoto, Hideki; Maeda, Fumihiko; Watanabe, Yoshio; Yamada, Koji; Kiyokura, Takanori 2005-01-01 A vacuum ultra-violet beamline for in situ angle-resolved photoemission spectroscopy of MBE-grown high-T c superconductors at low temperature has been constructed at beamline ABL-6B of the normal-conducting ring in the synchrotron radiation facility of the NTT Atsugi R and D Center. The constant-deviation-angle varied-line-spacing plane grating monochromator covers the energy range of 20-200 eV by using two gratings. A photon flux of the order of 10 11 s -1 with a resolving power of 2000 or more was achieved in the whole energy range. The endstation is equipped with an angle-resolved photoelectron spectrometer, an rf-stimulated He discharge lamp, a custom-designed sample manipulator for low-temperature measurements and a loadlock system for in situ measurements. Total energy resolution of about 13 meV has been obtained for the photoemission spectrum of the Au Fermi edge, in spite of the bending-magnet light source of a second-generation synchrotron radiation ring 16. Angle-resolved imaging of single-crystal materials with MeV helium ions International Nuclear Information System (INIS) Strathman, M.D.; Baumann, S. 1992-01-01 The simplest form of angle-resolved mapping for single-crystal materials is the creation of a channeling angular scan. Several laboratories have expanded this simple procedure to include mapping as a function of two independent tilts. These angle-resolved images are particularly suited to the assessment of crystal parameters including disorder, lattice location of impurities, and lattice stress. This paper will describe the use of the Charles Evans and Associates RBS-400 scattering chamber for acquisition, display, and analysis of angle-resolved images obtained from backscattered helium ions. Typical data acquisition times are 20 min for a ±2deg X-Y tilt scan with 2500 pixels (8/100deg resolution), and 10 nC per pixel. In addition, we will present a method for automatically aligning crystals for channeling measurements based on this imaging technology. (orig.) 17. An Angle Resolved Photoemission Study of a Mott Insulator and Its Evolution to a High Temperature Superconductor Energy Technology Data Exchange (ETDEWEB) Ronning, Filip 2002-03-19 One of the most remarkable facts about the high temperature superconductors is their close proximity to an antiferromagnetically ordered Mott insulating phase. This fact suggests that to understand superconductivity in the cuprates we must first understand the insulating regime. Due to material properties the technique of angle resolved photoemission is ideally suited to study the electronic structure in the cuprates. Thus, a natural starting place to unlocking the secrets of high Tc would appears to be with a photoemission investigation of insulating cuprates. This dissertation presents the results of precisely such a study. In particular, we have focused on the compound Ca{sub 2-x}Na{sub x}CuO{sub 2}Cl{sub 2}. With increasing Na content this system goes from an antiferromagnetic Mott insulator with a Neel transition of 256K to a superconductor with an optimal transition temperature of 28K. At half filling we have found an asymmetry in the integrated spectral weight, which can be related to the occupation probability, n(k). This has led us to identify a d-wave-like dispersion in the insulator, which in turn implies that the high energy pseudogap as seen by photoemission is a remnant property of the insulator. These results are robust features of the insulator which we found in many different compounds and experimental conditions. By adding Na we were able to study the evolution of the electronic structure across the insulator to metal transition. We found that the chemical potential shifts as holes are doped into the system. This picture is in sharp contrast to the case of La{sub 2-x}Sr{sub x}CuO{sub 4} where the chemical potential remains fixed and states are created inside the gap. Furthermore, the low energy excitations (ie the Fermi surface) in metallic Ca{sub 1.9}Na{sub 0.1}CuO{sub 2}Cl{sub 2} is most well described as a Fermi arc, although the high binding energy features reveal the presence of shadow bands. Thus, the results in this dissertation provide a 18. Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:Sapphire lasers International Nuclear Information System (INIS) Eich, S.; Stange, A.; Carr, A.V.; Urbancic, J.; Popmintchev, T.; Wiesenmayer, M.; Jansen, K.; Ruffing, A.; Jakobs, S.; Rohwer, T.; Hellmann, S.; Chen, C.; Matyba, P.; Kipp, L.; Rossnagel, K.; Bauer, M.; Murnane, M.M.; Kapteyn, H.C.; Mathias, S.; Aeschlimann, M. 2014-01-01 Highlights: • We present a scheme to generate high intensity XUV pulses from HHG with variable time-bandwidth product. • Shorter-wavelength driven high-harmonic XUV trARPES provides higher photon flux and increased energy resolution. • High-quality high-harmonic XUV trARPES data with sub 150 meV energy and sub 30 fs time resolution is presented. - Abstract: Time- and angle-resolved photoemission spectroscopy (trARPES) using femtosecond extreme ultraviolet high harmonics has recently emerged as a powerful tool for investigating ultrafast quasiparticle dynamics in correlated-electron materials. However, the full potential of this approach has not yet been achieved because, to date, high harmonics generated by 800 nm wavelength Ti:Sapphire lasers required a trade-off between photon flux, energy and time resolution. Photoemission spectroscopy requires a quasi-monochromatic output, but dispersive optical elements that select a single harmonic can significantly reduce the photon flux and time resolution. Here we show that 400 nm driven high harmonic extreme-ultraviolet trARPES is superior to using 800 nm laser drivers since it eliminates the need for any spectral selection, thereby increasing photon flux and energy resolution to <150 meV while preserving excellent time resolution of about 30 fs 19. Simulation and Measurement of Angle Resolved Reflectance from Black Si Surfaces DEFF Research Database (Denmark) Davidsen, Rasmus Schmidt; Wu, Kaiyu; Schmidt, Michael Stenbæk 2015-01-01 In this work angle-resolved reflectance from nanostructured Si surfaces realized by maskless RIE texturing has been simulated and measured. The simulation and experimental measurement data show the same trend. Experimentally a total reflectance below 1% for incident angles below 30o and specular... 20. Gauge invariance in the theoretical description of time-resolved angle-resolved pump/probe photoemission spectroscopy Energy Technology Data Exchange (ETDEWEB) Freericks, J. K.; Krishnamurthy, H. R.; Sentef, M. A.; Devereaux, T. P. 2015-10-01 Nonequilibrium calculations in the presence of an electric field are usually performed in a gauge, and need to be transformed to reveal the gauge-invariant observables. In this work, we discuss the issue of gauge invariance in the context of time-resolved angle-resolved pump/probe photoemission. If the probe is applied while the pump is still on, one must ensure that the calculations of the observed photocurrent are gauge invariant. We also discuss the requirement of the photoemission signal to be positive and the relationship of this constraint to gauge invariance. We end by discussing some technical details related to the perturbative derivation of the photoemission spectra, which involve processes where the pump pulse photoexcites electrons due to nonequilibrium effects. 1. Soft X-ray angle-resolved photoemission spectroscopy of heavily boron-doped superconducting diamond films Directory of Open Access Journals (Sweden) T. Yokoya, T. Nakamura, T. Matushita, T. Muro, H. Okazaki, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, Y. Takano, M. Nagao, T. Takenouchi, H. Kawarada and T. Oguchi 2006-01-01 Full Text Available We have performed soft X-ray angle-resolved photoemission spectroscopy (SXARPES of microwave plasma-assisted chemical vapor deposition diamond films with different B concentrations in order to study the origin of the metallic behavior of superconducting diamond. SXARPES results clearly show valence band dispersions with a bandwidth of ~23 eV and with a top of the valence band at gamma point in the Brillouin zone, which are consistent with the calculated valence band dispersions of pure diamond. Boron concentration-dependent band dispersions near the Fermi level (EF exhibit a systematic shift of EF, indicating depopulation of electrons due to hole doping. These SXARPES results indicate that diamond bands retain for heavy boron doping and holes in the diamond band are responsible for the metallic states leading to superconductivity at low temperature. A high-resolution photoemission spectroscopy spectrum near EF of a heavily boron-doped diamond superconductor is also presented. 2. Nano-Angle Resolved Photoemission Spectroscopy on Topological insulator Sb2Te3 nanowires responsible of quantum transport Science.gov (United States) Avila, José; Chen, Chaoyu; Arango, Yulieth C.; Huang, Liubing; Grützmacher, Detlev; Lüth, Hans; Lu, J. Grace; Schäpers, Thomas; Asensio, Maria C. 2017-06-01 Using high-resolution Nano-Angle Resolved Photoemission Spectroscopy (Nano-ARPES), we have determined the electronic structure of the surface and bulk states of topological insulator Sb2Te3 nanowires, which have been also characterized by magnetoresistance measurements. The observed Aharonov-Bohm-type oscillations could be unambiguously related to the transport by topological protected surface states directly recorded by photoemission. We have measured Nano-ARPES on individual nanowires of a few nanometers wide to provide direct evidence of the existence of the nontrivial topological surface states, as well as their doping. Our findings are consistent with theoretical predictions and confirm that the surface states of intrinsically doped unidimensional topological insulator nanowires are responsible for the quantum transport. 3. High-resolution angle-resolved photoemission studies of high Tc superconductor Bi2Sr2CaCu2O8 International Nuclear Information System (INIS) Liu, Rong. 1990-01-01 An angle-resolved photoemission study of the normal and superconducting states in Bi 2 Sr 2 CaCu 2 O 8 was performed. Measurements in the normal state show bands dispersing through the Fermi level from at least 350 meV below E F . The Fermi level crossings are consistant with local-density band calculation, including a point calculated to be of Bi-O character. Additional measurements were made where bands crossed the Fermi level between 100 and 250K, along with measurements on an adjacent Pt foil. The Fermi edges of both materials agree to within the noise. Below the Fermi level, the spectra show correlation effects on the form of an increased effective mass. The shape of the spectra can be explained by a lifetime-broadened photohole and secondary electrons. The effective inverse photohole lifetime is linear in energy. A superconducting gap has been measured at a number of points where there is density at the Fermi level in the normal state. By proper modeling, a gap of 24 meV was obtained for all these points, including points of Cu-O and Bi-O character respectively, according to band calculation. The lack of gap anisotropy in the basal plane suggests that pinning in this material is not d-wave pairing 4. Site-specific intermolecular valence-band dispersion in α-phase crystalline films of cobalt phthalocyanine studied by angle-resolved photoemission spectroscopy. Science.gov (United States) Yamane, Hiroyuki; Kosugi, Nobuhiro 2014-12-14 The valence band structure of α-phase crystalline films of cobalt phthalocyanine (CoPc) grown on Au(111) is investigated by using angle-resolved photoemission spectroscopy (ARPES) with synchrotron radiation. The photo-induced change in the ARPES peaks is noticed in shape and energy of the highest occupied molecular orbital (HOMO, C 2p) and HOMO-1 (Co 3d) of CoPc, and is misleading the interpretation of the electronic properties of CoPc films. From the damage-free normal-emission ARPES measurement, the clear valence-band dispersion has been first observed, showing that orbital-specific behaviors are attributable to the interplay of the intermolecular π-π and π-d interactions. The HOMO band dispersion of 0.1 eV gives the lower limit of the hole mobility for α-CoPc of 28.9 cm(2) V(-1) s(-1) at 15 K. The non-dispersive character of the split HOMO-1 bands indicates that the localization of the spin state is a possible origin of the antiferromagnetism. 5. Structural studies of molecular and metallic overlayers using angle- resolved photoemission extended fine structure International Nuclear Information System (INIS) Huang, Z. 1992-10-01 Angle-resolved photoemission extended fine structure (ARPEFS) was used to study molecular and metallic overlayers on metal surfaces through analysis of p2mg(2x1)CO/Ni(110) and the p(2x2)K/Ni(111) adsorption. For the dense p2mg(2x1)CO/Ni(110) surface layer, photoemission intensities from C 1s level were measured in three directions at photoelectron kinetic energies 60-400 eV. Using multiple-scattering spherical-wave (MSSW) modeling, it was found that CO molecules are adsorbed on short-bridge sites, with adjacent CO along the [110] direction displaced alternatively in opposite directions towards the [001] azimuths to form a zigzag chain geometry. The tilt angle is 16±2 degree from the surface normal for the direction linking the C atom and the center of the Ni bridge. The carbon C-Ni interatomic distance was determined to be 1.94±0.02 Angstrom. The first- to second-layer spacing of Ni is 1.27±0.04 Angstrom, up from 1.10 Angstrom for the clean Ni(110) surface, but close to the 1.25 Angstrom Ni interlayer spacing in the bulk. The C-O bond length and tilt angle were varied within small ranges (1.10--1.20 Angstrom and 15--23 degrees) in our MSSW simulations. Best agreement between experiment and simulations was achieved at 1.16 Angstrom and 19 degrees. This yields an O-O distance of 2.95 Angstrom for the two nearest CO molecules, (van der Waals' radius ∼ 1.5 Angstrom for oxygen). Two different partial-wave phase-shifts were used in MSSW, and structural results from both are in very good agreement. For the p(2x2)K/Ni(111) overlayer, ARPEFS χ(k) curves from K 1s level measured along [111] and [771] at 130K showed that the K atoms are preferentially adsorbed on the atop sites, in agreement with a LEED study of the same system 6. Angle resolved characterization of nanostructured and conventionally textured silicon solar cells DEFF Research Database (Denmark) Davidsen, Rasmus Schmidt; Ormstrup, Jeppe; Ommen, Martin Lind 2015-01-01 current, open circuit voltage, fill factor (FF) and power conversion efficiency are each measured as function of the relative incident angle between the solar cell and the light source. The relative incident angle is varied from 0° to 90° in steps of 10° in orthogonal axes, such that each solar cell......We report angle resolved characterization of nanostructured and conventionally textured silicon solar cells. The nanostructured solar cells are realized through a single step, mask-less, scalable reactive ion etching (RIE) texturing of the surface. Photovoltaic properties including short circuit... 7. Linear and circular dichroism in angle resolved Fe 3p photomission. Revision 1 International Nuclear Information System (INIS) Tamura, E.; Waddill, G.D.; Tobin, J.G.; Sterne, P.A. 1994-01-01 Using a recently developed spin-polarized, fully relativistic, multiple scattering approach based on the layer KKR Green function method, we have reproduced the Fe 3p angle-resolved soft x-ray photoemission spectra and analyzed the associated large magnetic dichroism effects for excitation with both linearly and circularly polarized light. Comparison between theory and experiment yields a spin-orbit splitting of 1.0--1.2 eV and an exchange splitting of 0.9-- 1.0 eV for Fe 3p. These values are 50--100% larger than those hitherto obtained experimentally 8. Angle-resolved reflection spectroscopy of high-quality PMMA opal crystal Science.gov (United States) Nemtsev, Ivan V.; Tambasov, Igor A.; Ivanenko, Alexander A.; Zyryanov, Victor Ya. 2018-02-01 PMMA opal crystal was prepared by a simple hybrid method, which includes sedimentation, meniscus formation and evaporation. We investigated three surfaces of this crystal by angle-resolved reflective light spectroscopy and SEM study. The angle-resolved reflective measurements were carried out in the 400-1100 nm range. We have determined the high-quality ordered surface of the crystal region. Narrow particle size distribution of the surface has been revealed. The average particle diameter obtained with SEM was nearly 361 nm. The most interesting result was that reflectivity of the surface turned out up to 98% at normal light incidence. Using a fit of dependences of the maximum reflectivity wavelength from an angle based on the Bragg-Snell law, the wavelength of maximum 0° reflectivity, the particle diameter and the fill factor have been determined. For the best surface maximum reflectivity wavelength of a 0° angle was estimated to be 869 nm. The particle diameter and fill factor were calculated as 372 nm and 0.8715, respectively. The diameter obtained by fitting is in excellent agreement with the particle diameter obtained with SEM. The reflectivity maximum is assumed to increase significantly when increasing the fill factor. We believe that using our simple approach to manufacture PMMA opal crystals will significantly increase the fabrication of high-quality photonic crystal templates and thin films. 9. Evidence for Itinerant Carriers in an Anisotropic Narrow-Gap Semiconductor by Angle-Resolved Photoemission Spectroscopy. Science.gov (United States) Ju, Sailong; Bai, Wei; Wu, Liming; Lin, Hua; Xiao, Chong; Cui, Shengtao; Li, Zhou; Kong, Shuai; Liu, Yi; Liu, Dayong; Zhang, Guobin; Sun, Zhe; Xie, Yi 2018-01-01 The ability to accurately determine the electronic structure of solids has become a key prerequisite for modern functional materials. For example, the precise determination of the electronic structure helps to balance the three thermoelectric parameters, which is the biggest challenge to design high-performance thermoelectric materials. Herein, by high-resolution, angle-resolved photoemission spectroscopy (ARPES), the itinerant carriers in CsBi 4 Te 6 (CBT) are revealed for the first time. CBT is a typical anisotropic, narrow-gap semiconductor used as a practical candidate for low-temperature thermoelectric applications, and p-doped CBT series show superconductivity at relatively low carrier concentrations. The ARPES results show a significantly larger bandwidth near the Fermi surface than calculations, which means the carriers transport anisotropically and itinerantly in CBT. It is reasonable to believe that these newly discovered features of carriers in narrow-gap semiconductors are promising for designing optimal thermoelectric materials and superconductors. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 10. Unusually large chemical potential shift in a degenerate semiconductor: Angle-resolved photoemission study of SnSe and Na-doped SnSe Science.gov (United States) Maeda, M.; Yamamoto, K.; Mizokawa, T.; Saini, N. L.; Arita, M.; Namatame, H.; Taniguchi, M.; Tan, G.; Zhao, L. D.; Kanatzidis, M. G. 2018-03-01 We have studied the electronic structure of SnSe and Na-doped SnSe by means of angle-resolved photoemission spectroscopy. The valence-band top reaches the Fermi level by the Na doping, indicating that Na-doped SnSe can be viewed as a degenerate semiconductor. However, in the Na-doped system, the chemical potential shift with temperature is unexpectedly large and is apparently inconsistent with the degenerate semiconductor picture. The large chemical potential shift and anomalous spectral shape are key ingredients for an understanding of the novel metallic state with the large thermoelectric performance in Na-doped SnSe. 11. Angle-resolved spin wave band diagrams of square antidot lattices studied by Brillouin light scattering Energy Technology Data Exchange (ETDEWEB) Gubbiotti, G.; Tacchi, S. [Istituto Officina dei Materiali del Consiglio Nazionale delle Ricerche (IOM-CNR), Sede di Perugia, c/o Dipartimento di Fisica e Geologia, Via A. Pascoli, I-06123 Perugia (Italy); Montoncello, F.; Giovannini, L. [Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via G. Saragat 1, I-44122 Ferrara (Italy); Madami, M.; Carlotti, G. [Dipartimento di Fisica e Geologia, Università di Perugia, Via A. Pascoli, I-06123 Perugia (Italy); Ding, J.; Adeyeye, A. O. [Information Storage Materials Laboratory, Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576 (Singapore) 2015-06-29 The Brillouin light scattering technique has been exploited to study the angle-resolved spin wave band diagrams of squared Permalloy antidot lattice. Frequency dispersion of spin waves has been measured for a set of fixed wave vector magnitudes, while varying the wave vector in-plane orientation with respect to the applied magnetic field. The magnonic band gap between the two most dispersive modes exhibits a minimum value at an angular position, which exclusively depends on the product between the selected wave vector magnitude and the lattice constant of the array. The experimental data are in very good agreement with predictions obtained by dynamical matrix method calculations. The presented results are relevant for magnonic devices where the antidot lattice, acting as a diffraction grating, is exploited to achieve multidirectional spin wave emission. 12. Robust depth selectivity in mesoscopic scattering regimes using angle-resolved measurements. Science.gov (United States) González-Rodríguez, P; Kim, A D; Moscoso, M 2013-03-01 We study optical imaging of tissues in the mesoscopic scattering regime in which light multiply scatters in tissues but is not fully diffusive. We use the radiative transport equation to model light propagation and an ℓ1-optimization method to solve the inverse source problem. We show that recovering the location and strength of several point-like sources that are close to each other is not possible when using angle-averaged measurements. The image reliability is limited by a spatial scale that is on the order of the transport mean-free path, even under the most ideal conditions. However, by using just a few angle-resolved measurements, the proposed method is able to overcome this limitation. 13. Angle-resolved photoemission spectroscopy for the study of two-dimensional materials Science.gov (United States) Mo, Sung-Kwan 2017-03-01 Quantum systems in confined geometries allow novel physical properties that cannot easily be attained in their bulk form. These properties are governed by the changes in the band structure and the lattice symmetry, and most pronounced in their single layer limit. Angle-resolved photoemission spectroscopy (ARPES) is a direct tool to investigate the underlying changes of band structure to provide essential information for understanding and controlling such properties. In this review, recent progresses in ARPES as a tool to study two-dimensional atomic crystals have been presented. ARPES results from few-layer and bulk crystals of material class often referred as "beyond graphene" are discussed along with the relevant developments in the instrumentation. 14. Direct observation of superconducting gaps in MgB 2 by angle-resolved photoemission spectroscopy Science.gov (United States) Souma, S.; Machida, Y.; Sato, T.; Takahashi, T.; Matsui, H.; Wang, S.-C.; Ding, H.; Kaminski, A.; Campuzano, J. C.; Sasaki, S.; Kadowaki, K. 2004-08-01 High-resolution angle-resolved photoemission spectroscopy has been carried out to clarify the anomalous superconductivity of MgB 2. We observed three bands crossing the Fermi level, which are ascribed to B2p-σ, π and surface bands. We have succeeded for the first time in directly observing the superconducting gaps of these bands separately. We have found that the superconducting-gap sizes of σ and surface bands are 6.5 ± 0.5 and 6.0 ± 0.5 meV, respectively, while that of the π band is much smaller (1.5 ± 0.5 meV). The present experimental result unambiguously demonstrates the validity of the two-band superconductivity in MgB 2. 15. Direct observation of superconducting gaps in MgB2 by angle-resolved photoemission spectroscopy International Nuclear Information System (INIS) Souma, S.; Machida, Y.; Sato, T.; Takahashi, T.; Matsui, H.; Wang, S.-C.; Ding, H.; Kaminski, A.; Campuzano, J.C.; Sasaki, S.; Kadowaki, K. 2004-01-01 High-resolution angle-resolved photoemission spectroscopy has been carried out to clarify the anomalous superconductivity of MgB 2 . We observed three bands crossing the Fermi level, which are ascribed to B2p-σ, π and surface bands. We have succeeded for the first time in directly observing the superconducting gaps of these bands separately. We have found that the superconducting-gap sizes of σ and surface bands are 6.5 ± 0.5 and 6.0 ± 0.5 meV, respectively, while that of the π band is much smaller (1.5 ± 0.5 meV). The present experimental result unambiguously demonstrates the validity of the two-band superconductivity in MgB 2 16. Angle-resolved and resonant photoemission spectroscopy of rare-earth and actinide intermetallics Science.gov (United States) Reihl, Bruno 1985-07-01 In this paper, some aspects of our angle-resolved and resonant photoemission work on rare-earth and actinide intermetallics will be summarized. The systems specifically mentioned are Gd(0001), UIr 3(100), UN(100), UO 2, α-γ- Ce 0.9Th 0.1, U xTh 1- xSb, USb xTe 1- x, UPd 3, UCu xNi 5- x, CeCu 2Si 2, UBe 13, U 2Zn 17 , SmAl 2, EuPd 13, YbBe 13, TmS, Yb xY 1- xAl 2, EuPd 2Si 2, TmSe, and UAs xSe 1- x. 17. Design of angle-resolved illumination optics using nonimaging bi-telecentricity for 193 nm scatterfield microscopy. Science.gov (United States) Sohn, Martin Y; Barnes, Bryan M; Silver, Richard M 2018-03-01 Accurate optics-based dimensional measurements of features sized well-below the diffraction limit require a thorough understanding of the illumination within the optical column and of the three-dimensional scattered fields that contain the information required for quantitative metrology. Scatterfield microscopy can pair simulations with angle-resolved tool characterization to improve agreement between the experiment and calculated libraries, yielding sub-nanometer parametric uncertainties. Optimized angle-resolved illumination requires bi-telecentric optics in which a telecentric sample plane defined by a Köhler illumination configuration and a telecentric conjugate back focal plane (CBFP) of the objective lens; scanning an aperture or an aperture source at the CBFP allows control of the illumination beam angle at the sample plane with minimal distortion. A bi-telecentric illumination optics have been designed enabling angle-resolved illumination for both aperture and source scanning modes while yielding low distortion and chief ray parallelism. The optimized design features a maximum chief ray angle at the CBFP of 0.002° and maximum wavefront deviations of less than 0.06 λ for angle-resolved illumination beams at the sample plane, holding promise for high quality angle-resolved illumination for improved measurements of deep-subwavelength structures using deep-ultraviolet light. 18. Electron energies in metals Energy Technology Data Exchange (ETDEWEB) Mahan, G.D. (Oak Ridge National Lab., TN (United States) Tennessee Univ., Knoxville, TN (United States). Dept. of Physics and Astronomy) 1991-07-10 The modern era of electron-electron interactions began a decade ago. Plummer's group initiated a program of using angular resolved photoemission to examine the band structure of the simple metals. Beginning with aluminum, and carrying on to sodium and potassium, they always found that the occupied energy bands were much narrower than expected. For example, the compressed energy bands for metallic potassium suggest a band effective mass of m = 1.33m{sub e}. This should be compared to the band mass found from optical conductivity m/m{sub e} = 1.01 {plus minus} 0.01. The discrepancy between these results is startling. It was this great difference which started my group doing calculations. Our program was two-fold. On one hand, we reanalyzed the experimental data, in order to see if Plummer's result was an experimental artifact. On the other hand, we completely redid the electron-electron self-energy calculations for simple metals, using the most modern choices of local-field corrections and vertex corrections. Our results will be reported in these lectures. They can be summarized as following: Our calculations give the same effective masses as the older calculations, so the theory is relatively unchanged; Our analysis of the experiments suggests that the recent measurements of band narrowing are an experimental artifact. 38 refs., 9 figs. 19. Angle-Resolved Electron Spectra of {{\\rm{F}}}^{-} Ions by Few-Cycle Laser Pulses Science.gov (United States) Chen, Jian-Hong; Zhao, Song-Feng; Wang, Guo-Li; Zheng, Xiao-Ping; Zhang, Zheng-Rong 2017-06-01 Not Available Supported by the National Natural Science Foundation of China under Grant Nos 11647150, 11464026, 11664035 and 11364038, the Young Talents Program of Gansu Province in 2016, the Scientific Research Program of the Higher Education Institutions of Gansu Province under Grant No 2016A-068, and the Doctoral Scientific Research Foundation of Lanzhou City University under Grant No LZCU-BS2015-04. 20. Enhanced ultrafast relaxation rate in the Weyl semimetal phase of MoTe2 measured by time- and angle-resolved photoelectron spectroscopy Science.gov (United States) Crepaldi, A.; Autès, G.; Gatti, G.; Roth, S.; Sterzi, A.; Manzoni, G.; Zacchigna, M.; Cacho, C.; Chapman, R. T.; Springate, E.; Seddon, E. A.; Bugnon, Ph.; Magrez, A.; Berger, H.; Vobornik, I.; Kalläne, M.; Quer, A.; Rossnagel, K.; Parmigiani, F.; Yazyev, O. V.; Grioni, M. 2017-12-01 MoTe2 has recently been shown to realize in its low-temperature phase the type-II Weyl semimetal (WSM). We investigated by time- and angle- resolved photoelectron spectroscopy (tr-ARPES) the possible influence of the Weyl points on the electron dynamics above the Fermi level EF, by comparing the ultrafast response of MoTe2 in the trivial and topological phases. In the low-temperature WSM phase, we report an enhanced relaxation rate of electrons optically excited to the conduction band, which we interpret as a fingerprint of the local gap closure when Weyl points form. By contrast, we find that the electron dynamics of the related compound WTe2 is slower and temperature independent, consistent with a topologically trivial nature of this material. Our results shows that tr-ARPES is sensitive to the small modifications of the unoccupied band structure accompanying the structural and topological phase transition of MoTe2. 1. Formation of complexes between functionalized chitosan membranes and copper: A study by angle resolved XPS Energy Technology Data Exchange (ETDEWEB) Jurado-López, Belén [Departamento de Química Inorgánica, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga (Spain); Vieira, Rodrigo Silveira [Chemical Engineering Department, Universidade Federal do Ceará, UFC, 60455-760 Fortaleza, CE (Brazil); Rabelo, Rodrigo Balloni; Beppu, Marisa Masumi [School of Chemical Engineering, University of Campinas, UNICAMP, P.O. Box 6066, 13081-970 Campinas, SP (Brazil); Casado, Juan [Departamento de Química-Física, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga (Spain); Rodríguez-Castellón, Enrique, E-mail: [email protected] [Departamento de Química Inorgánica, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga (Spain) 2017-01-01 Chitosan is a biopolymer with potential applications in various fields. Recently, it has been used for heavy metals removal like copper, due to the presence of amino and hydroxyl groups in its structure. Chitosan membranes were crosslinked with epichlorohydrin and bisoxirano and functionalized with chelating agents, such as iminodiacetic acid, aspartic acid and tris-(2-amino-ethyl) polyamine. These membranes were used for copper adsorption and the formed complexes were characterized. Thermal and crystalline properties of chitosan membranes were studied by TG-DCS and X-ray diffraction. Raman, XPS and FT-IR data confirmed that copper is linked to the modified chitosan membranes by the amino groups. The oxidation state of copper-chitosan membranes were also studied by angle resolved XPS, and by UV–Vis diffuse reflectance spectroscopy. - Highlights: • Chitosan membranes were crosslinked with epichlorohydrin and bisoxirano and functionalized with chelating agents. • The chelating agent were iminodiacetic acid, aspartic acid and tris-(2-amino-ethyl) polyamine. • The functionalized membranes were used for copper adsorption and studied by ARXPS, Raman, TG-DCS, FT-IR and XRD. • Spectroscopic data confirmed that copper is linked to the modified chitosan membranes by the amino groups. 2. Fourier-domain angle-resolved low coherence interferometry for clinical detection of dysplasia Science.gov (United States) Terry, Neil G.; Zhu, Yizheng; Wax, Adam 2010-02-01 Improved methods for detecting dysplasia, or pre-cancerous growth are a current clinical need, particularly in the esophagus. The currently accepted method of random biopsy and histological analysis provides only a limited examination of tissue in question while being coupled with a long time delay for diagnosis. Light scattering spectroscopy, in contrast, allows for inspection of the cellular structure and organization of tissue in vivo. Fourier-domain angle-resolved low-coherence interferometry (a/LCI) is a novel light scattering spectroscopy technique that provides quantitative depth-resolved morphological measurements of the size and optical density of the examined cell nuclei, which are characteristic biomarkers of dysplasia. Previously, clinical viability of the a/LCI system was demonstrated through analysis of ex vivo human esophageal tissue in Barrett's esophagus patients using a portable a/LCI, as was the development of a clinical a/LCI system. Data indicating the feasibility of the technique in other organ sites (colon, oral cavity) will be presented. We present an adaptation of the a/LCI system that will be used to investigate the presence of dysplasia in vivo in Barrett's esophagus patients. 3. Detection of intestinal dysplasia using angle-resolved low coherence interferometry Science.gov (United States) Terry, Neil; Zhu, Yizheng; Thacker, Julie K. M.; Migaly, John; Guy, Cynthia; Mantyh, Christopher R.; Wax, Adam 2011-10-01 Angle-resolved low coherence interferometry (a/LCI) is an optical biopsy technique that allows for depth-resolved, label-free measurement of the average size and optical density of cell nuclei in epithelial tissue to assess the tissue health. a/LCI has previously been used clinically to identify the presence of dysplasia in Barrett's Esophagus patients undergoing routine surveillance. We present the results of a pilot, ex vivo study of tissues from 27 patients undergoing partial colonic resection surgery, conducted to evaluate the ability of a/LCI to identify dysplasia. Performance was determined by comparing the nuclear morphology measurements with pathological assessment of co-located physical biopsies. A statistically significant correlation between increased average nuclear size, reduced nuclear density, and the presence of dysplasia was noted at the basal layer of the epithelium, at a depth of 200 to 300 μm beneath the tissue surface. Using a decision line determined from a receiver operating characteristic, a/LCI was able to separate dysplastic from healthy tissues with a sensitivity of 92.9% (13/14), a specificity of 83.6% (56/67), and an overall accuracy of 85.2% (69/81). The study illustrates the extension of the a/LCI technique to the detection of intestinal dysplasia, and demonstrates the need for future in vivo studies. 4. Angle Resolved Core-Level Spectroscopy of Zr1Nb Alloy Oxidation by Oxygen, Water and Hydrogen Peroxide Czech Academy of Sciences Publication Activity Database Bastl, Zdeněk; Senkevich, A. I.; Spirovová, Ilona; Vrtílková, V. 2002-01-01 Roč. 34, - (2002), s. 477-480 ISSN 0142-2421 Institutional research plan: CEZ:AV0Z4040901 Keywords : Zr-Nb alloy oxide films * angle-resolved x-ray photoelectron spectroscopy Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.071, year: 2002 5. Quasiparticle dynamics across the full Brillouin zone of Bi2Sr2CaCu2O8+δ traced with ultrafast time and angle-resolved photoemission spectroscopy Directory of Open Access Journals (Sweden) Georgi L. Dakovski 2015-09-01 Full Text Available A hallmark in the cuprate family of high-temperature superconductors is the nodal-antinodal dichotomy. In this regard, angle-resolved photoemission spectroscopy (ARPES has proven especially powerful, providing band structure information directly in energy-momentum space. Time-resolved ARPES (trARPES holds great promise of adding ultrafast temporal information, in an attempt to identify different interaction channels in the time domain. Previous studies of the cuprates using trARPES were handicapped by the low probing energy, which significantly limits the accessible momentum space. Using 20.15 eV, 12 fs pulses, we show for the first time the evolution of quasiparticles in the antinodal region of Bi2Sr2CaCu2O8+δ and demonstrate that non-monotonic relaxation dynamics dominates above a certain fluence threshold. The dynamics is heavily influenced by transient modification of the electron-phonon interaction and phase space restrictions, in stark contrast to the monotonic relaxation in the nodal and off-nodal regions. 6. Nodal gap structure of superconducting BaFe2(As1-xPx)2 from angle-resolved thermal conductivity in a magnetic field Science.gov (United States) Yamashita, M.; Senshu, Y.; Shibauchi, T.; Kasahara, S.; Hashimoto, K.; Watanabe, D.; Ikeda, H.; Terashima, T.; Vekhter, I.; Vorontsov, A. B.; Matsuda, Y. 2011-08-01 The structure of the superconducting order parameter in the iron-pnictide superconductor BaFe2(As0.67P0.33)2 (Tc=31 K) with line nodes is studied by the angle-resolved thermal conductivity measurements in a magnetic field rotated within the basal plane. We find that the thermal conductivity displays distinct fourfold oscillations with minima when the field is directed at ±45∘ with respect to the tetragonal a axis. We discuss possible gap structures that can account for the data, and conclude that the observed results are most consistent with the closed nodal loops located at the flat parts of the electron Fermi surface with high Fermi velocity. 7. Angle Resolved Photoemission Spectroscopy Studies of the Mott Insulator to Superconductor Evolution in Ca2-xNaxCuO2Cl2 Energy Technology Data Exchange (ETDEWEB) Shen, Kyle Michael 2005-09-02 It is widely believed that many of the exotic physical properties of the high-T{sub c} cuprate superconductors arise from the proximity of these materials to the strongly correlated, antiferromagnetic Mott insulating state. Therefore, one of the fundamental questions in the field of high-temperature superconductivity is to understand the insulator-to-superconductor transition and precisely how the electronic structure of Mott insulator evolves as the first holes are doped into the system. This dissertation presents high-resolution, doping dependent angle-resolved photoemission (ARPES) studies of the cuprate superconductor Ca{sub 2-x}Na{sub x}CuO{sub 2}Cl{sub 2}, spanning from the undoped parent Mott insulator to a high-temperature superconductor with a T{sub c} of 22 K. A phenomenological model is proposed to explain how the spectral lineshape, the quasiparticle band dispersion, and the chemical potential all progress with doping in a logical and self-consistent framework. This model is based on Franck-Condon broadening observed in polaronic systems where strong electron-boson interactions cause the quasiparticle residue, Z, to be vanishingly small. Comparisons of the low-lying states to different electronic states in the valence band strongly suggest that the coupling of the photohole to the lattice (i.e. lattice polaron formation) is the dominant broadening mechanism for the lower Hubbard band states. Combining this polaronic framework with high-resolution ARPES measurements finally provides a resolution to the long-standing controversy over the behavior of the chemical potential in the high-T{sub c} cuprates. This scenario arises from replacing the conventional Fermi liquid quasiparticle interpretation of the features in the Mott insulator by a Franck-Condon model, allowing the reassignment of the position of the quasiparticle pole. As a function of hole doping, the chemical potential shifts smoothly into the valence band while spectral weight is transferred 8. Measurements of polarization-dependent angle-resolved light scattering from individual microscopic samples using Fourier transform light scattering Science.gov (United States) Jung, JaeHwang; Kim, Jinhyung; Seo, Min-Kyo; Park, YongKeun 2018-03-01 We present a method to measure the vector-field light scattering of individual microscopic objects. The polarization-dependent optical field images are measured with quantitative phase imaging at the sample plane, and then numerically propagated to the far-field plane. This approach allows the two-dimensional polarization-dependent angle-resolved light scattered patterns from individual object to be obtained with high precision and sensitivity. Using this method, we present the measurements of the polarization-dependent light scattering of a liquid crystal droplet and individual silver nanowires over scattering angles of 50{\\deg}. In addition, the spectroscopic extension of the polarization-dependent angle-resolved light scattering is demonstrated using wavelength-scanning illumination. 9. Angle-resolved conical emission spectra from filamentation in a solid with an Airy pattern and a Gaussian laser beam. Science.gov (United States) Gong, Cheng; Li, ZiXi; Hua, LinQiang; Quan, Wei; Liu, XiaoJun 2016-09-15 Filamentation dynamics in fused silica are investigated using an Airy pattern and a Gaussian laser beam. The angle-resolved conical emission spectra are measured and compared with the predictions of several models. Our experimental observations are consistent with the X-waves model in both cases. This indicates that both laser beams spontaneously evolve into nonlinear X-waves and suggests a universal evolution of filaments in fused silica, regardless of the initial laser beam profile. 10. eqpair: Electron energy distribution calculator Science.gov (United States) Coppi, Paolo S. 2018-02-01 eqpair computes the electron energy distribution resulting from a balance between heating and direct acceleration of particles, and cooling processes. Electron-positron pair balance, bremstrahlung, and Compton cooling, including external soft photon input, are among the processes considered, and the final electron distribution can be hybrid, thermal, or non-thermal. 11. Theory of angle-resolved photoemission experiments on a two-band model OpenAIRE De Cao, Tian 2008-01-01 Considering the electron states inside and outside the solid, we derive a formula of photoemission intensity. A general theoretical way to determine electronic structures of solids from ARPES experiments is outlined. It is shown that the spectral function inside the solids cannot be measured directly by ARPES, the effects of free electron states on the electronic structure observed by ARPES measurements must be considered, and the results from ARPES experiments cannot be understood until thes... 12. Rapid high-resolution spin- and angle-resolved photoemission spectroscopy with pulsed laser source and time-of-flight spectrometer. Science.gov (United States) Gotlieb, K; Hussain, Z; Bostwick, A; Lanzara, A; Jozwiak, C 2013-09-01 A high-efficiency spin- and angle-resolved photoemission spectroscopy (spin-ARPES) spectrometer is coupled with a laboratory-based laser for rapid high-resolution measurements. The spectrometer combines time-of-flight (TOF) energy measurements with low-energy exchange scattering spin polarimetry for high detection efficiencies. Samples are irradiated with fourth harmonic photons generated from a cavity-dumped Ti:sapphire laser that provides high photon flux in a narrow bandwidth, with a pulse timing structure ideally matched to the needs of the TOF spectrometer. The overall efficiency of the combined system results in near-E(F) spin-resolved ARPES measurements with an unprecedented combination of energy resolution and acquisition speed. This allows high-resolution spin measurements with a large number of data points spanning multiple dimensions of interest (energy, momentum, photon polarization, etc.) and thus enables experiments not otherwise possible. The system is demonstrated with spin-resolved energy and momentum mapping of the L-gap Au(111) surface states, a prototypical Rashba system. The successful integration of the spectrometer with the pulsed laser system demonstrates its potential for simultaneous spin- and time-resolved ARPES with pump-probe based measurements. 13. Pitch angle resolved measurements of escaping charged fusion products in TFTR Energy Technology Data Exchange (ETDEWEB) Zweben, S.J. 1989-01-01 Measurements of the flux of charged fusion products escaping from the TFTR plasma have been made with a new type of detector which can resolve the particle flux vs. pitch angle, energy, and time. The design of this detector is described, and results from the 1987 TFTR run are presented. These results are roughly consistent with predictions from a simple first-orbit particle loss model with respect to the pitch angle, energy, time, and plasma current dependence of the signals. 11 refs., 9 figs. 14. Si(111)-sq root 21 x sq root 21 -(Ag+Cs) surface studied by scanning tunneling microscopy and angle-resolved photoemission spectroscopy CERN Document Server Liu, C; Morikawa, H; Okino, H; Hasegawa, S; Okuda, T; Kinoshita, T 2003-01-01 Scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES) were used to study the atomic and electronic structures of the Si(111)-sq root 21 x sq root 21-(Ag + Cs) surface (sq root 21-Cs in short), which was induced by depositing caesium atoms on the Si(111)-sq root 3 x sq root 3-Ag surface at room temperature (RT). Compared with previously reported STM images of noble-metal induced sq root 21 x sq root 21 phases including the Si(111)-sq root 21 x sq root 21-(Ag+Ag) and Si(111)-sq root 21 x sq root 21-(Ag+Au) surfaces (sq root 21-Ag and sq root 21-Au, respectively), the sq root 21-Cs surface displayed quite different features in STM images. The ARPES data of the sq root 21-Cs surface revealed an intrinsic dispersive surface-state band, together with a non-dispersive one near the Fermi level, which was also different from those of the sq root 21-Ag and sq root 21-Au surfaces. These results strongly suggest different atomic arrangements between Cs- and noble-metal induced sq root ... 15. Quantum Transport and Nano Angle-resolved Photoemission Spectroscopy on the Topological Surface States of Single Sb2Te3 Nanowires Science.gov (United States) Arango, Yulieth C.; Huang, Liubing; Chen, Chaoyu; Avila, Jose; Asensio, Maria C.; Grützmacher, Detlev; Lüth, Hans; Lu, Jia Grace; Schäpers, Thomas 2016-01-01 We report on low-temperature transport and electronic band structure of p-type Sb2Te3 nanowires, grown by chemical vapor deposition. Magnetoresistance measurements unravel quantum interference phenomena, which depend on the cross-sectional dimensions of the nanowires. The observation of periodic Aharonov-Bohm-type oscillations is attributed to transport in topologically protected surface states in the Sb2Te3 nanowires. The study of universal conductance fluctuations demonstrates coherent transport along the Aharonov-Bohm paths encircling the rectangular cross-section of the nanowires. We use nanoscale angle-resolved photoemission spectroscopy on single nanowires (nano-ARPES) to provide direct experimental evidence on the nontrivial topological character of those surface states. The compiled study of the bandstructure and the magnetotransport response unambiguosly points out the presence of topologically protected surface states in the nanowires and their substantial contribution to the quantum transport effects, as well as the hole doping and Fermi velocity among other key issues. The results are consistent with the theoretical description of quantum transport in intrinsically doped quasi-one-dimensional topological insulator nanowires. PMID:27581169 16. Angle-resolved light scattering of individual rod-shaped bacteria based on Fourier transform light scattering. Science.gov (United States) Jo, YoungJu; Jung, JaeHwang; Lee, Jee Woong; Shin, Della; Park, HyunJoo; Nam, Ki Tae; Park, Ji-Ho; Park, YongKeun 2014-05-28 Two-dimensional angle-resolved light scattering maps of individual rod-shaped bacteria are measured at the single-cell level. Using quantitative phase imaging and Fourier transform light scattering techniques, the light scattering patterns of individual bacteria in four rod-shaped species (Bacillus subtilis, Lactobacillus casei, Synechococcus elongatus, and Escherichia coli) are measured with unprecedented sensitivity in a broad angular range from -70° to 70°. The measured light scattering patterns are analyzed along the two principal axes of rod-shaped bacteria in order to systematically investigate the species-specific characteristics of anisotropic light scattering. In addition, the cellular dry mass of individual bacteria is calculated and used to demonstrate that the cell-to-cell variations in light scattering within bacterial species is related to the cellular dry mass and growth. 17. Direct observation of superconducting gaps in MgB{sub 2} by angle-resolved photoemission spectroscopy Energy Technology Data Exchange (ETDEWEB) Souma, S.; Machida, Y.; Sato, T.; Takahashi, T.; Matsui, H.; Wang, S.-C.; Ding, H.; Kaminski, A.; Campuzano, J.C.; Sasaki, S.; Kadowaki, K 2004-08-01 High-resolution angle-resolved photoemission spectroscopy has been carried out to clarify the anomalous superconductivity of MgB{sub 2}. We observed three bands crossing the Fermi level, which are ascribed to B2p-{sigma}, {pi} and surface bands. We have succeeded for the first time in directly observing the superconducting gaps of these bands separately. We have found that the superconducting-gap sizes of {sigma} and surface bands are 6.5 {+-} 0.5 and 6.0 {+-} 0.5 meV, respectively, while that of the {pi} band is much smaller (1.5 {+-} 0.5 meV). The present experimental result unambiguously demonstrates the validity of the two-band superconductivity in MgB{sub 2}. 18. Characterization of the α-SN/CDTE(110) interface by angle-resolved X-ray photoemission International Nuclear Information System (INIS) Lin, T.S.; Partin, W.J.; Chung, Y.W. 1987-01-01 Stoichiometric and atomically clean CdTe(110) surfaces have been prepared by suitable chemical etching, followed by argon sputtering, and sample annealing in ultra-high vacuum. Cubic (α) -tin was grown on CdTe(110) by tin evaporation from a tungsten filament at a substrate temperature of 30 0 C. Angle-resolved X-ray photoelectron spectroscopy (ARXPS) was used to determine the α-Sn growth mechanism and the composition profile of this semiconductor heterostructure nondestructively. From their analyses, the authors conclude that α-Sn grows on CdTe(110) at 30 0 C by a layer by layer mechanism and forms an abrupt junction with CdTe(110) 19. Direct Observation of Localized Spin Antiferromagnetic Transition in PdCrO2 by Angle-Resolved Photoemission Spectroscopy Science.gov (United States) Noh, Han-Jin; Jeong, Jinwon; Chang, Bin; Jeong, Dahee; Moon, Hyun Sook; Cho, En-Jin; Ok, Jong Mok; Kim, Jun Sung; Kim, Kyoo; Min, B. I.; Lee, Han-Koo; Kim, Jae-Young; Park, Byeong-Gyu; Kim, Hyeong-Do; Lee, Seongsu 2014-01-01 We report the first case of the successful measurements of a localized spin antiferromagnetic transition in delafossite-type PdCrO2 by angle-resolved photoemission spectroscopy (ARPES). This demonstrates how to circumvent the shortcomings of ARPES for investigation of magnetism involved with localized spins in limited size of two-dimensional crystals or multi-layer thin films that neutron scattering can hardly study due to lack of bulk compared to surface. Also, our observations give direct evidence for the spin ordering pattern of Cr3+ ions in PdCrO2 suggested by neutron diffraction and quantum oscillation measurements, and provide a strong constraint that has to be satisfied by a microscopic mechanism for the unconventional anomalous Hall effect recently reported in this system. PMID:24419488 20. Evidence of the nature of core-level photoemission satellites using angle-resolved photoemission extended fine structure International Nuclear Information System (INIS) Moler, E.J.; Kellar, S.A.; Huff, W.R.A. 1997-01-01 The authors present a unique method of experimentally determining the angular momentum and intrinsic/extrinsic origin of core-level photoemission satellites by examining the satellite diffraction pattern in the Angle Resolved Photoemission Extended Fine Structure (ARPEFS) mode. They show for the first time that satellite peaks not associated with chemically differentiated atomic species display an ARPEFS intensity oscillation. They present ARPEFS data for the carbon 1s from (√3x√3)R30 CO/Cu(111) and p2mg(2xl)CO/Ni(110), nitrogen 1s from c(2x2) N 2 /Ni(100), cobalt 1s from p(1x1)Co/Cu(100), and nickel 3p from clean nickel (111). The satellite peaks and tails of the Doniach-Sunjic line shapes in all cases exhibit ARPEFS curves which indicate an angular momentum identical to the main peak and are of an intrinsic nature 1. Evidence of the nature of core-level photoemission satellites using angle-resolved photoemission extended fine structure Energy Technology Data Exchange (ETDEWEB) Moler, E.J.; Kellar, S.A.; Huff, W.R.A. [Lawrence Berkeley National Lab., CA (United States)] [and others 1997-04-01 The authors present a unique method of experimentally determining the angular momentum and intrinsic/extrinsic origin of core-level photoemission satellites by examining the satellite diffraction pattern in the Angle Resolved Photoemission Extended Fine Structure (ARPEFS) mode. They show for the first time that satellite peaks not associated with chemically differentiated atomic species display an ARPEFS intensity oscillation. They present ARPEFS data for the carbon 1s from ({radical}3x{radical}3)R30 CO/Cu(111) and p2mg(2xl)CO/Ni(110), nitrogen 1s from c(2x2) N{sub 2}/Ni(100), cobalt 1s from p(1x1)Co/Cu(100), and nickel 3p from clean nickel (111). The satellite peaks and tails of the Doniach-Sunjic line shapes in all cases exhibit ARPEFS curves which indicate an angular momentum identical to the main peak and are of an intrinsic nature. 2. Angle-resolved photoemission spectroscopy for VO{sub 2} thin films grown on TiO{sub 2} (0 0 1) substrates Energy Technology Data Exchange (ETDEWEB) Muraoka, Y., E-mail: [email protected] [Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530 (Japan); Faculty of Science, Research Laboratory for Surface Science, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530 (Japan); Saeki, K.; Yao, Y. [Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530 (Japan); Wakita, T. [Faculty of Science, Research Laboratory for Surface Science, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530 (Japan); Hirai, M.; Yokoya, T. [Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530 (Japan); Faculty of Science, Research Laboratory for Surface Science, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530 (Japan); Eguchi, R.; Shin, S. [RIKEN/SPring-8, 1-1-1 Kouto, Sayo, Hyogo 679-5148 (Japan) 2010-08-15 We present the results of angle-resolved photoemission spectroscopy (ARPES) measurements of metallic VO{sub 2} thin films. The VO{sub 2} thin films have been grown on TiO{sub 2} (0 0 1) single crystal substrates using pulsed laser deposition. The films exhibit a first-order metal-insulator transition (MIT) at 305 K. In the ARPES spectra of the metallic phase for the films, the O 2p band shows highly dispersive feature in the binding energy range of 3-8 eV along the {Gamma}-Z direction. The periodicity of the dispersive band is found to be 2.2 A{sup -1} which is almost identical with the periodicity expected from the c-axis length of the VO{sub 2} thin films. The overall feature of the experimental band structure is similar to the band structure calculations, supporting that we have succeeded in observing the dispersive band of the O 2p state in the metallic VO{sub 2} thin film. The present work indicates that the ARPES measurements using epitaxial thin films are promising for determining the band structure of VO{sub 2}. 3. Diffraction of high energy electrons International Nuclear Information System (INIS) Bourret, A. 1981-10-01 The diffraction of electrons by a crystal is examined to study its structure. As the electron-substance interaction is strong, it must be treated in a dynamic manner. Using the N waves theory and physical optics the base equations giving the wave at the outlet are deduced for a perfect crystal and their equivalence is shown. The more complex case of an imperfect crystal is then envisaged in these two approaches. In both cases, only the diffraction of high energy electrons ( > 50 KeV) are considered since in the diffraction of slow electrons back scattering cannot be ignored. Taking into account an increasingly greater number of beams, through fast calculations computer techniques, enables images to be simulated in very varied conditions. The general use of the Fast Fourier Transform has given a clear cut practical advantage to the multi-layer method [fr 4. Studies of Dirac and Weyl fermions by angle resolved photoemission spectroscopy Energy Technology Data Exchange (ETDEWEB) Huang, Lunan [Iowa State Univ., Ames, IA (United States) 2016-01-01 This dissertation consists of three parts. First, we study magnetic domains in Nd2Fe14B single crystals using high resolution magnetic force microscopy (MFM). In addition to the elongated, wavy nano-domains reported by a previous MFM study, we found that the micrometer size, star-shaped fractal pattern is constructed of an elongated network of nano-domains about 20 nm in width, with resolution-limited domain walls thinner than 2 nm. Second, we studied extra Dirac cones of multilayer graphene on SiC surface by ARPES and SPA-LEED. We discovered extra Dirac cones on Fermi surface due to SiC 6 x 6 and graphene 6√ 3 6√ 3 coincidence lattice on both single-layer and three-layer graphene sheets. We interpreted the position and intensity of the Dirac cone replicas, based on the scattering vectors from LEED patterns. We found the positions of replica Dirac cones are determined mostly by the 6 6 SiC superlattice even graphene layers grown thicker. Finally, we studied the electronic structure of MoTe2 by ARPES and experimentally con rmed the prediction of type II Weyl state in this material. By combining the result of Density Functional Theory calculations and Berry curvature calculations with out experimental data, we identi ed Fermi arcs, track states and Weyl points, all features predicted to exist in a type II Weyl semimetal. This material is an excellent playground for studies of exotic Fermions. 5. Low-energy electron potentiometry. Science.gov (United States) Jobst, Johannes; Kautz, Jaap; Mytiliniou, Maria; Tromp, Rudolf M; van der Molen, Sense Jan 2017-10-01 In a lot of systems, charge transport is governed by local features rather than being a global property as suggested by extracting a single resistance value. Consequently, techniques that resolve local structure in the electronic potential are crucial for a detailed understanding of electronic transport in realistic devices. Recently, we have introduced a new potentiometry method based on low-energy electron microscopy (LEEM) that utilizes characteristic features in the reflectivity spectra of layered materials [1]. Performing potentiometry experiments in LEEM has the advantage of being fast, offering a large field of view and the option to zoom in and out easily, and of being non-invasive compared to scanning-probe methods. However, not all materials show clear features in their reflectivity spectra. Here we, therefore, focus on a different version of low-energy electron potentiometry (LEEP) that uses the mirror mode transition, i.e. the drop in electron reflectivity around zero electron landing energy when they start to interact with the sample rather than being reflected in front of it. This transition is universal and sensitive to the local electrostatic surface potential (either workfunction or applied potential). It can consequently be used to perform LEEP experiments on a broader range of material compared to the method described in Ref[1]. We provide a detailed description of the experimental setup and demonstrate LEEP on workfunction-related intrinsic potential variations on the Si(111) surface and for a metal-semiconductor-metal junction with external bias applied. In the latter, we visualize the Schottky effect at the metal-semiconductor interface. Finally, we compare how robust the two LEEP techniques discussed above are against image distortions due to sample inhomogeneities or contamination. Copyright © 2017 Elsevier B.V. All rights reserved. 6. Photoelectron spectra of N2 +: Rotational line profiles studied with He;I endash excited angle-resolved spectroscopy and with synchrotron radiation International Nuclear Information System (INIS) Oehrwall, G.; Baltzer, P.; Bozek, J. 1999-01-01 We have recorded angle-resolved He I photoelectron spectra of the three outermost valence states in N 2 + , with high enough resolution to observe rotational line profiles. For the two Σ states, the X 2 Σ g + and the B 2 Σ u + , we found that the rotational branches corresponding to different changes in rotational quantum number can differ dramatically in β value. The well-known difference in β value for the ν=0 and ν=1 vibrations of the X 2 Σ g + state was found to be due to different rotational branching ratios and also different β values of the rotational branches. For the ν=0 endash 2 vibrations of the A 2 Π u state, the β value difference between rotational branches is much less pronounced than in the X and B states. We have also recorded synchrotron-radiation-excited photoelectron spectra of the ν=0 vibrational peaks of the X 2 Σ g + and B 2 Σ u + states where rotational line profiles are resolved. The intensities of the rotational branches were studied as function of photon energy, the X state between 23 and 65 eV, and the B state between 23 and 45 eV. The results for the X state have recently been presented in a Letter [G. Oehrwall, P. Baltzer, and J. Bozek, Phys. Rev. Lett. 81, 546, 1998]. The rotational branching ratios of the two states have very different behaviors as functions of photon energy. The relative intensities of the rotational branches in the X state change significantly over the studied energy range. The 3σ g →kσ u shape resonance apparently gives rise to a non-Franck-Condon-like behavior for the rotational branching ratio of the X state. In the B state, the rotational branching ratios remain essentially constant over the studied energy range. copyright 1999 The American Physical Society 7. Vicinage effects in energy loss and electron emission during grazing scattering of heavy molecular ions from a solid surface International Nuclear Information System (INIS) Song Yuanhong; Wang Younian; Miskovic, Z.L. 2005-01-01 Vicinage effects in the energy loss and the electron emission spectra are studied in the presence of Coulomb explosion of swift, heavy molecular ions, during their grazing scattering from a solid surface. The dynamic response of the surface is treated by means of the dielectric theory within the specular reflection model using the plasmon pole approximation for the bulk dielectric function, whereas the angle-resolved energy spectra of the electrons emitted from the surface are obtained on the basis of the first-order, time-dependent perturbation theory. The evolution of the charge states of the constituent ions in the molecule during scattering is described by a nonequilibrium extension of the Brandt-Kitagawa model. The molecule scattering trajectories and the corresponding Coulomb explosion dynamics are evaluated for the cases of the internuclear axis being either aligned in the beam direction or randomly oriented in the directions parallel to the surface. Our calculations show that the vicinage effect in the energy loss is generally weaker for heavy molecules than for light molecules. In addition, there is clear evidence of the negative vicinage effect in both the energy loss and the energy spectra of the emitted electrons for molecular ions at lower speeds and with the axis aligned in the direction of motion 8. Combined angle-resolved X-ray photoelectron spectroscopy, density functional theory and kinetic study of nitridation of gallium arsenide Science.gov (United States) Mehdi, H.; Monier, G.; Hoggan, P. E.; Bideux, L.; Robert-Goumet, C.; Dubrovskii, V. G. 2018-01-01 The high density of interface and surface states that cause the strong Fermi pinning observed on GaAs surfaces can be reduced by depositing GaN ultra-thin films on GaAs. To further improve this passivation, it is necessary to investigate the nitridation phenomena by identifying the distinct steps occurring during the process and to understand and quantify the growth kinetics of GaAs nitridation under different conditions. Nitridation of the cleaned GaAs substrate was performed using N2 plasma source. Two approaches have been combined. Firstly, an AR-XPS (Angle Resolved X-ray Photoelectron Spectroscopy) study is carried out to determine the chemical environments of the Ga, As and N atoms and the composition depth profile of the GaN thin film which allow us to summarize the nitridation process in three steps. Moreover, the temperature and time treatment have been investigated and show a significant impact on the formation of the GaN layer. The second approach is a refined growth kinetic model which better describes the GaN growth as a function of the nitridation time. This model clarifies the exchange mechanism of arsenic with nitrogen atoms at the GaN/GaAs interface and the phenomenon of quasi-saturation of the process observed experimentally. 9. Characterization of weakly absorbing thin films by multiple linear regression analysis of absolute unwrapped phase in angle-resolved spectral reflectometry. Science.gov (United States) Dong, Jingtao; Lu, Rongsheng 2018-04-30 The simultaneous determination of t, n(λ), and κ(λ) of thin films can be a tough task for the high correlation of fit parameters. The strong assumptions about the type of dispersion relation are commonly used as a consequence to alleviate correlation concerns by reducing the free parameters before the nonlinear regression analysis. Here we present an angle-resolved spectral reflectometry for the simultaneous determination of weakly absorbing thin film parameters, where a reflectance interferogram is recorded in both angular and spectral domains in a single-shot measurement for the point of the sample being illuminated. The variations of the phase recovered from the interferogram as functions of t, n, and κ reveals that the unwrapped phase is monotonically related to t, n, and κ, thereby allowing the problem of correlation to be alleviated by multiple linear regression. After removing the 2π ambiguity of the unwrapped phase, the merit function based on the absolute unwrapped phase performs a 3D data cube with variables of t, n and κ at each wavelength. The unique solution of t, n, and κ can then be directly determined from the extremum of the 3D data cube at each wavelength with no need of dispersion relation. A sample of GaN thin film grown on a polished sapphire substrate is tested. The experimental data of t and [n(λ), κ(λ)] are confirmed by the scanning electron microscopy and the comparison with the results of other related works, respectively. The consistency of the results shows the proposed method provides a useful tool for the determination of the thickness and optical constants of weakly absorbing thin films. 10. Thermal Stability of Au/NbOx/Nb and Au/Nb2O5/W Model Catalysts Studied by Angle-resolved X-ray Photoelectron Spectroscopy Czech Academy of Sciences Publication Activity Database Lykhach, Yaroslava; Plšek, Jan; Spirovová, Ilona; Bastl, Zdeněk 2003-01-01 Roč. 68, č. 10 (2003), s. 1791-1804 ISSN 0010-0765 R&D Projects: GA ČR GA104/02/0664 Institutional research plan: CEZ:AV0Z4040901 Keywords : model metal catalysts * angle resolved photoemission * depth profiles Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.041, year: 2003 11. Energy electron analyzers raster electron microscope International Nuclear Information System (INIS) Dremova, N.N.; Raj, Eh.I.; Robinson, V.N. 1995-01-01 Spectrometers of back-scattered and secondary electrons used in a raster electron microscope designed to study multilayer structures and potential relief at the solid-state body surface, are described. Their possible applications are demonstrated using microelectronics devices as an example 12. Power Electronics, Energy Harvesting and Renewable Energies Laboratory Data.gov (United States) Federal Laboratory Consortium — The research in the Power Electronics, Energy Harvesting and Renewable Energies Laboratory (PEHREL) is mainly focused on investigation, modeling, simulation, design,... 13. Absence of a holelike fermi surface for the iron-based K0.8F1.7Se2 superconductor revealed by angle-resolved photoemission spectroscopy. Science.gov (United States) Qian, T; Wang, X-P; Jin, W-C; Zhang, P; Richard, P; Xu, G; Dai, X; Fang, Z; Guo, J-G; Chen, X-L; Ding, H 2011-05-06 We have performed an angle-resolved photoemission spectroscopy study of the new iron-based superconductor K(0.8)Fe(1.7)Se(2) (T(c)∼30 K). Clear band dispersion is observed with the overall bandwidth renormalized by a factor of 2.5 compared to our local density approximation calculations, indicating relatively strong correlation effects. Only an electronlike band crosses the Fermi energy, forming a nearly circular Fermi surface (FS) at M (π, 0). The holelike band at Γ sinks ∼90 meV below the Fermi energy, with an indirect band gap of 30 meV, to the bottom of the electronlike band. The observed FS topology in this superconductor favors (π, π) inter-FS scattering between the electronlike FSs at the M points, in sharp contrast to other iron-based superconductors which favor (π, 0) inter-FS scattering between holelike and electronlike FSs. 14. High-energy electron diffraction and microscopy CERN Document Server Peng, L M; Whelan, M J 2011-01-01 This book provides a comprehensive introduction to high energy electron diffraction and elastic and inelastic scattering of high energy electrons, with particular emphasis on applications to modern electron microscopy. Starting from a survey of fundamental phenomena, the authors introduce the most important concepts underlying modern understanding of high energy electron diffraction. Dynamical diffraction in transmission (THEED) and reflection (RHEED) geometries is treated using ageneral matrix theory, where computer programs and worked examples are provided to illustrate the concepts and to f 15. Very low energy scanning electron microscopy Czech Academy of Sciences Publication Activity Database Frank, Luděk; Hovorka, Miloš; Konvalina, Ivo; Mikmeková, Šárka; Müllerová, Ilona 2011-01-01 Roč. 645, č. 1 (2011), s. 46-54 ISSN 0168-9002 R&D Projects: GA MŠk OE08012 Institutional research plan: CEZ:AV0Z20650511 Keywords : scanning electron microscopy * low energy electrons * cathode lens * very low energy STEM * grain contrast Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.207, year: 2011 16. Reaffirming the d(x2-y2) superconducting gap using the autocorrelation angle-resolved photoemission spectroscopy of Bi1.5Pb0.55Sr1.6La0.4CuO(6+δ). Science.gov (United States) Hashimoto, M; He, R-H; Testaud, J P; Meevasana, W; Moore, R G; Lu, D H; Yoshida, Y; Eisaki, H; Devereaux, T P; Hussain, Z; Shen, Z-X 2011-04-22 Knowledge of the gap function is important to understand the pairing mechanism for high-temperature (T(c)) superconductivity. However, Fourier transform scanning tunneling spectroscopy (FT STS) and angle-resolved photoemission spectroscopy (ARPES) in the cuprates have reported contradictory gap functions, with FT-STS results deviating strongly from a canonical d(x2-y2) form. By applying an "octet model" analysis to autocorrelation ARPES, we reveal that a contradiction occurs because the octet model does not consider the effects of matrix elements and the pseudogap. This reaffirms the canonical d(x2-y2) superconducting gap around the node, which can be directly determined from ARPES. Further, our study suggests that the FT-STS reported fluctuating superconductivity around the node at far above T(c) is not necessary to explain the existence of the quasiparticle interference at low energy. 17. Power Electronics for Renewable Energy Systems DEFF Research Database (Denmark) Choi, U. M.; Lee, K. B.; Blaabjerg, Frede 2012-01-01 The use of renewable energy sources are increased because of the depletion of natural resources and the increasing pollution level from energy production. The wind energy and the solar energy are most widely used among the renewable energy sources. Power electronics is needed in almost all kinds...... of renewable energy system. It controls the renewable source and interfaces with the load effectively, which can be grid-connected or van work in stand-alone mode. In this presentation, overview of wind and photovoltaic energy systems are introduced. Next, the power electronic circuits behind the most common... 18. Relaxation of strongly coupled electron and phonon fields after photoemission and high-energy part of ARPES spectra of cuprates Science.gov (United States) Myasnikova, A. E.; Zhileeva, E. A.; Moseykin, D. V. 2018-03-01 An approach to considering systems with a high concentration of correlated carriers and strong long-range electron–phonon interaction and to calculating the high-energy part of the angle-resolved photoemission spectroscopy (ARPES) spectra of such systems is suggested. Joint relaxation of strongly coupled fields—a field of correlated electrons and phonon field—after photoemission is studied to clarify the nature of characteristic features observed in the high-energy part of the ARPES spectra of cuprate superconductors. Such relaxation occurs in systems with strong predominantly long-range electron–phonon interaction at sufficiently high carrier concentration due to the coexistence of autolocalized and delocalized carriers. A simple method to calculate analytically a high-energy part of the ARPES spectrum arising is proposed. It takes advantage of using the coherent states basis for the phonon field in the polaron and bipolaron states. The approach suggested yields all the high-energy spectral features like broad Gaussian band and regions of ‘vertical dispersion’ being in good quantitative agreement with the experiments on cuprates at any doping with both types of carriers. Demonstrated coexistence of autolocalized and delocalized carriers in superconducting cuprates changes the idea about their ground state above the superconducting transition temperature that is important for understanding transport and magnetic properties. High density of large-radius autolocalized carriers revealed may be a key to the explanation of charge ordering in doped cuprates. 19. Attainment of Electron Beam Suitable for Medium Energy Electron Cooling Energy Technology Data Exchange (ETDEWEB) Seletskiy, Sergei M. [Univ. of Rochester, NY (United States) 2005-01-01 Electron cooling of charged particle beams is a well-established technique at electron energies of up to 300 keV. However, up to the present time the advance of electron cooling to the MeV-range energies has remained a purely theoretical possibility. The electron cooling project at Fermilab has recently demonstrated the ¯rst cooling of 8.9 GeV/c antiprotons in the Recycler ring, and therefore, has proved the validity of the idea of relativistic electron cool- ing. The Recycler Electron Cooler (REC) is the key component of the Teva- tron Run II luminosity upgrade project. Its performance depends critically on the quality of electron beam. A stable electron beam of 4.3 MeV car- rying 0.5 A of DC current is required. The beam suitable for the Recycler Electron Cooler must have an angular spread not exceeding 200 ¹rad. The full-scale prototype of the REC was designed, built and tested at Fermilab in the Wideband laboratory to study the feasibility of attaining the high-quality electron beam. In this thesis I describe various aspects of development of the Fermilab electron cooling system, and the techniques used to obtain the electron beam suitable for the cooling process. In particular I emphasize those aspects of the work for which I was principally responsible. 20. Study of the local structure of binary surfaces by electron diffraction (XPS, LEED) OpenAIRE Gereová, Katarína 2006-01-01 Study of local structure of binary surface with usage of ultra-thin film of cerium deposited on a Pd (111) single-crystal surface is presented. X-ray photoelectron spectroscopy and diffraction (XPS, XPD), angle resolved UV photoemission spectroscopy (ARUPS) and low energy electron diffraction (LEED) was used for our investigations. LEED and X-ray excited photoemission intensities results represent a surface-geometrical structure. As well, mapping of ultra-violet photoelectron intensities as a... 1. Electron correlation energy in confined two-electron systems Energy Technology Data Exchange (ETDEWEB) Wilson, C.L. [Chemistry Program, Centre College, 600 West Walnut Street, Danville, KY 40422 (United States); Montgomery, H.E., E-mail: [email protected] [Chemistry Program, Centre College, 600 West Walnut Street, Danville, KY 40422 (United States); Sen, K.D. [School of Chemistry, University of Hyderabad, Hyderabad 500 046 (India); Thompson, D.C. [Chemistry Systems and High Performance Computing, Boehringer Ingelheim Pharamaceuticals Inc., 900 Ridgebury Road, Ridgefield, CT 06877 (United States) 2010-09-27 Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted Hartree-Fock and radial limit energies over a range of confinement radii from 0.05-10a{sub 0}. At small R, the correlation energies approach limiting values that are independent of Z while at intermediate R, systems with Z{>=}1 exhibit a characteristic maximum in the correlation energy resulting from an increase in the angular correlation energy which is offset by a decrease in the radial correlation energy. 2. Electron capture and energy-gain spectroscopy Energy Technology Data Exchange (ETDEWEB) Taulbjerg, K. 1989-01-01 The applicability of translation energy spectroscopy as a tool to determine individual reaction cross sections in atomic collisions is analyzed with special emphasis on the electron capture process in highly charged ion collisions. A condition is derived to separate between higher collision energies where translation energy spectroscopy is problem free and lower energies where strong overlap of individual spectra features prohibits an analysis of the total translation energy spectrum by means of a simple deconvolution procedure. 8 refs., 6 figs. 3. Energy Saving and Efficient Energy Use By Power Electronic Systems DEFF Research Database (Denmark) Blaabjerg, Frede; Wang, Huai; Davari, Pooya 2017-01-01 energy in different applications. This chapter will give an overview of challenges and possibilities in terms of energy saving and also energy efficient use. This includes a discussion on high efficiency power electronics devices and the systems they are used for energy loss reduction. The key enabling......In the development of the modern society, one of the key factors is to save energy in order to become more independent of other energy resources. Two important approaches can be taken—one is to change behavior and thereby save energy—the second one is to develop new technology which is able to save...... technologies are power electronics, Information and Communication Technology (ICT) as well as systems to carry the electrical energy through power transmission, conversion and distribution. A couple of examples will be given to demonstrate the energy saving possibilities by power electronics systems... 4. Power electronics for renewable energy systems DEFF Research Database (Denmark) Iov, Florin; Blaabjerg, Frede 2009-01-01 sources from the conventional, fossil (and short term) based energy sources to renewable energy resources. Another is to use high efficient power electronics in power generation, power transmission/distribution and end-user application. This paper discuss some of the most emerging renewable energy sources... 5. Ultrafast Electron Dynamics in Solar Energy Conversion. Science.gov (United States) Ponseca, Carlito S; Chábera, Pavel; Uhlig, Jens; Persson, Petter; Sundström, Villy 2017-08-23 Electrons are the workhorses of solar energy conversion. Conversion of the energy of light to electricity in photovoltaics, or to energy-rich molecules (solar fuel) through photocatalytic processes, invariably starts with photoinduced generation of energy-rich electrons. The harvesting of these electrons in practical devices rests on a series of electron transfer processes whose dynamics and efficiencies determine the function of materials and devices. To capture the energy of a photogenerated electron-hole pair in a solar cell material, charges of opposite sign have to be separated against electrostatic attractions, prevented from recombining and being transported through the active material to electrodes where they can be extracted. In photocatalytic solar fuel production, these electron processes are coupled to chemical reactions leading to storage of the energy of light in chemical bonds. With the focus on the ultrafast time scale, we here discuss the light-induced electron processes underlying the function of several molecular and hybrid materials currently under development for solar energy applications in dye or quantum dot-sensitized solar cells, polymer-fullerene polymer solar cells, organometal halide perovskite solar cells, and finally some photocatalytic systems. 6. Structural and electronic analysis of Hf on Si(1 1 1) surface studied by XPS, LEED and XPD Energy Technology Data Exchange (ETDEWEB) Carazzolle, M.F. [Experimentelle Physik 1, Universitaet Dortmund, Otto-Hahn-Str. 4, D44221 Dortmund (Germany); Instituto de Fisica, Universidade Estadual de Campinas, C.P. 6165, 13083-970 Campinas, SP (Brazil)], E-mail: [email protected]; Schuermann, M.; Fluechter, C.R.; Weier, D. [Experimentelle Physik 1, Universitaet Dortmund, Otto-Hahn-Str. 4, D44221 Dortmund (Germany); Berges, U. [Experimentelle Physik 1, Universitaet Dortmund, Otto-Hahn-Str. 4, D44221 Dortmund (Germany); DELTA, Universitaet Dortmund, Maria-Goeppert-Mayer-Str. 2, D44227 Dortmund (Germany); Siervo, A. de [Laboratorio Nacional de Luz Sincrotron, C.P. 6192, 13084-971 Campinas, SP (Brazil); Landers, R. [Instituto de Fisica, Universidade Estadual de Campinas, C.P. 6165, 13083-970 Campinas, SP (Brazil); Laboratorio Nacional de Luz Sincrotron, C.P. 6192, 13084-971 Campinas, SP (Brazil); Kleiman, G.G. [Instituto de Fisica, Universidade Estadual de Campinas, C.P. 6165, 13083-970 Campinas, SP (Brazil); Westphal, C. [Experimentelle Physik 1, Universitaet Dortmund, Otto-Hahn-Str. 4, D44221 Dortmund (Germany); DELTA, Universitaet Dortmund, Maria-Goeppert-Mayer-Str. 2, D44227 Dortmund (Germany) 2007-05-15 In this work, we present a systematic electronic and structural study of the Hf-silicide formation upon annealing on Si(1 1 1) surface. The electronic structure and surface composition were determined by X-ray photoelectron spectroscopy (XPS) and angle-resolved X-ray photoelectron spectroscopy (ARXPS). To determine the atomic structure of the surface alloy we used low energy electron diffraction (LEED) and angle-resolved photoelectron diffraction (XPD). It was possible to verify that, after 600 deg. C annealing, there is alloy formation and after 700 deg. C the Hf diffusion process is predominant. Using LEED and XPD measurements we detected the ordered island formation simultaneously with alloy formation. 7. NaI(Tl) electron energy resolution CERN Document Server Mengesha, W 2002-01-01 NaI(Tl) electron energy resolution eta sub e was measured using the Modified Compton Coincidence Technique (MCCT). The MCCT allowed detection of nearly monoenergetic internal electrons resulting from the scattering of incident 662 keV gamma rays within a primary NaI(Tl) detector. Scattered gamma rays were detected using a secondary HPGe detector in a coincidence mode. Measurements were carried out for electron energies ranging from 16 to 438 keV, by varying the scattering angle. Measured HPGe coincidence spectra were deconvolved to determine the scattered energy spectra from the NaI(Tl) detector. Subsequently, the NaI(Tl) electron energy spectra were determined by subtracting the energy of scattered spectra from the incident source energy (662 keV). Using chi-squared minimization, iterative deconvolution of the internal electron energy spectra from the measured NaI(Tl) spectra was then used to determine eta sub e at the electron energy of interest. eta sub e values determined using this technique represent va... 8. High energy electron multibeam diffraction and imaging International Nuclear Information System (INIS) Bourret, Alain. 1980-04-01 The different theories of dynamical scattering of electrons are firstly reviewed with special reference to their basis and the validity of the different approximations. Then after a short description of the different experimental set ups, structural analysis and the investigation of the optical potential by means of high energy electrons will be surveyed 9. Electron energy-distribution functions in gases International Nuclear Information System (INIS) Pitchford, L.C. 1981-01-01 Numerical calculation of the electron energy distribution functions in the regime of drift tube experiments is discussed. The discussion is limited to constant applied fields and values of E/N (ratio of electric field strength to neutral density) low enough that electron growth due to ionization can be neglected 10. Angle-resolved spectral Fabry-Pérot interferometer for single-shot measurement of refractive index dispersion over a broadband spectrum Science.gov (United States) Dong, J. T.; Ji, F.; Xia, H. J.; Liu, Z. J.; Zhang, T. D.; Yang, L. 2018-01-01 An angle-resolved spectral Fabry-Pérot interferometer is reported for fast and accurate measurement of the refractive index dispersion of optical materials with parallel plate shape. The light sheet from the wavelength tunable laser is incident on the parallel plate with converging angles. The transmitted interference light for each angle is dispersed and captured by a 2D sensor, in which the rows and the columns are used to simultaneously record the intensities as a function of wavelength and incident angle, respectively. The interferogram, named angle-resolved spectral intensity distribution, is analyzed by fitting the phase information instead of finding the fringe peak locations that present periodic ambiguity. The refractive index dispersion and the physical thickness can be then retrieved from a single-shot interferogram within 18 s. Experimental results of an optical substrate standard indicate that the accuracy of the refractive index dispersion is less than 2.5 × 10-5 and the relative uncertainty of the thickness is 6 × 10-5 mm (3σ) due to the high stability and the single-shot measurement of the proposed system. 11. Low Energy Electron Cooler for NICA Booster CERN Document Server Denisov, A P 2017-01-01 BINP has developed an electron cooler to increase the ion accumulation efficiency in the NICA (Nuclotron-based Ion Collider fAcility) heavy ion booster (JINR, Dubna). Adjustment of the cooler magnetic system provides highly homogeneous magnetic field in the cooling section B trans/B long ≤ 4∙10-5 which is vital for efficient electron cooling. First experiments with an electron beam performed at BINP demonstrated the target DC current of 500 mA and electron energy 6 keV. 12. Electronic and structural characterizations of unreconstructed {0001} surfaces and the growth of graphene overlayers International Nuclear Information System (INIS) Emtsev, Konstantin 2009-01-01 The present work is focused on the characterization of the clean unreconstructed SiC{0001} surfaces and the growth of graphene overlayers thereon. Electronic properties of SiC surfaces and their interfaces with graphene and few layer graphene films were investigated by means of angle resolved photoelectron spectroscopy, X-ray photoelectron spectroscopy and low energy electron diffraction. Structural characterizations of the epitaxial graphene films grown on SiC were carried out by atomic force microscopy and low energy electron microscopy. Supplementary data was obtained by scanning tunneling microscopy. (orig.) 13. Stability of electron energy in the Fermilab electron cooler Energy Technology Data Exchange (ETDEWEB) Shemyakin, A.; Carlson, K.; Prost, L.R.; Saewert, G.; /Fermilab 2009-02-01 A powerful electron beam (4.3 MeV, 0.1 A DC) generated by an electrostatic accelerator has been used at Fermilab for three years to cool antiprotons in the Recycler ring. For electron cooling to be effective, the electron energy should not deviate from its optimum value by more than 500V. The main tool for studying the energy stability is the electron beam position in a high-dispersion area. The energy ripple (frequencies above 0.2 Hz) was found to be less than 150 eV rms; the main cause of the ripple is the fluctuations of the chain current. In addition, the energy can drift to up to several keV that is traced to two main sources. One of them is a drift of the charging current, and another is a temperature dependence of generating voltmeter readings. The paper describes the efforts to reach the required level of stability as well as the setup, diagnostics, results of measurements, and operational experience. 14. Stability of electron energy in the Fermilab electron cooler International Nuclear Information System (INIS) Shemyakin, A.; Carlson, K.; Prost, L.R.; Saewert, G. 2009-01-01 A powerful electron beam (4.3 MeV, 0.1 A DC) generated by an electrostatic accelerator has been used at Fermilab for three years to cool antiprotons in the Recycler ring. For electron cooling to be effective, the electron energy should not deviate from its optimum value by more than 500V. The main tool for studying the energy stability is the electron beam position in a high-dispersion area. The energy ripple (frequencies above 0.2 Hz) was found to be less than 150 eV rms; the main cause of the ripple is the fluctuations of the chain current. In addition, the energy can drift to up to several keV that is traced to two main sources. One of them is a drift of the charging current, and another is a temperature dependence of generating voltmeter readings. The paper describes the efforts to reach the required level of stability as well as the setup, diagnostics, results of measurements, and operational experience 15. Low energy electron scattering from fuels International Nuclear Information System (INIS) Lopes, M. Cristina A.; Silva, Daniel G.M.; Coelho, Rafael F.; Duque, Humberto V.; Santos, Rodrigo R. dos; Ribeiro, Thiago M. 2011-01-01 Full text. Accurate and precise values of absolute total cross section (TCS) represent important information in many scientific and technological applications. In our case, for example, we are motivated to provide such information for electron-fuel collision processes which are specifically relevant to modeling spark ignition in alcohol-fuelled internal combustion engines. Many electron scattering TCS measurements are presently available for a diverse range of atomic and molecular targets. However, lack of data for important bio-molecular targets still remains. Disagreements between the available TCS data for the alcohols have prompted several studies of electron scattering collision of slow electrons with these molecules which are currently important in applications as bio- fuels. This relevance, which has attracted much attention, has been one of the subjects of a recent collaboration between experimental and theoretical groups in the USA and Brazil. Recently this collaboration reported first measurements and calculations of differential cross sections for elastic low-energy (rotationally unresolved) electron scattering by several primary alcohols. In this work we address methanol and ethanol TCSs at low energy range and report additional studies of resonant structure in ethanol using the detection of metastable states produced by electron impact excitation with high energy resolution. We have recently constructed a TCS apparatus in our laboratory at Universidade Federal de Juiz de Fora, Brazil, based on the well-known linear transmission technique. The experimental setup is based on the measurement of the attenuation of a collimated electron beam through a gas cell containing the atoms or molecules to be studied at a given pressure. It consists essentially of an electron gun, a gas cell and an electron energy analyzer composed of an array of decelerating electrostatic lenses, a cylindrical dispersive 127o analyzer and a Faraday cup. To our knowledge, there exist 16. Low energy electron scattering from fuels Energy Technology Data Exchange (ETDEWEB) Lopes, M. Cristina A.; Silva, Daniel G.M.; Coelho, Rafael F.; Duque, Humberto V.; Santos, Rodrigo R. dos; Ribeiro, Thiago M. [Universidade Federal de Juiz de Fora (UFJF), MG (Brazil). Dept. de Fisica; Yates, Brent; Hong, Ling; Khakoo, Murtadha A. [California State University at Fullerton, CA (US). Physics Department; Bettega, Marcio H.F. [Universidade Federal do Parana (UFPR), Curitiba, PR (Brazil). Dept. de Fisica; Costa, Romarly F. da [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil). Centro de Ciencias Naturais e Humanas; Lima, Marco A.P. [Laboratorio Nacional de Ciencia e Tecnologia do Bioetanol (CTBE/CNPEM), Campinas, SP (Brazil) 2011-07-01 Full text. Accurate and precise values of absolute total cross section (TCS) represent important information in many scientific and technological applications. In our case, for example, we are motivated to provide such information for electron-fuel collision processes which are specifically relevant to modeling spark ignition in alcohol-fuelled internal combustion engines. Many electron scattering TCS measurements are presently available for a diverse range of atomic and molecular targets. However, lack of data for important bio-molecular targets still remains. Disagreements between the available TCS data for the alcohols have prompted several studies of electron scattering collision of slow electrons with these molecules which are currently important in applications as bio- fuels. This relevance, which has attracted much attention, has been one of the subjects of a recent collaboration between experimental and theoretical groups in the USA and Brazil. Recently this collaboration reported first measurements and calculations of differential cross sections for elastic low-energy (rotationally unresolved) electron scattering by several primary alcohols. In this work we address methanol and ethanol TCSs at low energy range and report additional studies of resonant structure in ethanol using the detection of metastable states produced by electron impact excitation with high energy resolution. We have recently constructed a TCS apparatus in our laboratory at Universidade Federal de Juiz de Fora, Brazil, based on the well-known linear transmission technique. The experimental setup is based on the measurement of the attenuation of a collimated electron beam through a gas cell containing the atoms or molecules to be studied at a given pressure. It consists essentially of an electron gun, a gas cell and an electron energy analyzer composed of an array of decelerating electrostatic lenses, a cylindrical dispersive 127o analyzer and a Faraday cup. To our knowledge, there exist 17. Relativistic energy loss in a dispersive medium DEFF Research Database (Denmark) 2002-01-01 The electron energy loss in a dispersive medium is obtained using macroscopic electrodynamics taking advantage of a static frame of reference. Relativistic corrections are described in terms of a dispersive Lorentz factor obtained by replacing the vacuum velocity c by the characteristic phase...... velocity c/n, where n is the complex index of refraction. The angle-resolved energy-loss spectrum of a Drude conductor is analyzed in detail and it is shown that the low-energy peak due to Ohmic losses is enhanced compared to the classical approximation.... 18. Angle - resolved photoemission study of two phases of the GaAs(100)-c(4x4) surface Czech Academy of Sciences Publication Activity Database Cukr, Miroslav; Jiříček, Petr; Bartoš, Igor; Sadowski, J. 2008-01-01 Roč. 100, - (2008), 072017/1-072017/4 ISSN 1742-6588 R&D Projects: GA AV ČR IAA100100628; GA ČR GA202/07/0601 Institutional research plan: CEZ:AV0Z10100521 Keywords : gallium arsenide * molecular beam epitaxy * photoelectron spectroscopy * surface reconstruction * surface phases * electron states Subject RIV: BM - Solid Matter Physics ; Magnetism 19. Electron scattering from sodium at intermediate energies International Nuclear Information System (INIS) Mitroy, J.; McCarthy, I.E. 1986-10-01 A comprehensive comparison is made between theoretical calculations and experimental data for intermediate energy (≥ 10 eV) electron scattering from sodium vapour. The theoretical predictions of coupled-channels calculations (including one, two or four channels) do not agree with experimental values of the differential cross sections for elastic scattering or the resonant 3s to 3p excitation. Increasingly-more-sophisticated calculations, incorporating electron correlations in the target states, and also including core-excited states in the close-coupling expansion, are done at a few selected energies in an attempt to isolate the cause of the discrepancies between theory and experiment. It is found that these more-sophisticated calculations give essentially the same results as the two- and four-channel calculations using Hartree-Fock wavefunctions. Comparison of the sodium high-energy elastic differential cross sections with those of neon suggests that the sodium differential cross section experiments may suffer from systematic errors. There is also disagreement, at the higher energies, between theoretical values for the scattering parameters and those that are derived from laser-excited superelastic scattering and electron photon coincidence experiments. When allowance is made for the finite acceptance angle of the electron spectrometers used in the experiments by convoluting the theory with a function representing the distribution of electrons entering the electron spectrometer it is found that the magnitudes of the differences between theory and experiment are reduced 20. Ultrasound Attenuation in Sr2RuO4: An Angle-Resolved Study of the Superconducting Gap Function Science.gov (United States) Lupien, C.; Macfarlane, W. A.; Proust, Cyril; Taillefer, Louis; Mao, Z. Q.; Maeno, Y. 2001-06-01 We present a study of the electronic ultrasound attenuation α in the unconventional superconductor Sr2RuO4. The power law behavior of α at temperatures down to Tc/30 clearly indicates the presence of nodes in the gap. In the normal state, we find an enormous anisotropy of α in the basal plane of the tetragonal structure. In the superconducting state, the temperature dependence of α also exhibits significant anisotropy. We discuss these results in relation to possible gap functions. 1. Superconducting gap structure of heavy-Fermion compound URu2Si2 determined by angle-resolved thermal conductivity Science.gov (United States) Kasahara, Y.; Shishido, H.; Shibauchi, T.; Haga, Y.; Matsuda, T. D.; Onuki, Y.; Matsuda, Y. 2009-05-01 In heavy-Fermion compound URu2Si2, unusual superconductivity is embedded in an enigmatic 'hidden order' phase. Recently, it has been shown that URu2Si2 is essentially a multiband superconductor associated with the semimetallic compensated electronic structure. Here, to pin down the detailed superconducting gap structure, we have performed thermal transport measurements on ultraclean URu2Si2 single crystals in magnetic fields rotating various directions relative to the crystal axes. By changing the amplitude of magnetic fields, we determined the nodal topology of electron and hole band separately. The results indicate a new type of unconventional superconductivity with two distinct gaps, in which horizontal line nodes lie within the basal ab plane of the light-hole band with small gap and point nodes along the c-axis in the heavy electron band with large gap. This gap structure is consistent with 'chiral' d-wave symmetry with a form {\\hat{k}}_{z}({\\hat{k}}_{x}+i{\\hat{k}}_{y}) . 2. Superconducting gap structure of heavy-Fermion compound URu2Si2 determined by angle-resolved thermal conductivity International Nuclear Information System (INIS) Kasahara, Y; Shishido, H; Shibauchi, T; Matsuda, Y; Haga, Y; Matsuda, T D; Onuki, Y 2009-01-01 In heavy-Fermion compound URu 2 Si 2 , unusual superconductivity is embedded in an enigmatic 'hidden order' phase. Recently, it has been shown that URu 2 Si 2 is essentially a multiband superconductor associated with the semimetallic compensated electronic structure. Here, to pin down the detailed superconducting gap structure, we have performed thermal transport measurements on ultraclean URu 2 Si 2 single crystals in magnetic fields rotating various directions relative to the crystal axes. By changing the amplitude of magnetic fields, we determined the nodal topology of electron and hole band separately. The results indicate a new type of unconventional superconductivity with two distinct gaps, in which horizontal line nodes lie within the basal ab plane of the light-hole band with small gap and point nodes along the c-axis in the heavy electron band with large gap. This gap structure is consistent with 'chiral' d-wave symmetry with a form k-circumflex z (k-circumflex x +ik-circumflex y ). 3. Simulations of High-Energy Electron Cooling CERN Document Server Fedotov, Alexei V; Bruhwiler, David L; Eidelman, Yury I; Litvinenko, Vladimir N; Malitsky, Nikolay; Meshkov, Igor; Sidorin, Anatoly O; Smirnov, Alexander V; Troubnikov, Grigory 2005-01-01 High-energy electron cooling of RHIC presents many unique features and challenges. An accurate estimate of the cooling times requires a detailed calculation of the cooling process, which takes place simultaneously with various diffusive mechanisms in RHIC. In addition, many unexplored effects of high-energy cooling in a collider complicate the task of getting very accurate estimates of cooling times. To address these high-energy cooling issues, a detailed study of cooling dynamics based on computer codes is underway at Brookhaven National Laboratory. In this paper, we present an update on code development and its application to the high-energy cooling dynamics studies for RHIC. 4. SIMULATIONS OF HIGH-ENERGY ELECTRON COOLING. Energy Technology Data Exchange (ETDEWEB) FEDOTOV,A.V.; BEN-ZVI,I.; EIDELMAN, YU.; LITVINENKO, V.; MALITSKY, N. 2005-05-16 High-energy electron cooling of RHIC presents many unique features and challenges. An accurate estimate of the cooling times requires a detailed calculation of the cooling process, which takes place simultaneously with various diffusive mechanisms in RHIC. In addition, many unexplored effects of high-energy cooling in a collider complicate the task of getting very accurate estimates of cooling times. To address these high-energy cooling issues, a detailed study of cooling dynamics based on computer codes is underway at Brookhaven National Laboratory. In this paper, we present an update on code development and its application to the high-energy cooling dynamics studies for RHIC. 5. SIMULATIONS OF HIGH-ENERGY ELECTRON COOLING International Nuclear Information System (INIS) FEDOTOV, A.V.; BEN-ZVI, I.; EIDELMAN, YU.; LITVINENKO, V.; MALITSKY, N. 2005-01-01 High-energy electron cooling of RHIC presents many unique features and challenges. An accurate estimate of the cooling times requires a detailed calculation of the cooling process, which takes place simultaneously with various diffusive mechanisms in RHIC. In addition, many unexplored effects of high-energy cooling in a collider complicate the task of getting very accurate estimates of cooling times. To address these high-energy cooling issues, a detailed study of cooling dynamics based on computer codes is underway at Brookhaven National Laboratory. In this paper, we present an update on code development and its application to the high-energy cooling dynamics studies for RHIC 6. Electronic market places in the energy International Nuclear Information System (INIS) Mons, L. 2001-12-01 Electronic market places in the energy domain occurred at the end of the 90's in the US and have started to develop in Europe in the year 2000. About 60 platforms are registered today and this development can be explained by the advantages raised by such an infrastructure: simplification of purchase procedures, reduction of delays in the purchase decision, reduction of administrative costs etc.. However, today none of these electronic market places is profitable and several have closed down. On the other hand, this tool will certainly become necessary in the future and all energy actors are developing projects in this way. This study analyzes the electronic market places phenomenon in the energy domain using 10 market places examples with their key-factors of success. It draws out a complete status of the initiatives developed today and presents some scenarios of evolution. (J.S.) 7. Energy and electron transfers in photosensitive chitosan. Science.gov (United States) Wu, Shuizhu; Zeng, Fang; Zhu, Hongping; Tong, Zhen 2005-02-23 Novel photosensitive chitosan was synthesized. The modified chitosan contains photoactive anthracene chromophore moieties. Because of the presence of anthracene chromophores, the polymer absorbs light in the UV-vis spectral region. Electronically excited polymeric chromophores could participate in energy and electron transfer processes to the suitable acceptor molecules. The photosensitive chitosan developed herein could could act as an efficient photosensitizer and lead to the application of the environmentally friendly photocatalytic system for an efficient degradation of a wide range of pollutants. 8. Multiple Nodeless Superconducting Gaps in (Ba0.6K0.4)Fe2As2 Superconductor from Angle-Resolved Photoemission Spectroscopy International Nuclear Information System (INIS) Lin, Zhao; Hai-Yun, Liu; Wen-Tao, Zhang; Jian-Qiao, Meng; Xiao-Wen, Jia; Guo-Dong, Liu; Xiao-Li, Dong; Wei, Lu; Xing-Jiang, Zhou; Gen-Fu, Chen; Jian-Lin, Luo; Nan-Lin, Wang; Gui-Ling, Wang; Yong, Zhou; Zu-Yan, Xu; Yong, Zhu; Xiao-Yang, Wang; Chuang-Tian, Chen 2008-01-01 High resolution angle-resolved photoemission measurements have been carried out to study the superconducting gap in the (Ba 0.6 K 0.4 )Fe 2 As 2 superconductor with T e = 35 K. Two hole-like Fermi surface sheets around the I' point exhibit different superconducting gaps. The inner Fermi surface sheet shows larger (10 ∼ 12 meV) and slightly momentum-dependent gap while the outer one has smaller (7 ∼ 8meV) and nearly isotropic gap. The lack of gap node in both Fermi surface sheets favours s-wave superconducting gap symmetry. Superconducting gap opening is also observed at the M(π, π) point. The two Fermi surface spots near the M point are gapped below T e but the gap persists above T e. The rich and detailed superconducting gap information will provide key insights and constraints in understanding pairing mechanism in the iron-based superconductors 9. The complementary nature of x-ray photoelectron spectroscopy and angle-resolved x-ray diffraction part II: Analysis of oxides on dental alloys Science.gov (United States) Kerber, S. J.; Barr, T. L.; Mann, G. P.; Brantley, W. A.; Papazoglou, E.; Mitchell, J. C. 1998-06-01 X-ray photoelectron spectroscopy (XPS) and angle-resolved x-ray diffraction (ARXRD) were used to analyze the oxide layer on three palladium-gallium-based dental casting alloys. The oxide layers were approximately 10 Μm thick. The use of the techniques helped to determine which mechanism was responsible for oxide formation—either (a) oxide layer growth via diffusion of oxygen through the scale to the metal, causing the scale to grow at the metal-oxide interface, or (b) an oxide layer formed by metal ions diffusing through the scale to the surface and reacting with oxygen, causing the scale to grow at the oxide-air interface. The oxide growth mechanisms were correlated to previous layer adhesion results determined with biaxial flexure testing. 10. Electronic and structural characterizations of unreconstructed {l_brace}0001{r_brace} surfaces and the growth of graphene overlayers Energy Technology Data Exchange (ETDEWEB) Emtsev, Konstantin 2009-06-03 The present work is focused on the characterization of the clean unreconstructed SiC{l_brace}0001{r_brace} surfaces and the growth of graphene overlayers thereon. Electronic properties of SiC surfaces and their interfaces with graphene and few layer graphene films were investigated by means of angle resolved photoelectron spectroscopy, X-ray photoelectron spectroscopy and low energy electron diffraction. Structural characterizations of the epitaxial graphene films grown on SiC were carried out by atomic force microscopy and low energy electron microscopy. Supplementary data was obtained by scanning tunneling microscopy. (orig.) 11. High energy electron irradiation of flowable materials International Nuclear Information System (INIS) Offermann, B.P. 1975-01-01 In order to efficiently irradiate a flowable material with high energy electrons, a hollow body is disposed in a container for the material and the material is caused to flow in the form of a thin layer across a surface of the body from or to the interior of the container while the material flowing across the body surface is irradiated. (U.S.) 12. Applications for Energy Recovering Free Electron Lasers Energy Technology Data Exchange (ETDEWEB) George Neil 2007-08-01 The availability of high-power, high-brilliance sources of tunable photons from energy-recovered Free Electron Lasers is opening up whole new fields of application of accelerators in industry. This talk will review some of the ideas that are already being put into production, and some of the newer ideas that are still under development. 13. Crank-angle resolved imaging of biacetyl laser-induced fluorescence in an optical internal combustion engine Science.gov (United States) Smith, J. D.; Sick, V. 2005-09-01 The use of a frequency-tripled, diode-pumped Nd:YAG laser in combination with a CMOS camera lens-coupled to a three-stage image intensifier allowed the visualization of the fuel distribution with crank angle resolution for hundreds of consecutive engine cycles. Biacetyl, doped into iso-octane, was excited at rates of 12 kHz with 100 ns pulses. Pulse energies are high enough to allow single-pulse imaging of the vapor-phase fuel distribution for motored and fired operation in an optical engine. The repetition rate of the setup is adequate to resolve critical steps in the development of the fuel cloud around the spark plug of a direct-injection gasoline engine. 14. Electron clouds in high energy hadron accelerators Energy Technology Data Exchange (ETDEWEB) Petrov, Fedor 2013-08-29 The formation of electron clouds in accelerators operating with positrons and positively charge ions is a well-known problem. Depending on the parameters of the beam the electron cloud manifests itself differently. In this thesis the electron cloud phenomenon is studied for the CERN Super Proton Synchrotron (SPS) and Large Hadron Collider (LHC) conditions, and for the heavy-ion synchrotron SIS-100 as a part of the FAIR complex in Darmstadt, Germany. Under the FAIR conditions the extensive use of slow extraction will be made. After the acceleration the beam will be debunched and continuously extracted to the experimental area. During this process, residual gas electrons can accumulate in the electric field of the beam. If this accumulation is not prevented, then at some point the beam can become unstable. Under the SPS and LHC conditions the beam is always bunched. The accumulation of electron cloud happens due to secondary electron emission. At the time when this thesis was being written the electron cloud was known to limit the maximum intensity of the two machines. During the operation with 25 ns bunch spacing, the electron cloud was causing significant beam quality deterioration. At moderate intensities below the instability threshold the electron cloud was responsible for the bunch energy loss. In the framework of this thesis it was found that the instability thresholds of the coasting beams with similar space charge tune shifts, emittances and energies are identical. First of their kind simulations of the effect of Coulomb collisions on electron cloud density in coasting beams were performed. It was found that for any hadron coasting beam one can choose vacuum conditions that will limit the accumulation of the electron cloud below the instability threshold. We call such conditions the ''good'' vacuum regime. In application to SIS-100 the design pressure 10{sup -12} mbar corresponds to the good vacuum regime. The transition to the bad vacuum 15. Angle-Resolved Photoemission Study of the Evolution of Band Structure And Charge Density Wave Properties in Rte (3) (R=Y, La, Ce, Sm, Gd, Tb, And Dy) Energy Technology Data Exchange (ETDEWEB) Brouet, V.; Yang, W.L.; Zhou, X.J.; Hussain, Z.; Moore, R.G.; He, R.; Lu, D.H.; Shen, Z.X.; Laverock, J.; Dugdale, S.B.; Ru, N.; Fisher, I.R. 2009-05-12 We present a detailed angle-resolved photoemission spectroscopy (ARPES) investigation of the RTe{sub 3} family, which sets this system as an ideal 'textbook' example for the formation of a nesting driven charge density wave (CDW). This family indeed exhibits the full range of phenomena that can be associated to CDW instabilities, from the opening of large gaps on the best nested parts of Fermi surface (up to 0.4 eV), to the existence of residual metallic pockets. ARPES is the best suited technique to characterize these features, thanks to its unique ability to resolve the electronic structure in k space. An additional advantage of RTe{sub 3} is that the band structure can be very accurately described by a simple two dimensional tight-binding (TB) model, which allows one to understand and easily reproduce many characteristics of the CDW. In this paper, we first establish the main features of the electronic structure by comparing our ARPES measurements with the linear muffin-tin orbital band calculations. We use this to define the validity and limits of the TB model. We then present a complete description of the CDW properties and of their strong evolution as a function of R. Using simple models, we are able to reproduce perfectly the evolution of gaps in k space, the evolution of the CDW wave vector with R, and the shape of the residual metallic pockets. Finally, we give an estimation of the CDW interaction parameters and find that the change in the electronic density of states n(E{sub F}), due to lattice expansion when different R ions are inserted, has the correct order of magnitude to explain the evolution of the CDW properties. 16. Low Energy Electron Scattering from Fuels Science.gov (United States) Lopes, M. C. A.; Silva, D. G. M.; Bettega, M. H. F.; da Costa, R. F.; Lima, M. A. P.; Khakoo, M. A.; Winstead, C.; McKoy, V. 2012-11-01 In order to understand and optimize processes occurring during the ignition of plasma and its consequences in post-discharge for an internal combustion engine, especially considering the spark plug, we have produced in this work some basic information necessary to modeling spark ignition in alcohol- fuelled engines. Total cross sections of electron scattering by methanol and ethanol molecules in the energy range from 60 to 500 eV are reported, using the linear transmission method based on the Beer-Lambert law to first approximation. Aditionally to that, measurements and calculations of differential cross sections for elastic low-energy (rotationally unresolved) electron scattering were also discussed, for impact energies of 1, 2, 5, 10, 15, 20, 30, 50, and 100 eV and for scattering angles of 5°-130°. The measurements were obtained using the relative flow method with an aperture source, and calculations using two different implementations of the Schwinger multichannel method, one that takes all electrons into account and is adapted for parallel computers, and another that uses pseudopotentials and considers only the valence electrons. 17. Electron-ion recombination at low energy International Nuclear Information System (INIS) Andersen, L.H. 1993-01-01 The work is based on results obtained with a merged-beams experiment. A beam of electronics with a well characterized density and energy distribution was merged with a fast, monoenergetic ion beam. Results have been obtained for radiative recombination and dielectronic recombination at low relative energies (0 to ∼70eV). The obtained energy resolution was improved by about a factor of 30. High vacuum technology was used to suppress interactions with electrons from the environments. The velocity distribution of the electron beam was determined. State-selective dielectronic-recombination measurements were performable. Recombination processes were studied. The theoretical background for radiative recombination and Kramers' theory are reviewed. The quantum mechanical result and its relation to the semiclassical theory is discussed. Radiative recombination was also measured with several different non-bare ions, and the applicability of the semiclassical theory to non-bare ions was investigated. The use of an effective charge is discussed. For dielectronic recombination, the standard theoretical approach in the isolated resonance and independent-processes approximation is debated. The applicability of this method was tested. The theory was able to reproduce most of the experimental data except when the recombination process was sensitive to couplings between different electronic configurations. The influence of external perturbing electrostatic fields is discussed. (AB) (31 refs.) 18. Energy Saving and Efficient Energy Use By Power Electronic Systems DEFF Research Database (Denmark) Blaabjerg, Frede; Wang, Huai; Davari, Pooya 2017-01-01 , such as in the applications of adjustable speed drives and solid-state lighting systems. Power electronics gives also a high flexibility when renewable power production is introduced to electrical energy systems. Future research opportunities and challenges will finally be discussed.... 19. Reprint of Low-energy electron potentiometry. Science.gov (United States) Jobst, Johannes; Kautz, Jaap; Mytiliniou, Maria; Tromp, Rudolf M; van der Molen, Sense Jan 2017-12-01 In a lot of systems, charge transport is governed by local features rather than being a global property as suggested by extracting a single resistance value. Consequently, techniques that resolve local structure in the electronic potential are crucial for a detailed understanding of electronic transport in realistic devices. Recently, we have introduced a new potentiometry method based on low-energy electron microscopy (LEEM) that utilizes characteristic features in the reflectivity spectra of layered materials [1]. Performing potentiometry experiments in LEEM has the advantage of being fast, offering a large field of view and the option to zoom in and out easily, and of being non-invasive compared to scanning-probe methods. However, not all materials show clear features in their reflectivity spectra. Here we, therefore, focus on a different version of low-energy electron potentiometry (LEEP) that uses the mirror mode transition, i.e. the drop in electron reflectivity around zero electron landing energy when they start to interact with the sample rather than being reflected in front of it. This transition is universal and sensitive to the local electrostatic surface potential (either workfunction or applied potential). It can consequently be used to perform LEEP experiments on a broader range of material compared to the method described in Ref[1]. We provide a detailed description of the experimental setup and demonstrate LEEP on workfunction-related intrinsic potential variations on the Si(111) surface and for a metal-semiconductor-metal junction with external bias applied. In the latter, we visualize the Schottky effect at the metal-semiconductor interface. Finally, we compare how robust the two LEEP techniques discussed above are against image distortions due to sample inhomogeneities or contamination. Copyright © 2017. Published by Elsevier B.V. 20. Low Energy Electron Scattering from Fuels Science.gov (United States) Lopes, M. Cristina A. 2012-06-01 We report an investigation of processes that occur during the ignition of the plasma and its consequences in post-discharge time for an internal combustion engine, in order to find the appropriate parameters to be used in cars that operate with lean mixtures air-fuel. The relevance of this theme has attracted much attention, and has been one of the subjects of collaboration between experimental and theoretical groups in the USA and Brazil. We have produced some basic information necessary to modeling spark ignition in alcohol- fuelled engines. Total cross sections of electron scattering by methanol and ethanol molecules were obtained, using the linear transmission method based on the Beer-Lambert law to first approximation. Measurements and calculations of differential cross sections for low-energy (rotationally unresolved) electron scattering were also obtained, for scattering angles of 5 --130 . The measurements were taken using the relative flow method with an aperture source, and calculations using two different implementations of the Schwinger multichannel method, one that takes all electrons into account and is adapted for parallel computers, and another that uses pseudopotentials and considers only the valence electrons. Additionally to these, computer simulation studies of electronic discharge in mixtures of ethanol were performed, using a Zero-Dimensional Plasma Kinetic solver. Previous reported models for combustion of ethanol and cross sections data for momentum transfer of electron collisions with ethanol were used. The time evolutions of the main species densities are reported and the ignition time delay discussed. 1. Reflection electron energy loss spectroscopy of aluminum Czech Academy of Sciences Publication Activity Database Jiříček, Petr; Bartoš, Igor; Zemek, Josef; Werner, W. S. M. 2010-01-01 Roč. 604, 11-12 (2010), s. 1006-1009 ISSN 0039-6028 R&D Projects: GA ČR GA202/07/0601; GA MŠk MEB060809 Institutional research plan: CEZ:AV0Z10100521 Keywords : Al(111) * polycrystalline Al * electron energy loss spectroscopy * photoelectron diffraction * PHD * REELS Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.010, year: 2010 2. Energy Transformation in Molecular Electronic Systems Energy Technology Data Exchange (ETDEWEB) Kasha, Michael 1999-05-17 This laboratory has developed many new ideas and methods in the electronic spectroscopy of molecules. This report covers the contract period 1993-1995. A number of the projects were completed in 1996, and those papers are included in the report. The DOE contract was terminated at the end of 1995 owing to a reorganizational change eliminating nationally the projects under the Office of Health and Environmental Research, U. S. Department of Energy. 3. Cation profiling of passive films on stainless steel formed in sulphuric and acetic acid by deconvolution of angle-resolved X-ray photoelectron spectra Energy Technology Data Exchange (ETDEWEB) Högström, Jonas, E-mail: [email protected]; Fredriksson, Wendy, E-mail: [email protected]; Edstrom, Kristina, E-mail: [email protected]; Björefors, Fredrik, E-mail: [email protected]; Nyholm, Leif, E-mail: [email protected]; Olsson, Claes-Olof A., E-mail: [email protected] 2013-11-01 An approach for determining depth gradients of metal-ion concentrations in passive films on stainless steel using angle-resolved X-ray photoelectron spectroscopy (ARXPS) is described. The iterative method, which is based on analyses of the oxidised metal peaks, provides increased precision and hence allows faster ARXPS measurements to be carried out. The method was used to determine the concentration depth profiles for molybdenum, iron and chromium in passive films on 316L/EN 1.4432 stainless steel samples oxidised in 0.5 M H{sub 2}SO{sub 4} and acetic acid diluted with 0.02 M Na{sub 2}B{sub 4}O{sub 7} · 10H{sub 2}O and 1 M H{sub 2}O, respectively. The molybdenum concentration in the film is pin-pointed to the oxide/metal interface and the films also contained an iron-ion-enriched surface layer and a chromium-ion-dominated middle layer. Although films of similar composition and thickness (i.e., about 2 nm) were formed in the two electrolytes, the corrosion currents were found to be three orders of magnitude larger in the acetic acid solution. The differences in the layer composition, found for the two electrolytes as well as different oxidation conditions, can be explained based on the oxidation potentials of the metals and the dissolution rates of the different metal ions. 4. Multiple π-bands and Bernal stacking of multilayer graphene on C-face SiC, revealed by nano-Angle Resolved Photoemission. Science.gov (United States) Johansson, Leif I; Armiento, Rickard; Avila, Jose; Xia, Chao; Lorcy, Stephan; Abrikosov, Igor A; Asensio, Maria C; Virojanadara, Chariya 2014-02-24 Only a single linearly dispersing π-band cone, characteristic of monolayer graphene, has so far been observed in Angle Resolved Photoemission (ARPES) experiments on multilayer graphene grown on C-face SiC. A rotational disorder that effectively decouples adjacent layers has been suggested to explain this. However, the coexistence of μm-sized grains of single and multilayer graphene with different azimuthal orientations and no rotational disorder within the grains was recently revealed for C-face graphene, but conventional ARPES still resolved only a single π-band. Here we report detailed nano-ARPES band mappings of individual graphene grains that unambiguously show that multilayer C-face graphene exhibits multiple π-bands. The band dispersions obtained close to the K-point moreover clearly indicate, when compared to theoretical band dispersion calculated in the framework of the density functional method, Bernal (AB) stacking within the grains. Thus, contrary to earlier claims, our findings imply a similar interaction between graphene layers on C-face and Si-face SiC. 5. Determining the thickness of aliphatic alcohol monolayers covalently attached to silicon oxide surfaces using angle-resolved X-ray photoelectron spectroscopy Science.gov (United States) Lee, Austin W. H.; Kim, Dongho; Gates, Byron D. 2018-04-01 The thickness of alcohol based monolayers on silicon oxide surfaces were investigated using angle-resolved X-ray photoelectron spectroscopy (ARXPS). Advantages of using alcohols as building blocks for the formation of monolayers include their widespread availability, ease of handling, and stability against side reactions. Recent progress in microwave assisted reactions demonstrated the ease of forming uniform monolayers with alcohol based reagents. The studies shown herein provide a detailed investigation of the thickness of monolayers prepared from a series of aliphatic alcohols of different chain lengths. Monolayers of 1-butanol, 1-hexanol, 1-octanol, 1-decanol, and 1-dodecanol were each successfully formed through microwave assisted reactions and characterized by ARXPS techniques. The thickness of these monolayers consistently increased by ∼1.0 Å for every additional methylene (CH2) within the hydrocarbon chain of the reagents. Tilt angles of the molecules covalently attached to silicon oxide surfaces were estimated to be ∼35° for each type of reagent. These results were consistent with the observations reported for thiol based or silane based monolayers on either gold or silicon oxide surfaces, respectively. The results of this study also suggest that the alcohol based monolayers are uniform at a molecular level. 6. Adsorption site and structure determination of c(2x2) N{sub 2}/Ni(100) using angle-resolved photoemission extended fine structure Energy Technology Data Exchange (ETDEWEB) Moler, E.J.; Kellar, S.A.; Huff, W.R.A. [Lawrence Berkeley National Lab., CA (United States)] [and others 1997-04-01 The authors have determined the atomic spatial structure of c(2x2) N2Ni(100) with Angle-Resolved Photoemission Extended Fine Structure (ARPEFS) from the nitrogen 1s core level using monochromatized x-rays from beamline 6.1 at SSRL and beamline 9.3.2 at the ALS. The chemically shifted N 1s peak intensities were summed together to obtain ARPEFS curves for both nitrogen atoms in the molecule. They used a new, highly-optimized program based on the Rehr-Albers scattering matrix formalism to find the adsorption site and to quantitatively determine the bond-lengths. The nitrogen molecule stands upright at an atop site, with a N-Ni bond length of 2.25(1) {angstrom}, a N-N bond length of 1.10(7) {angstrom}, and a first layer Ni-Ni spacing of 1.76(4) {angstrom}. The shake-up peak shows an identical ARPEFS diffraction pattern, confirming its intrinsic nature and supporting a previous use of this feature to decompose the peak into contributions from the chemically inequivalent nitrogen atoms. Comparison to a previously published theoretical treatment of N-N-Ni and experimental structures of analogous adsorbate systems demonstrates the importance of adsorbate-adsorbate interactions in weakly chemisorbed systems. 7. Time- and angle-resolved x-ray diffraction to probe structural and chemical evolution during Al-Ni intermetallic reactions. Science.gov (United States) Yoo, Choong-Shik; Wei, Haoyan; Chen, Jing-Yin; Shen, Guoyin; Chow, Paul; Xiao, Yuming 2011-11-01 We present novel time- and angle-resolved x-ray diffraction (TARXD) capable of probing structural and chemical evolutions during rapidly propagating exothermic intermetallic reactions between Ni-Al multilayers. The system utilizes monochromatic synchrotron x-rays and a two-dimensional (2D) pixel array x-ray detector in combination of a fast-rotating diffraction beam chopper, providing a time (in azimuth) and angle (in distance) resolved x-ray diffraction image continuously recorded at a time resolution of ~30 μs over a time period of 3 ms. Multiple frames of the TARXD images can also be obtained with time resolutions between 30 and 300 μs over three to several hundreds of milliseconds. The present method is coupled with a high-speed camera and a six-channel optical pyrometer to determine the reaction characteristics including the propagation speed of 7.6 m/s, adiabatic heating rate of 4.0 × 10(6) K/s, and conductive cooling rate of 4.5 × 10(4) K/s. These time-dependent structural and temperature data provide evidences for the rapid formation of intermetallic NiAl alloy within 45 μs, thermal expansion coefficient of 1.1 × 10(-6) K for NiAl, and crystallization of V and Ag(3)In in later time. © 2011 American Institute of Physics 8. Low-energy electron scattering from methane International Nuclear Information System (INIS) Bundschu, C.T.; Gibson, J.C.; Buckman, S.J.; Brunger, M.J.; Gianturco, F.A. 1997-01-01 Absolute differential cross sections for elastic scattering and vibrational excitation (ν 2.4 , ν 1.3 ) of CH 4 have been measured at incident energies between 0.6 and 5.4 eV. These cross sections have also been extrapolated and integrated in order to derive integral and momentum transfer cross sections which are compared with the results of previous single-collision and electron swarm experiments. Elastic differential cross sections have also been calculated using a body-fixed (BF), single-centre expansion (SCE) for the close-coupled (CC) equations. There is excellent agreement between the present data and the most recent elastic scattering results of Boesten and Tanaka, but substantial discrepancies between these two data sets and several previous measurements. There is also excellent agreement at most energies between the present measured and calculated elastic cross sections. (author) 9. Electron-impact electronic-state excitation of para-benzoquinone Science.gov (United States) Jones, D. B.; da Costa, R. F.; Kossoski, F.; Varella, M. T. do N.; Bettega, M. H. F.; Ferreira da Silva, F.; Limão-Vieira, P.; García, G.; Lima, M. A. P.; White, R. D.; Brunger, M. J. 2018-03-01 Angle resolved electron energy loss spectra (EELS) for para-benzoquinone (C6H4O2) have been recorded for incident electron energies of 20, 30, and 40 eV. Measured differential cross sections (DCSs) for electronic band features, composed of a combination of energetically unresolved electronic states, are subsequently derived from those EELS. Where possible, the obtained DCSs are compared with those calculated using the Schwinger multichannel method with pseudopotentials. These calculations were performed using a minimum orbital basis single configuration interaction framework at the static exchange plus polarisation level. Here, quite reasonable agreement between the experimental cross sections and the theoretical cross sections for the summation of unresolved states was observed. 10. Anisotropic Electron-Photon and Electron-Phonon Interactions in Black Phosphorus. Science.gov (United States) Ling, Xi; Huang, Shengxi; Hasdeo, Eddwi H; Liang, Liangbo; Parkin, William M; Tatsumi, Yuki; Nugraha, Ahmad R T; Puretzky, Alexander A; Das, Paul Masih; Sumpter, Bobby G; Geohegan, David B; Kong, Jing; Saito, Riichiro; Drndic, Marija; Meunier, Vincent; Dresselhaus, Mildred S 2016-04-13 Orthorhombic black phosphorus (BP) and other layered materials, such as gallium telluride (GaTe) and tin selenide (SnSe), stand out among two-dimensional (2D) materials owing to their anisotropic in-plane structure. This anisotropy adds a new dimension to the properties of 2D materials and stimulates the development of angle-resolved photonics and electronics. However, understanding the effect of anisotropy has remained unsatisfactory to date, as shown by a number of inconsistencies in the recent literature. We use angle-resolved absorption and Raman spectroscopies to investigate the role of anisotropy on the electron-photon and electron-phonon interactions in BP. We highlight, both experimentally and theoretically, a nontrivial dependence between anisotropy and flake thickness and photon and phonon energies. We show that once understood, the anisotropic optical absorption appears to be a reliable and simple way to identify the crystalline orientation of BP, which cannot be determined from Raman spectroscopy without the explicit consideration of excitation wavelength and flake thickness, as commonly used previously. 11. Triple Hybrid Energy Harvesting Interface Electronics Science.gov (United States) Uluşan, H.; Chamanian, S.; Pathirana, W. M. P. R.; Zorlu, Ö.; Muhtaroğlu, A.; Külah, H. 2016-11-01 This study presents a novel triple hybrid system that combines simultaneously generated power from thermoelectric (TE), vibration-based electromagnetic (EM) and piezoelectric (PZT) harvesters for a relatively high power supply capability. In the proposed solution each harvesting source utilizes a distinct power management circuit that generates a DC voltage suitable for combining the three parallel supplies. The circuits are designed and implemented in 180 nm standard CMOS technology, and are terminated with a schottky diode to avoid reverse current flow. The harvested AC signal from the EM harvester is rectified with a self-powered AC-DC doubler, which utilizes active diode structures to minimize the forward- bias voltage drop. The PZT interface electronics utilizes a negative voltage converter as the first stage, followed by synchronous power extraction and DC-to-DC conversion through internal switches, and an external inductor. The ultra-low voltage DC power harvested by the TE generator is stepped up through a charge-pump driven by an LC oscillator with fully- integrated center-tapped differential inductors. Test results indicate that hybrid energy harvesting circuit provides more than 1 V output for load resistances higher than 100 kΩ (10 μW) where the stand-alone harvesting circuits are not able to reach 1 V output. This is the first hybrid harvester circuit that simultaneously extracts energy from three independent sources, and delivers a single DC output. 12. Study and realization of an electron gun at low energy International Nuclear Information System (INIS) Camus, P. 1977-01-01 This work presents the theoretical concepts and experimental design of an electron gun. This gun is working in the weak energy range and the focus position is independant of electron energy measurements and analysis methods of the electron beam are described [fr 13. Energy and angular distributions of backscattered electrons from ... Abstract. The energy and angular distributions of backscattered electrons produced under the impact of 5 keV electrons with thick Al, Ti, Ag, W and Pt targets are measured. The energy range of backscattered electrons is considered between EB = 50 eV and 5000. eV. The angle of incidence α and take-off angle θ are ... 14. Energy and angular distributions of backscattered electrons from ... The energy and angular distributions of backscattered electrons produced under the impact of 5 keV electrons with thick Al, Ti, Ag, W and Pt targets are measured. The energy range of backscattered electrons is considered between B = 50 eV and 5000 eV. The angle of incidence α and take-off angle are chosen to have ... 15. Ionization By Impact Electrons in Solids: Electron Mean Free Path Fitted Over A Wide Energy Range Energy Technology Data Exchange (ETDEWEB) Ziaja, B; London, R A; Hajdu, J 2005-06-09 We propose a simple formula for fitting the electron mean free paths in solids both at high and at low electron energies. The free-electron-gas approximation used for predicting electron mean free paths is no longer valid at low energies (E < 50 eV), as the band structure effects become significant at those energies. Therefore we include the results of the band structure calculations in our fit. Finally, we apply the fit to 9 elements and 2 compounds. 16. Electronic energy distribution function at high electron swarm energies in neon International Nuclear Information System (INIS) Brown, K.L.; Fletcher, J. 1995-01-01 Electron swarms moving through a gas under the influence of an applied electric field have been extensively investigated. Swarms at high energies, as measured by the ratio of the applied field to the gas number density, E/N, which are predominant in many applications have, in general, been neglected. Discharges at E/N in the range 300 0 < 133 Pa using a differentially pumped vacuum system in which the swarm electrons are extracted from the discharge and energy analysed in both a parallel plate retarded potential analyser and a cylindrical electrostatic analyser. Both pre-breakdown and post-breakdown discharges have been studied. Initial results indicate that as the discharge traverses breakdown no sudden change in the nature of the discharge occurs and that the discharge can be described by both a Monte Carlo simulation and by a Boltzmann treatment given by Phelps et al. (1987). 18 refs., 8 figs 17. Electronic configurations and energies in some thermodynamically correlated laves compounds International Nuclear Information System (INIS) Campbell, G.M. 1979-04-01 The known electronic configurations of simple elements in Laves compounds are correlated with those of the more complex systems to determine their electronic configurations and gaseous state promotion energies 18. Dynamics of Low-Energy Electron Induced Reactions in Condensed Science.gov (United States) Boyer, Michael; Soe, Chanmyaemyae; Chamberlain, Kristal; Shyur, Yomay; Arumainayagam, Christopher 2011-03-01 We present insights into the dynamics of low-energy electron-induced reactions in thin films of methanol (CH3 OH). Low-energy electrons in matter can initiate chemical reactions though electron impact ionization of a molecule, electron impact excitation of a molecule, or through dissociation of a transient negative ion formed by electron attachment to a molecule. Our studies focus on the dynamics by which low-energy electron interaction with condensed methanol initiates chemical reactions which lead to the formation of methoxymethanol (CH3 O CH2 OH) and ethylene glycol (HO CH2 CH2 OH). The results of our post-irradiation temperature programmed desorption experiments indicate that both products can form from irradiating methanol with electrons at subionization energies. In addition, we find evidence that dissociative electron attachment plays a role in the formation of methoxymethanol but not in ethylene glycol. 19. Self-consistent electronic structure of the contracted tungsten (001) surface International Nuclear Information System (INIS) Posternak, M.; Krakauer, H.; Freeman, A.J. 1982-01-01 Self-consistent linearized-augmented-plane-wave energy-band studies using the warped muffin-tin approximation for a seven-layer W(001) single slab with the surface-layer separation contracted by 6% of the bulk interlayer spacing are reported. Surface electronic structure, local densities of states, generalized susceptibility for the surface, work function, and core-level shifts are found to have insignificant differences with corresponding results for the unrelaxed surface. Several differences in surface states between theory and recent angle-resolved photoemission experiments are discussed in the light of new proposed models of the actual unreconstructed surface structure at high temperatures 20. Sterilization of foods with low-energy electrons ('soft-electrons') Energy Technology Data Exchange (ETDEWEB) Hayashi, Toru; Takahashi, Yoko; Todoriki, Setsuko 1998-06-01 Electrons with an energy of 300 keV or lower were defined as 'Soft-electrons', which showed several advantages over conventional irradiation with gamma-rays or high-energy electrons in decontamination of grains and spices. Energies of electrons necessary to reduce microbial loads to levels lower than 10 CFU/g were 60 keV for brown rice, 75 keV for wheat, 100 keV for white pepper, coriander and basil, 130 keV for buckwheat, 160 keV for rough rice, and 210 keV for black pepper. Electrons with such energies did not significantly influence the quality. 1. Electron polarimetry at low energies in Hall C at JLab International Nuclear Information System (INIS) 2013-01-01 Although the majority of Jefferson Lab experiments require multi-GeV electron beams, there have been a few opportunities to make electron beam polarization measurements at rather low energies. This proceedings will discuss some of the practical difficulties encountered in performing electron polarimetry via Mo/ller scattering at energies on the order of a few hundred MeV. Prospects for Compton polarimetry at very low energies will also be discussed. While Mo/ller scattering is likely the preferred method for electron polarimetry at energies below 500 MeV, there are certain aspects of the polarimeter and experiment design that must be carefully considered 2. Low-energy electron beams through ultra-thin foils, applications for electron microscopy NARCIS (Netherlands) Van Aken, R.H. 2005-01-01 This thesis has discussed two electron microscopy applications that make use of ultra-thin foils: the tunnel junction emitter and the low-energy foil corrector. Both applications have in common that the electron beam is sent through the thin foil at low energy. Part of the electrons will scatter in 3. A magnetic electron energy analyser for fast data acquisition Energy Technology Data Exchange (ETDEWEB) Zha, X.; Walker, C.G.H. [Department of Electronics, University of York, Heslington, York YO10 5DD (United Kingdom); El-Gomati, M.M., E-mail: [email protected] [Department of Electronics, University of York, Heslington, York YO10 5DD (United Kingdom) 2011-07-21 A new approach to the acquisition of Auger electron spectra is introduced. Electrons emitted from a sample illuminated by a primary electron beam are dispersed by a magnetic field which immerses both sample and electron energy analyser. The analyser is broadly based on the 180{sup o} magnetic spectrometer, but can acquire spectra with good energy resolution for electrons with a significant component of velocity parallel to the magnetic field. An Active Pixel Sensor is used to acquire the electron spectrum without the use of a microchannel plate as in most currently used analysers. An example spectrum of an elastic peak is given. 4. Tantalum surface oxidation: Bond relaxation, energy entrapment, and electron polarization Energy Technology Data Exchange (ETDEWEB) Guo, Yongling [Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education), Hunan Provincial Key Laboratory of Thin Film Materials and Devices, Faculty of Materials Science and Engineering, Xiangtan University, Hunan 411105 (China); Bo, Maolin [Yangtze Normal University, College of Mechanical and Electrical Engineering, Chongqing 408100 (China); Wang, Yan [School of Information and Electronic Engineering, Hunan University of Science and Technology, Hunan 411201 (China); Liu, Yonghui [Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education), Hunan Provincial Key Laboratory of Thin Film Materials and Devices, Faculty of Materials Science and Engineering, Xiangtan University, Hunan 411105 (China); Sun, Chang Q. [NOVITAS, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (Singapore); Huang, Yongli, E-mail: [email protected] [Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education), Hunan Provincial Key Laboratory of Thin Film Materials and Devices, Faculty of Materials Science and Engineering, Xiangtan University, Hunan 411105 (China) 2017-02-28 Graphical abstract: The bond, electron and energy relaxation result in core level energy shift, local densification, quantum entrapment and electron polarization of bonding electrons. - Highlights: • Increasing the oxygen coverage lowers the adsorption energy associated with lattice reconstruction. • Electrons transfer from Ta surface atoms to sp-hydrated oxygen, creating dipole moment that decreases the work function. • Oxygen chemisorption modified valence density-of-state (DOS) for Ta with four excessive DOS features: O−Ta bonding, O{sup 2−} lone pairs, Ta+ electron holes, and the lone-pair polarized Ta dipoles. • The bond, electron and energy relaxation between surface undercoordinated atoms are responsible for core level energy shift, local densification, quantum entrapment and electron polarization of bonding electrons. - Abstract: A combination of photoelectron spectrometric analysis and density functional theory calculations has enabled reconciliation of the bond-energy-electron relaxation for the Ta(100, 110, 111) surfaces chemisorbed with oxygen at different coverages. Results show that increasing oxygen coverage lowers the adsorption energy associated with lattice reconstruction. Valence electrons transfer from Ta surface atoms to oxygen to create four excessive DOS features in terms of O−Ta bonding, lone pairs of oxygen, Ta{sup +} electron holes, and polarized Ta dipoles. Oxidation proceeds in the following dynamics: oxygen gets electrons from two neighboring Ta atoms left behind Ta{sup +}; the sp{sup 3}-orbital hybridization takes place with additional two electron lone pairs, the lone pairs polarize the other two Ta neighbors becoming dipoles. X-ray photoelectron spectral analysis results in the 4f binding energy of an isolated Ta atom and its shift upon bond formation and oxidation. Exercises provide not only a promising numerical approach for the quantitative information about the bond and electronic behavior but also consistent 5. Power electronic converter systems for direct drive renewable energy applications DEFF Research Database (Denmark) Chen, Zhe 2013-01-01 This chapter presents power electronic conversion systems for wind and marine energy generation applications, in particular, direct drive generator energy conversion systems. Various topologies are presented and system design optimization and reliability are briefly discussed.......This chapter presents power electronic conversion systems for wind and marine energy generation applications, in particular, direct drive generator energy conversion systems. Various topologies are presented and system design optimization and reliability are briefly discussed.... 6. Electron emission from materials at low excitation energies International Nuclear Information System (INIS) Urma, N.; Kijek, M.; Millar, J.J. 1996-01-01 Full text: An experimental system has been designed and developed with the purpose of measuring the total electron emission yield from materials at low energy excitation. In the first instance the reliability of the system was checked by measuring the total electron emission yield for a well defined surface (aluminium 99.45%). The obtained data was in the expected range given by the literature, and consequently the system will be used further for measuring the total electron yield for a range of materials with interest in the instrumentation industry. We intend to measure the total electron emission yield under electron bombardment as a function of incident electron energy up to 1200 eV, angle of incidence, state of the surface and environment to which the surface has been exposed. Dependence of emission on total electron irradiated dose is also of interest. For many practical application of the 'Secondary Electron Emission', the total electron yield is desired to be as large as possible. The above phenomenon has practical applicability in electron multiplier tube and Scanning electron microscopy - when by means of the variation of the yield of the emitted electrons one may produce visible images of small sample areas. The electron multiplier tube, is a device which utilises the above effect to detect and amplify both single particles and low currents streams of charged particles. The majority of electron tubes use electrons with low energy, hundreds of eV. Not a lot has been published in the literature about this regime and also about the emission when the impinging electrons have small energy, up to 1 KeV. The information obtained from the experimental measurements concerning the total electron emission yield is used to asses the investigated materials as a potential electron emitting surfaces or dynodes in an electron multiplier tube 7. ELEC-2005: Electronics in High Energy Physics CERN Multimedia Monique Duval 2004-01-01 ELEC-2005 is a new course series on modern electronics, given by CERN physicists and engineers in the format of the successful ELEC-2002 course series, and within the framework of the 2005 Technical Training Programme. This comprehensive course series is designed for people who are not electronics specialists, for example physicists, engineers and technicians working at or visiting the laboratory, who use or will use electronics in their present or future activities, in particular in the context of the LHC accelerator and experiments. ELEC-2005 will composed of four Terms throughout the year: Winter Term: Introduction to electronics in HEP (January-February, 6 lectures) Spring Term: Integrated circuits and VLSI technology for physics (March, 6 lectures) Summer Term: System electronics for physics: Issues (May, 7 lectures) Winter Term: Electronics applications in HEP experiments (November-December, 10 lectures) Lectures within each Term will take place on Tuesdays and Thursdays, from 10:00 to 12:30. The... 8. Electrospun Fibers for Energy, Electronic, & Environmental Applications Science.gov (United States) Bedford, Nicholas M. Electrospinning is an established method for creating polymer and bio-polymer fibers of dimensions ranging from ˜10 nanometers to microns. The process typically involves applying a high voltage between a solution source (usually at the end of a capillary or syringe) and a substrate on which the nanofibers are deposited. The high electric field distorts the shape of the liquid droplet, creating a Taylor cone. Additional applied voltage ejects a liquid jet of the polymer solution in the Taylor cone toward the counter electrode. The formation of fibers is generated by the rapid electrostatic elongation and solvent evaporation of this viscoelastic jet, which typically generates an entangled non-woven mesh of fibers with a high surface area to volume ratio. Electrospinning is an attractive alternative to other processes for creating nano-scale fibers and high surface area to volume ratio surfaces due to its low start up cost, overall simplicity, wide range of processable materials, and the ability to generate a moderate amount of fibers in one step. It has also been demonstrated that coaxial electrospinning is possible, wherein the nanofiber has two distinct phases, one being the core and another being the sheath. This method is advantageous because properties of two materials can be combined into one fiber, while maintaining two distinct material phases. Materials that are inherently electrospinable could be made into fibers using this technique as well. The most common applications areas for electrospun fibers are in filtration and biomedical areas, with a comparatively small amount of work done in energy, environmental, and sensor applications. Furthermore, the use of biologically materials in electrospun fibers is an avenue of research that needs more exploration, given the unique properties these materials can exhibit. The research aim of this thesis is to explore the use of electrospun fibers for energy, electrical and environmental applications. For energy 9. An extension of the Eisberg-Resnick treatment for electron energies in many-electron atoms Science.gov (United States) Whitaker, M. A. B.; Bennett, I. 1989-03-01 Eisberg and Resnick present a simple argument for the energy of an electron in a multielectron atom using the concept of shielding from electrons in inner shells. The results of such a treatment are unfortunately confined so as to be out of range of experimental values. Here, the effect of electrons in outer shells is included, and, in the nonrelativistic region, energies are obtained for electrons in the first and second shells in reasonable agreement with experiment. 10. Characteristic energy range of electron scattering due to plasmaspheric hiss Science.gov (United States) Ma, Q.; Li, W.; Thorne, R. M.; Bortnik, J.; Reeves, G. D.; Kletzing, C. A.; Kurth, W. S.; Hospodarsky, G. B.; Spence, H. E.; Baker, D. N.; Blake, J. B.; Fennell, J. F.; Claudepierre, S. G.; Angelopoulos, V. 2016-12-01 We investigate the characteristic energy range of electron flux decay due to the interaction with plasmaspheric hiss in the Earth's inner magnetosphere. The Van Allen Probes have measured the energetic electron flux decay profiles in the Earth's outer radiation belt during a quiet period following the geomagnetic storm that occurred on 7 November 2015. The observed energy of significant electron decay increases with decreasing L shell and is well correlated with the energy band corresponding to the first adiabatic invariant μ = 4-200 MeV/G. The electron diffusion coefficients due to hiss scattering are calculated at L = 2-6, and the modeled energy band of effective pitch angle scattering is also well correlated with the constant μ lines and is consistent with the observed energy range of electron decay. Using the previously developed statistical plasmaspheric hiss model during modestly disturbed periods, we perform a 2-D Fokker-Planck simulation of the electron phase space density evolution at L = 3.5 and demonstrate that plasmaspheric hiss causes the significant decay of 100 keV-1 MeV electrons with the largest decay rate occurring at around 340 keV, forming anisotropic pitch angle distributions at lower energies and more flattened distributions at higher energies. Our study provides reasonable estimates of the electron populations that can be most significantly affected by plasmaspheric hiss and the consequent electron decay profiles. 11. A compact, versatile low-energy electron beam ion source Energy Technology Data Exchange (ETDEWEB) Zschornack, G., E-mail: [email protected] [Department of Physics, Dresden University of Technology, 01062 Dresden, Germany and Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, 01328 Dresden (Germany); König, J.; Schmidt, M.; Thorn, A. [DREEBIT GmbH, 01109 Dresden (Germany) 2014-02-15 A new compact Electron Beam Ion Source, the Dresden EBIT-LE, is introduced as an ion source working at low electron beam energies. The EBIT-LE operates at an electron energy ranging from 100 eV to some keV and can easily be modified to an EBIT also working at higher electron beam energies of up to 15 keV. We show that, depending on the electron beam energy, electron beam currents from a few mA in the low-energy regime up to about 40 mA in the high-energy regime are possible. Technical solutions as well as first experimental results of the EBIT-LE are presented. In ion extraction experiments, a stable production of low and intermediate charged ions at electron beam energies below 2 keV is demonstrated. Furthermore, X-ray spectroscopy measurements confirm the possibility of using the machine as a source of X-rays from ions excited at low electron energies. 12. Low energy electron imaging using Medipix 2 detector NARCIS (Netherlands) Sikharulidze, I.; van Gastel, Raoul; Schramm, S.; Abrahams, J.P.; Poelsema, Bene; Tromp, R.M.; van der Molen, S.J. 2011-01-01 Low Energy Electron Microscopy (LEEM) and Photo-Emission Electron Microscopy (PEEM) predominantly use a combination of microchannel plate (MCP), phosphor screen and optical camera to record images formed by 10–20 keV electrons. We have tested the performance of a LEEM/PEEM instrument with a Medipix2 13. Scattering of polarized low-energy electrons by ferromagnetic metals International Nuclear Information System (INIS) Helman, J.S. 1981-01-01 A source of spin polarized electrons with remarkable characteristics based on negative electron affinity (NEA) GaAs has recently been developed. It constitutes a unique tool to investigate spin dependent interactions in electron scattering processes. The characteristics and working principles of the source are briefly described. Some theoretical aspects of the scattering of polarized low-energy electrons by ferromagnetic metals are discussed. Finally, the results of the first polarized low-energy electron diffraction experiment using the NEA GaAs source are reviewed; they give information about the surface magnetization of ferromagnetic Ni (110). (Author) [pt 14. Energy and angular distributions of electrons ejected from CH Relative cross sections, differential in energy and angle, for electrons ejected from CH4 and C3H8 molecules under 16.0 keV electron impact have been measured. Electrons were analyzed by a 45° parallel plate electrostatic analyzer at emission angles varying from 60° to 135° with energies from 50 eV to 1000 eV. 15. Low-energy electron microdosimetry of CS-137 International Nuclear Information System (INIS) Paschoa, A.S.; Wrenn, M.E. 1980-09-01 The mass of tissue irradiated by an internal emitter depends upon the distribution of the radionuclide within the organism and the type of radiation emitted. The range (95% absorption) of low-energy electron effectively defines the sensitive volume in which the energy of the emitted electron is deposited. Accordingly, in the case of Auger electron microdosimetry of internal emitters the correct definition of the sensitive volume is of paramount importance. The amount of energy delivered by the monoenergetic electrons emitted by the decay system 137 Cs → sup(137m)Ba to spherical volumes of water-like tissue media of radii equivalent to the estimated ranges of those electrons in water is calculated and discussed as far as the variations of the estimated ranges of electrons as a function of the initial energy of emission are concerned. Although there are still many uncertainties on the actual ranges of low-energy electrons, one can state confidently that the ranges of the Auger electrons of the decay system 137 Cs → 137 sup(m) Ba → 137 Ba can be considered to be in the same order of magnitude of the diameter of a cell. The energy deposition in spherical volumes of water-like tissue media, considered equivalent to the sensitive volumes for the Auger electrons of the decay system 137 Cs → 137 sub(m) Ba → 137 Ba, range for several orders of magnitude from 10 2 to about 10 10 times higher than the energy deposition in similar media by the internal conversion electrons of this decay system. If equivalent variations of energy deposition per unit mass occur when the masses considered are cellular, and subcellular structures, then the effects into the sensitive volume should be taken into biological consideration as far as the microdosimetry of low-energy electrons (approximately equal to 10 keV) is considered, whenever there is internal localization of Auger emitters. (Author) [pt 16. Electron energy-loss spectra in molecular fluorine Science.gov (United States) Nishimura, H.; Cartwright, D. C.; Trajmar, S. 1979-01-01 Electron energy-loss spectra in molecular fluorine, for energy losses from 0 to 17.0 eV, have been taken at incident electron energies of 30, 50, and 90 eV and scattering angles from 5 to 140 deg. Features in the spectra above 11.5 eV energy loss agree well with the assignments recently made from optical spectroscopy. Excitations of many of the eleven repulsive valence excited electronic states are observed and their location correlates reasonably well with recent theoretical results. Several of these excitations have been observed for the first time and four features, for which there are no identifications, appear in the spectra. 17. Electron cooling for low-energy RHIC program Energy Technology Data Exchange (ETDEWEB) Fedotov, A.; Ben-Zvi, I.; Chang, X.; Kayran, D.; Litvinenko, V.N.; Pendzick, A.; Satogata, T. 2009-08-31 Electron cooling was proposed to increase luminosity of the RHIC collider for heavy ion beam energies below 10 GeV/nucleon. Providing collisions at such energies, termed RHIC 'low-energy' operation, will help to answer one of the key questions in the field of QCD about existence and location of critical point on the QCD phase diagram. The electron cooling system should deliver electron beam of required good quality over energies of 0.9-5 MeV. Several approaches to provide such cooling were considered. The baseline approach was chosen and design work started. Here we describe the main features of the cooling system and its expected performance. We have started design work on a low-energy RHIC electron cooler which will operate with kinetic electron energy range 0.86-2.8 (4.9) MeV. Several approaches to an electron cooling system in this energy range are being investigated. At present, our preferred scheme is to transfer the Fermilab Pelletron to BNL after Tevatron shutdown, and to use it for DC non-magnetized cooling in RHIC. Such electron cooling system can significantly increase RHIC luminosities at low-energy operation. 18. Performance of the electron energy-loss spectrometer International Nuclear Information System (INIS) Tanaka, H.; Huebner, R.H. 1977-01-01 Performance characteristics of the electron energy-loss spectrometer incorporating a new high-resolution hemispherical monochromator are reported. The apparatus achieved an energy-resolution of 25 meV in the elastic scattering mode, and angular distributions of elastically scattered electrons were in excellent agreement with previous workers. Preliminary energy-loss spectra for several atmospheric gases demonstrate the excellent versatility and stable operation of the improved system. 12 references 19. Electronically droplet energy harvesting using piezoelectric cantilevers KAUST Repository 2012-01-01 A report is presented on free falling droplet energy harvesting using piezoelectric cantilevers. The harvester incorporates a multimorph clamped-free cantilever which is composed of five layers of lead zirconate titanate piezoelectric thick films. During the impact, the droplet kinetic energy is transferred into the form of mechanical stress forcing the piezoelectric structure to vibrate. Experimental results show energy of 0.3 μJ per droplet. The scenario of moderate falling drop intensity, i.e. 230 drops per second, yields a total energy of 400 μJ. © 2012 The Institution of Engineering and Technology. 20. Trends in Power Electronics and Control of Renewable Energy Systems DEFF Research Database (Denmark) Blaabjerg, Frede; Iov, Florin; Kerekes, Tamas 2010-01-01 by means of power electronics are changing the future electrical infrastructure but also contributes steadily more to non-carbon based electricity production. Most focus is on the power electronics technologies used. In the case of photovoltaics transformer-less systems are discussed as they have...... term) based energy sources to renewable energy sources. Another is to use high efficient power electronics in power generation, power transmission/distribution and end-user application. This paper discuss trends of the most emerging renewable energy sources, wind energy and photovoltaics, which......The electrical energy consumption continues to grow and more applications will be based on electricity in the next decades. We can expect that more 60 % of all energy consumption will be converted and used as electricity. It is a demand that production, distribution and use of electrical energy... 1. Applications of Electronstatic Lenses to Electron Gun and Energy Analyzers International Nuclear Information System (INIS) Sise, O. 2004-01-01 Focal properties and geometries are given for several types of electrostatic lens systems commonly needed in electron impact studies. One type is an electron gun which focuses electrons over a wide range of energy onto a fixed point, such as target, and the other type is an analyzer system which focuses scattered electrons of variable energy onto a fixed position, such as the entrance plane of an analyzer. There are many different types and geometries of these lenses for controlling and focusing of the electron beams. In this presentation we discussed the criteria used for the design of the electrostatic lenses associated with the electron gun and energy analyzers and determined the fundamental relationships between the operation and behaviour of multi-element electrostatic lenses, containing five, six and seven elements. The focusing of the electron beam was achieved by applying suitable voltages to the series of these lens elements, Design of the lens system for electron gun was based on our requirements that the beam at the target had a small spot size and zero beam angle, that is, afocal mode. For energy analyzer systems we considered the entrance of the hemispherical analyzer which determines the energy of the electron beam and discussed the focusing condition of this lens systems 2. CAMAC high energy physics electronics hardware International Nuclear Information System (INIS) Kolpakov, I.F. 1977-01-01 CAMAC hardware for high energy physics large spectrometers and control systems is reviewed as is the development of CAMAC modules at the High Energy Laboratory, JINR (Dubna). The total number of crates used at the Laboratory is 179. The number of CAMAC modules of 120 different types exceeds 1700. The principles of organization and the structure of developed CAMAC systems are described. (author) 3. Power Electronics and Control of Renewable Energy Systems DEFF Research Database (Denmark) Iov, Florin; Ciobotaru, Mihai; Sera, Dezso 2007-01-01 sources from the conventional, fossil (and short term) based energy sources to renewable energy resources. Another is to use high efficient power electronics in power generation, power transmission/distribution and end-user application. This paper discuss some of the most emerging renewable energy sources... 4. Development of laser-based scanning µ-ARPES system with ultimate energy and momentum resolutions. Science.gov (United States) Iwasawa, Hideaki; Schwier, Eike F; Arita, Masashi; Ino, Akihiro; Namatame, Hirofumi; Taniguchi, Masaki; Aiura, Yoshihiro; Shimada, Kenya 2017-11-01 We have developed a laser-based scanning angle-resolved photoemission spectroscopy system (µ-ARPES) equipped with a high precision 6-axis control system, realizing not only high-resolution photoemission spectroscopy in energy and momentum, but also spatial resolution of a µm scale. This enables our µ-ARPES system to probe fine details of intrinsic electronic states near the Fermi level such as the superconducting gaps and lifetime broadening. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved. 5. Energy degradation of fast electrons in hydrogen gas Science.gov (United States) Xu, Yueming; Mccray, Richard 1991-01-01 An equation is derived for calculating the energy distribution of fast electrons in a partially ionized gas and a method is provided to solve for the electron degradation spectrum and the energy deposition in different forms (ionization, excitation, or heating). As an example, the energy degradation of fast electrons in a gas of pure hydrogen is calculated, considering excitations to the lowest 10 atomic levels. The Bethe approximation and the continuous slowing-down approximation are discussed and it is concluded that these approximations are accurate to the order of 20 percent for electrons with initial energy of greater than about keV. The method and results can be used to determine heating, excitations, and ionizations by high-energy photoelectrons or cosmic-ray particles in various astrophysical circumstances, such as the interstellar medium, supernova envelopes, and QSO emission-line clouds. 6. Nonequilibrium electron energy-loss kinetics in metal clusters CERN Document Server Guillon, C; Fatti, N D; Vallee, F 2003-01-01 Ultrafast energy exchanges of a non-Fermi electron gas with the lattice are investigated in silver clusters with sizes ranging from 4 to 26 nm using a femtosecond pump-probe technique. The results yield evidence for a cluster-size-dependent slowing down of the short-time energy losses of the electron gas when it is strongly athermal. A constant rate is eventually reached after a few hundred femtoseconds, consistent with the electron gas internal thermalization kinetics, this behaviour reflecting evolution from an individual to a collective electron-lattice type of coupling. The timescale of this transient regime is reduced in small nanoparticles, in agreement with speeding up of the electron-electron interactions with size reduction. The experimental results are in quantitative agreement with numerical simulations of the electron kinetics. 7. Thermalisation of high energy electrons and positrons in water vapour Science.gov (United States) Munoz, A.; Blanco, F.; Limao-Vieira, P.; Thorn, P. A.; Brunger, M. J.; Buckman, S. J.; Garcia, G. 2008-07-01 In this study we describe a method to simulate single electron tracks of electrons in molecular gases, particularly in water vapour, from relatively high energies, where Born (Inokuti 1971) approximation is supposed to be valid, down to thermal energies paying special attention to the low energy secondary electrons which are abundantly generated along the energy degradation procedure. Experimental electron scattering cross sections (Munoz et al. 2007) and energy loss spectra (Thorn et al. 2007) have been determined, where possible, to be used as input parameters of the simulating program. These experimental data have been complemented with optical potential calculation (Blanco and Garcia 2003) providing a complete set of interaction probability functions for each type of collision which could take place in the considered energy range: elastic, ionization, electronic excitation, vibrational and rotational excitation. From the simulated track structure (Munoz et al. 2005) information about energy deposition and radiation damage at the molecular level can be derived. A similar procedure is proposed to the study of single positron tracks in gases. Due to the lack of experimental data for positron interaction with molecules, especially for those related to energy loss and excitation cross sections, some distribution probability data have been derived from those of electron scattering by introducing positron characteristics as positroniun formation. Preliminary results for argon are presented discussing also the utility of the model to biomedical applications based on positron emitters. 8. HIGH-ENERGY ELECTRON COOLING BASED ON REALISTIC SIX-DIMENSIONAL DISTRIBUTION OF ELECTRONS Energy Technology Data Exchange (ETDEWEB) FEDOTOV,A.; BEN-ZVI, I.; ET AL. 2007-06-25 The high-energy electron cooling system for RHIC-II is unique compared to standard coolers. It requires bunched electron beam. Electron bunches are produced by an Energy Recovery Linac (ERL), and cooling is planned without longitudinal magnetic field. To address unique features of the RHIC cooler, a generalized treatment of cooling force was introduced in BETACOOE code which allows us to calculate friction force for an arbitrary distribution of electrons. Simulations for RHIC cooler based on electron distribution from ERL are presented. 9. Energy Spread Reduction of Electron Beams Produced via Laser Wake Energy Technology Data Exchange (ETDEWEB) Pollock, Bradley Bolt [Univ. of California, San Diego, CA (United States) 2012-01-01 Laser wakefield acceleration of electrons holds great promise for producing ultra-compact stages of GeV scale, high quality electron beams for applications such as x-ray free electron lasers and high energy colliders. Ultra-high intensity laser pulses can be self-guided by relativistic plasma waves over tens of vacuum diffraction lengths, to give >1 GeV energy in cm-scale low density plasma using ionization-induced injection to inject charge into the wake at low densities. This thesis describes a series of experiments which investigates the physics of LWFA in the self-guided blowout regime. Beginning with high density gas jet experiments the scaling of the LWFA-produced electron beam energy with plasma electron density is found to be in excellent agreement with both phenomenological theory and with 3-D PIC simulations. It is also determined that self-trapping of background electrons into the wake exhibits a threshold as a function of the electron density, and at the densities required to produce electron beams with energies exceeding 1 GeV a different mechanism is required to trap charge into low density wakes. By introducing small concentrations of high-Z gas to the nominal He background the ionization-induced injection mechanism is enabled. Electron trapping is observed at densities as low as 1.3 x 1018 cm-3 in a gas cell target, and 1.45 GeV electrons are demonstrated for the first time from LWFA. This is currently the highest electron energy ever produced from LWFA. The ionization-induced trapping mechanism is also shown to generate quasi-continuous electron beam energies, which is undesirable for accelerator applications. By limiting the region over which ionization-induced trapping occurs, the energy spread of the electron beams can be controlled. The development of a novel two-stage gas cell target provides the capability to tailor the gas composition in the longitudinal direction, and confine the trapping process to occur only in a 10. Secondary electron emission yield in the limit of low electron energy CERN Document Server Andronov, A.N.; Kaganovich, I.D.; Startsev, E.A.; Raitses, Y.; Demidov, V.I. 2013-04-22 Secondary electron emission (SEE) from solids plays an important role in many areas of science and technology.1 In recent years, there has been renewed interest in the experimental and theoretical studies of SEE. A recent study proposed that the reflectivity of very low energy electrons from solid surface approaches unity in the limit of zero electron energy2,3,4, If this was indeed the case, this effect would have profound implications on the formation of electron clouds in particle accelerators,2-4 plasma measurements with electrostatic Langmuir probes, and operation of Hall plasma thrusters for spacecraft propulsion5,6. It appears that, the proposed high electron reflectivity at low electron energies contradicts to numerous previous experimental studies of the secondary electron emission7. The goal of this note is to discuss possible causes of these contradictions. 11. Tests of an electron monitor for routine quality control measurements of electron energies International Nuclear Information System (INIS) Ramsay, E.B.; Reinstein, L.E.; Meek, A.G. 1991-01-01 The depth dose for electrons is sensitive to energy and the AAPM Task Group 24 has recommended that tests be performed at monthly intervals to assure electron beam energy constancy by verifying the depth for the 80% dose to within ±3 mm. Typically, this is accomplished by using a two-depth dose ratio technique. Recently, a new device, the Geske monitor, has been introduced that is designed for verifying energy constancy in a single reading. The monitor consists of nine parallel plate detectors that alternate with 5-mm-thick absorbers made of an aluminum alloy. An evaluation of the clinical usefulness of this monitor for the electron beams available on a Varian Clinac 20 has been undertaken with respect to energy discrimination. Beam energy changes of 3 mm of the 80% dose give rise to measurable output changes ranging from 1.7% for 20-MeV electron beams to 15% for 6-MeV electron beams 12. Scattering of high energy electrons on deuteron International Nuclear Information System (INIS) Grossetete, B. 1964-12-01 The aim of this work is to obtain information on the neutron form factor from the study of the scattering of electrons on deuterium. The first part is dedicated to the theoretical study of the elastic and inelastic scattering. We introduce different form factors: Sachs form factor, the Pauli and Dirac form factors, they appear in the analytic expression of the scattering cross-section. We show how the deuteron form factors can be deduced from neutron's and proton's form factors. In the case of the inelastic scattering we show how the cross section can be broken into components associated to partial waves and we obtain different formulas for the inelastic cross-section based on the Breit formula or the Durand formalism. The second part is dedicated to the experiment setting of electron scattering on deuterium. The elastic scattering experiment has been made on solid or liquid CD 2 targets while inelastic scattering has been studied on a liquid target. We have used an electron beam produced by the Orsay linear accelerator and the scattered electrons have been analysed by a magnetic spectrometer and a Cerenkov detector. The results give a very low value (slightly positive)for the charge form factor of the neutron and a magnetic form factor for the neutron slightly below that of the proton [fr 13. Scanning transmission low-energy electron microscopy Czech Academy of Sciences Publication Activity Database Müllerová, Ilona; Hovorka, Miloš; Konvalina, Ivo; Unčovský, M.; Frank, Luděk 2011-01-01 Roč. 55, č. 4 (2011), 2:1-6 ISSN 0018-8646 R&D Projects: GA AV ČR IAA100650902; GA MŠk ED0017/01/01 Institutional research plan: CEZ:AV0Z20650511 Keywords : TEM * STEM * SEM Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 0.723, year: 2011 14. Secondary electrons monitor for continuous electron energy measurements in UHF linac International Nuclear Information System (INIS) Zimek, Zbigniew; Bulka, Sylwester; Mirkowski, Jacek; Roman, Karol 2001-01-01 Continuous energy measurements have now became obligatory in accelerator facilities devoted to radiation sterilization process. This is one of several accelerator parameters like dose rate, beam current, bean scan parameters, conveyer speed which must be recorded as it is a required condition of accelerator validation procedure. Electron energy measurements are rather simple in direct DC accelerator, where the applied DC voltage is directly related to electron energy. High frequency linacs are not offering such opportunity in electron energy measurements. The analyzing electromagnet is applied in some accelerators but that method can be used only in off line mode before or after irradiation process. The typical solution is to apply the non direct method related to control and measurements certain accelerator parameters like beam current and microwave energy pulse power. The continuous evaluation of electron energy can be performed on the base of calculation and result comparison with calibration curve 15. Power Electronics Control of Wind Energy in Distributed Power System DEFF Research Database (Denmark) Iov, Florin; Ciobotaru, Mihai; Blaabjerg, Frede 2008-01-01 emerging renewable energy sources, wind energy, which by means of power electronics are changing from being a minor energy source to be acting as an important power source in the energy system. Power electronics is the enabling technology and the presentation will cover the development in wind turbine......The global electrical energy consumption is still rising and there is an urgent demand to increase the power capacity. It is expected that the power capacity has to be doubled within 20 years. The production, distribution and use of energy should be as efficient as possible and incentives to save...... energy at the end-user should also be set up. Deregulation of energy has in the past lowered the investment in larger power plants, which means the need for new electrical power sources will be high in the near future. Two major technologies will play important roles to solve the future problems. One... 16. Design, development and characterization of tetrode type electron gun system for generation of low energy electrons International Nuclear Information System (INIS) Deore, A.V.; Bhoraskar, V.N.; Dhole, S.D. 2011-01-01 A tetrode type electron gun system for the generation of low energy electrons was designed, developed and characterized. An electron gun having four electrodes namely cathode, focusing electrode, control electrode and anode has been designed for the irradiation experiments. This electron gun is capable to provide electrons of energy over the range of 1 keV to 20 keV, with current maximum upto 100 μA. The electron gun and a faraday cup are mounted in the evacuated cylindrical chamber. The samples are fixed on the faraday cup and irradiated with low energy electrons at a pressure around 10 -6 mbar. In this electron gun system, at any electron energy over the entire range, the electron beam diameter can be varied from 5 to 120 mm on the Faraday cup mounted at a distance of 200 mm from the anode in the chamber. Also, the circular shape of the beam spot was maintained, even though the beam current and beam diameter are varied. The uniformity of the electron beam over the entire beam area was measured with a multi electrode assembly and found to be well within 15%. This system is being used for the synthesis and diffusion of metal and semiconductor nanoparticles in polymeric materials. (author) 17. Simulations and measurements in scanning electron microscopes at low electron energy. Science.gov (United States) Walker, Christopher G H; Frank, Luděk; Müllerová, Ilona 2016-11-01 The advent of new imaging technologies in Scanning Electron Microscopy (SEM) using low energy (0-2 keV) electrons has brought about new ways to study materials at the nanoscale. It also brings new challenges in terms of understanding electron transport at these energies. In addition, reduction in energy has brought new contrast mechanisms producing images that are sometimes difficult to interpret. This is increasing the push for simulation tools, in particular for low impact energies of electrons. The use of Monte Carlo calculations to simulate the transport of electrons in materials has been undertaken by many authors for several decades. However, inaccuracies associated with the Monte Carlo technique start to grow as the energy is reduced. This is not simply associated with inaccuracies in the knowledge of the scattering cross-sections, but is fundamental to the Monte Carlo technique itself. This is because effects due to the wave nature of the electron and the energy band structure of the target above the vacuum energy level become important and these are properties which are difficult to handle using the Monte Carlo method. In this review we briefly describe the new techniques of scanning low energy electron microscopy and then outline the problems and challenges of trying to understand and quantify the signals that are obtained. The effects of charging and spin polarised measurement are also briefly explored. SCANNING 38:802-818, 2016. © 2016 Wiley Periodicals, Inc. © Wiley Periodicals, Inc. 18. Treatment of foods with 'soft-electrons' (low-energy electrons) Energy Technology Data Exchange (ETDEWEB) Hayashi, Toru [Japan International Research Center for Agricultural Sciences (JIRCAS), Tsukuba, Ibaraki (Japan); Todoriki, Setsuko [National Food Research Institute (NFRI), Tsukuba, Ibaraki (Japan) 2003-02-01 Electrons with energies of 300 keV or lower were defined as soft-electrons'. Soft-electrons can eradicate microorganisms residing on the surface of grains, pulses, spices, dehydrated vegetables, tea leaves and seeds, and reduce their microbial loads to levels lower than 10 CFU/g with little quality deterioration. Soft-electrons can inactivate insect pests infesting grains and pulses and inhibit sprouting of potatoes. (author) 19. Electronic Energy Transfer in Polarizable Heterogeneous Environments DEFF Research Database (Denmark) Svendsen, Casper Steinmann; Kongsted, Jacob 2015-01-01 such couplings provide important insight into the strength of interaction between photo-active pigments in protein-pigment complexes. Recently, attention has been payed to how the environment modifies or even controls the electronic couplings. To enable such theoretical predictions, a fully polarizable embedding......-order multipole moments. We use this extended model to systematically examine three different ways of obtaining EET couplings in a heterogeneous medium ranging from use of the exact transition density to a point-dipole approximation. Several interesting observations are made including that explicit use...... of transition densities in the calculation of the electronic couplings - also when including the explicit environment contribution - can be replaced by a much simpler transition point charge description without comprising the quality of the model predictions.... 20. Studies on electronic structure of GaN(0001) surface CERN Document Server Xie Chang Kun; Xu Fa Qiang; Deng Rui; Liu Feng; Yibulaxin, K 2002-01-01 An electronic structure investigation on GaN(0001) is reported. The authors employ a full-potential linearized augmented plane-wave (FPLAPW) approach to calculate the partial density of state, which is in agreement with previous experimental results. The effects of the Ga3d semi-core levels on the electronic structure of GaN are discussed. The valence-electronic structure of the wurtzite GaN(0001) surface is investigated using synchrotron radiation excited angle-resolved photoemission spectroscopy. The bulk bands dispersion along GAMMA A direction in the Brillouin zones is measured using normal-emission spectra by changing photon-energy. The band structure derived from authors' experimental data is compared well with the results of authors' FPLAPW calculation. Furthermore, off-normal emission spectra are also measured along the GAMMA K and GAMMA M directions. Two surface states are identified, and their dispersions are characterized 1. Electron energy spectrum in core-shell elliptic quantum wire Directory of Open Access Journals (Sweden) V.Holovatsky 2007-01-01 Full Text Available The electron energy spectrum in core-shell elliptic quantum wire and elliptic semiconductor nanotubes are investigated within the effective mass approximation. The solution of Schrodinger equation based on the Mathieu functions is obtained in elliptic coordinates. The dependencies of the electron size quantization spectrum on the size and shape of the core-shell nanowire and nanotube are calculated. It is shown that the ellipticity of a quantum wire leads to break of degeneration of quasiparticle energy spectrum. The dependences of the energy of odd and even electron states on the ratio between semiaxes are of a nonmonotonous character. The anticrosing effects are observed at the dependencies of electron energy spectrum on the transversal size of the core-shell nanowire. 2. Development of total-skin electron therapy at two energies International Nuclear Information System (INIS) Cox, R.S.; Heck, R.J.; Fessenden, P.; Karzmark, C.J.; Rust, D.C. 1990-01-01 Total-Skin Electron Therapy (TSET) modalities have been developed at two energies on a Varian Clinac 1800. The physical criteria for the beams were determined mainly from the requirement of continuing the Stanford treatment technique, which was 12 Total-Skin Electron Therapy portals combined in six pairs. The penetration of the lower energy mode matches that previously obtained at Stanford on the Varian Clinac 10, (about 4 mm for the 80% isodose contour in the 12-field treatment). The penetration of the higher energy mode is about 8 mm at the 80% contour. The Total-Skin Electron Therapy modes necessarily use electrons produced by the two standard electron-beam modes of lowest energy, nominally 6 and 9 MeV. Measurements to verify the beam specifications were carried out with diodes, a variety of ionization chambers, and a specially constructed circular phantom for film dosimetry. Initially, the penetration of the Total-Skin Electron Therapy beams was too large to match our criteria, so two methods of reducing it were explored: (a) the energies of the electron beams produced by the machine were reduced (which also reduced the energies of the corresponding standard electron modes) and (b) a large polymethylmethacrylate degrader (2.4 m X 1.2 m) 1 cm thick was placed just in front of the patient plane. Acceptable Total-Skin Electron Therapy beams could be produced by either method and the latter was finally used. The use of the standard dose monitoring system for the Total-Skin Electron Therapy modes considerably simplifies the daily treatment delivery as well as the implementation. However, the need for reasonable dose rates at the treatment plane (3.5 meters beyond the isocenter) requires dose rates of 24 Gy/min at the isocenter. Nevertheless, it is possible to use the internal dose monitor provided the problems associated with high dose rates are addressed 3. Treatment of basal cell epithelioma with high energy electron beam Energy Technology Data Exchange (ETDEWEB) Ogawa, Y. (Hyogo-ken Cancer Center, Kobe (Japan)); Kumano, M.; Kumano, K. 1981-11-01 Thirty patients with basal cell epithelioma received high energy electron beam therapy. They were irradiated with a dose ranging from 4,800 rad (24 fractions, 35 days) to 12,000 rad (40 fractions, 57 days). Tumors disappeared in all cases. These were no disease-related deaths; in one patient there was recurrence after 2 years. We conclude that radiotherapy with high energy electron beam is very effective in the treatment of basal cell epithelioma. 4. International Conference on Power Electronics and Renewable Energy Systems CERN Document Server Suresh, L; Dash, Subhransu; Panigrahi, Bijaya 2015-01-01 The book is a collection of high-quality peer-reviewed research papers presented in Proceedings of International Conference on Power Electronics and Renewable Energy Systems (ICPERES 2014) held at Rajalakshmi Engineering College, Chennai, India. These research papers provide the latest developments in the broad area of Power Electronics and Renewable Energy. The book discusses wide variety of industrial, engineering and scientific applications of the emerging techniques. It presents invited papers from the inventors/originators of new applications and advanced technologies. 5. Electronic structures of elements according to ionization energies. Science.gov (United States) 2017-11-28 The electronic structures of elements in the periodic table were analyzed using available experimental ionization energies. Two new parameters were defined to carry out the study. The first parameter-apparent nuclear charge (ANC)-quantified the overall charge of the nucleus and inner electrons observed by an outer electron during the ionization process. This parameter was utilized to define a second parameter, which presented the shielding ability of an electron against the nuclear charge. This second parameter-electron shielding effect (ESE)-provided an insight into the electronic structure of atoms. This article avoids any sort of approximation, interpolation or extrapolation. First experimental ionization energies were used to obtain the two aforementioned parameters. The second parameter (ESE) was then graphed against the electron number of each element, and was used to read the corresponding electronic structure. The ESE showed spikes/peaks at the end of each electronic shell, providing insight into when an electronic shell closes and a new one starts. The electronic structures of elements in the periodic table were mapped using this methodology. These graphs did not show complete agreement with the previously known "Aufbau" filling rule. A new filling rule was suggested based on the present observations. Finally, a new way to organize elements in the periodic table is suggested. Two earlier topics of effective nuclear charge, and shielding factor were also briefly discussed and compared numerically to demonstrate the capability of the new approach. 6. Beam-Based Calibration of the Electron Energy in the Fermilab Electron Cooler CERN Document Server Seletsky, Sergey 2005-01-01 Electron cooling of 8.9 GeV antiprotons in the Fermilab's Recycler ring requires precise matching of electron and antiproton velocities. While the final match can be done by optimization of the cooling process, for the very first cooling one should rely on the knowledge of absolute values of electron and antiproton energies. The upper limit for the energy uncertainty of both beams is determined by the Recycler's momentum aperture and is equal to 0.3%. The paper discusses a method of the electron energy calibration that is based on the measurement of the electron's Larmor wavelength in the field of the cooling section solenoid. The method was tested in an 18 m long cooling section prototype with 3.5 MeV electrons. An accuracy of 0.3% was demonstrated. 7. Generation of Low-Energy High-Current Electron Beams in Plasma-Anode Electron Guns Science.gov (United States) Ozur, G. E.; Proskurovsky, D. I. 2018-01-01 This paper is a review of studies on the generation of low-energy high-current electron beams in electron guns with a plasma anode and an explosive-emission cathode. The problems related to the initiation of explosive electron emission under plasma and the formation and transport of high-current electron beams in plasma-filled systems are discussed consecutively. Considerable attention is given to the nonstationary effects that occur in the space charge layers of plasma. Emphasis is also placed on the problem of providing a uniform energy density distribution over the beam cross section, which is of critical importance in using electron beams of this type for surface treatment of materials. Examples of facilities based on low-energy high-current electron beam sources are presented and their applications in materials science and practice are discussed. 8. Evaluation of Miscellaneous and Electronic Device Energy Use in Hospitals Energy Technology Data Exchange (ETDEWEB) Black, Douglas R.; Lanzisera, Steven M.; Lai, Judy; Brown, Richard E.; Singer, Brett C. 2012-09-01 Miscellaneous and electronic loads (MELs) consume about one-thirdof the primary energy used in US buildings, and their energy use is increasing faster than other end-uses. In healthcare facilities, 30percent of the annual electricity was used by MELs in 2008. This paper presents methods and challenges for estimating medical MELs energy consumption along with estimates of energy use in a hospital by combining device-level metered data with inventories and usage information. An important finding is that common, small devices consume large amounts of energy in aggregate and should not be ignored when trying to address hospital energy use. 9. Charge-coupled device area detector for low energy electrons International Nuclear Information System (INIS) Horacek, Miroslav 2003-01-01 A fast position-sensitive detector was designed for the angle- and energy-selective detection of signal electrons in the scanning low energy electron microscope (SLEEM), based on a thinned back-side directly electron-bombarded charged-coupled device (CCD) sensor (EBCCD). The principle of the SLEEM operation and the motivation for the development of the detector are explained. The electronics of the detector is described as well as the methods used for the measurement of the electron-bombarded gain and of the dark signal. The EBCCD gain of 565 for electron energy 5 keV and dynamic range 59 dB for short integration time up to 10 ms at room temperature were obtained. The energy dependence of EBCCD gain and the detection efficiency are presented for electron energy between 2 and 5 keV, and the integration time dependence of the output signals under dark conditions is given for integration time from 1 to 500 ms 10. Ion induced high energy electron emission from copper International Nuclear Information System (INIS) Ruano, G.; Ferron, J. 2008-01-01 We present measurements of secondary electron emission from Cu induced by low energy bombardment (1-5 keV) of noble gas (He + , Ne + and Ar + ) and Li + ions. We identify different potential and kinetic mechanisms and find the presence of high energetic secondary electrons for a couple of ion-target combinations. In order to understand the presence of these fast electrons we need to consider the Fermi shuttle mechanism and the different ion neutralization efficiencies. 11. Reactions induced by low energy electrons in cryogenic films International Nuclear Information System (INIS) Bass, A.D.; Sanche, L. 2003-01-01 We review recent research on reactions (including dissociation) initiated by low-energy electron bombardment of monolayer and multilayer molecular solids at cryogenic temperatures. With incident electrons of energies below 20 eV, dissociation is observed by the electron stimulated desorption (ESD) of anions from target films and is attributed to the processes of dissociative electron attachment (DEA) and to dipolar dissociation. It is shown that DEA to condensed molecules is sensitive to environmental factors such as the identity of co-adsorbed species and film morphology. The effects of image-charge induced polarization on cross-sections for DEA to CH3Cl are also discussed. Taking as examples, the electron-induced production of CO within multilayer films of methanol and acetone, it is shown that the detection of electronic excited states by high resolution electron energy loss spectroscopy can be used to monitor electron beam damage. In particular, the incident energy dependence of the CO indicates that below 19 eV, dissociation proceeds via the decay of transient negative ions (TNI) into electronically excited dissociative states. The electron induced dissociation of biomolecular targets is also considered, taking as examples the ribose analog tetrahydrofuran and DNA bases adenine and thymine, cytosine and guanine. The ESD of anions from such films also show dissociation via the formation of TNI. In multilayer molecular solids, fragment species resulting from dissociation, may react with neighboring molecules, as is demonstrated in anion ESD measurements from films containing O 2 and various hydrocarbon molecules. X-ray photoelectron spectroscopy measurements reported for electron irradiated monolayers of H 2 O and CF 4 on a Si - H passivated surface further show that DEA is an important initial step in the electron-induced chemisorption of fragment species 12. Energy and angular distributions of electrons ejected from CH and ... Abstract. Relative cross sections, differential in energy and angle, for electrons ejected from CH4 and C3H8 molecules under 16.0 keV electron impact have been measured. Electrons were analyzed by a 45Ж parallel plate electrostatic analyzer at emission angles varying from 60Ж to 135Ж with en- ergies from 50 eV to ... 13. Charge-coupled device area detector for low energy electrons Czech Academy of Sciences Publication Activity Database Horáček, Miroslav 2003-01-01 Roč. 74, č. 7 (2003), s. 3379 - 3384 ISSN 0034-6748 R&D Projects: GA ČR GA102/00/P001 Institutional research plan: CEZ:AV0Z2065902 Keywords : low energy electrons * charged-coupled device * detector Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.343, year: 2003 14. Utilization of low-energy electron accelerators in Korea Energy Technology Data Exchange (ETDEWEB) Lee, Byung Cheol [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of) 2003-02-01 There are more than 20 electron accelerators in Korea. Most of those are installed in factories for heat-resistant cables, heat-shrinkable cables, radial tires, foams, tube/ films, curing, etc. Four low-energy electron accelerators are in operation for research purposes such as polymer modification, purification of flue gas, waste water treatment, modification of semiconductor characteristics, etc. (author) 15. Electronic structure analysis and vertical ionization energies of ... Electronic structure analysis and vertical ionization energies of thiophene and ethynylthiophenes. RAMAN K SINGH and MANOJ K MISHRA. Department of Chemistry, Indian Institute of Technology Bombay, Powai 400 076 e-mail: [email protected]. Abstract. Results from different decouplings of the electron propagator ... 16. Computation of the average energy for LXY electrons International Nuclear Information System (INIS) Grau Carles, A.; Grau, A. 1996-01-01 The application of an atomic rearrangement model in which we only consider the three shells K, L and M, to compute the counting efficiency for electron capture nuclides, requires a fine averaged energy value for LMN electrons. In this report, we illustrate the procedure with two example, ''125 I and ''109 Cd. (Author) 4 refs 17. Electron energy and electron trajectories in an inverse free-electron laser accelerator based on a novel electrostatic wiggler Science.gov (United States) Nikrah, M.; Jafari, S. 2016-06-01 We expand here a theory of a high-gradient laser-excited electron accelerator based on an inverse free-electron laser (inverse-FEL), but with innovations in the structure and design. The electrostatic wiggler used in our scheme, namely termed the Paul wiggler, is generated by segmented cylindrical electrodes with applied oscillatory voltages {{V}\\text{osc}}(t) over {{90}\\circ} segments. The inverse-FEL interaction can be described by the equations that govern the electron motion in the combined fields of both the laser pulse and Paul wiggler field. A numerical study of electron energy and electron trajectories has been made using the fourth-order Runge-Kutta method. The results indicate that the electron attains a considerable energy at short distances in this device. It is found that if the electron has got sufficient suitable wiggler amplitude intensities, it can not only gain higher energy in longer distances, but also can retain it even after the passing of the laser pulse. In addition, the results reveal that the electron energy gains different peaks for different initial axial velocities, so that a suitable small initial axial velocity of e-beam produces substantially high energy gain. With regard to the transverse confinement of the electron beam in a Paul wiggler, there is no applied axial guide magnetic field in this device. 18. Properties of the electron cloud in a high-energy positron and electron storage ring Directory of Open Access Journals (Sweden) K. C. Harkay 2003-03-01 Full Text Available Low-energy, background electrons are ubiquitous in high-energy particle accelerators. Under certain conditions, interactions between this electron cloud and the high-energy beam can give rise to numerous effects that can seriously degrade the accelerator performance. These effects range from vacuum degradation to collective beam instabilities and emittance blowup. Although electron-cloud effects were first observed two decades ago in a few proton storage rings, they have in recent years been widely observed and intensely studied in positron and proton rings. Electron-cloud diagnostics developed at the Advanced Photon Source enabled for the first time detailed, direct characterization of the electron-cloud properties in a positron and electron storage ring. From in situ measurements of the electron flux and energy distribution at the vacuum chamber wall, electron-cloud production mechanisms and details of the beam-cloud interaction can be inferred. A significant longitudinal variation of the electron cloud is also observed, due primarily to geometrical details of the vacuum chamber. Such experimental data can be used to provide realistic limits on key input parameters in modeling efforts, leading ultimately to greater confidence in predicting electron-cloud effects in future accelerators. 19. Properties of the electron cloud in a high-energy positron and electron storage ring International Nuclear Information System (INIS) Harkay, K.C.; Rosenberg, R.A. 2003-01-01 Low-energy, background electrons are ubiquitous in high-energy particle accelerators. Under certain conditions, interactions between this electron cloud and the high-energy beam can give rise to numerous effects that can seriously degrade the accelerator performance. These effects range from vacuum degradation to collective beam instabilities and emittance blowup. Although electron-cloud effects were first observed two decades ago in a few proton storage rings, they have in recent years been widely observed and intensely studied in positron and proton rings. Electron-cloud diagnostics developed at the Advanced Photon Source enabled for the first time detailed, direct characterization of the electron-cloud properties in a positron and electron storage ring. From in situ measurements of the electron flux and energy distribution at the vacuum chamber wall, electron-cloud production mechanisms and details of the beam-cloud interaction can be inferred. A significant longitudinal variation of the electron cloud is also observed, due primarily to geometrical details of the vacuum chamber. Such experimental data can be used to provide realistic limits on key input parameters in modeling efforts, leading ultimately to greater confidence in predicting electron-cloud effects in future accelerators. 20. Variation of kinetic energy release with temperature and electron energy for unimolecular ionic transitions International Nuclear Information System (INIS) Rabia, M.A.; Fahmy, M.A. 1992-01-01 The kinetic energy released during seven unimolecular ionic transitions, generated from benzyl alcohol and benzyl amine have been studied as a function of ion source temperature and ionizing electron energy. Only, the kinetic energy released during H CN elimination from fragment [C 7 H 8 N]+ ion of benzyl amine displays a temperature dependence. For only two transitions, generated from benzyl alcohol, the kinetic energy released show a significant ionizing electron energy dependence. These results may reveal the role of the internal energy of reacting ions in producing the kinetic energy released some transitions produced from benzyl alcohol 1. Estimation of the characteristic energy of electron precipitation Directory of Open Access Journals (Sweden) C. F. del Pozo 2002-09-01 Full Text Available Data from simultaneous observations (on 13 February 1996, 9 November 1998, and 12 February 1999 with the IRIS, DASI and EISCAT systems are employed in the study of the energy distribution of the electron precipitation during substorm activity. The estimation of the characteristic energy of the electron precipitation over the common field of view of IRIS and DASI is discussed. In particular, we look closely at the physical basis of the correspondence between the characteristic energy, the flux-averaged energy, as defined below, and the logarithm of the ratio of the green-light intensity to the square of absorption. This study expands and corrects results presented in the paper by Kosch et al. (2001. It is noticed, moreover, that acceleration associated with diffusion processes in the magnetosphere long before precipitation may be controlling the shape of the energy spectrum. We propose and test a "mixed" distribution for the energy-flux spectrum, exponential at the lower energies and Maxwellian or modified power-law at the higher energies, with a threshold energy separating these two regimes. The energy-flux spectrum at Tromsø, in the 1–320 keV range, is derived from EISCAT electron density profiles in the 70–140 km altitude range and is applied in the "calibration" of the optical intensity and absorption distributions, in order to extrapolate the flux and characteristic energy maps.Key words. Ionosphere (auroral ionosphere; particle precipitation; particle acceleration 2. FNAL R and D in medium energy electron cooling CERN Document Server Nagaitsev, S; Crawford, A C; Kroc, T; MacLachlan, J; Saewert, G; Schmidt, C W; Shemyakin, A; Warner, A 2000-01-01 The first stage of the Fermilab Electron Cooling R and D program is now complete: a technology necessary to generate hundreds of milliamps of electron beam current at MeV energies has been demonstrated. Conceptual design studies show that with an electron beam current of 200 mA and with a cooling section of 20 m electron cooling in the 8.9 GeV/c Fermilab Recycler ring can provide antiproton stacking rates suitable for the Tevatron upgrades beyond Run II luminosity goals. A novel electron beam transport scheme with a weak magnetic field at the cathode and in the cooling section, and with discrete focusing elements in between will be used. A prototype of such an electron cooling system is now being built at Fermilab as part of the continuing R and D program. This paper describes the status of the electron cooling R and D program at Fermilab. 3. Very low energy scanning electron microscopy in nanotechnology Czech Academy of Sciences Publication Activity Database Müllerová, Ilona; Hovorka, Miloš; Mika, Filip; Mikmeková, Eliška; Mikmeková, Šárka; Pokorná, Zuzana; Frank, Luděk 2012-01-01 Roč. 9, 8/9 (2012), s. 695-716 ISSN 1475-7435 R&D Projects: GA MŠk OE08012; GA MŠk ED0017/01/01; GA AV ČR IAA100650902 Institutional research plan: CEZ:AV0Z20650511 Keywords : scanning electron microscopy very low energy electrons * cathode lens * grain contrast * strain contrast * imaging of participates * dopant contrast * very low energy STEM * graphene Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.087, year: 2012 4. Ultra-low-energy wide electron exposure unit International Nuclear Information System (INIS) Yonago, Akinobu; Oono, Yukihiko; Tokunaga, Kazutoshi; Kishimoto, Junichi; Wakamoto, Ikuo 2001-01-01 Heat and ultraviolet ray processes are used in surface dryness of paint, surface treatment of construction materials and surface sterilization of food containers. A process using a low-energy wide-area electron beam (EB) has been developed that features high speed and low drive cost. EB processing is not widespread in general industry, however, due to high equipment cost and difficult maintenance. We developed an ultra-low-energy wide-area electron beam exposure unit, the Mitsubishi Wide Electron Exposure Unit (MIWEL) to solve these problems. (author) 5. Toward Defect Engineering Strategies to Optimize Energy and Electronic Materials Directory of Open Access Journals (Sweden) Efstratia N. Sgourou 2017-06-01 Full Text Available The technological requirement to optimize materials for energy and electronic materials has led to the use of defect engineering strategies. These strategies take advantage of the impact of composition, disorder, structure, and mechanical strain on the material properties. In the present review, we highlight key strategies presently employed or considered to tune the properties of energy and electronic materials. We consider examples from electronic materials (silicon and germanium, photocatalysis (titanium oxide, solid oxide fuel cells (cerium oxide, and nuclear materials (nanocomposites. 6. Energy Dependence of Near-relativistic Electron Spectrum at ... Abstract. In view of the renewed interest in the study of energetic par- ticles in the outer radiation belt of the earth, we feel it will be helpful in looking for the energy dependence of the electron energy spectrum at geo- stationary orbit. This may give us some insight into how we can safeguard geostationary satellites from ... 7. Quantitative energy-dispersive electron probe X-ray microanalysis ... Abstract. An energy-dispersive electron probe X-ray microanalysis (ED-EPMA) technique us- ing an energy-dispersive X-ray detector with an ultra-thin window, designated as low-Z particle. EPMA, has been developed. The low-Z particle EPMA allows the quantitative determination of concentrations of low-Z elements such ... 8. Electron energy distribution in a weakly ionized plasma International Nuclear Information System (INIS) Cesari, C. 1967-03-01 The aim of this work is to determine from both the theoretical and experimental points of view the type of distribution function for the electronic energies existing in a positive-column type cold laboratory plasma having an ionization rate of between 10 -6 and 10 -7 . The theoretical analysis, based on the imperfect Lorentz model and taking into account inelastic collisions is developed from the Boltzmann equation. The experimental method which we have employed for making an electrostatic analysis of the electronic energies makes use of a Langmuir probe used in conjunction with a transistorized electronic device. A comparison between the experimental and theoretical results yields information concerning the mechanisms governing electronic energy transfer on a microscopic scale. (author) [fr 9. Household energy consumption and consumer electronics: The case of television International Nuclear Information System (INIS) Crosbie, Tracey 2008-01-01 In recent years, there has been a dramatic rise in the number of consumer electronics in households. These new technologies and the services that support them enable new highly energy intensive behaviours. Using in-depth interview data collected from 20 households in 2006, this paper explores these energy intensive behaviours, using the example of the use of televisions. In doing so, it illustrates how the design and marketing of consumer electronics, and the services which support them, actively encourage energy intensive behaviours and how householders are reconfiguring their homes and lifestyles to fit these behaviours. This latter point is significant because, as householders change their homes and daily lives to fit energy intensive consuming behaviours, it will become increasingly difficult to encourage people to reduce their household energy consumption. This paper concludes with the implications of the research findings for policies designed to reduce household energy consumption 10. Low energy electron attachment to the uracil molecule International Nuclear Information System (INIS) Hanel, G.; Gstir, B.; Denifl, S.; Scheier, P.; Maerk, T.D.; Farizon, B.; Farizon, M. 2002-01-01 Using a recently constructed high resolution crossed beam apparatus involving a hemispherical electron monochromator, electron attachment to the uracil molecule C 4 H 4 N 2 O 2 was studied. The electron energy range investigated was in the region between 0 and 12 eV. What will happen when slow electrons are colliding with the cellular RNA compound uracil was the objective of this investigation. The following anion fragments were detected: (C 4 H 3 N 2 O 2 ) - , OCN - , (H 2 C 3 NO) - , CN - , O - . The most important result was that within the detection efficiency any traces of the parent anion were observed. The most intense fragment anion appeared on a mass to charge ratio 111 amu., it corresponds to a uracil molecule missing one hydrogen. Another observation was whereas the parent minus H anion is observed at zero electron energy, all other fragments appear in other range. (nevyjel) 11. Sterilization of experimental animal feeds with high energy electron beam International Nuclear Information System (INIS) Takekawa, Tetsuya; Shakudo, Taketomi; Furuta, Masakazu; Tada, Mikiro 2005-01-01 Penetration range and depth-dose distribution of 10 MeV electrons within commercial packages of experimental animal feeds were examined with a high power electron accelerator for verification of the application of high energy electron beam irradiation to sterilize experimental animal feeds. Optimum packaging sizes were proposed based on the experimental results. The change of the vitamins and the efficacy of the sterilization by the irradiation were also studied. It is confirmed that the sterilization of experimental animal feeds by 10 MeV electron beam has been completely practical. (author) 12. Low-energy elastic electron interactions with pyrimidine International Nuclear Information System (INIS) Palihawadana, Prasanga; Sullivan, James; Buckman, Stephen; Brunger, Michael; Winstead, Carl; McKoy, Vincent; Garcia, Gustavo; Blanco, F. 2011-01-01 We present results of measurements and calculations of elastic electron scattering from pyrimidine in the energy range 3-50 eV. Absolute differential and integral elastic cross sections have been measured using a crossed electron-molecule beam spectrometer and the relative flow technique. The measured cross sections are compared with results of calculations using the well-known Schwinger variational technique and an independent-atom model. Agreement between the measured differential cross sections and the results of the Schwinger calculations is good at lower energies but less satisfactory at higher energies where inelastic channels that should be open are kept closed in the calculations. 13. GEANT4 simulation of electron energy deposition in extended media CERN Document Server Kadri, O; Gharbi, F; Trabelsi, A 2007-01-01 The present work demonstrates that GEANT4 yields a consistent description of electron transport processes in semi-infinite homogeneous and heterogeneous extended media. This comparison covers the e− energy deposition profiles in a range of elements from aluminum to tantalum through molybdenum at source energies from 0.3 to 1.0 MeV and at incident angles from 0° to 60°. The good agreement between simulation results and data confirms that the Monte Carlo used code is capable of accurate electron beam energy deposition calculation even under such conditions. 14. Electron and photon energy measurement calibration with the ATLAS detector CERN Document Server Manzoni, Stefano; The ATLAS collaboration 2016-01-01 An accurate calibration of the energy measurement of electron and photon is paramount for many ATLAS physics analysis. The calibration of the energy measurement is performed in-situ using a large statistics of Z->ee events. The results obtained with the pp collisions data recorded in 2015 and 2016 at sqrt(s)= 13 TeV, corresponding to an integrated luminosity of 3.2 fb-1 and 2.7 fb-1 respectively , as well as the corresponding uncertainties on the electron and photon energy scales, are presented. 15. Electron and photon energy measurement calibration with the ATLAS detector CERN Document Server AUTHOR\|(INSPIRE)INSPIRE-00436885; The ATLAS collaboration 2016-01-01 An accurate calibration of the energy measurement of electrons and photons is paramount for many ATLAS physics analyses. The calibration of the energy measurement is performed $in$-$situ$ using a large statistics of $Z \\rightarrow ee$ events. The results obtained with the $pp$ collisions data recorded in 2015 and 2016 at $\\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 3.2 fb$^{-1}$ and 2.7 fb$^{-1}$ respectively, as well as the corresponding uncertainties on the electron and photon energy scales, are presented 16. Energy of auroral electrons and Z mode generation Science.gov (United States) Krauss-Varban, D.; Wong, H. K. 1990-01-01 The present consideration of Z-mode radiation generation, in light of observational results indicating that the O mode and second-harmonic X-mode emissions can prevail over the X-mode fundamental radiation when suprathermal electron energy is low, gives attention to whether the thermal effect on the Z-mode dispersion can be equally important, and whether the Z-mode can compete for the available free-energy source. It is found that, under suitable circumstances, the growth rate of the Z-mode can be substantial even for low suprathermal auroral electron energies. Growth is generally maximized for propagation perpendicular to the magnetic field. 17. Electron Identification and Energy Measurement with Emulsion Cloud Chamber Science.gov (United States) Kitagawa, Nobuko; Komatsu, Masahiro Charged particles undergo the Multiple Coulomb Scattering (MCS) when passing through a material. Their momentum can be estimated from the distribution of the scattering angle directly. Angle of electrons (or positrons) largely changes because of the energy loss in bremsstrahlung, and they are distinguished from other charged particles by making use of its feature. Electron energy is generally measured by counting of electromagnetic shower (e.m. shower) tracks in Emulsion Cloud Chamber (ECC), so enough absorber material is needed to develop the shower. In the range from sub-GeV to a few GeV, electrons don't develop noticeable showers. In order to estimate the energy of electrons in this range with a limited material, we established the new method which is based on the scattering angle considering the energy loss in bremsstrahlung. From the Monte Carlo simulation (MC) data, which is generated by electron beam (0.5 GeV, 1 GeV, 2 GeV) exposure to ECC, we derived the correlation between energy and scattering angle in each emulsion layer. We fixed the function and some parameters which 1 GeV MC sample would return 1 GeV as the center value, and then applied to 0.5 GeV and 2 GeV sample and confirmed the energy resolution about 50% within two radiation length. 18. A method of dopant electron energy spectrum parameterization for calculation of single-electron nanodevices Science.gov (United States) Shorokhov, V. V. 2017-05-01 Solitary dopants in semiconductors and dielectrics that possess stable electron structures and interesting physical properties may be used as building blocks of quantum computers and sensor systems that operate based on new physical principles. This study proposes a phenomenological method of parameterization for a single-particle energy spectrum of dopant valence electrons in crystalline semiconductors and dielectrics that takes electron-electron interactions into account. It is proposed to take electron-electron interactions in the framework of the outer electron shell model into account. The proposed method is applied to construct the procedure for the determination of the effective dopant outer shell capacity and the method for calculation of the tunneling current in a single-electron device with one or several active dopants-charge centers. 19. Temporal and spatial distribution of high energy electrons at Jupiter Science.gov (United States) Jun, I.; Garrett, H. B.; Ratliff, J. M. 2003-04-01 Measurements of the high energy, omni-directional electron environment by the Galileo spacecraft Energetic Particle Detector (EPD) were used to study the high energy electron environment in the Jovian magnetosphere, especially in the region between 8 to 18 Rj (1 Rj = 1 Jovian radius = 71,400 km). 10-minute averages of the EPD data collected between Jupiter orbit insertion (JOI) in 1995 and the orbit number 33 (I33) in 2002 form an extensive dataset, which has been extremely useful to observe temporal and spatial variability of the Jovian high energy electron environment. The count rates of the EPD electron channels (0.174, 0.304, 0.527, 1.5, 2.0, and 11 MeV) were grouped into 0.5 Rj or 0.5 L bins and analyzed statistically. The results indicate that: (1) a log-normal Gaussian distribution well describes the statistics of the high energy electron environment (for example, electron differential fluxes) in the Jovian magnetosphere, in the region studied here; (2) the high energy electron environments inferred by the Galileo EPD measurements are in a close agreement with the data obtained using the Divine model, which was developed more than 30 years ago from Pioneer 10, 11 and Voyager 1, 2 data; (3) the data are better organized when plotted against magnetic radial parameter L than Rj; (4) the standard deviations of the 0.174, 0.304, 0.527 MeV channel count rates are larger than those of the 1.5, 2.0, 11 MeV count rates in 12 Rj. These observations are very helpful to understand short- and long-term, and local variability of the Jovian high energy electron environment, and are discussed in detail. 20. Power electronics - key technology for renewable energy systems DEFF Research Database (Denmark) Blaabjerg, Frede; Iov, Florin; Kerekes, Tamas 2011-01-01 are changing and challenging the future electrical infrastructure but also contributes steadily more to non-carbon based electricity production. Most focus in the paper is on the power electronics technologies used. In the case of photovoltaics transformer-less systems are discussed as they have the potential...... as efficient as possible. Further, the emerging climate changes is arguing to find sustainable future solutions. Of many options, two major technologies will play important roles to solve parts of those future problems. One is to change the electrical power production from conventional, fossil based energy...... sources to renewable energy sources. Another is to use high efficient power electronics in power generation, power transmission/distribution and end-user application. This paper discuss trends of the most emerging renewable energy sources, wind energy and photovoltaics, which by means of power electronics... 1. Power electronics for renewable energy systems, transportation and industrial applications CERN Document Server 2014-01-01 Power Electronics for Renewable Energy, Transportation, and Industrial Applications combines state-of-the-art global expertise to present the latest research on power electronics and its application in transportation, renewable energy, and different industrial applications. This timely book aims to facilitate the implementation of cutting-edge techniques to design problems offering innovative solutions to the growing power demands in small- and large-size industries. Application areas in the book range from smart homes and electric and plug-in hybrid electrical vehicles (PHEVs), to smart distribution and intelligence operation centers where significant energy efficiency improvements can be achieved through the appropriate use and design of power electronics and energy storage devices. 2. Modeling power electronics and interfacing energy conversion systems CERN Document Server Simões, Marcelo Godoy 2017-01-01 Discusses the application of mathematical and engineering tools for modeling, simulation and control oriented for energy systems, power electronics and renewable energy. This book builds on the background knowledge of electrical circuits, control of dc/dc converters and inverters, energy conversion and power electronics. The book shows readers how to apply computational methods for multi-domain simulation of energy systems and power electronics engineering problems. Each chapter has a brief introduction on the theoretical background, a description of the problems to be solved, and objectives to be achieved. Block diagrams, electrical circuits, mathematical analysis or computer code are covered. Each chapter concludes with discussions on what should be learned, suggestions for further studies and even some experimental work. 3. On the possibility of obtaining high-energy polarized electrons on Yerevan synchrotron International Nuclear Information System (INIS) Melikyan, R.A. 1975-01-01 A possibility of producing high-energy polarized electrons on the Yerevan synchrotron is discussed. A review of a number of low-energy polarized electron sources and of some of experiments with high-energy polarized electrons is given 4. Transfer of chirality from adsorbed chiral molecules to the substrates highlighted by circular dichroism in angle-resolved valence photoelectron spectroscopy DEFF Research Database (Denmark) Contini, G.; Turchini, S.; Sanna, Simone 2012-01-01 Studies of self-assembled chiral molecules on achiral metallic surfaces have mostly focused on the determination of the geometry of adsorbates and their electronic structure. The aim of this paper is to provide direct information on the chirality character of the system and on the chirality trans... 5. Communication: Investigation of the electron momentum density distribution of nanodiamonds by electron energy-loss spectroscopy Energy Technology Data Exchange (ETDEWEB) Feng, Zhenbao; Yang, Bing; Lin, Yangming; Su, Dangsheng, E-mail: [email protected] [Shenyang National Laboratory of Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Wenhua Road 72, Shenyang 110016 (China) 2015-12-07 The electron momentum distribution of detonation nanodiamonds (DND) was investigated by recording electron energy-loss spectra at large momentum transfer in the transmission electron microscope (TEM), which is known as electron Compton scattering from solid (ECOSS). Compton profile of diamond film obtained by ECOSS was found in good agreement with prior photon experimental measurement and theoretical calculation that for bulk diamond. Compared to the diamond film, the valence Compton profile of DND was found to be narrower, which indicates a more delocalization of the ground-state charge density for the latter. Combining with other TEM characterizations such as high-resolution transmission electron spectroscopy, diffraction, and energy dispersive X-ray spectroscopy measurements, ECOSS was shown to be a great potential technique to study ground-state electronic properties of nanomaterials. 6. Dissipation and energy balance in electronic dynamics of Na clusters Science.gov (United States) Vincendon, Marc; Suraud, Eric; Reinhard, Paul-Gerhard 2017-06-01 We investigate the impact of dissipation on the energy balance in the electron dynamics of metal clusters excited by strong electro-magnetic pulses. The dynamics is described theoretically by Time-Dependent Density-Functional Theory (TDDFT) at the level of Local Density Approximation (LDA) augmented by a self interaction correction term and a quantum collision term in Relaxation-Time Approximation (RTA). We evaluate the separate contributions to the total excitation energy, namely energy exported by electron emission, potential energy due to changing charge state, intrinsic kinetic and potential energy, and collective flow energy. The balance of these energies is studied as function of the laser parameters (frequency, intensity, pulse length) and as function of system size and charge. We also look at collisions with a highly charged ion and here at the dependence on the impact parameter (close versus distant collisions). Dissipation turns out to be small where direct electron emission prevails namely for laser frequencies above any ionization threshold and for slow electron extraction in distant collisions. Dissipation is large for fast collisions and at low laser frequencies, particularly at resonances. Contribution to the Topical Issue "Dynamics of Systems at the Nanoscale", edited by Andrey Solov'yov and Andrei Korol. 7. Total electron scattering cross section of Fluorocarbons at intermediate electron energies Science.gov (United States) Palihawadana, Prasanga; Villela, Gilberto; Ariyasinghe, Wickramasinghe 2008-10-01 Total electron scattering cross sections (TCS) of Tetrafluoromethane (CF4), Trifluoromethane (CHF3), Hexafluoroethane (C2F6) and Octafluorocyclobutane (C4F8) have been measured using the linear transmission technique for impact energies 0.10 -- 4.00 keV. These TCS are compared to existing experimental and theoretical TCS in the literature. Based on the present measurements, an empirical formula is developed to predict the TCS of fluorocarbons as a function of incident electron energy. 8. Electron beam directed energy device and methods of using same Science.gov (United States) Retsky, Michael W. 2007-10-16 A method and apparatus is disclosed for an electron beam directed energy device. The device consists of an electron gun with one or more electron beams. The device includes one or more accelerating plates with holes aligned for beam passage. The plates may be flat or preferably shaped to direct each electron beam to exit the electron gun at a predetermined orientation. In one preferred application, the device is located in outer space with individual beams that are directed to focus at a distant target to be used to impact and destroy missiles. The aimings of the separate beams are designed to overcome Coulomb repulsion. A method is also presented for directing the beams to a target considering the variable terrestrial magnetic field. In another preferred application, the electron beam is directed into the ground to produce a subsurface x-ray source to locate and/or destroy buried or otherwise hidden objects including explosive devices. 9. Technical Training: ELEC-2005: Electronics in High Energy Physics CERN Multimedia Monique Duval 2005-01-01 CERN Technical Training 2005: Learning for the LHC! ELEC-2005: Electronics in High Energy Physics - Spring Term ELEC-2005 is a new course series on modern electronics, given by CERN physicists and engineers within the framework of the 2005 Technical Training Programme, in an extended format of the successful ELEC-2002 course series. This comprehensive course series is designed for people who are not electronics specialists, for example physicists, engineers and technicians working at or visiting the laboratory, who use or will use electronics in their present or future activities, in particular in the context of the LHC accelerator and experiments. ELEC-2005 is composed of four Terms: the Winter Term, Introduction to electronics in HEP, already took place; the next three Terms will run throughout the year: Spring Term: Integrated circuits and VLSI technology for physics (March, 6 lectures) - now open for registration Summer Term: System electronics for physics: Issues (May, 7 lectures) Autumn Term: Ele... 10. Design for Reliability of Power Electronics in Renewable Energy Systems DEFF Research Database (Denmark) Ma, Ke; Yang, Yongheng; Wang, Huai 2014-01-01 Power electronics is the enabling technology for maximizing the power captured from renewable electrical generation, e.g., the wind and solar technology, and also for an efficient integration into the grid. Therefore, it is important that the power electronics are reliable and do not have too many...... electronics technology as well as to know how the power electronics technology is loaded in terms of temperature and other stressors relevant, to reliability. Hence, this chapter will show the basics of power electronics technology for renewable energy systems, describe the mission profile of the technology...... failures during operation which otherwise will increase cost for operation, maintenance and reputation. Typically, power electronics in renewable electrical generation has to be designed for 20–30 years of operation, and in order to do that, it is crucial to know about the mission profile of the power... 11. Low-Energy Electron Induced Reactions in Condensed Methanol Science.gov (United States) Boyer, Michael; Boamah, Mavis; Chamberlain, Kristal; Myae Soe, Chanmaye; Bass, Andrew; Sanche, Leon; Arumainayagam, Christopher 2012-02-01 We investigate the dynamics of low-energy electron-induced reactions in condensed thin films of methanol (CH3OH) through electron stimulated desorption (ESD) and post-irradiation temperature programmed desorption (TPD) experiments. ESD experiments indicate that the anions which desorb from the methanol thin film during electron irradiation are predominantly formed through the dissociation of temporary negative ions formed by electron capture by methanol molecules, a process known as dissociative electron attachment (DEA). However, based on investigation of reaction products remaining in the methanol thin film post-irradiation through TPD experiments, DEA is not the obvious primary mechanism by which methoxymethanol (CH3OCH2OH) and ethylene glycol (HOCH2CH2OH) are formed. Evidence indicates formation of these molecules may be driven by both DEA and electron impact excitation. 12. Energy and temperature fluctuations in the single electron box International Nuclear Information System (INIS) Berg, Tineke L van den; Brange, Fredrik; Samuelsson, Peter 2015-01-01 In mesoscopic and nanoscale systems at low temperatures, charge carriers are typically not in thermal equilibrium with the surrounding lattice. The resulting, non-equilibrium dynamics of electrons has only begun to be explored. Experimentally the time-dependence of the electron temperature (deviating from the lattice temperature) has been investigated in small metallic islands. Motivated by these experiments, we investigate theoretically the electronic energy and temperature fluctuations in a metallic island in the Coulomb blockade regime, tunnel coupled to an electronic reservoir, i.e. a single electron box. We show that electronic quantum tunnelling between the island and the reservoir, in the absence of any net charge or energy transport, induces fluctuations of the island electron temperature. The full distribution of the energy transfer as well as the island temperature is derived within the framework of full counting statistics. In particular, the low-frequency temperature fluctuations are analysed, fully accounting for charging effects and non-zero reservoir temperature. The experimental requirements for measuring the predicted temperature fluctuations are discussed. (paper) 13. High-energy electron irradiation of NdFeB permanent magnets: Dependence of radiation damage on the electron energy Energy Technology Data Exchange (ETDEWEB) Bizen, Teruhiko [JASRI SPring-8, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5198 (Japan)]. E-mail: [email protected]; Asano, Yoshihiro [JASRI SPring-8, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5198 (Japan); RIKEN SPring-8 Center, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5148 (Japan); Marechal, Xavier-Marie [JASRI SPring-8, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5198 (Japan); Seike, Takamitsu [JASRI SPring-8, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5198 (Japan); Aoki, Tsuyoshi [JASRI SPring-8, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5198 (Japan); Fukami, Kenji [JASRI SPring-8, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5198 (Japan); Hosoda, Naoyasu [JASRI SPring-8, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5198 (Japan); Yonehara, Hiroto [JASRI SPring-8, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5198 (Japan); Takagi, Tetsuya [JASRI SPring-8, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5198 (Japan); Hara, Toru [RIKEN SPring-8 Center, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5148 (Japan); Tanaka, Takashi [RIKEN SPring-8 Center, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5148 (Japan); Kitamura, Hideo [RIKEN SPring-8 Center, 1-1-1 Kouto Sayo-cho, Sayo-gun, Hyogo 679-5148 (Japan) 2007-05-11 High-energy electron-beam bombardment of Nd{sub 2}Fe{sub 14}B-type permanent magnets induces radiation damage characterized by a drop in the magnetic field. Experiments carried out at the SPring-8 booster synchrotron, with 4, 6, and 8 GeV electrons, show that the drop in magnetic field is energy dependent. Electromagnetic shower simulations suggest that most of the radiation damage happens in a small region around the irradiation axis, and that the contribution of neutrons with large scattering angles or with low energies to the magnetic field change is small. 14. Proposal to detect an emission of unusual super-high energy electrons in electron storage rings Directory of Open Access Journals (Sweden) Da-peng Qian 2014-01-01 Full Text Available According to an extended Lorentz–Einstein mass formula taken into the uncertainty principle, it is predicted that the electron beams passing accelerating electric field should with a small probability generate abnormal super-high energy electrons which are much higher than the beam energy. Author’s preliminary experiment result at electron storage ring has hinted these signs, so suggests to more strictly detect this unusual phenomenon, and thus to test the extended mass formula as well as a more perfect special relativity. 15. Angle-resolved photoemission spectroscopy of (Ca, Na) sub 2 CuO sub 2 Cl sub 2 crystals: Fingerprints of a magnetic insulator in a heavily underdoped superconductor CERN Document Server Kohsaka, Y; Ronning, F 2003-01-01 Electric evolution from an antiferromagnet to a high-T sub c superconductor is revealed by angle-resolved photoemission experiments on tetragonal Ca sub 1 sub . sub 9 Na sub 0 sub . sub 1 CuO sub 2 Cl sub 2 single crystals, which were successfully grown for the first time under high pressures. In this underdoped superconductor, we found clear fingerprints of the parent insulator: a shadow band and a large pseudogap. These observations are most likely described by a 'chemical potential shift', which contrasts clearly with the prevailing wisdom of the pinned chemical potential' learned from the prototype La sub 2 sub - sub x Sr sub x CuO sub 4 , demonstrating that the route to a high-T sub c superconductor is not unique. (author) 16. Power Electronics and Reliability in Renewable Energy Systems DEFF Research Database (Denmark) Blaabjerg, Frede; Ma, Ke; Zhou, Dao 2012-01-01 Power Electronics are needed in almost all kind of renewable energy systems. It is used both for controlling the renewable source and also for interfacing to the load, which can be grid-connected or working in stand-alone mode. More and more efforts are put into making renewable energy systems...... better in terms of reliability in order to ensure a high availability of the power sources, in this case the knowledge of mission profile of a certain application is crucial for the reliability evaluation/design of power electronics. In this paper an overview on the power electronic circuits behind...... the most common converter configurations for wind turbine and photovoltaic is done. Next different aspects of improving the system reliability are mapped. Further on examples of how to control the chip temperature in different power electronic configurations as well as operation modes for wind power... 17. Angle-resolved photoemission study of the evolution of band structure and charge density wave properties in RTe3 (R= Y, La, Ce, Sm, Gd, Tb and Dy) Energy Technology Data Exchange (ETDEWEB) Brouet, V.; Yang, W.L.; Zhou, X.J.; Hussain, Z.; Moore, R.G.; He, R.; Lu, D.H.; Shen, Z.X.; Laverock, J.; Dugdale, S.; Ru, N.; Fisher, I.R. 2010-02-15 We present a detailed ARPES investigation of the RTe{sub 3} family, which sets this system as an ideal 'textbook' example for the formation of a nesting driven Charge Density Wave (CDW). This family indeed exhibits the full range of phenomena that can be associated to CDW instabilities, from the opening of large gaps on the best nested parts of Fermi Surface (FS) (up to 0.4eV), to the existence of residual metallic pockets. ARPES is the best suited technique to characterize these features, thanks to its unique ability to resolve the electronic structure in k-space. An additional advantage of RTe{sub 3} is that the band structure can be very accurately described by a simple 2D tight-binding (TB) model, which allows one to understand and easily reproduce many characteristics of the CDW. In this paper, we first establish the main features of the electronic structure, by comparing our ARPES measurements with Linear Muffin-Tin Orbital band calculations. We use this to define the validity and limits of the TB model. We then present a complete description of the CDW properties and, for the first time, of their strong evolution as a function of R. Using simple models, we are able to reproduce perfectly the evolution of gaps in k-space, the evolution of the CDW wave vector with R and the shape of the residual metallic pockets. Finally, we give an estimation of the CDW interaction parameters and find that the change in the electronic density of states n(Ef), due to lattice expansion when different R ions are inserted, has the correct order of magnitude to explain the evolution of the CDW properties. 18. Tesla energy space for Mie–Schwinger continuous electron OpenAIRE Bulyzhenkov, I. 2013-01-01 Tesla reading of electricity through invisible energy ether between visible bodies corresponds to the found radial solution for a continuous source. The Mie–Schwinger distributed electron extends over the very structure of its Coulomb radial ﬁeld. The electric charge is not a basic concept of Maxwell-Tesla electrodynamics but is the ﬁeld energy distribution under the uniﬁed, non-dual approach to matter-energy in the nonempty world space. Electric self-energy of such a uniﬁed nonlocal carrier ... 19. Power electronics - The key technology for Renewable Energy Systems DEFF Research Database (Denmark) Blaabjerg, Frede; Ma, Ke; Yang, Yongheng 2014-01-01 The energy paradigms in many countries (e.g. Germany and Denmark) have experienced a significant change from fossil-based resources to clean renewables (e.g. wind turbines and photovoltaics) in the past few decades. The scenario of highly penetrated renewables is going to be further enhanced...... solutions, can pave the way for renewable energies. In light of this, some of the most emerging renewable energies, e.g. wind energy and photovoltaic, which by means of power electronics are changing character as a major part in the electricity generation, are explored in this paper. Issues like technology... 20. Stochasticity of the energy absorption in the electron cyclotron resonance International Nuclear Information System (INIS) Gutierrez T, C.; Hernandez A, O. 1998-01-01 The energy absorption mechanism in cyclotron resonance of the electrons is a present problem, since it could be considered from the stochastic point of view or this related with a non-homogeneous but periodical of plasma spatial structure. In this work using the Bogoliubov average method for a multi periodical system in presence of resonances, the drift equations were obtained in presence of a RF field for the case of electron cyclotron resonance until first order terms with respect to inverse of its cyclotron frequency. The absorbed energy equation is obtained on part of electrons in a simple model and by drift method. It is showed the stochastic character of the energy absorption. (Author) 1. Data Acquisition System for Electron Energy Loss Coincident Spectrometers International Nuclear Information System (INIS) Zhang Chi; Yu Xiaoqi; Yang Tao 2005-01-01 A Data Acquisition System (DAQ) for electron energy loss coincident spectrometers (EELCS) has been developed. The system is composed of a Multiplex Time-Digital Converter (TDC) that measures the flying time of positive and negative ions and a one-dimension position-sensitive detector that records the energy loss of scattering electrons. The experimental data are buffered in a first-in-first-out (FIFO) memory module, then transferred from the FIFO memory to PC by the USB interface. The DAQ system can record the flying time of several ions in one collision, and allows of different data collection modes. The system has been demonstrated at the Electron Energy Loss Coincident Spectrometers at the Laboratory of Atomic and Molecular Physics, USTC. A detail description of the whole system is given and experimental results shown 2. Elastic scattering of low energy electrons by hydrogen molecule International Nuclear Information System (INIS) Freitas, L.C.G.; Mu-Tao, L.; Botelho, L.F. 1987-01-01 The coherent version of the Renormalized Multiple-Centre Potential Model (RMPM) has been extended to treat the elastic scattering of low energy electrons by H2 molecule. The intramolecular Multiple Scattering (MS) effect has also been included. The comparison against the experimental data shows that the inclusion of the MS improves significantly with experiment. The extension of the present method to study electron-polyatomic molecule interaction is also discussed. (author) [pt 3. Differences between GaAs/GaInP and GaAs/AlInP interfaces grown by movpe revealed by depth profiling and angle-resolved X-ray photoelectron spectroscopies Energy Technology Data Exchange (ETDEWEB) López-Escalante, M.C., E-mail: [email protected] [Nanotech Unit, Laboratorio de Materiales y Superficies, Departamento de Ingeniería Química, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga (Spain); Gabás, M. [The Nanotech Unit, Depto. de Física Aplicada I, Andalucía Tech, Universidad de Málaga, Campus de Teatinos s/n, 29071 Málaga Spain (Spain); García, I.; Barrigón, E.; Rey-Stolle, I.; Algora, C. [Instituto de Energía Solar, Universidad Politécnica de Madrid, Avda. Complutense 30, 28040 Madrid Spain (Spain); Palanco, S.; Ramos-Barrado, J.R. [The Nanotech Unit, Depto. de Física Aplicada I, Andalucía Tech, Universidad de Málaga, Campus de Teatinos s/n, 29071 Málaga Spain (Spain) 2016-01-01 Graphical abstract: - Highlights: • GaAs, AlInP and GaInP epi-layers grown in a MOVPE facility. • GaAs/GaInP and GaAs/AlInP interfaces studied through the combination of angle resolved and depth profile X-ray photoelectros spectroscopies. • GaAs/GaInP interface shows no features appart from GaAs, GaInP and mixed GaInAs or GaInAsP phases. • GaAs/AlInP interface shows traces of an anomalous P environment, probably due to P-P clusters. - Abstract: GaAs/GaInP and GaAs/AlInP interfaces have been studied using photoelectron spectroscopy tools. The combination of depth profile through Ar{sup +} sputtering and angle resolved X-ray photoelectron spectroscopy provides reliable information on the evolution of the interface chemistry. Measurement artifacts related to each particular technique can be ruled out on the basis of the results obtained with the other technique. GaAs/GaInP interface spreads out over a shorter length than GaAs/AlInP interface. The former could include the presence of the quaternary GaInAsP in addition to the nominal GaAs and GaInP layers. On the contrary, the GaAs/AlInP interface exhibits a higher degree of compound mixture. Namely, traces of P atoms in a chemical environment different to the usual AlInP coordination were found at the top of the GaAs/AlInP interface, as well as mixed phases like AlInP, GaInAsP or AlGaInAsP, located at the interface. 4. Superconductor digital electronics: Scalability and energy efficiency issues (Review Article) Science.gov (United States) Tolpygo, Sergey K. 2016-05-01 Superconductor digital electronics using Josephson junctions as ultrafast switches and magnetic-flux encoding of information was proposed over 30 years ago as a sub-terahertz clock frequency alternative to semiconductor electronics based on complementary metal-oxide-semiconductor (CMOS) transistors. Recently, interest in developing superconductor electronics has been renewed due to a search for energy saving solutions in applications related to high-performance computing. The current state of superconductor electronics and fabrication processes are reviewed in order to evaluate whether this electronics is scalable to a very large scale integration (VLSI) required to achieve computation complexities comparable to CMOS processors. A fully planarized process at MIT Lincoln Laboratory, perhaps the most advanced process developed so far for superconductor electronics, is used as an example. The process has nine superconducting layers: eight Nb wiring layers with the minimum feature size of 350 nm, and a thin superconducting layer for making compact high-kinetic-inductance bias inductors. All circuit layers are fully planarized using chemical mechanical planarization (CMP) of SiO2 interlayer dielectric. The physical limitations imposed on the circuit density by Josephson junctions, circuit inductors, shunt and bias resistors, etc., are discussed. Energy dissipation in superconducting circuits is also reviewed in order to estimate whether this technology, which requires cryogenic refrigeration, can be energy efficient. Fabrication process development required for increasing the density of superconductor digital circuits by a factor of ten and achieving densities above 107 Josephson junctions per cm2 is described. 5. Dose controlled low energy electron irradiator for biomolecular films. Science.gov (United States) Kumar, S V K; Tare, Satej T; Upalekar, Yogesh V; Tsering, Thupten 2016-03-01 We have developed a multi target, Low Energy Electron (LEE), precise dose controlled irradiator for biomolecular films. Up to seven samples can be irradiated one after another at any preset electron energy and dose under UHV conditions without venting the chamber. In addition, one more sample goes through all the steps except irradiation, which can be used as control for comparison with the irradiated samples. All the samples are protected against stray electron irradiation by biasing them at -20 V during the entire period, except during irradiation. Ethernet based communication electronics hardware, LEE beam control electronics and computer interface were developed in house. The user Graphical User Interface to control the irradiation and dose measurement was developed using National Instruments Lab Windows CVI. The working and reliability of the dose controlled irradiator has been fully tested over the electron energy range of 0.5 to 500 eV by studying LEE induced single strand breaks to ΦX174 RF1 dsDNA. 6. Electronic transport of molecular nanowires by considering of electron hopping energy between the second neighbors Directory of Open Access Journals (Sweden) H Rabani 2015-07-01 Full Text Available In this paper, we study the electronic conductance of molecular nanowires by considering the electron hopping between the first and second neighbors with the help Green’s function method at the tight-binding approach. We investigate three types of structures including linear uniform and periodic chains as well as poly(p-phenylene molecule which are embedded between two semi-infinite metallic leads. The results show that in the second neighbor approximation, the resonance, anti-resonance and Fano phenomena occur in the conductance spectra of these structures. Moreover, a new gap is observed at edge of the lead energy band wich its width depends on the value of the electron hopping energy between the second neighbors. In the systems including intrinsic gap, this hopping energy shifts the gap in the energy spectra. 7. Energy spectra variations of high energy electrons in magnetic storms observed by ARASE and HIMAWARI Science.gov (United States) Takashima, T.; Higashio, N.; Mitani, T.; Nagatsuma, T.; Yoshizumi, M. 2017-12-01 The ARASE spacecraft was launched in December 20, 2016 to investigate mechanisms for acceleration and loss of relativistic electrons in the radiation belts during space storms. The six particle instruments with wide energy range (a few eV to 10MeV) are onboard the ARASE spacecraft. Especially, two particle instruments, HEP and XEP observe high energy electron with energy range from 70keV to over 10Mev. Those instruments observed several geomagnetic storms caused by coronal hole high speed streams or coronal mass ejections from March in 2017. The relativistic electrons in the outer radiation belt were disappeared/increased and their energy spectra were changed dynamically in some storms observed by XEP/HEP onboard the ARASE spacecraft. In the same time, SEDA-e with energy range 200keV-4.5MeV for electron on board the HIMAWARI-8, Japanese weather satellite on GEO, observed increase of relativistic electron in different local time. We will report on energy spectra variations of high energy electrons including calibrations of differential flux between XEP and HEP and discuss comparisons with energy spectra between ARAE and HIMAWARI that observed each storm in different local time. 8. Treatment of surfaces with low-energy electrons Czech Academy of Sciences Publication Activity Database Frank, Luděk; Mikmeková, Eliška; Lejeune, M. 2017-01-01 Roč. 407, JUN 15 (2017), s. 105-108 ISSN 0169-4332 R&D Projects: GA TA ČR(CZ) TE01020118; GA MŠk(CZ) LO1212; GA MŠk ED0017/01/01 Institutional support: RVO:68081731 Keywords : Low-energy electrons * Electron beam induced release * Graphene * Ultimate cleaning of surfaces Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering OBOR OECD: Nano-processes (applications on nano-scale) Impact factor: 3.387, year: 2016 9. Electron energy loss spectrometers the technology of high performance CERN Document Server Ibach, Harald 1991-01-01 Electron energy loss spectroscopy has become an indispensable tool in surface analysis Although the basic physics of this technique is well understood, instrument design has previously largely been left to intuition This book is the first to provide a comprehensive treatment of the electron optics involved in the production of intense monochromatic beams and the detection of scattered electrons It includes a full three-dimensional analysis of the electron optical properties of electron emission systems, monochromators and lens systems, placing particular emphasis on the procedures for matching the various components The description is kept mathematically simple and focuses on practical aspects, with many hints for writing computer codes to calculate and optimize electrostatic lens elements 10. Wettability Modification of Nanomaterials by Low-Energy Electron Flux Directory of Open Access Journals (Sweden) Torchinsky I 2009-01-01 Full Text Available Abstract Controllable modification of surface free energy and related properties (wettability, hygroscopicity, agglomeration, etc. of powders allows both understanding of fine physical mechanism acting on nanoparticle surfaces and improvement of their key characteristics in a number of nanotechnology applications. In this work, we report on the method we developed for electron-induced surface energy and modification of basic, related properties of powders of quite different physical origins such as diamond and ZnO. The applied technique has afforded gradual tuning of the surface free energy, resulting in a wide range of wettability modulation. In ZnO nanomaterial, the wettability has been strongly modified, while for the diamond particles identical electron treatment leads to a weak variation of the same property. Detailed investigation into electron-modified wettability properties has been performed by the use of capillary rise method using a few probing liquids. Basic thermodynamic approaches have been applied to calculations of components of solid–liquid interaction energy. We show that defect-free, low-energy electron treatment technique strongly varies elementary interface interactions and may be used for the development of new technology in the field of nanomaterials. 11. Free electron lasers for transmission of energy in space Science.gov (United States) Segall, S. B.; Hiddleston, H. R.; Catella, G. C. 1981-01-01 A one-dimensional resonant-particle model of a free electron laser (FEL) is used to calculate laser gain and conversion efficiency of electron energy to photon energy. The optical beam profile for a resonant optical cavity is included in the model as an axial variation of laser intensity. The electron beam profile is matched to the optical beam profile and modeled as an axial variation of current density. Effective energy spread due to beam emittance is included. Accelerators appropriate for a space-based FEL oscillator are reviewed. Constraints on the concentric optical resonator and on systems required for space operation are described. An example is given of a space-based FEL that would produce 1.7 MW of average output power at 0.5 micrometer wavelength with over 50% conversion efficiency of electrical energy to laser energy. It would utilize a 10 m-long amplifier centered in a 200 m-long optical cavity. A 3-amp, 65 meV electrostatic accelerator would provide the electron beam and recover the beam after it passes through the amplifier. Three to five shuttle flights would be needed to place the laser in orbit. 12. Dose characteristics of high-energy electrons, muons and photons International Nuclear Information System (INIS) Britvich, G.I.; Krupnyj, G.I.; Peleshko, V.N.; Rastsvetalov, Ya.N. 1980-01-01 Differential distribution of energy release at different depth of tissue-equivalent phantoms (plexiglas, polystyrene, polyethylene) at the energy of incident electrons, muons of 0.2-40 GeV and photons with the mean energy of 3.6 GeV are measured. The error of experimental results does not exceed 7%. On the basis of the data obtained dose characteristics of electrons, muons and photons for standard geometry are estimated. For all types of irradiation the maximum value of specific equivalent dose, nremxcm 2 /part. is presented. It is shown that published values of specific equivalent dose of electron radiation are higher in all the investigated energy range from 0.2 to 40 GeV, and for muon radiation a good agreement with the present experiment is observed. The highly precise results obtained which cover the wide dynamic range according to the energy of incident particles can serve as the basis for reconsidering the existing recommendations for dose characteristics of electron radiation [ru 13. Electron correlations in narrow energy bands: modified polar model approach Directory of Open Access Journals (Sweden) L. Didukh 2008-09-01 Full Text Available The electron correlations in narrow energy bands are examined within the framework of the modified form of polar model. This model permits to analyze the effect of strong Coulomb correlation, inter-atomic exchange and correlated hopping of electrons and explain some peculiarities of the properties of narrow-band materials, namely the metal-insulator transition with an increase of temperature, nonlinear concentration dependence of Curie temperature and peculiarities of transport properties of electronic subsystem. Using a variant of generalized Hartree-Fock approximation, the single-electron Green's function and quasi-particle energy spectrum of the model are calculated. Metal-insulator transition with the change of temperature is investigated in a system with correlated hopping. Processes of ferromagnetic ordering stabilization in the system with various forms of electronic DOS are studied. The static conductivity and effective spin-dependent masses of current carriers are calculated as a function of electron concentration at various DOS forms. The correlated hopping is shown to cause the electron-hole asymmetry of transport and ferromagnetic properties of narrow band materials. 14. Electron and photon energy calibration with the ATLAS detector CERN Document Server 2017-01-01 An accurate calibration of the energy measurement of electron and photon is needed for many ATLAS physics analysis. The calibration of the energy measurement is performed in-situ using a large statistics of Z->ee events. A pre-requisite of this calibration is a good understanding of the material in front of the calorimeter and of the inter-calibration of the different calorimeter layers. The Z->ee sample is also used to measure the energy resolution. The results obtained with the pp collisions data at sqrt(s)=13 TeV in 2016 (2015) corresponding to an integrated luminosity of 33.9 (3.1)fb-1 of sqrt(s)=13 TeV are presented as well as the corresponding uncertainties on the electron and photon energy scales. 15. High energy primary electron spectrum observed by the emulsion chamber Science.gov (United States) Nishimura, J.; Fujii, M.; Aizu, H.; Hiraiwa, N.; Taira, T.; Kobayashi, T.; Niu, K.; Koss, T. A.; Lord, J. J.; Golden, R. L. 1978-01-01 A detector of the emulsion chamber type is used to measure the energy spectrum of cosmic-ray electrons. Two large emulsion chambers, each having an area of 40 by 50 sq cm, are exposed for about 25.5 hr at an average pressure altitude of 3.9 mbar. About 500 high-energy cascades (no less than about 600 GeV) are detected by searching for dark spots on the X-ray films. A power-law energy dependence formula is derived for the spectrum of primary cosmic-ray electrons in the energy region over 100 GeV. The results are in good agreement with the transition curves obtained previously by theoretical and Monte Carlo calculations. 16. Magnetic properties and core electron binding energies of liquid water Science.gov (United States) Galamba, N.; Cabral, Benedito J. C. 2018-01-01 The magnetic properties and the core and inner valence electron binding energies of liquid water are investigated. The adopted methodology relies on the combination of molecular dynamics and electronic structure calculations. Born-Oppenheimer molecular dynamics with the Becke and Lee-Yang-Parr functionals for exchange and correlation, respectively, and includes an empirical correction (BLYP-D3) functional and classical molecular dynamics with the TIP4P/2005-F model were carried out. The Keal-Tozer functional was applied for predicting magnetic shielding and spin-spin coupling constants. Core and inner valence electron binding energies in liquid water were calculated with symmetry adapted cluster-configuration interaction. The relationship between the magnetic shielding constant σ(17O), the role played by the oxygen atom as a proton acceptor and donor, and the tetrahedral organisation of liquid water are investigated. The results indicate that the deshielding of the oxygen atom in water is very dependent on the order parameter (q) describing the tetrahedral organisation of the hydrogen bond network. The strong sensitivity of magnetic properties on changes of the electronic density in the nuclei environment is illustrated by a correlation between σ(17O) and the energy gap between the 1a1[O1s] (core) and the 2a1 (inner valence) orbitals of water. Although several studies discussed the eventual connection between magnetic properties and core electron binding energies, such a correlation could not be clearly established. Here, we demonstrate that for liquid water this correlation exists although involving the gap between electron binding energies of core and inner valence orbitals. 17. From electron energy-loss spectroscopy to multi-dimensional and multi-signal electron microscopy. Science.gov (United States) Colliex, Christian 2011-01-01 This review intends to illustrate how electron energy-loss spectroscopy (EELS) techniques in the electron microscope column have evolved over the past 60 years. Beginning as a physicist tool to measure basic excitations in solid thin foils, EELS techniques have gradually become essential for analytical purposes, nowadays pushed to the identification of individual atoms and their bonding states. The intimate combination of highly performing techniques with quite efficient computational tools for data processing and ab initio modeling has opened the way to a broad range of novel imaging modes with potential impact on many different fields. The combination of Angström-level spatial resolution with an energy resolution down to a few tenths of an electron volt in the core-loss spectral domain has paved the way to atomic-resolved elemental and bonding maps across interfaces and nanostructures. In the low-energy range, improved energy resolution has been quite efficient in recording surface plasmon maps and from them electromagnetic maps across the visible electron microscopy (EM) domain, thus bringing a new view to nanophotonics studies. Recently, spectrum imaging of the emitted photons under the primary electron beam and the spectacular introduction of time-resolved techniques down to the femtosecond time domain, have become innovative keys for the development and use of a brand new multi-dimensional and multi-signal electron microscopy. 18. Where is electronic energy stored in adenosine triphosphate? Science.gov (United States) Arabi, Alya A; Matta, Chérif F 2009-04-09 The gas-phase electronic energy of the hydrolysis of methyl triphosphate, a model of adenosine 5'-triphosphate (ATP), is partitioned into local (atomic and group) contributions. A modified definition of Lipmann's "group transfer potential" is proposed on the basis of the partitioning of the total electronic energy into atomic contributions within the framework of the quantum theory of atoms in molecules (QTAIM). The group transfer potential is defined here as the sum of the atomic energies forming the group in ATP minus the sum of the energies of the same atoms in inorganic phosphate. It is found that the transfer potential of the terminal phosphate group in ATP is significantly reduced, from +241.7 to +73.1 kcal/mol, as a result of complexation with magnesium. This is accompanied by a concomitant change in the energy of reaction from -168.6 to -24.9 kcal/mol. Regions within ATP where the electronic energy changes the most upon hydrolysis are identified. The study is conducted at the DFT/B3LYP/6-31+G(d,p) level of theory. 19. Low energy electron beam processing of YBCO thin films Energy Technology Data Exchange (ETDEWEB) Chromik, Š., E-mail: [email protected] [Institute of Electrical Engineering, SAS, Dúbravská cesta 9, 841 04 Bratislava (Slovakia); Camerlingo, C. [CNR-SPIN, Istituto Superconduttori, Materiali Innovativi e Dispositivi, via Campi Flegrei 34, 80078 Pozzuoli (Italy); Sojková, M.; Štrbík, V.; Talacko, M. [Institute of Electrical Engineering, SAS, Dúbravská cesta 9, 841 04 Bratislava (Slovakia); Malka, I.; Bar, I.; Bareli, G. [Department of Physics, Ben Gurion University of the Negev, P.O.B. 653, 84105 Beer Sheva (Israel); Jung, G. [Department of Physics, Ben Gurion University of the Negev, P.O.B. 653, 84105 Beer Sheva (Israel); Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw (Poland) 2017-02-15 Highlights: • Improvement of superconducting properties of irradiated bridges under certain conditions. • 30 keV irradiation influence CuO{sub 2} planes as well as oxygen chains. • Direct confirmation of changes in oxygen chains using micro-Raman spectroscopy. • Possibility of electron writing. - Abstract: Effects of low energy 30 keV electron irradiation of superconducting YBa{sub 2}Cu{sub 3}O{sub 7−δ} thin films have been investigated by means of transport and micro-Raman spectroscopy measurements. The critical temperature and the critical current of 200 nm thick films initially increase with increasing fluency of the electron irradiation, reach the maximum at fluency 3 − 4 × 10{sup 20} electrons/cm{sup 2}, and then decrease with further fluency increase. In much thinner films (75 nm), the critical temperature increases while the critical current decreases after low energy electron irradiation with fluencies below 10{sup 20} electrons/cm{sup 2}. The Raman investigations suggest that critical temperature increase in irradiated films is due to healing of broken Cu−O chains that results in increased carrier’s concentration in superconducting CuO{sub 2} planes. Changes in the critical current are controlled by changes in the density of oxygen vacancies acting as effective pinning centers for flux vortices. The effects of low energy electron irradiation of YBCO turned out to result from a subtle balance of many processes involving oxygen removal, both by thermal activation and kick-off processes, and ordering of chains environment by incident electrons. 20. Microsecond Electron Beam Source with Electron Energy Up to 400 Kev and Plasma Anode Science.gov (United States) Abdullin, É. N.; Basov, G. F.; Shershnev, S. 2017-12-01 A new high-power source of electrons with plasma anode for producing high-current microsecond electron beams with electron energy up to 400 keV has been developed, manufactured, and put in operation. To increase the cross section and pulse current duration of the beam, a multipoint explosive emission cathode is used in the electron beam source, and the beam is formed in an applied external guiding magnetic field. The Marx generator with vacuum insulation is used as a high-voltage source. Electron beams with electron energy up to 300-400 keV, current of 5-15 kA, duration of 1.5-3 μs, energy up to 4 kJ, and cross section up to 150 cm2 have been produced. The operating modes of the electron beam source are realized in which the applied voltage is influenced weakly on the current. The possibility of source application for melting of metal surfaces is demonstrated. 1. Electronic excitation of some silicium compounds in the vacuum ultravi olet region International Nuclear Information System (INIS) Rocco, M.L.M. 1986-01-01 Angle-resolved electron energy-loss spectra have been measured for the tetramethylsilane, trimethylchlorosilane and dimethyldichloresilane molecules in the 5 - 300 eV energy range. The spectra have been obtained at 1 KeV incident energy, with an energy resolution of about 0.5 eV (valense region) and 0.8 eV (inner-shell region). Both the valence and core-level excitation bands can be as associated to transitions to Rydber and valence states. No dipole-allowed transition has been observed in the spectra measured in the angular range of 1 to 9 degrees (valence region) and 3 to 7 degrees (inner-shell region). (Author) [pt 2. Evaluation of high-energy brachytherapy source electronic disequilibrium and dose from emitted electrons. Science.gov (United States) Ballester, Facundo; Granero, Domingo; Pérez-Calatayud, José; Melhus, Christopher S; Rivard, Mark J 2009-09-01 The region of electronic disequilibrium near photon-emitting brachytherapy sources of high-energy radionuclides (60Co, 137CS, 192Ir, and 169Yb) and contributions to total dose from emitted electrons were studied using the GEANT4 and PENELOPE Monte Carlo codes. Hypothetical sources with active and capsule materials mimicking those of actual sources but with spherical shape were examined. Dose contributions due to source photons, x rays, and bremsstrahlung; source beta-, Auger electrons, and internal conversion electrons; and water collisional kerma were scored. To determine if conclusions obtained for electronic equilibrium conditions and electron dose contribution to total dose for the representative spherical sources could be applied to actual sources, the 192Ir mHDR-v2 source model (Nucletron B.V., Veenendaal, The Netherlands) was simulated for comparison to spherical source results and to published data. Electronic equilibrium within 1% is reached for 60Co, 137CS, 192Ir, and 169Yb at distances greater than 7, 3.5, 2, and 1 mm from the source center, respectively, in agreement with other published studies. At 1 mm from the source center, the electron contributions to total dose are 1.9% and 9.4% for 60Co and 192Ir, respectively. Electron emissions become important (i.e., > 0.5%) within 3.3 mm of 60Co and 1.7 mm of 192Ir sources, yet are negligible over all distances for 137Cs and 169Yb. Electronic equilibrium conditions along the transversal source axis for the mHDR-v2 source are comparable to those of the spherical sources while electron dose to total dose contribution are quite different. Electronic equilibrium conditions obtained for spherical sources could be generalized to actual sources while electron contribution to total dose depends strongly on source dimensions, material composition, and electron spectra. 3. Atomic excitation and molecular dissociation by low energy electron collisions International Nuclear Information System (INIS) Weyland, Marvin 2016-01-01 In this work, momentum imaging experiments have been conducted for the electron impact excitation of metastable states in noble gases and for dissociative electron attachment (DEA) in polyatomic molecules. For the electron impact excitation study a new experimental technique has been developed which is able to measure the scattering angle distribution of the electrons by detection of the momentum transfer to the atoms. Momentum transfer images have been recorded for helium and neon at fixed electron impact energy close to the excitation threshold and good agreement with current R-matrix theory calculations was found. A new momentum imaging apparatus for negative ions has been built for the purpose of studying DEA in biologically relevant molecules. During this work, DEA was investigated in the molecules ammonia, water, formic acid, furan, pyridine and in two chlorofluorocarbons. Furthermore, the change of DEA resonance energies when molecules form clusters compared to monomers was investigated in ammonia and formic acid. The experimental results of most studied molecules could be compared to recent theoretical calculations and they support further development in the theoretical description of DEA. The new apparatus built in this work also delivered a superior momentum resolution compared to existing setups. This allows the momentum imaging of heavier fragments and fragments with lower kinetic energy. 4. Atomic excitation and molecular dissociation by low energy electron collisions Energy Technology Data Exchange (ETDEWEB) Weyland, Marvin 2016-11-16 In this work, momentum imaging experiments have been conducted for the electron impact excitation of metastable states in noble gases and for dissociative electron attachment (DEA) in polyatomic molecules. For the electron impact excitation study a new experimental technique has been developed which is able to measure the scattering angle distribution of the electrons by detection of the momentum transfer to the atoms. Momentum transfer images have been recorded for helium and neon at fixed electron impact energy close to the excitation threshold and good agreement with current R-matrix theory calculations was found. A new momentum imaging apparatus for negative ions has been built for the purpose of studying DEA in biologically relevant molecules. During this work, DEA was investigated in the molecules ammonia, water, formic acid, furan, pyridine and in two chlorofluorocarbons. Furthermore, the change of DEA resonance energies when molecules form clusters compared to monomers was investigated in ammonia and formic acid. The experimental results of most studied molecules could be compared to recent theoretical calculations and they support further development in the theoretical description of DEA. The new apparatus built in this work also delivered a superior momentum resolution compared to existing setups. This allows the momentum imaging of heavier fragments and fragments with lower kinetic energy. 5. Treatment of surfaces with low-energy electrons Energy Technology Data Exchange (ETDEWEB) Frank, L., E-mail: [email protected] [Institute of Scientific Instruments of the CAS, v.v.i., Královopolská 147, 61264 Brno (Czech Republic); Mikmeková, E. [Institute of Scientific Instruments of the CAS, v.v.i., Královopolská 147, 61264 Brno (Czech Republic); FEI Company, Achtseweg Noord 5, 5651 GG Eindhoven (Netherlands); Lejeune, M. [LPMC – Faculte des Sciences d’Amiens, Universite de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens Cedex 2 (France) 2017-06-15 Highlights: • Using proper irradiation parameters, adsorbed hydrocarbons are released from surfaces. • Slow electrons remove hydrocarbons instead of depositing carbon. • Prolonged irradiation with very slow electrons does not create defects in graphene. - Abstract: Electron-beam-induced deposition of various materials from suitable precursors has represented an established branch of nanotechnology for more than a decade. A specific alternative is carbon deposition on the basis of hydrocarbons as precursors that has been applied to grow various nanostructures including masks for subsequent technological steps. Our area of study was unintentional electron-beam-induced carbon deposition from spontaneously adsorbed hydrocarbon molecules. This process traditionally constitutes a challenge for scanning electron microscopy practice preventing one from performing any true surface studies outside an ultrahigh vacuum and without in-situ cleaning of samples, and also jeopardising other electron-optical devices such as electron beam lithographs. Here we show that when reducing the energy of irradiating electrons sufficiently, the e-beam-induced deposition can be converted to e-beam-induced release causing desorption of hydrocarbons and ultimate cleaning of surfaces in both an ultrahigh and a standard high vacuum. Using series of experiments with graphene samples, we demonstrate fundamental features of e-beam-induced desorption and present results of checks for possible radiation damage using Raman spectroscopy that led to optimisation of the electron energy for damage-free cleaning. The method of preventing carbon contamination described here paves the way for greatly enhanced surface sensitivity of imaging and substantially reduced demands on vacuum systems for nanotechnological applications. 6. Electron Energy Level Statistics in Graphene Quantum Dots NARCIS (Netherlands) De Raedt, H.; Katsnellson, M. I.; Katsnelson, M.I. 2008-01-01 Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots [7] we investigate the level statistics in the simplest tight-binding model for different dot shapes by computer simulation. The results are in a reasonable agreement with the 7. Energy Dependence of Near-relativistic Electron Spectrum at ... 2016-01-27 Jan 27, 2016 ... This may give us some insight into how we can safeguard geostationary satellites from functional anomalies of the deep dielectric charging type, which are caused by charge accumulation and subsequent discharge of relativistic electrons. In this study we examine whether there is any energy dependence ... 8. High Energy Electron Dosimetry by Alanine/ESR Spectroscopy International Nuclear Information System (INIS) Chu, Sung Sil 1989-01-01 Dosimetry based on electron spin resonance(ESR) analysis of radiation induced free radicals in amino acids is relevant to biological dosimetry applications. Alanine detectors are without walls and are tissue equivalent. Therefore, alanine ESR dosimetry looks promising for use in the therapy level. The dose range of the alanine/ESR dosimetry system can be extended down to l Gy. In a water phantom the absorbed dose of electrons generated by a medical linear accelerator of different initial energies (6-21 MeV) and therapeutic dose levels(1-60 Gy) was measured. Furthermore, depth dose measurements carried out with alanine dosimeters were compared with ionization chamber measurements. As the results, the measured absorbed doses for shallow depth of initial electron energies above 15 MeV were higher by 2-5% than those calculated by nominal energy CE factors. This seems to be caused by low energy scattered beams generated from the scattering foil and electron cones of beam projecting device in medical linear accelerator 9. Electron emission in collisions of intermediate energy ions with atoms International Nuclear Information System (INIS) Garibotti, C.R. 1988-01-01 The aim of this work, is the analysis of the processes of electronic emission produced in the collisions of small ions (H + , He ++ ) of intermediate energy (50 a 200 KeV/amu) with light gaseous targets. (A.C.A.G.) [pt 10. Scanning electron microscopy-energy dispersive X-ray spectrometer ... African Journals Online (AJOL) Results suggest that the SEM-EDX is one of the potential tools for rapid detection of metals, namely, As and Cd in himematsutake. Key words: Arsenic (As), cadmium (Cd), scanning electron microscopy-energy dispersive X-ray spectrometer (SEM-EDX), coupled plasma-mass spectrometer (ICP-MS), himematsutake. 11. Preliminary investigations on high energy electron beam tomography Energy Technology Data Exchange (ETDEWEB) Baertling, Yves; Hoppe, Dietrich; Hampel, Uwe 2010-12-15 In computed tomography (CT) cross-sectional images of the attenuation distribution within a slice are created by scanning radiographic projections of an object with a rotating X-ray source detector compound and subsequent reconstruction of the images from these projection data on a computer. CT can be made very fast by employing a scanned electron beam instead of a mechanically moving X-ray source. Now this principle was extended towards high-energy electron beam tomography with an electrostatic accelerator. Therefore a dedicated experimental campaign was planned and carried out at the Budker Institute of Nuclear Physics (BINP), Novosibirsk. There we investigated the capabilities of BINP's accelerators as an electron beam generating and scanning unit of a potential high-energy electron beam tomography device. The setup based on a 1 MeV ELV-6 (BINP) electron accelerator and a single detector. Besides tomographic measurements with different phantoms, further experiments were carried out concerning the focal spot size and repeat accuracy of the electron beam as well as the detector's response time and signal to noise ratio. (orig.) 12. Renewable Energy Systems in the Power Electronics Curriculum DEFF Research Database (Denmark) Blaabjerg, Frede; Chen, Zhe; Teodorescu, Remus 2005-01-01 , magnetics, electrical machines, power systems, analogue and digital control, materials, power converters, electronics, materials, thermal design and EMC. However, those fields may not be enough in order to give the students enough skills. It is also necessary to learn about systems and for the moment one...... of the most important area is renewable energy systems. This paper will discuss the basic courses for the power electronics curriculum. It will also discuss how to teach power electronic systems efficiently through a projectoriented and problem-based learning approach with Aalborg University in Denmark...... as a full-scale example. Different project examples will be given as well as important laboratories for adjustable speed drives and renewable energy systems which are used at the university are described.... 13. Penetration of an electron beam into material and energy dissipation International Nuclear Information System (INIS) Kral, V.; Pelzbauer, Z. 1986-01-01 The contribution is concerned with penetration of an electron beam having energy between 5 and 25 keV into the polymer and with energy dissipation inside the interaction volume of the polymer. The experimentally observed shape on the interaction volume has been theoretically substantiated, the range has been calculated, and a comparison with Gruen's empirical relation has been carried out. It is shown that with increasing accelerating voltage the centre of the core of the interaction volume is shifted more deeply under the sample surface and the dissipated energy decreases. Extension of the neck of the interaction volume caused by back scattering is discussed. (author) 14. Radiation effect of low energy electron beam on plant growth International Nuclear Information System (INIS) Takeshita, Hidefumi; Yoshii, Fumio; Kume, Tamikazu 2000-01-01 Radiation effect of low energy electron beam (EB) on the growth of maize, barley and soybean was investigated. Seeds of maize, barley and soybean were irradiated in the dose range of 2 to 20 kGy using EB with different energy from 150 to 250 keV. Growth promotion was observed for irradiated seeds of maize and soybean at the dose up to 10 kGy. Especially, significant promotion of root growth was observed for irradiated barley and soybean. It was also found for soybean that phytoalexin induction activity was clearly enhanced by low energy EB irradiation. (author) 15. Radiated energy calculation in free electron lasers without inversion International Nuclear Information System (INIS) Oganesyan, K.B. 2017-01-01 The equations of particle motion in the free electron lasers without inversion are derived using the Hamiltonian formalism. In small signal regime the uncoupled one dimensional phase equation is derived in the form of pendulum equation. For the practical estimations the same equation along with the equation of particle energy change are solved using perturbation theory and the expressions for gain in FEL regime and particle angle dependence of energy at the exit of first undulator are obtained. Results for gain, particle phase and energy change depending on beam parameters and device are presented 16. Studies of space charge effects on operating electron beam ion trap at low electron beam energy Energy Technology Data Exchange (ETDEWEB) Jin, Xuelong; Fei, Zejie; Xiao, Jun; Lu, Di; Hutton, Roger [The Key Lab of Applied Ion Beam Physics, Ministry of Education (China); Shanghai EBIT Laboratory, Modern Physics Institute, Fudan University, Shanghai (China); Zou, Yaming, E-mail: [email protected] [The Key Lab of Applied Ion Beam Physics, Ministry of Education (China); Shanghai EBIT Laboratory, Modern Physics Institute, Fudan University, Shanghai (China) 2013-08-21 An electron beam ion trap (EBIT) is a powerful machine for disentangling studies of atomic processes in plasmas. To assist studies on edge plasma spectroscopic diagnostics, a very low energy EBIT, SH-PermEBIT, has been set up at the Shanghai EBIT lab. Large amounts of simulation works were done to study the factors which hinder the EBIT from operation at very low electron beam energies. Under the guide line of the simulation results, we finally managed to successfully reach 60 eV for the lower end of the electron beam energy with a beam transmission above 57%. In this presentation, simulation studies of the space charge effect, which is one of the most important causes of beam loss, was made based on Tricomp (Field precision) 17. Secondary Electrons as an Energy Source for Life. Science.gov (United States) Stelmach, Kamil B; Neveu, Marc; Vick-Majors, Trista J; Mickol, Rebecca L; Chou, Luoth; Webster, Kevin D; Tilley, Matt; Zacchei, Federica; Escudero, Cristina; Flores Martinez, Claudio L; Labrado, Amanda; Fernández, Enrique J G 2018-01-01 Life on Earth is found in a wide range of environments as long as the basic requirements of a liquid solvent, a nutrient source, and free energy are met. Previous hypotheses have speculated how extraterrestrial microbial life may function, among them that particle radiation might power living cells indirectly through radiolytic products. On Earth, so-called electrophilic organisms can harness electron flow from an extracellular cathode to build biomolecules. Here, we describe two hypothetical mechanisms, termed "direct electrophy" and "indirect electrophy" or "fluorosynthesis," by which organisms could harness extracellular free electrons to synthesize organic matter, thus expanding the ensemble of potential habitats in which extraterrestrial organisms might be found in the Solar System and beyond. The first mechanism involves the direct flow of secondary electrons from particle radiation to a microbial cell to power the organism. The second involves the indirect utilization of impinging secondary electrons and a fluorescing molecule, either biotic or abiotic in origin, to drive photosynthesis. Both mechanisms involve the attenuation of an incoming particle's energy to create low-energy secondary electrons. The validity of the hypotheses is assessed through simple calculations showing the biomass density attainable from the energy supplied. Also discussed are potential survival strategies that could be used by organisms living in possible habitats with a plentiful supply of secondary electrons, such as near the surface of an icy moon. While we acknowledge that the only definitive test for the hypothesis is to collect specimens, we also describe experiments or terrestrial observations that could support or nullify the hypotheses. Key Words: Radiation-Electrophiles-Subsurface life. Astrobiology 18, 73-85. 18. Secondary Electrons as an Energy Source for Life Science.gov (United States) Stelmach, Kamil B.; Neveu, Marc; Vick-Majors, Trista J.; Mickol, Rebecca L.; Chou, Luoth; Webster, Kevin D.; Tilley, Matt; Zacchei, Federica; Escudero, Cristina; Flores Martinez, Claudio L.; Labrado, Amanda; Fernández, Enrique J. G. 2018-01-01 Life on Earth is found in a wide range of environments as long as the basic requirements of a liquid solvent, a nutrient source, and free energy are met. Previous hypotheses have speculated how extraterrestrial microbial life may function, among them that particle radiation might power living cells indirectly through radiolytic products. On Earth, so-called electrophilic organisms can harness electron flow from an extracellular cathode to build biomolecules. Here, we describe two hypothetical mechanisms, termed "direct electrophy" and "indirect electrophy" or "fluorosynthesis," by which organisms could harness extracellular free electrons to synthesize organic matter, thus expanding the ensemble of potential habitats in which extraterrestrial organisms might be found in the Solar System and beyond. The first mechanism involves the direct flow of secondary electrons from particle radiation to a microbial cell to power the organism. The second involves the indirect utilization of impinging secondary electrons and a fluorescing molecule, either biotic or abiotic in origin, to drive photosynthesis. Both mechanisms involve the attenuation of an incoming particle's energy to create low-energy secondary electrons. The validity of the hypotheses is assessed through simple calculations showing the biomass density attainable from the energy supplied. Also discussed are potential survival strategies that could be used by organisms living in possible habitats with a plentiful supply of secondary electrons, such as near the surface of an icy moon. While we acknowledge that the only definitive test for the hypothesis is to collect specimens, we also describe experiments or terrestrial observations that could support or nullify the hypotheses. 19. Electronic structure of the quasi-one-dimensional organic conductor TTF-TCNQ DEFF Research Database (Denmark) Sing, M.; Schwingenschlögl, U.; Claessen, R. 2003-01-01 We study the electronic structure of the quasi-one-dimensional organic conductor TTF-TCNQ by means of density-functional band theory, Hubbard model calculations, and angle-resolved photoelectron spectroscopy (ARPES). The experimental spectra reveal significant quantitative and qualitative...... discrepancies to band theory. We demonstrate that the dispersive behavior as well as the temperature dependence of the spectra can be consistently explained by the finite-energy physics of the one-dimensional Hubbard model at metallic doping. The model description can even be made quantitative, if one accounts......-dimensional Hubbard model for the low-energy spectral behavior is attributed to interchain coupling and the additional effect of electron-phonon interaction.... 20. Interplay between electronic and structural properties in the Pb/Ag(1 0 0) interface. Science.gov (United States) Crepaldi, A; Zhan, R R; Moser, S; Sheverdyaeva, P M; Carbone, C; Papagno, M; Moras, P; Baraldi, A; Grioni, M 2015-11-18 We report an investigation of the structural and electronic properties of a Pb monolayer (ML) grown on Ag(1 0 0), by combining x-ray photoelectron diffraction (XPD) and angle resolved photoelectron spectroscopy (ARPES). The Pb atoms are found to arrange in a pseudo-hexagonal adlayer commensurate to the underlying square Ag substrate, resulting in a coincidence cell with c([Formula: see text]) periodicity. The electronic structure of the Pb ML in proximity of the Fermi level consists in three p-derived bands, which show different degrees of hybridization with the substrate for their different orbital characters. In particular, we report that the p xy states disperse without forming energy gap, in contrast to previous ARPES studies of the Pb ML on different metallic substrates. We attribute the absence of energy gap to the commensurability between substrate and adlayer, resulting in a higher two-dimensionality of the Pb ML. 1. Time-resolved ARPES at LACUS: Band Structure and Ultrafast Electron Dynamics of Solids. Science.gov (United States) Crepaldi, Alberto; Roth, Silvan; Gatti, Gianmarco; Arrell, Christopher A; Ojeda, José; van Mourik, Frank; Bugnon, Philippe; Magrez, Arnaud; Berger, Helmuth; Chergui, Majed; Grioni, Marco 2017-05-31 The manipulation of the electronic properties of solids by light is an exciting goal, which requires knowledge of the electronic structure with energy, momentum and temporal resolution. Time- and angle-resolved photoemission spectroscopy (tr-ARPES) is the most direct probe of the effects of an optical excitation on the band structure of a material. In particular, tr-ARPES in the extreme ultraviolet (VUV) range gives access to the ultrafast dynamics over the entire Brillouin zone. VUV tr-ARPES experiments can now be performed at the ASTRA (ARPES Spectrometer for Time-Resolved Applications) end station of Harmonium, at LACUS. Its capabilities are illustrated by measurements of the ultrafast electronic response of ZrSiTe, a novel topological semimetal characterized by linearly dispersing states located at the Brillouin zone boundary. 2. Precision measurements of high-energy conversion electron lines and determination of neutron binding energies International Nuclear Information System (INIS) Braumandl, F. 1979-01-01 The paper first discusses the energy accuracy of the BILL conversion electron spectrometer at the Grenoble high flux reactor. With an improved temperature stabilisation of the magnets, an energy accuracy of ΔE/E -5 can be reached. After this, highly exact measurements of high-energy conversion electron lines of the 200 Hg, 114 Cd, 165 Dy, 168 Er, 239 U nuclei and the 13 C, 28 Al 3 H and 92 Zr photoelectron lines were carried out. Energy calibration of the spectrometer was carried out in the 1.5 MeV to 6.5 MeV range with intensive high-energy transitions of the 200 Hg nucleus. Systematic calibration errors could be investigated by means of combinations between the calibration lines. A calibration for absolute energies was obtained by comparing low-energy gamma transitions of 200 Hg with the 411.8 keV gold standard. (orig.) [de 3. Controlled cooling of an electronic system for reduced energy consumption Energy Technology Data Exchange (ETDEWEB) David, Milnes P.; Iyengar, Madhusudan K.; Schmidt, Roger R. 2018-01-30 Energy efficient control of a cooling system cooling an electronic system is provided. The control includes automatically determining at least one adjusted control setting for at least one adjustable cooling component of a cooling system cooling the electronic system. The automatically determining is based, at least in part, on power being consumed by the cooling system and temperature of a heat sink to which heat extracted by the cooling system is rejected. The automatically determining operates to reduce power consumption of the cooling system and/or the electronic system while ensuring that at least one targeted temperature associated with the cooling system or the electronic system is within a desired range. The automatically determining may be based, at least in part, on one or more experimentally obtained models relating the targeted temperature and power consumption of the one or more adjustable cooling components of the cooling system. 4. Energy-weighted dynamical scattering simulations of electron diffraction modalities in the scanning electron microscope. Science.gov (United States) Pascal, Elena; Singh, Saransh; Callahan, Patrick G; Hourahine, Ben; Trager-Cowan, Carol; Graef, Marc De 2018-04-01 Transmission Kikuchi diffraction (TKD) has been gaining momentum as a high resolution alternative to electron back-scattered diffraction (EBSD), adding to the existing electron diffraction modalities in the scanning electron microscope (SEM). The image simulation of any of these measurement techniques requires an energy dependent diffraction model for which, in turn, knowledge of electron energies and diffraction distances distributions is required. We identify the sample-detector geometry and the effect of inelastic events on the diffracting electron beam as the important factors to be considered when predicting these distributions. However, tractable models taking into account inelastic scattering explicitly are lacking. In this study, we expand the Monte Carlo (MC) energy-weighting dynamical simulations models used for EBSD [1] and ECP [2] to the TKD case. We show that the foil thickness in TKD can be used as a means of energy filtering and compare band sharpness in the different modalities. The current model is shown to correctly predict TKD patterns and, through the dictionary indexing approach, to produce higher quality indexed TKD maps than conventional Hough transform approach, especially close to grain boundaries. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved. 5. Power Electronics as Efficient Interface of Renewable Energy Sources DEFF Research Database (Denmark) Blaabjerg, Frede; Chen, Zhe; Kjær, Søren Bækhøj 2004-01-01 renewable energy conversion system, will play an important part in our future energy supply. But other sources like microturbines, photovoltaics and fuel cell systems may also be serious contributor to the power supply. Characteristically, power electronics will be an efficient and important interface...... to the grid and this paper will first briefly discuss three different alternative/ renewable energy sources. Next, various configurations of the wind turbine technology are presented, as this technology seems to be most developed and cost-effective. Finally, the developments and requirements from the grid......The global electrical energy consumption is steadily rising and consequently there is a demand to increase the power generation capacity. A significant percentage of the required capacity increase can be based on renewable energy sources. Wind turbine technology, as the most cost effective... 6. Power Electronics as Efficient Interface of Renewable Energy Sources DEFF Research Database (Denmark) Blaabjerg, Frede; Chen, Zhe; Kjær, Søren Bækhøj 2004-01-01 to the grid and this paper will first briefly discuss three different alternative/ renewable energy sources. Next, various configurations of the wind turbine technology are presented, as this technology seems to be most developed and cost-effective. Finally, the developments and requirements from the grid......The global electrical energy consumption is steadily rising and consequently there is a demand to increase the power generation capacity. A significant percentage of the required capacity increase can be based on renewable energy sources. Wind turbine technology, as the most cost effective...... renewable energy conversion system, will play an important part in our future energy supply. But other sources like microturbines, photovoltaics and fuel cell systems may also be serious contributor to the power supply. Characteristically, power electronics will be an efficient and important interface... 7. High-energy electron impact apparatus utilizing a simple diode electron gun assembly International Nuclear Information System (INIS) Peterson, R.B.; Pidwerbekki, D. 1992-01-01 An electron impact facility based on a ribbon filament cathode, simple diode gun, and thin aluminium foil window is described. The facility is designed for the study of gas phase electron impact phenomena at pressures up to one atmosphere in a variety of gases. Of particular interest is the simple design of the electron gun for generating electron beams having energies up to 100 keV and currents up to 5 mA. The beam is magnetically collimated and directed through a thin aluminium foil which is used as the vacuum-gas interface to an impact chamber. Maximum power delivered to the impact region depends on the thickness of the foil window. Using an 8.4 μm thick aluminium foil, approximately 150 W can be delivered to the impact chamber. Thermal heating of the foil by the electron beam is the limiting factor restricting higher effective power transmission. (Author) 8. Measuring the electron beam energy in a magnetic bunch compressor International Nuclear Information System (INIS) Hacker, Kirsten 2010-09-01 Within this thesis, work was carried out in and around the first bunch compressor chicane of the FLASH (Free-electron LASer in Hamburg) linear accelerator in which two distinct systems were developed for the measurement of an electron beams' position with sub-5 μm precision over a 10 cm range. One of these two systems utilized RF techniques to measure the difference between the arrival-times of two broadband electrical pulses generated by the passage of the electron beam adjacent to a pickup antenna. The other system measured the arrival-times of the pulses from the pickup with an optical technique dependent on the delivery of laser pulses which are synchronized to the RF reference of the machine. The relative advantages and disadvantages of these two techniques are explored and compared to other available approaches to measure the same beam property, including a time-of-flight measurement with two beam arrival-time monitors and a synchrotron light monitor with two photomultiplier tubes. The electron beam position measurement is required as part of a measurement of the electron beam energy and could be used in an intra-bunch-train beam-based feedback system that would stabilize the amplitude of the accelerating field. By stabilizing the accelerating field amplitude, the arrival-time of the electron beam can be made more stable. By stabilizing the electron beam arrival-time relative to a stable reference, diagnostic, seeding, and beam-manipulation lasers can be synchronized to the beam. (orig.) 9. Energy transfer from lower energy to higher-energy electrons mediated by whistler waves in the radiation belts Science.gov (United States) Shklyar, D. R. 2017-01-01 We study the problem of energy exchange between waves and particles, which leads to energization of the latter, in an unstable plasma typical of the radiation belts. The ongoing Van Allen Probes space mission brought this problem among the most discussed in space physics. A free energy which is present in an unstable plasma provides the indispensable condition for energy transfer from lower energy particles to higher-energy particles via resonant wave-particle interaction. This process is studied in detail by the example of electron interactions with whistler mode wave packets originated from lightning-induced emission. We emphasize that in an unstable plasma, the energy source for electron energization is the energy of other particles, rather than the wave energy as is often assumed. The way by which the energy is transferred from lower energy to higher-energy particles includes two processes that operate concurrently, in the same space-time domain, or sequentially, in different space-time domains, in which a given wave packet is located. In the first process, one group of resonant particles gives the energy to the wave. The second process consists in wave absorption by another group of resonant particles, whose energy therefore increases. We argue that this mechanism represents an efficient means of electron energization in the radiation belts. 10. Application of low energy electron beam to precoated steel plates International Nuclear Information System (INIS) Koshiishi, Kenji 1989-01-01 Recently in the fields of home electric appliances, machinery and equipment and interior building materials, the needs for the precoated steel plates having the design and function of high class increase rapidly. In order to cope with such needs, the authors have advanced the examination on the application of electron beam hardening technology to precoated steel plates, and developed the precoated steel plates of high grade and high design 'Super Tecstar EB Series' by utilizing low energy electron beam. The features of this process are (1) hardening can be done at room temperature in a short time-thermally weak films can be adhered, (2) high energy irradiation-the hardening of thick enamel coating and the adhesion of colored films are feasible, (3) the use of monomers of low molecular weight-by high crosslinking, the performance of high sharpness, high hardness, anti-contamination property and so on can be given. The application to precoated steel plate production process is the coating and curing of electron beam hardening type paints, the coating of films with electron beam hardening type adhesives, and the reforming of surface polymer layers by impregnating monomers and causing graft polymerization with electron beam irradiation. The outline of the Super Tecstar EB Series is described. (K.I.) 11. Modern electron microscopy resolved in space, energy and time Science.gov (United States) Carbone, F. 2011-06-01 Recent pioneering experiments combining ultrafast lasers with electron-based technology demonstrated the possibility to obtain real-time information about chemical bonds and their dynamics during reactions and phase transformation. These techniques have been successfully applied to several states of matter including gases, liquids, solids and biological samples showing a unique versatility thanks to the high sensitivity of electrons to tiny amounts of material and their low radiation damage. A very powerful tool, the time-resolved Transmission Electron Microscope (TEM), is capable of delivering information on the structure of ordered and disordered matter through diffraction and imaging, with a spatial resolution down to the atomic limit (10-10 m); the same apparatus can distinguish dynamical phenomena happening on the time-scales between fs and ms, with a dynamic range of 12 orders of magnitude. At the same time, spectroscopic information can be obtained from the loss of kinetic energy of electrons interacting with specimens in the range of interband transitions and plasmons in solids, or charge transfers in molecules, all the way up to the atomic core levels with the same time-resolution. In this contribution, we focus on the recent advances in fs Electron Energy Loss Spectroscopy (FEELS), discussing the main results and their implications for future studies. 12. Silicon passivation study under low energy electron irradiation conditions International Nuclear Information System (INIS) Cluzel, R. 2010-01-01 Backside illuminated thinned CMOS (Complementary Metal Oxide Semiconductor) imaging system is a technology developed to increase the signal to noise ratio and the sensibility of such sensors. This configuration is adapted to the electrons detection from the energy range of [1 - 12 keV]. The impinging electron creates by multiplication several hundreds of secondary electrons close to the surface. A P ++ highly-doped passivation layer of the rear face is required to reduce the secondary electron surface recombination rate. Thanks to the potential barrier induced by the P ++ layer, the passivation layer increases the collected charges number and so the sensor collection gain. The goal of this study is to develop some experimental methods in order to determine the effect of six different passivation processes on the collection gain. Beforehand, the energy profile deposited by an incident electron is studied with the combination of Monte-Carlo simulations and some analytical calculations. The final collection gain model shows that the mirror effect from the passivation layer is a key factor at high energies whereas the passivation layer has to be as thin as possible at low energies. A first experimental setup which consists in irradiating P ++ /N large diodes allows to study the passivation process impacts on the surface recombinations. Thanks to a second setup based on a single event upset directly on thinned CMOS sensor, passivation techniques are discriminated in term of mirror effect and the implied spreading charges. The doping atoms activation laser annealing is turn out to be a multiplication gain inhomogeneity source impacting directly the matrix uniformity. (author) 13. Inverse planning of energy-modulated electron beams in radiotherapy International Nuclear Information System (INIS) Gentry, John R.; Steeves, Richard; Paliwal, Bhudatt A. 2006-01-01 The use of megavoltage electron beams often poses a clinical challenge in that the planning target volume (PTV) is anterior to other radiosensitive structures and has variable depth. To ensure that skin as well as the deepest extent of the PTV receives the prescribed dose entails prescribing to a point beyond the depth of peak dose for a single electron energy. This causes dose inhomogeneities and heightened potential for tissue fibrosis, scarring, and possible soft tissue necrosis. Use of bolus on the skin improves the entrant dose at the cost of decreasing the therapeutic depth that can be treated. Selection of a higher energy to improve dose homogeneity results in increased dose to structures beyond the PTV, as well as enlargement of the volume receiving heightened dose. Measured electron data from a linear accelerator was used as input to create an inverse planning tool employing energy and intensity modulation using bolus (e-IMRT TM ). Using tools readily available in a radiotherapy department, the applications of energy and intensity modulation on the central axis makes it possible to remove hot spots of 115% or more over the depths clinically encountered. The e-IMRT TM algorithm enables the development of patient-specific dose distributions with user-defined positions of peak dose, range, and reduced dose to points beyond the prescription point 14. Low energy electron beams for industrial and environmental applications CERN Document Server 2017-01-01 EuCARD-2 Workshop, 8-9 December 2016, Warsaw, Poland. Organizers: Science and Technology Facilities Council, UK CERN - The European Organization for Nuclear Research, Switzerland, Institute of Nuclear Chemistry and Technology, Poland, Fraunhofer Institute for Electron Beam and Plasma Technology, Germany, Warsaw University of Technology, Poland. An article presents short information about EuCARD-2 Workshop “Low energy electron beams for industrial and environmental applications”, which was held in December 2016 in Warsaw. Objectives, main topics and expected output of meeting are described. List of organizers is included. International Nuclear Information System (INIS) Yoshii, Fumio; Nagasawa, Naotsugu; Kume, Tamikazu 2003-01-01 The radiation degradations of marine polysaccharides by both gamma Co-60 and electron beam irradiations are investigated. Polysaccharides and oligosaccharides can be produced by degradation of corresponding polysaccharides including marine polysaccharides such as alginates, chitin chitosan and carrageenan. The viscosity of alginate, chitosan and carrageenan solution decreases markedly with increase of the low energy electron beam irradiation time and the beam current. Furthermore, the viscosity is reduced sharply in short time for polysaccharide solution with low concentration, for instance carrageenan solution of 1%. (author) 16. Low-energy electron scattering from molecules, biomolecules and surfaces CERN Document Server Carsky, Petr 2011-01-01 Since the turn of the 21st century, the field of electron molecule collisions has undergone a renaissance. The importance of such collisions in applications from radiation chemistry to astrochemistry has flowered, and their role in industrial processes such as plasma technology and lighting are vital to the advancement of next generation devices. Furthermore, the development of the scanning tunneling microscope highlights the role of such collisions in the condensed phase, in surface processing, and in the development of nanotechnology.Low-Energy Electron Scattering from Molecules, Biomolecule 17. Introduction to the theory of low-energy electron diffraction International Nuclear Information System (INIS) Fingerland, A.; Tomasek, M. 1975-01-01 An elementary introduction to the basic principles of the theory of low-energy electron diffraction is presented. General scattering theory is used to classify the hitherto known approaches to the problem (optical potential and one-electron approximation; formal scattering theory: Born expansion and multiple scattering; translational symmetry: Ewald construction; classification of LEED theories by means of the T matrix; pseudokinematical theory for crystal with clean surface and with an adsorbed monomolecular layer; dynamical theory; inclusion of inelastic collisions; discussion of a simple example by means of the band-structure approach) 18. Low energy intense electron beams with extra-low energy spread International Nuclear Information System (INIS) Aleksandrov, A.V.; Calabrese, R.; Ciullo, G.; Dikansky, N.S.; Guidi, V.; Kot, N.C.; Kudelainen, V.I.; Lamanna, G.; Lebedev, V.A.; Logachov, P.V.; Tecchio, L.; Yang, B. 1994-01-01 Maximum achievable intensity for low energy electron beams is a feature that is not very often compatible with low energy spread. We show that a proper choice of the source and the acceleration optics allows one to match them together. In this scheme, a GaAs photocathode excited by a single-mode infrared laser and adiabatic acceleration in fully magnetised optics enables the production of a low-energy-spread electron beam with relatively high intensity. The technological problems associated with the method are discussed together with its limitations. (orig.) 19. Electron energy distribution function, effective electron temperature, and dust charge in the temporal afterglow of a plasma Energy Technology Data Exchange (ETDEWEB) Denysenko, I. B.; Azarenkov, N. A. [School of Physics and Technology, V. N. Karazin Kharkiv National University, Svobody sq. 4, 61022 Kharkiv (Ukraine); Kersten, H. [Institut für Experimentelle und Angewandte Physik, Leibnizstr. 19, Kiel D-24098 (Germany) 2016-05-15 Analytical expressions describing the variation of electron energy distribution function (EEDF) in an afterglow of a plasma are obtained. Especially, the case when the electron energy loss is mainly due to momentum-transfer electron-neutral collisions is considered. The study is carried out for different EEDFs in the steady state, including Maxwellian and Druyvesteyn distributions. The analytical results are not only obtained for the case when the rate for momentum-transfer electron-neutral collisions is independent on electron energy but also for the case when the collisions are a power function of electron energy. Using analytical expressions for the EEDF, the effective electron temperature and charge of the dust particles, which are assumed to be present in plasma, are calculated for different afterglow durations. An analytical expression for the rate describing collection of electrons by dust particles for the case when the rate for momentum-transfer electron-neutral collisions is independent on electron energy is also derived. The EEDF profile and, as a result, the effective electron temperature and dust charge are sufficiently different in the cases when the rate for momentum-transfer electron-neutral collisions is independent on electron energy and when the rate is a power function of electron energy. 20. Electron energy-loss spectroscopy of coupled plasmonic systems: beyond the standard electron perspective Science.gov (United States) Bernasconi, G. D.; Flauraud, V.; Alexander, D. T. L.; Brugger, J.; Martin, O. J. F.; Butet, J. 2016-09-01 Electron energy-loss spectroscopy (EELS) has become an experimental method of choice for the investigation of localized surface plasmon resonances, allowing the simultaneous mapping of the associated field distributions and their resonant energies with a nanoscale spatial resolution. The experimental observations have been well-supported by numerical models based on the computation of the Lorentz force acting on the impinging electrons by the scattered field. However, in this framework, the influence of the intrinsic properties of the plasmonic nanostructures studied with the electron energy-loss (EEL) measurements is somehow hidden in the global response. To overcome this limitation, we propose to go beyond this standard, and well-established, electron perspective and instead to interpret the EELS data using directly the intrinsic properties of the nanostructures, without regard to the force acting on the electron. The proposed method is particularly well-suited for the description of coupled plasmonic systems, because the role played by each individual nanoparticle in the observed EEL spectrum can be clearly disentangled, enabling a more subtle understanding of the underlying physical processes. As examples, we consider different plasmonic geometries in order to emphasize the benefits of this new conceptual approach for interpreting experimental EELS data. In particular, we use it to describe results from samples made by traditional thin film patterning and by arranging colloidal nanostructures. 1. Energy analyzer for Auger electron spectroscopy and low-energy backscattering ion spectroscopy International Nuclear Information System (INIS) Volkov, S.S.; Gorelik, V.A.; Gutenko, V.T.; Protopopov, O.D.; Trubitsin, A.A.; Shuvalova, Z.A.; Yakushev, G.A. 1988-01-01 Energy analyzer for electron Auger spectroscopy and low-energy backscattering ion spectroscopy is described. Analyzer presents one-cascade variant of cylindrical mirror with second-order focusing. Energy relative resolution is continuously adjusted within 0.2-1.2% limits. Signal/noise relation by Cu Auger-line at 1 muA current of exciting beam changes upper limit of range 150-450 2. Anisotropic plasmons, excitons, and electron energy loss spectroscopy of phosphorene Science.gov (United States) Ghosh, Barun; Kumar, Piyush; Thakur, Anmol; Chauhan, Yogesh Singh; Bhowmick, Somnath; Agarwal, Amit 2017-07-01 In this article, we explore the anisotropic electron energy loss spectrum (EELS) in monolayer phosphorene based on ab initio time-dependent density-functional-theory calculations. Similarly to black phosphorus, the EELS of undoped monolayer phosphorene is characterized by anisotropic excitonic peaks for energies in the vicinity of the band gap and by interband plasmon peaks for higher energies. On doping, an additional intraband plasmon peak also appears for energies within the band gap. Similarly to other two-dimensional systems, the intraband plasmon peak disperses as ωpl∝√{q } in both the zigzag and armchair directions in the long-wavelength limit and deviates for larger wave vectors. The anisotropy of the long-wavelength plasmon intraband dispersion is found to be inversely proportional to the square root of the ratio of the effective masses: ωpl(q y ̂) /ωpl(q x ̂) =√{mx/my } . 3. EELOSS: the program for calculation of electron energy loss data International Nuclear Information System (INIS) Tanaka, Shun-ichi 1980-10-01 A computer code EELOSS has been developed to obtain the electron energy loss data required for shielding and dosimetry of beta- and gamma-rays in nuclear plants. With this code, the following data are obtainable for any energy from 0.01 to 15 MeV in any medium (metal, insulator, gas, compound, or mixture) composed of any choice of 69 elements with atomic number 1 -- 94: a) Collision stopping power, b) Restricted collision stopping power, c) Radiative stopping power, and d) Bremsstrahlung production cross section. The availability of bremsstrahlung production cross section data obtained by the EELOSS code is demonstrated by the comparison of calculated gamma-ray spectrum with measured one in Pb layer, where electron-photon cascade is included implicitly. As a result, it is concluded that the uncertainty in the bremsstrahlung production cross sections is negligible in the practical shielding calculations of gamma rays of energy less than 15 MeV, since the bremsstrahlung production cross sections increase with the gamma-ray energy and the uncertainty for them decreases with increasing the gamma-ray energy. Furthermore, the accuracy of output data of the EELOSS code is evaluated in comparison with experimental data, and satisfactory agreements are observed concerning the stopping power. (J.P.N.) 4. Narrow beam dosimetry for high-energy hadrons and electrons CERN Document Server Pelliccioni, M; Ulrici, Luisa 2001-01-01 Organ doses and effective dose were calculated with the latest version of the Monte Carlo transport code FLUKA in the case of an anthropomorphic mathematical model exposed to monoenergetic narrow beams of protons, pions and electrons in the energy range 10°— 400 GeV. The target organs considered were right eye, thyroid, thymus, lung and breast. Simple scaling laws to the calculated values are given. The present data and formula should prove useful for dosimetric estimations in case of accidental exposures to high-energy beams. 5. LDRD project 151362 : low energy electron-photon transport. Energy Technology Data Exchange (ETDEWEB) Kensek, Ronald Patrick; Hjalmarson, Harold Paul; Magyar, Rudolph J.; Bondi, Robert James; Crawford, Martin James 2013-09-01 At sufficiently high energies, the wavelengths of electrons and photons are short enough to only interact with one atom at time, leading to the popular %E2%80%9Cindependent-atom approximation%E2%80%9D. We attempted to incorporate atomic structure in the generation of cross sections (which embody the modeled physics) to improve transport at lower energies. We document our successes and failures. This was a three-year LDRD project. The core team consisted of a radiation-transport expert, a solid-state physicist, and two DFT experts. 6. Pulse energy control through dual loop electronic feedback CSIR Research Space (South Africa) Jacobs, Cobus 2006-07-01 7. Exchange energy of inhomogenous electron gas near a metal surface International Nuclear Information System (INIS) Miglio, L.; Tosi, M.P.; March, N.H. 1980-12-01 Using the first-order density matrix of an infinite-barrier model of a metal surface, the exchange energy density can be evaluated exactly as a function of distance z from the barrier. This result is compared with the local approximation -3/4e 2 (3/π)sup(1/3) rhosup(4/3)(z) where rho is the electron density in the model. The local approximation is demonstrated to be quantitatively accurate at all z. The integrated surface exchange energy is given to within 3% by the local theory. (author) 8. Power Electronics for Renewable Energy Systems - Status and Trends DEFF Research Database (Denmark) Blaabjerg, Frede; Ma, Ke; Yang, Yongheng 2014-01-01 In the past few decades, the energy paradigms in many countries are experiencing significant change from fossil-based resources to cleaner renewables. It is expected that the scenario of highly penetrated renewables is going to be further enhanced. This requires that the production, distribution...... electronics in generation, transmission/distribution and end-user application, together with advanced controls, can pave the way for renewable energy resources. In view of this, some of the most promising renewable candidates like wind power and photovoltaic, which are becoming a significant part... 9. Construction of an energy selector for slow electrons International Nuclear Information System (INIS) Chatel, S. 1968-01-01 After a presentation of the principles on which are built mono-kinetic electron selectors and the difficulties peculiar to low energies, a review of the equipment built by other authors is given. The apparatus described here uses a cylindrical condenser with an angle of π/2. It can be fitted to a mass spectrometer. The measurements carried out with an analyzer identical to the selector show the separating power to be between 0.12 and 0. 14 V for energies of between 6 and 42 V. (author) [fr 10. Experimental investigation about energy balance of electron emission from materials under electron impacts at low energy: application to silver, graphite and SiO2 Science.gov (United States) Villemant, M.; Sarrailh, P.; Belhaj, M.; Garrigues, L.; Boniface, C. 2017-12-01 The energy balance measurement of electron emission at a wall submitted to electron impact at low incident energy is a topic of interest for miscellaneous technological applications. This article points out the experimental protocol, biases corrections and post-process needed to obtain reproducible and quantitative electron emission measurements. The measurements have been performed for incident electrons energy between 5 eV and 105 eV and for three samples materials: silver, graphite and SiO2. These measurements show that wall absorbs more energy at high incident electrons energy and that graphite absorbs more energy than silver, than SiO2. Results are presented for mono-energetic incident electron beam and for a Lambertian energy distribution. Analytical laws fitted from experimental results and applicable for modelling issue are proposed for a Lambertian distribution of incident electrons. 11. LEETECH facility as a flexible source of low energy electrons CERN Document Server Attie, D; Bezshyyko, O; Burmistrov, L; Chaus, A; Colas, P; Fedorchuk, O; Golinka-Bezshyyko, L; Kadenko, I; Krylov, V; Kubytskyi, V; Lopez, R; Monard, H; Rodin, V; Titov, M; Tomassini, D; Variola, A 2016-01-01 A new versatile facility LEETECH for detector R&D, tests and calibration is designed and constructed. It uses electrons produced by the photoinjector PHIL at LAL, Orsay and provides a powerful tool for wide range R&D studies of different detector concepts delivering "mono-chromatic" samples of low energy electrons with adjustable energy and intensity. Among other innovative instrumentation techniques, LEETECH will be used for testing various gaseous tracking detectors and studying new Micromegas/InGrid concept which has very promising characteristics of spatial resolution and can be a good candidate for particle tracking and identification. In this paper the importance and expected characteristics of such facility based on detailed simulation studies are addressed. 12. Recommended Auger-electron kinetic energies for 42 elemental solids International Nuclear Information System (INIS) Powell, C.J. 2010-01-01 An analysis is presented of Auger-electron kinetic energies (KEs) from four data sources for 65 Auger transitions in 45 elemental solids. For each data source, a single instrument had been used to measure KEs for many elements. In order to compare KEs from two sources, it was necessary to recalibrate the energy scales of each instrument using recommended reference data. Mean KEs are given for most of the Auger transitions for which there were at least two independent measurements and for which differences from the mean KEs were considered acceptably small. In several cases, comparisons were made to published KE data to resolve discrepancies. We are able to recommend mean KEs for 59 Auger transitions from 42 elemental solids and to provide estimates of the uncertainties of these KEs. This compilation should be useful for the determination of chemical shifts of Auger peaks in Auger electron spectroscopy and X-ray photoelectron spectroscopy. 13. General theory for environmental effects on (vertical) electronic excitation energies. Science.gov (United States) Schwabe, Tobias 2016-10-21 Almost 70 years ago, the first theoretical model for environmental effects on electronic excitation energies has been derived. Since then, several different interpretations and refined models have been proposed for the perichromic shift of a chromophore due to its surrounding medium. Some of these models are contradictory. Here, the contributing terms are derived within the framework of long-range perturbation theory with the least approximations so far. The derivation is based on a state-specific interpretation of the interaction energies and all terms can be identified with individual properties of either the chromophore or the surroundings, respectively. Further, the much debated contribution due to transition moments coupled to the environment can be verified in the form of a non-resonant excitonic coupling to the dynamic polarizabilities in the environment. These general insights should clarify discussions and interpretations of environmental effects on electronic excitations and should foster the development of new models for the computation of these effects. 14. Imaging and electron energy-loss spectroscopy using single nanosecond electron pulses. Science.gov (United States) Picher, Matthieu; Bücker, Kerstin; LaGrange, Thomas; Banhart, Florian 2018-03-13 We implement a parametric study with single electron pulses having a 7 ns duration to find the optimal conditions for imaging, diffraction, and electron energy-loss spectroscopy (EELS) in the single-shot approach. Photoelectron pulses are generated by illuminating a flat tantalum cathode with 213 nm nanosecond laser pulses in a 200 kV transmission electron microscope (TEM) with thermionic gun and Wehnelt electrode. For the first time, an EEL spectrometer is used to measure the energy distribution of single nanosecond electron pulses which is crucial for understanding the ideal imaging conditions of the single-shot approach. By varying the laser power, the Wehnelt bias, and the condenser lens settings, the optimum TEM operation conditions for the single-shot approach are revealed. Due to space charge and the Boersch effect, the energy width of the pulses under maximized emission conditions is far too high for imaging or spectroscopy. However, by using the Wehnelt electrode as an energy filter, the energy width of the pulses can be reduced to 2 eV, though at the expense of intensity. The first EEL spectra taken with nanosecond electron pulses are shown in this study. With 7 ns pulses, an image resolution of 25 nm is attained. It is shown how the spherical and chromatic aberrations of the objective lens as well as shot noise limit the resolution. We summarize by giving perspectives for improving the single-shot time-resolved approach by using aberration correction. Copyright © 2018 Elsevier B.V. All rights reserved. 15. Electron Beam Energy Compensation by Controlling RF Pulse Shape CERN Document Server Kii, T; Kusukame, K; Masuda, K; Nakai, Y; Ohgaki, H; Yamazaki, T; Yoshikawa, K; Zen, H 2005-01-01 We have studied on improvement of electron beam macropulse properties from a thermionic RF gun. Though a thermionic RF gun has many salient features, there is a serious problem that back-bombardment effect worsens quality of the beam. To reduce beam energy degradation by this effect, we tried to feed non-flat RF power into the gun. As a result, we successfully obtained about 1.5 times longer macropulse and two times larger total charge per macropulse. On the other hand, we calculated transient evolution of RF power considering non-constant beam loading. The beam loading is evaluated from time evolution of cathode temperature, by use of one dimensional heat conduction model and electron trajectories' calculations by a particle simulation code. Then we found good agreement between the experimental and calculation results. Furthermore, with the same way, we studied the electron beam output dependence on the cathode radius. 16. Theoretical characterization of electron energy distribution function in RF plasmas International Nuclear Information System (INIS) Capitelli, M.; Capriati, G.; Dilonardo, M.; Gorse, C.; Longo, S. 1993-01-01 Different methods for the modeling of low-temperature plasmas of both technological and fundamental interest are discussed. The main concept of all these models is the electron energy distribution function (eedf) which is necessary to calculate the rate coefficients for any chemical reaction involving electrons. Results of eedf calculations in homogeneous SF 6 and SiH 4 plasmas are discussed based on solution of the time-dependent Boltzmann equation. The space-dependent eedf in an RF discharge in He is calculated taking into account the sheath oscillations by a Monte Carlo model assuming the plasma heating mechanism and the electric field determined by using a fluid model. The need to take into account the ambipolar diffusion of electrons in RF discharge modeling is stressed. A self-consistent model based on coupling the equations of the fluid model and the chemical kinetics ones is presented. (orig.) 17. Nanobiotechnology in energy, environment and electronics methods and applications CERN Document Server Nicolini, Claudio 2015-01-01 Introduction: Present Challenges and Future Solutions via Nanotechnology for Electronics, Environment and Energy; Claudio NicoliniPart A: MethodsInfluence of Chromosome Translocation on Yeast Life Span: Implications for Long-Term Industrial Biofermentation; Jason Sims, Dmitri Nikitin, and Carlo V. BruschiPulsed Power Nanotechnologies for Disintegration and Breaking Up of Refractory Precious Metals Ores; Valentin A. Chanturiya and Igor Zh. BuninModeling of Software Sensors in Bioprocess; Luca Belmonte and Claudio NicoliniN 18. Parity nonconservation in polarized electron scattering at high energies Energy Technology Data Exchange (ETDEWEB) Prescott, C.Y. 1979-10-01 Recent observations of parity violation in inelastic scattering of electrons at high energy is discussed with reference to the process e(polarized) + D(unpolarized) ..-->.. e + X. The kinetics of this process, the idealized case of scattering from free quark targets, experimental techniques and results, and relations to atomic physics of parity violation in bismuth and thallium atoms with a model independent analysis. 17 references. (JFP) 19. Parity nonconservation in polarized electron scattering at high energies International Nuclear Information System (INIS) Prescott, C.Y. 1979-10-01 Recent observations of parity violation in inelastic scattering of electrons at high energy is discussed with reference to the process e(polarized) + D(unpolarized) → e + X. The kinetics of this process, the idealized case of scattering from free quark targets, experimental techniques and results, and relations to atomic physics of parity violation in bismuth and thallium atoms with a model independent analysis. 17 references 20. Practical Use of Scanning Low Energy Electron Microscope (SLEEM) Czech Academy of Sciences Publication Activity Database Müllerová, Ilona; Mikmeková, Eliška; Mikmeková, Šárka; Konvalina, Ivo; Frank, Luděk 2016-01-01 Roč. 22, S3 (2016), s. 1650-1651 ISSN 1431-9276 R&D Projects: GA TA ČR(CZ) TE01020118; GA MŠk(CZ) LO1212; GA MŠk ED0017/01/01 Institutional support: RVO:68081731 Keywords : scanning low energy * SLEEM Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.891, year: 2016 1. Experimental electron binding energies for thulium in different matrices Czech Academy of Sciences Publication Activity Database Inoyatov, A. K.; Kovalík, Alojz; Filosofov, D. V.; Ryšavý, Miloš; Perevoshchikov, L. L.; Yushkevich, Yu. V.; Zbořil, M. 2015-01-01 Roč. 202, JUL (2015), s. 46-55 ISSN 0368-2048 R&D Projects: GA MŠk LG14004; GA ČR(CZ) GAP203/12/1896 Institutional support: RVO:61389005 Keywords : Tm-169 * (169)yb * atomic environment * electron binding energy * chemical shift * natural atomic level width Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.561, year: 2015 2. Nanocellulose as Material Building Block for Energy and Flexible Electronics Science.gov (United States) Hu, Liangbing 2014-03-01 In this talk, I will discuss the fabrications, properties and device applications of functional nanostructured paper based on nanocellulose. Nanostructures with tunable optical, electrical, ionic and mechanical properties will be discussed. Lab-scale demonstration devices, including low-cost Na-ion batteries, microbial fuel cells, solar cells, transparent transistors, actuators and touch screens will be briefly mentioned. These studies show that nanocellulose is a promising green material for electronics and energy devices. 3. Direct angle resolved photoemission spectroscopy and ... [3] Karl Alex Mueller, personal communications (2006). In contrast, see P W Anderson, Nature Phys. 2, 626 (2006) or the whole issue Nature. Phys. - 20 years of HTSC (March 2006). [4] G Baskaran, personal communication, Kanpur (2006), also CM9910161v1. [5] T Timusk and B Statt, Rep. Prog. Phys. 62(1), 61 (1999). 4. Direct angle resolved photoemission spectroscopy and ... We gratefully acknowledge financial support by the EPFL and the Swiss National. Fund for Scientific Research. This work is based upon research conducted at the. Synchrotron Radiation Center, University of Wisconsin-Madison, which is sup- ported by the NSF under Award No. DMR-0084402. DP gratefully acknowledges. 5. Angle-resolved catholdoluminescence imaging polarimetry NARCIS (Netherlands) Osorio, C.I.; Coenen, T.; Brenny, B.J.M.; Polman, A.; Koenderink, A.F. 2015-01-01 Cathodoluminescence spectroscopy (CL) allows characterizing light emission in bulk and nanostructured materials and is a key tool in fields ranging from materials science to nanophotonics. Previously, CL measurements focused on the spectral content and angular distribution of emission, while the 6. Imaging properties and energy aberrations of a double-pass cylindrical-mirror electron energy analyzer International Nuclear Information System (INIS) Erickson, N.E.; Powell, C.J. 1986-01-01 The imaging properties and energy aberrations of a commercial double-pass cylindrical-mirror analyzer have been characterized using an extension of the method recently reported by Seah and Mathieu. The electron beam from the coaxial electron gun was rastered across a test surface and the intensity of either elastically scattered electrons or of electrons at other selected energies was stored in a computer as a function of beam position on the specimen and other experimental parameters. The intensity data were later plotted to provide an ''image'' of the detected intensity. Images of this type are presented for electron energies of 100, 500, and 1000 eV and for the application of small offset voltages (typically between -1 and +5 V) between the analyzer and the gun cathode with the instrument operated in conditions appropriate for XPS or AES. Small offset voltages ( or approx. =5 V) lead to image shapes similar to those for the elastic peak but with 20%--40% increased widths. Deflection of the incident beam by up to 2 mm from the axis caused variations of up to +-0.15 eV in the measured positions of the elastic peak. Our observations can be interpreted qualitatively in terms of the known relationship between detected signal and combinations of position of electron emission from the specimen, angle of emission, and electron energy. The images obtained with elastically and inelastically scattered electrons provide a convenient and quantitative means of assessing instrument performance and of defining the specimen area being analyzed for the particular combination of instrument operating conditions and the energy width of AES or XPS features from the specimen 7. Low energy electron scattering from atoms: Search for nanocatalysts Science.gov (United States) Msezane, A. Z.; Felfli, Z.; Sokolovski, D. 2011-05-01 Manipulating the structure and the dynamics of metallic nanoparticles, attractive due to their optical, electronic and magnetic properties, including applications in catalysis, requires a fundamental understanding of the dynamic processes at the atomic level. The fundamental mechanism of catalysis at the atomic scale has already been proposed and demonstrated in Au, Pd and Au-Pd catalysis of H2O2 through the scrutiny of low energy electron elastic total cross sections (TCSs). The use of mixed precious metal catalysts can produce even higher activities compared to Au alone. Here the interplay between negative ion resonances and Ramsauer-Townsend minima that characterize low energy electron TCSs for Au is identified as the fundamental signature of nanoscale catalysts. Calculated electron elastic TCSs for Ag, Pt, Pd, Ru and Y atoms are presented as illustrations. The recent complex angular momentum methodology is used for the calculations. It is concluded that these atoms are suitable candidates for nanocatalysts individually or in combinations. Supported by U.S. DOE, AFOSR and CAU CFNM, NSF-CREST. 8. A generalized electron energy probability function for inductively coupled plasmas under conditions of nonlocal electron kinetics Science.gov (United States) Mouchtouris, S.; Kokkoris, G. 2018-01-01 A generalized equation for the electron energy probability function (EEPF) of inductively coupled Ar plasmas is proposed under conditions of nonlocal electron kinetics and diffusive cooling. The proposed equation describes the local EEPF in a discharge and the independent variable is the kinetic energy of electrons. The EEPF consists of a bulk and a depleted tail part and incorporates the effect of the plasma potential, Vp, and pressure. Due to diffusive cooling, the break point of the EEPF is eVp. The pressure alters the shape of the bulk and the slope of the tail part. The parameters of the proposed EEPF are extracted by fitting to measure EEPFs (at one point in the reactor) at different pressures. By coupling the proposed EEPF with a hybrid plasma model, measurements in the gaseous electronics conference reference reactor concerning (a) the electron density and temperature and the plasma potential, either spatially resolved or at different pressure (10-50 mTorr) and power, and (b) the ion current density of the electrode, are well reproduced. The effect of the choice of the EEPF on the results is investigated by a comparison to an EEPF coming from the Boltzmann equation (local electron kinetics approach) and to a Maxwellian EEPF. The accuracy of the results and the fact that the proposed EEPF is predefined renders its use a reliable alternative with a low computational cost compared to stochastic electron kinetic models at low pressure conditions, which can be extended to other gases and/or different electron heating mechanisms. 9. Electron-beam broadening in amorphous carbon films in low-energy scanning transmission electron microscopy. Science.gov (United States) Drees, H; Müller, E; Dries, M; Gerthsen, D 2018-02-01 Resolution in scanning transmission electron microscopy (STEM) is ultimately limited by the diameter of the electron beam. The electron beam diameter is not only determined by the properties of the condenser lens system but also by electron scattering in the specimen which leads to electron-beam broadening and degradation of the resolution with increasing specimen thickness. In this work we introduce a new method to measure electron-beam broadening which is based on STEM imaging with a multi-segmented STEM detector. We focus on STEM at low electron energies between 10 and 30 keV and use an amorphous carbon film with known thickness as test object. The experimental results are compared with calculated beam diameters using different analytical models and Monte-Carlo simulations. We find excellent agreement of the experimental data with the recently published model by Gauvin and Rudinsky [1] for small t/λ el (thickness to elastic mean free path) values which are considered in our study. Copyright © 2017 Elsevier B.V. All rights reserved. 10. Spatial structure determination of ({radical}3 x {radical}3)R30{degrees} and (1.5 x 1.5)R18{degrees}CO on Cu(111) using angle-resolved photoemission extended fine structure Energy Technology Data Exchange (ETDEWEB) Moler, E.J.; Kellar, S.A.; Huff, W.R.A. [Lawrence Berkeley National Lab., CA (United States)] [and others 1997-04-01 The authors report a study of the spatial structure of ({radical}3 x {radical}3)R30{degrees} (low coverage) and (1.5 x 1.5)R18{degrees} (intermediate coverage) CO adsorbed on Cu(111), using the Angle-Resolved Photoemission Extended Fine Structure (ARPEFS) technique at beamline 9.3.2 at the Advanced Light Source. The CO molecule adsorbs on an atop site for both adsorption phases. Full multiple-scattering spherical-wave (MSSW) calculations were used to extract the C-Cu. bond length and the first Cu-Cu layer spacing for each adsorption phase. The authors find that the C-Cu bond length remains unchanged with increasing coverage, but the 1st Cu-Cu layer spacing contracts at the intermediate coverage. They calculate the bending mode force constant in the (1.5 x 1.5)R18{degrees} phase to be K{sub {delta}} = 2.2 (1) x 10{sup {minus}12} dyne-cm/rad from their experimentally determined bond lengths combined with previously published infra-red absorption frequencies. 11. Electron energy distributions in a magnetized inductively coupled plasma International Nuclear Information System (INIS) Song, Sang-Heon; Yang, Yang; Chabert, Pascal; Kushner, Mark J. 2014-01-01 Optimizing and controlling electron energy distributions (EEDs) is a continuing goal in plasma materials processing as EEDs determine the rate coefficients for electron impact processes. There are many strategies to customize EEDs in low pressure inductively coupled plasmas (ICPs), for example, pulsing and choice of frequency, to produce the desired plasma properties. Recent experiments have shown that EEDs in low pressure ICPs can be manipulated through the use of static magnetic fields of sufficient magnitudes to magnetize the electrons and confine them to the electromagnetic skin depth. The EED is then a function of the local magnetic field as opposed to having non-local properties in the absence of the magnetic field. In this paper, EEDs in a magnetized inductively coupled plasma (mICP) sustained in Ar are discussed with results from a two-dimensional plasma hydrodynamics model. Results are compared with experimental measurements. We found that the character of the EED transitions from non-local to local with application of the static magnetic field. The reduction in cross-field mobility increases local electron heating in the skin depth and decreases the transport of these hot electrons to larger radii. The tail of the EED is therefore enhanced in the skin depth and depressed at large radii. Plasmas densities are non-monotonic with increasing pressure with the external magnetic field due to transitions between local and non-local kinetics 12. Electron energy-loss spectroscopy on fullerenes and fullerene compounds International Nuclear Information System (INIS) Armbruster, J. 1996-03-01 A few years ago, a new form of pure carbon, the fullerenes, has been discovered, which shows many fascinating properties. Within this work the spatial and electronic structure of some selected fullerene compounds have been investigated by electron-energy-loss spectroscopy in transmission. Phase pure samples of alkali intercalated fullerides A x C 60 (A=Na, K, Cs) have been prepared using vacuum distillation. Measruements of K 3 C 60 show a dispersion of the charge carrier plasmon close to zero. This can be explained by calculations, which take into account both band structure and local-field (inhomogeneity) effects. The importance of the molecular structure can also be seen from the A 4 C 60 compounds, where the non-metallic properties are explained by a splitting of the t 1u and t 1g derived bands that is caused by electron-correlation and Jahn-Teller effects. First measurements of the electronic structure of Na x C 60 (x>6) are presented and reveal a complete transfer from the sodium atoms but an incomplete transfer onto the C 60 molecules. This behaviour can be explained by taking into account additional electronic states that are situated between the sodium atoms in the octahedral sites and are predicted by calculations using local density approximation. The crystal structure of the higher fullerenes C 76 and C 84 is found to be face-centered cubic 13. Spin polarization effects in low-energy elastic electron scattering International Nuclear Information System (INIS) Beerlage, M.J.M. 1982-01-01 This work describes experiments on the role of spin polarization in elastic electron scattering. Chapter I introduces the topic and in chapter II elastic scattering of 10-50 eV electrons from Ar and Kr in the angular range between 40 0 and 110 0 is studied. Noble gases have been chosen as targets in view of their relative theoretical simplicity. Below 25 eV scattered intensities measured by various authors exhibit severe disagreements. However, in the entire energy range, the spin polarization results can reasonably well be used to point out the shortcomings of the available theoretical data. The main topic of chapter III is the first attempt to determine the magnitude of a polarization phenomenon - in elastic electron scattering from the optically active camphor molecule - of which the existence has recently been predicted qualitatively from the absence of parity symmetry in such molecules. Besides these studies on gaseous targets the author has initiated a scattering experiment on crystal surfaces, using spin polarized electrons. Within the framework of this project a large new experimental arrangement has been built up. It consists of a spin polarized electron source and a LEED scattering chamber. Design, construction and test results, showing the usefulness of the set-up, are described in the last chapter. (Auth.) 14. Simulating electron energy loss spectroscopy with the MNPBEM toolbox Science.gov (United States) Hohenester, Ulrich 2014-03-01 Within the MNPBEM toolbox, we show how to simulate electron energy loss spectroscopy (EELS) of plasmonic nanoparticles using a boundary element method approach. The methodology underlying our approach closely follows the concepts developed by García de Abajo and coworkers (Garcia de Abajo, 2010). We introduce two classes eelsret and eelsstat that allow in combination with our recently developed MNPBEM toolbox for a simple, robust, and efficient computation of EEL spectra and maps. The classes are accompanied by a number of demo programs for EELS simulation of metallic nanospheres, nanodisks, and nanotriangles, and for electron trajectories passing by or penetrating through the metallic nanoparticles. We also discuss how to compute electric fields induced by the electron beam and cathodoluminescence. Catalogue identifier: AEKJ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKJ_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 38886 No. of bytes in distributed program, including test data, etc.: 1222650 Distribution format: tar.gz Programming language: Matlab 7.11.0 (R2010b). Computer: Any which supports Matlab 7.11.0 (R2010b). Operating system: Any which supports Matlab 7.11.0 (R2010b). RAM:≥1 GB Classification: 18. Catalogue identifier of previous version: AEKJ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 370 External routines: MESH2D available at www.mathworks.com Does the new version supersede the previous version?: Yes Nature of problem: Simulation of electron energy loss spectroscopy (EELS) for plasmonic nanoparticles. Solution method: Boundary element method using electromagnetic potentials. Reasons for new version: The new version of the toolbox includes two additional classes for the simulation of electron energy 15. Structure, electronic properties and electron energy loss spectra of transition metal nitride films Energy Technology Data Exchange (ETDEWEB) Koutsokeras, L.E.; Matenoglou, G.M.; Patsalas, P., E-mail: [email protected] 2013-01-01 We present a thorough and critical study of the electronic properties of the mononitrides of the group IV–V–VI metals (TiN, ZrN, HfN, NbN, TaN, MoN, and WN) grown by Pulsed Laser Deposition (PLD). The microstructure and density of the films have been studied by X-Ray Diffraction (XRD) and Reflectivity (XRR), while their optical properties were investigated by spectral reflectivity at vertical incidence and in-situ reflection electron energy loss spectroscopy (R-EELS). We report the R-EELS spectra for all the binary TMN and we identify their features (metal-d plasmon and N-p + metal-d loss) based on previous ab-initio band structure calculations. The spectral positions of p + d loss peak are rationally grouped according to the electron configuration (i.e. of the respective quantum numbers) of the constituent metal. The assigned and reported R-EELS spectra can be used as a reference database for the colloquial in-situ surface analysis performed in most laboratories. - Highlights: ► Identification of the effect of ionization potential to the structure of PLD nitride films. ► Report of low energy electron loss spectra of NbN, MoN, HfN, TaN, WN. ► Correlation of the Np+Med loss peak with the metal’s valence electron configuration. 16. Measuring the electron beam energy in a magnetic bunch compressor Energy Technology Data Exchange (ETDEWEB) Hacker, Kirsten 2010-09-15 Within this thesis, work was carried out in and around the first bunch compressor chicane of the FLASH (Free-electron LASer in Hamburg) linear accelerator in which two distinct systems were developed for the measurement of an electron beams' position with sub-5 {mu}m precision over a 10 cm range. One of these two systems utilized RF techniques to measure the difference between the arrival-times of two broadband electrical pulses generated by the passage of the electron beam adjacent to a pickup antenna. The other system measured the arrival-times of the pulses from the pickup with an optical technique dependent on the delivery of laser pulses which are synchronized to the RF reference of the machine. The relative advantages and disadvantages of these two techniques are explored and compared to other available approaches to measure the same beam property, including a time-of-flight measurement with two beam arrival-time monitors and a synchrotron light monitor with two photomultiplier tubes. The electron beam position measurement is required as part of a measurement of the electron beam energy and could be used in an intra-bunch-train beam-based feedback system that would stabilize the amplitude of the accelerating field. By stabilizing the accelerating field amplitude, the arrival-time of the electron beam can be made more stable. By stabilizing the electron beam arrival-time relative to a stable reference, diagnostic, seeding, and beam-manipulation lasers can be synchronized to the beam. (orig.) 17. Resolving runaway electron distributions in space, time, and energy Science.gov (United States) Paz-Soldan, C.; Cooper, C. M.; Aleynikov, P.; Eidietis, N. W.; Lvovskiy, A.; Pace, D. C.; Brennan, D. P.; Hollmann, E. M.; Liu, C.; Moyer, R. A.; Shiraki, D. 2018-05-01 Areas of agreement and disagreement with present-day models of runaway electron (RE) evolution are revealed by measuring MeV-level bremsstrahlung radiation from runaway electrons (REs) with a pinhole camera. Spatially resolved measurements localize the RE beam, reveal energy-dependent RE transport, and can be used to perform full two-dimensional (energy and pitch-angle) inversions of the RE phase-space distribution. Energy-resolved measurements find qualitative agreement with modeling on the role of collisional and synchrotron damping in modifying the RE distribution shape. Measurements are consistent with predictions of phase-space attractors that accumulate REs, with non-monotonic features observed in the distribution. Temporally resolved measurements find qualitative agreement with modeling on the impact of collisional and synchrotron damping in varying the RE growth and decay rate. Anomalous RE loss is observed and found to be largest at low energy. Possible roles for kinetic instability or spatial transport to resolve these anomalies are discussed. 18. Power electronics for renewable and distributed energy systems a sourcebook of topologies, control and integration CERN Document Server Chakraborty, Sudipta; Kramer, William E 2013-01-01 While most books approach power electronics and renewable energy as two separate subjects, Power Electronics for Renewable and Distributed Energy Systems takes an integrative approach; discussing power electronic converters topologies, controls and integration that are specific to the renewable and distributed energy system applications. An overview of power electronic technologies is followed by the introduction of various renewable and distributed energy resources that includes photovoltaics, wind, small hydroelectric, fuel cells, microturbines and variable speed generation. Energy storage s 19. Low Energy Electrons as Probing Tool for Astrochemical Reaction Mechanisms Science.gov (United States) Hendrik Bredehöft, Jan; Swiderek, Petra; Hamann, Thorben 20. Radiation processing of natural polymers using low energy electron beam International Nuclear Information System (INIS) Kume, Tamikazu 2004-01-01 Radiation processing is widely used in Japan and the economic scale of radiation application amounted to about 71 b$(ratio relative to GDP: 1.7%) in total. It consisted of 60 b$ (85%) in industry, 10 b$(14%) in medicine and 1 b$ (1%) in agriculture. Irradiation using gamma-ray from 60 Co and electron beam is commercially used for the sterilization and modification of materials. Utilization of natural polymers by radiation has been investigated for recycling the natural resources and reducing the environmental pollution. Polysaccharides such as chitosan, sodium alginate, carrageenan, cellulose, pectin were easily degraded by irradiation and induced various kinds of biological activities, i.e. anti-bacterial activity, elicitor activity, plant growth promotion, suppression of environmental stress on plants. Radiation degraded chitosan was effective to enhance the growth of plants in tissue culture. Low energy electron beam (EB) irradiation has a variety of applications and good safety. A self-shielded low energy electron accelerator system needs an initial investment much lower than a 60 Co facility. It was demonstrated that the liquid sample irradiation system using low energy EB was effective not only for the preparation of degraded polysaccharides but also for radiation vulcanization of natural rubber latex (RVNRL). Some carbohydrate derivatives, carboxymethylcellulose (CMC), carboxymethyl-starch and carboxymethyl-chitin/chitosan, can be crosslinked under certain radiation condition and produced the biodegradable hydrogel for medical and agricultural use. Treatment of soybean seeds by low energy EB enhanced the growth and the number of rhizobia on the root. (author) 1. Sturmian theory of electron energy distributions in low energy ion-atom collisions Energy Technology Data Exchange (ETDEWEB) Ovchinnikov, S.Yu. [Department of Physics and Astronomy, University of Tennessee, 401 Nielsen Physics Building, Knoxville, TN 37996-1200 (United States) and Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 (United States)]. E-mail: [email protected]; Macek, J.H. [Department of Physics and Astronomy, University of Tennessee, 401 Nielsen Physics Building, Knoxville, TN 37996-1200 (United States); Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 (United States) 2005-12-15 The energy and angular distributions of electrons ejected from targets and projectiles in the collisions of slow H and H{sup -} with He targets has been calculated exactly in a model that treats electron interactions with neutral targets via zero-range interactions. These calculations employ two-center Sturmian functions for collisions at non-zero impact parameters. The computed distributions are compared with recent measurements for He targets. Total ionization cross sections are also computed and compared with experiment over a broad energy range for proton, alpha particle and neutral hydrogen impact on helium atoms. The calculations are in generally good agreement with experiment. 2. Secondary-electron-emission spectroscopy of tungsten: Angular dependence and phenomenology DEFF Research Database (Denmark) Willis, Roy F.; Christensen, Niels Egede 1978-01-01 Angle-resolved energy-distribution measurements of secondary-electron emission (SEE) from metals reveal spectral fine structure that relates directly to the density distribution of the one-electron states throughout E-K→ space located above the vacuum level Ev. The angular dependence of the SEE...... of basically two contributions JSEEtotal=∫0πdΩ∫0EmaxjSEE (E, Ω)dE=JSEEbulk+JSEEsurface. The bulk contribution represents emission due to Bloch waves propagating out of states in the semi-infinite crystal; the surface contribution represents that part of the current due to evanescent waves at the metal-vacuum...... interface. In addition, transmission-induced spectral features are observed (transmission resonances), which are not related to the density-of-states fine structure, but are due to a quantum-mechanical enhancement in the escape probability arising from wave-function matching at the emitter-vacuum interface... 3. Electronic energy transfer through non-adiabatic vibrational-electronic resonance. I. Theory for a dimer. Science.gov (United States) Tiwari, Vivek; Peters, William K; Jonas, David M 2017-10-21 Non-adiabatic vibrational-electronic resonance in the excited electronic states of natural photosynthetic antennas drastically alters the adiabatic framework, in which electronic energy transfer has been conventionally studied, and suggests the possibility of exploiting non-adiabatic dynamics for directed energy transfer. Here, a generalized dimer model incorporates asymmetries between pigments, coupling to the environment, and the doubly excited state relevant for nonlinear spectroscopy. For this generalized dimer model, the vibrational tuning vector that drives energy transfer is derived and connected to decoherence between singly excited states. A correlation vector is connected to decoherence between the ground state and the doubly excited state. Optical decoherence between the ground and singly excited states involves linear combinations of the correlation and tuning vectors. Excitonic coupling modifies the tuning vector. The correlation and tuning vectors are not always orthogonal, and both can be asymmetric under pigment exchange, which affects energy transfer. For equal pigment vibrational frequencies, the nonadiabatic tuning vector becomes an anti-correlated delocalized linear combination of intramolecular vibrations of the two pigments, and the nonadiabatic energy transfer dynamics become separable. With exchange symmetry, the correlation and tuning vectors become delocalized intramolecular vibrations that are symmetric and antisymmetric under pigment exchange. Diabatic criteria for vibrational-excitonic resonance demonstrate that anti-correlated vibrations increase the range and speed of vibronically resonant energy transfer (the Golden Rule rate is a factor of 2 faster). A partial trace analysis shows that vibronic decoherence for a vibrational-excitonic resonance between two excitons is slower than their purely excitonic decoherence. 4. Electron flux models for different energies at geostationary orbit Science.gov (United States) Boynton, R. J.; Balikhin, M. A.; Sibeck, D. G.; Walker, S. N.; Billings, S. A.; Ganushkina, N. 2016-10-01 Forecast models were derived for energetic electrons at all energy ranges sampled by the third-generation Geostationary Operational Environmental Satellites (GOES). These models were based on Multi-Input Single-Output Nonlinear Autoregressive Moving Average with Exogenous inputs methodologies. The model inputs include the solar wind velocity, density and pressure, the fraction of time that the interplanetary magnetic field (IMF) was southward, the IMF contribution of a solar wind-magnetosphere coupling function proposed by Boynton et al. (2011b), and the Dst index. As such, this study has deduced five new 1 h resolution models for the low-energy electrons measured by GOES (30-50 keV, 50-100 keV, 100-200 keV, 200-350 keV, and 350-600 keV) and extended the existing >800 keV and >2 MeV Geostationary Earth Orbit electron fluxes models to forecast at a 1 h resolution. All of these models were shown to provide accurate forecasts, with prediction efficiencies ranging between 66.9% and 82.3%. 5. Low-energy collisions between electrons and BeD+ Science.gov (United States) Niyonzima, S.; Pop, N.; Iacob, F.; Larson, Å; Orel, A. E.; Mezei, J. Zs; Chakrabarti, K.; Laporta, V.; Hassouni, K.; Benredjem, D.; Bultel, A.; Tennyson, J.; Reiter, D.; Schneider, I. F. 2018-02-01 Multichannel quantum defect theory is applied in the treatment of the dissociative recombination and vibrational excitation processes for the BeD+ ion in the 24 vibrational levels of its ground electronic state ({{X}}{}1{{{Σ }}}+,{v}{{i}}+=0\\ldots 23). Three electronic symmetries of BeD** states ({}2{{\\Pi }}, {}2{{{Σ }}}+, and {}2{{Δ }}) are considered in the calculation of cross sections and the corresponding rate coefficients. The incident electron energy range is 10‑5–2.7 eV and the electron temperature range is 100–5000 K. The vibrational dependence of these collisional processes is highlighted. The resulting data are useful in magnetic confinement fusion edge plasma modeling and spectroscopy, in devices with beryllium based main chamber materials, such as ITER and JET, and operating with the deuterium–tritium fuel mix. An extensive rate coefficients database is presented in graphical form and also by analytic fit functions whose parameters are tabulated in the supplementary material. 6. The relevance of the vertex bremsstrahlung photon detection in the electron-neutrino (antineutrino) electron scattering experiments at low energy CERN Document Server Broggini, C; Moretti, M 1999-01-01 We discuss the size of the electron-antineutrino electron into electron-antineutrino electron cross section reduction due to the rejection of the events with a vertex bremsstrahlung photon above a certain energy in the final state. In particular we analyze the effect in experiments designed to detect the low energy electron-antineutrino and electron-neutrino from a nuclear reactor and from the Sun. We find that such reduction has to be considered in a relatively high statistic reactor experiment, while it is negligible for pp and 7Be solar neutrino detection. 7. Ultrafast electronic energy relaxation in a conjugated dendrimer leading to inter-branch energy redistribution. Science.gov (United States) Ondarse-Alvarez, D; Kömürlü, S; Roitberg, A E; Pierdominici-Sottile, G; Tretiak, S; Fernandez-Alberti, S; Kleiman, V D 2016-09-14 Dendrimers are arrays of coupled chromophores, where the energy of each unit depends on its structure and conformation. The light harvesting and energy funneling properties are strongly dependent on their highly branched conjugated architecture. Herein, the photoexcitation and subsequent ultrafast electronic energy relaxation and redistribution of a first generation dendrimer (1) are analyzed combining theoretical and experimental studies. Dendrimer 1 consists of three linear phenylene-ethynylene (PE) units, or branches, attached in the meta position to a central group opening up the possibility of inter-branch energy transfer. Excited state dynamics are explored using both time-resolved spectroscopy and non-adiabatic excited state molecular dynamics simulations. Our results indicate a subpicosecond loss of anisotropy due to an initial excitation into several states with different spatial localizations, followed by exciton self-trapping on different units. This exciton hops between branches. The absence of an energy gradient leads to an ultrafast energy redistribution among isoenergetic chromophore units. At long times we observe similar probabilities for each branch to retain significant contributions of the transition density of the lowest electronic excited-state. The observed unpolarized emission is attributed to the contraction of the electronic wavefunction onto a single branch with frequent interbranch hops, and not to its delocalization over the whole dendrimer. 8. Electronic structure and electron energy-loss spectroscopy of ZrO2 zirconia Science.gov (United States) Dash, L. K.; Vast, Nathalie; Baranek, Philippe; Cheynet, Marie-Claude; Reining, Lucia 2004-12-01 The atomic and electronic structures of zirconia are calculated within density functional theory, and their evolution is analyzed as the crystal-field symmetry changes from tetrahedral [cubic (c-ZrO2) and tetragonal (t-ZrO2) phases] to octahedral (hypothetical rutile ZrO2 ), to a mixing of these symmetries (monoclinic phase, m-ZrO2 ). We find that the theoretical bulk modulus in c-ZrO2 is 30% larger than the experimental value, showing that the introduction of yttria in zirconia has a significant effect. Electronic structure fingerprints which characterize each phase from their electronic spectra are identified. We have carried out electron energy-loss spectroscopy experiments at low momentum transfer and compared these results to the theoretical spectra calculated within the random phase approximation. We show a dependence of the valence and 4p ( N2,3 edge) plasmons on the crystal structure, the dependence of the latter being brought into the spectra by local-field effects. Last, we attribute low energy excitations observed in EELS of m-ZrO2 to defect states 2eV above the top of the intrinsic valence band, and the EELS fundamental band gap value is reconciled with the 5.2 or 5.8eV gaps determined by vacuum ultraviolet spectroscopy. 9. Cost analysis of low energy electron accelerator for film curing International Nuclear Information System (INIS) Ochi, Masafumi 2003-01-01 Low energy electron accelerators are recognized as one of the advanced curing means of converting processes for films and papers. In the last three years the price of the accelerator equipment has been greatly reduced. The targeted application areas are mainly processes of curing inks, coatings, and adhesives to make packaging materials. The operating cost analyses were made for electron beam (EB) processes over the conventional ones without EB. Then three new proposals for cost reduction of EB processes are introduced. Also being developed are new EB chemistries such as coatings, laminating adhesives and inks. EB processes give instantaneous cure and EB chemistries are basically non solvent causing less VOC emission to the environment. These developments of both equipment and chemistries might have a potential to change conventional packaging film industries. (author) 10. On selection rules and inelastic electron scattering at intermediate energies International Nuclear Information System (INIS) Nuroh, K. 1986-12-01 Correlation effects are included in the Bethe-Born theory for the generalized oscillator strength of inelastic scattering of electrons on atoms. The formulation is such as to allow for the calculation of relative line strengths of multiplets. It is used to analyze line strengths of the 4d → 4f transition in La 3+ and Ce 4+ within LS-coupling. The analysis indicates that only singlet states of the intermediate 4d 9 4f configuration are allowed. Calculated line strengths are compared with a recent core electron energy loss spectra of metallic La and tetravalent CeO 2 and there is an overall qualitative agreement between theory and experiment. (author). 11 refs, 4 figs, 2 tabs 11. Maximum wind energy extraction strategies using power electronic converters Science.gov (United States) Wang, Quincy Qing 2003-10-01 This thesis focuses on maximum wind energy extraction strategies for achieving the highest energy output of variable speed wind turbine power generation systems. Power electronic converters and controls provide the basic platform to accomplish the research of this thesis in both hardware and software aspects. In order to send wind energy to a utility grid, a variable speed wind turbine requires a power electronic converter to convert a variable voltage variable frequency source into a fixed voltage fixed frequency supply. Generic single-phase and three-phase converter topologies, converter control methods for wind power generation, as well as the developed direct drive generator, are introduced in the thesis for establishing variable-speed wind energy conversion systems. Variable speed wind power generation system modeling and simulation are essential methods both for understanding the system behavior and for developing advanced system control strategies. Wind generation system components, including wind turbine, 1-phase IGBT inverter, 3-phase IGBT inverter, synchronous generator, and rectifier, are modeled in this thesis using MATLAB/SIMULINK. The simulation results have been verified by a commercial simulation software package, PSIM, and confirmed by field test results. Since the dynamic time constants for these individual models are much different, a creative approach has also been developed in this thesis to combine these models for entire wind power generation system simulation. An advanced maximum wind energy extraction strategy relies not only on proper system hardware design, but also on sophisticated software control algorithms. Based on literature review and computer simulation on wind turbine control algorithms, an intelligent maximum wind energy extraction control algorithm is proposed in this thesis. This algorithm has a unique on-line adaptation and optimization capability, which is able to achieve maximum wind energy conversion efficiency through 12. The energy distribution of electrons in radio jets Science.gov (United States) Tsouros, Alexandros; Kylafis, Nikolaos D. 2017-07-01 Context. Black-hole and neutron-star X-ray binaries exhibit compact radio jets, when they are in the so called quiescent, hard, or hard intermediate states. The radio spectrum in these states is flat to slightly inverted, I.e., the spectral index of the observed flux density is in the range 0 ≲ α ≲ 0.5. It is widely accepted that the energy distribution of the electrons, in the rest frame of the jet, is a power law with index in the range 3 ≲ p ≲ 5. Aims: Contrary to what our thinking was decades ago, now we know that the jets originate in the hot, inner flow around black holes and neutron stars. So it is worth investigating the radio spectrum that is emitted by a thermal jet as a function of direction. Methods: As an example, we consider a parabolic jet and, with the assumption of flux freezing, we compute the emitted spectrum in all directions, from radio to near infrared, using either a thermal distribution of electrons or a power-law one. Results: We have found that parabolic jets with a thermal distribution of electrons give also flat to slightly inverted spectra. In particular, for directions along the jet (θ = 0), both distributions of electron energies give α = 0 ± 0.01. The index α increases as the viewing angle θ increases and for directions perpendicular to the jet (θ = π/ 2), the thermal distribution gives α = 0.40 ± 0.05, while the power-law distribution gives α = 0.20 ± 0.05. The break frequency νb, which marks the transition from partially optically thick to optically thin synchrotron emission, is comparable for the power-law and the thermal distributions. Conclusions: Contrary to common belief, it is not necessary to invoke a power-law energy distribution of the electrons in a jet to explain its flat to slightly inverted radio spectrum. A relativistic Maxwellian produces similar radio spectra. Thus, the jet may be the widely invoked "corona" around black holes in X-ray binaries. 13. Interpretation of diffuse low-energy electron diffraction intensities International Nuclear Information System (INIS) Saldin, D.K.; Pendry, J.B.; Van Hove, M.A.; Somorjai, G.A. 1985-01-01 It is shown that the diffuse low-energy electron diffraction (LEED) that occurs between sharp LEED beams can be used to determine the local bonding configuration near disordered surface atoms. Two approaches to the calculation of diffuse LEED intensities are presented for the case of lattice-gas disorder of an adsorbate on a crystalline substrate. The capabilities of this technique are most similar to those of near-edge extended x-ray absorption fine structure, but avoid the restrictions due to the use of photons 14. Low power electronic interface for electrostatic energy harvesters International Nuclear Information System (INIS) Phan, Tra Nguyen; Azadmehr, Mehdi; Le, Cuong Phu; Halvorsen, Einar 2015-01-01 This paper presents design and simulation of a power electronic interface circuit for MEMS electrostatic energy harvesters. The designed circuit is applicable to highly miniaturized electrostatic harvesters with small transducer capacitances below 10 pF. It is based on comb- drive harvesters with two anti-phase capacitors that are connected as charge pumps and uses a flyback-path scheme. Controlled activation and deactivation of sub-circuits, some by help of clocking, were exploited to reduce power consumption down to 1.03 μW. Net power generation can be achieved with as low initial voltage as 3.0 V. (paper) 15. Measurement of the Electron Structure Function at LEP energies CERN Document Server Abdallah, J; Adam, W; Adzic, P; Albrecht, T; Alemany-Fernandez, R; Allmendinger, T; Allport, P P; Amaldi, U; Amapane, N; Amato, S; Anashkin, E; Andreazza, A; Andringa, S; Anjos, N; Antilogus, P; Apel, W-D; Arnoud, Y; Ask, S; Asman, B; Augustin, J E; Augustinus, A; Baillon, P; Ballestrero, A; Bambade, P; Barbier, R; Bardin, D; Barker, G J; Baroncelli, A; Battaglia, M; Baubillier, M; Becks, K-H; Begalli, M; Behrmann, A; Ben-Haim, E; Benekos, N; Benvenuti, A; Berat, C; Berggren, M; Bertrand, D; Besancon, M; Besson, N; Bloch, D; Blom, M; Bluj, M; Bonesini, M; Boonekamp, M; Booth, P S L; Borisov, G; Botner, O; Bouquet, B; Bowcock, T J V; Boyko, I; Bracko, M; Brenner, R; Brodet, E; Bruckman, P; Brunet, J M; Buschbeck, B; Buschmann, P; Calvi, M; Camporesi, T; Canale, V; Carena, F; Castro, N; Cavallo, F; Chapkin, M; Charpentier, Ph; Checchia, P; Chierici, R; Chliapnikov, P; Chudoba, J; Chung, S U; Cieslik, K; Collins, P; Contri, R; Cosme, G; Cossutti, F; Costa, M J; Crennell, D; Cuevas, J; D'Hondt, J; da Silva, T; Da Silva, W; Della Ricca, G; De Angelis, A; De Boer, W; De Clercq, C; De Lotto, B; De Maria, N; De Min, A; de Paula, L; Di Ciaccio, L; Di Simone, A; Doroba, K; Drees, J; Eigen, G; Ekelof, T; Ellert, M; Elsing, M; Espirito Santo, M C; Fanourakis, G; Fassouliotis, D; Feindt, M; Fernandez, J; Ferrer, A; Ferro, F; Flagmeyer, U; Foeth, H; Fokitis, E; Fulda-Quenzer, F; Fuster, J; Gandelman, M; Garcia, C; Gavillet, Ph; Gazis, E; Gokieli, R; Golob, B; Gomez-Ceballos, G; Goncalves, P; Graziani, E; Grosdidier, G; Grzelak, K; Guy, J; Haag, C; Hallgren, A; Hamacher, K; Hamilton, K; Haug, S; Hauler, F; Hedberg, V; Hennecke, M; Hoffman, J; Holmgren, S-O; Holt, P J; Houlden, M A; Jackson, J N; Jarlskog, G; Jarry, P; Jeans, D; Johansson, E K; Jonsson, P; Joram, C; Jungermann, L; Kapusta, F; Katsanevas, S; Katsoufis, E; Kernel, G; Kersevan, B P; Kerzel, U; King, B T; Kjaer, N J; Kluit, P; Kokkinias, P; Kourkoumelis, C; Kouznetsov, O; Krumstein, Z; Kucharczyk, M; Lamsa, J; Leder, G; Ledroit, F; Leinonen, L; Leitner, R; Lemonne, J; Lepeltier, V; Lesiak, T; Liebig, W; Liko, D; Lipniacka, A; Lopes, J H; Lopez, J M; Loukas, D; Lutz, P; Lyons, L; MacNaughton, J; Malek, A; Maltezos, S; Mandl, F; Marco, J; Marco, R; Marechal, B; Margoni, M; Marin, J-C; Mariotti, C; Markou, A; Martinez-Rivero, C; Masik, J; Mastroyiannopoulos, N; Matorras, F; Matteuzzi, C; Mazzucato, F; Mazzucato, M; Mc Nulty, R; Meroni, C; Migliore, E; Mitaroff, W; Mjoernmark, U; Moa, T; Moch, M; Moenig, K; Monge, R; Montenegro, J; Moraes, D; Moreno, S; Morettini, P; Mueller, U; Muenich, K; Mulders, M; Mundim, L; Murray, W; Muryn, B; Myatt, G; Myklebust, T; Nassiakou, M; Navarria, F; Nawrocki, K; Nemecek, S; Nicolaidou, R; Nikolenko, M; Oblakowska-Mucha, A; Obraztsov, V; Olshevski, A; Onofre, A; Orava, R; Osterberg, K; Ouraou, A; Oyanguren, A; Paganoni, M; Paiano, S; Palacios, J P; Palka, H; Papadopoulou, Th D; Pape, L; Parkes, C; Parodi, F; Parzefall, U; Passeri, A; Passon, O; Peralta, L; Perepelitsa, V; Perrotta, A; Petrolini, A; Piedra, J; Pieri, L; Pierre, F; Pimenta, M; Piotto, E; Podobnik, T; Poireau, V; Pol, M E; Polok, G; Pozdniakov, V; Pukhaeva, N; Pullia, A; Radojicic, D; Rebecchi, P; Rehn, J; Reid, D; Reinhardt, R; Renton, P; Richard, F; Ridky, J; Rivero, M; Rodriguez, D; Romero, A; Ronchese, P; Roudeau, P; Rovelli, T; Ruhlmann-Kleider, V; Ryabtchikov, D; Sadovsky, A; Salmi, L; Salt, J; Sander, C; Savoy-Navarro, A; Schwickerath, U; Sekulin, R; Siebel, M; Sisakian, A; Slominski, W; Smadja, G; Smirnova, O; Sokolov, A; Sopczak, A; Sosnowski, R; Spassov, T; Stanitzki, M; Stocchi, A; Strauss, J; Stugu, B; Szczekowski, M; Szeptycka, M; Szumlak, T; Szwed, J; Tabarelli, T; Tegenfeldt, F; Timmermans, J; Tkatchev, L; Tobin, M; Todorovova, S; Tome, B; Tonazzo, A; Tortosa, P; Travnicek, P; Treille, D; Tristram, G; Trochimczuk, M; Troncon, C; Turluer, M L; Tyapkin, I A; Tyapkin, P; Tzamarias, S; Uvarov, V; Valenti, G; Van Dam, P; Van Eldik, J; van Remortel, N; Van Vulpen, I; Vegni, G; Veloso, F; Venus, W; Verdier, P; Verzi, V; Vilanova, D; Vitale, L; Vrba, V; Wahlen, H; Washbrook, A J; Weiser, C; Wicke, D; Wickens, J; Wilkinson, G; Winter, M; Witek, M; Yushchenko, O; Zalewska, A; Zalewski, P; Zavrtanik, D; Zhuravlov, V; Zimin, N I; Zintchenko, A; Zupan, M 2010-01-01 The hadronic part of the Electron Structure Function (ESF) has been measured for the first time, using e+e- data collected by the DELPHI experiment at LEP, at centre-of-mass energies sqrt(s) = 91.2-209.5 GeV. The data analysis is simpler than that of the measurement of the photon structure function. The ESF data are compared to predictions of phenomenological models based on the photon structure function. It is shown that the quasi-real photon virtuality contribution is significant. The presented data can serve as a cross-check of the photon structure function analyses and help in refining existing parametrizations. 16. Two-electron photoionization cross sections at high energies International Nuclear Information System (INIS) Amusia, M.Ya.; Krivec, R.; Mandelzweig, V.B. 2003-01-01 Double and single electron photoionization cross sections and their ratios at high and ultra-relativistic energies are calculated for H - , He and helium-like ions in ground and excited states including triplet states. The ratios contain shake-off and quasi-free terms. A high precision non-variational wave function is used. The quasi-free mechanism increases the ratios impressively: for He we get 0.0762 instead of 0.0164 in the non-relativistic case. Ratios are inversely proportional to Z 2 , with a factor increasing from 0.094 in the nonrelativistic to 0.595 in the ultra-relativistic limit. (author) 17. Electron energy loss spectroscopy microanalysis and imaging in the transmission electron microscope: example of biological applications International Nuclear Information System (INIS) Diociaiuti, Marco 2005-01-01 This paper reports original results obtained in our laboratory over the past few years in the application of both electron energy loss spectroscopy (EELS) and electron spectroscopy imaging (ESI) to biological samples, performed in two transmission electron microscopes (TEM) equipped with high-resolution electron filters and spectrometers: a Gatan model 607 single magnetic sector double focusing EEL serial spectrometer attached to a Philips 430 TEM and a Zeiss EM902 Energy Filtering TEM. The primary interest was on the possibility offered by the combined application of these spectroscopic techniques with those offered by the TEM. In particular, the electron beam focusing available in a TEM allowed us to perform EELS and ESI on very small sample volumes, where high-resolution imaging and electron diffraction techniques can provide important structural information. I show that ESI was able to improve TEM performance, due to the reduced chromatic aberration and the possibility of avoiding the sample staining procedure. Finally, the analysis of the oscillating extended energy loss fine structure (EXELFS) beyond the ionization edges characterizing the EELS spectra allowed me, in a manner very similar to the extended X-ray absorption fine structure (EXAFS) analysis of the X-ray absorption spectra, to obtain short-range structural information for such light elements of biological interest as O or Fe. The Philips EM430 (250-300 keV) TEM was used to perform EELS microanalysis on Ca, P, O, Fe, Al and Si. The assessment of the detection limits of this method was obtained working with well-characterized samples containing Ca and P, and mimicking the actual cellular matrix. I applied EELS microanalysis to Ca detection in bone tissue during the mineralization process and to P detection in the cellular membrane of erythrocytes treated with an anti-tumoral drug, demonstrating that the cellular membrane is a drug target. I applied EELS microanalysis and selected area electron 18. Radiation processing of liquid with low energy electron accelerator Energy Technology Data Exchange (ETDEWEB) Makuuchi, Keizo [Japan Atomic Energy Research Inst., Takasaki, Gunma (Japan). Takasaki Radiation Chemistry Research Establishment 2003-02-01 19. Beam Profile Diagnostics for the Fermilab Medium Energy Electron Cooler Science.gov (United States) Warner, A.; Kazakevich, G.; Nagaitsev, S.; Tassotto, G.; Gai, W.; Konecny, R. 2005-10-01 The Fermilab Recycler ring will employ an electron cooler to store and cool 8.9 GeV antiprotons. The cooler will be based on a Pelletron electrostatic accelerator working in an energy-recovery regime. Several techniques for determining the characteristics of the beam dynamics are being investigated. Beam profiles have been measured as a function of the beam line optics at the energy of 3.5 MeV in the current range of 10/sup -4/-1 A, with a pulse duration of 2 /spl mu/s. The profiles were measured using optical transition radiation produced at the interface of a 250-/spl mu/m aluminum foil and also from YAG crystal luminescence. In addition, beam profiles measured using multiwire detectors were investigated. These three diagnostics will be used together to determine the profile dynamics of the beam. In this paper we report the results so far obtained using these techniques. 20. Radiation processing of liquid with low energy electron accelerator International Nuclear Information System (INIS) Makuuchi, Keizo 2003-01-01 1. Advanced Power Electronics Interfaces for Distributed Energy Workshop Summary: August 24, 2006, Sacramento, California Energy Technology Data Exchange (ETDEWEB) Treanton, B.; Palomo, J.; Kroposki, B.; Thomas, H. 2006-10-01 The Advanced Power Electronics Interfaces for Distributed Energy Workshop, sponsored by the California Energy Commission Public Interest Energy Research program and organized by the National Renewable Energy Laboratory, was held Aug. 24, 2006, in Sacramento, Calif. The workshop provided a forum for industry stakeholders to share their knowledge and experience about technologies, manufacturing approaches, markets, and issues in power electronics for a range of distributed energy resources. It focused on the development of advanced power electronic interfaces for distributed energy applications and included discussions of modular power electronics, component manufacturing, and power electronic applications. 2. Electron Attachment to POCl3: Measurement and Theoretical Analysis of Rate Constants and Branching Ratios as a Function of Gas Pressure and Temperature, Electron Temperature, and Electron Energy National Research Council Canada - National Science Library Van Doren, Jane M; Friedman, Jeffrey F; Miller, Thomas M; Viggiano, A. A; Denifl, S; Scheier, P; Mark, T. D; Troe, J 2006-01-01 ... of the resonant POCl3 state and collisional stabilization of the parent anion. In the electron beam experiment at zero electron energy, the fragment ion POCl2- is the dominant ion product of attachment (96... 3. A study of angle-resolved photoemission extended fine structure as applied to the Ni 3p, Cu 3s, and Cu 3p core levels of the respective clean (111) surfaces Energy Technology Data Exchange (ETDEWEB) Huff, W.R.A.; Moler, E.J.; Kellar, S.A. [Lawrence Berkeley National Lab., CA (United States)] [and others 1997-04-01 The first non-s initial state angle-resolved photoemission extended fine structure (ARPEFS) study of clean surfaces for the purpose of further understanding the technique is reported. The surface structure sensitivity of ARPEFS applied to clean surfaces and to arbitrary initial states is studied using normal photoemission data taken from the Ni 3p core levels of a Ni(111) single crystal and the Cu 3s and the Cu 3p core-levels of a Cu(111) single crystal. The Fourier transforms of these clean surface data are dominated by backscattering. Unlike the s initial state data, the p initial state data show a peak in the Fourier transform corresponding to in-plane scattering from the six nearest-neighbors to the emitter. Evidence was seen for single-scattering events from in the same plane as the emitters and double-scattering events. Using a newly developed, multiple-scattering calculation program, ARPEFS data from clean surfaces and from p initial states can be modeled to high precision. Although there are many layers of emitters when measuring photoemission from a clean surface, test calculations show that the ARPEFS signal is dominated by photoemission from atoms in the first two crystal layers. Thus, ARPEFS applied to clean surfaces is sensitive to surface reconstruction. The known contraction of the first two Cu(111) layers is confirmed. The best-fit calculation for clean Ni(111) indicates an expansion of the first two layers. To better understand the ARPEFS technique, the authors studied s and non-s initial state photoemission from clean metal surfaces. 4. Electron beam induced Hg desorption and the electronic structure of the Hg depleted surface of Hg1/sub -//sub x/Cd/sub x/Te International Nuclear Information System (INIS) Shih, C.K.; Friedman, D.J.; Bertness, K.A.; Lindau, I.; Spicer, W.E.; Wilson, J.A. 1986-01-01 Auger electron spectroscopy (AES), x-ray photoemission spectroscopy (XPS), low energy electron diffraction (LEED), and angle-resolved ultraviolet photoemission spectroscopy (ARPES) were used to study the electron beam induced Hg desorption from a cleaved (110)Hg/sub 1-//sub x/Cd/sub x/Te surface and the electronic structure of the Hg depleted surface. Solid state recrystallized Hg/sub 1-//sub x/Cd/sub x/Te single crystals were used. It was found that the electron beam heating dominated the electron beam induced Hg desorption on Hg/sub 1-//sub x/Cd/sub x/Te. At the electron beam energy used, the electron beam heating extended several thousand angstroms deep. However, the Hg depletion saturated after a few monolayers were depleted of Hg atoms. At the initial stage of Hg loss (only 3%), the surface band bends upward (more p type). The ARPES spectrum showed the loss of some E vs k dispersion after 22% Hg atoms were removed from the surface region, and no dispersion was observed after 43% Hg atoms were removed. These results have important implications on the electronic structure of the surfaces and interfaces of which the stoichiometry is altered 5. Low energy electron point source microscopy: beyond imaging. Science.gov (United States) Beyer, André; Gölzhäuser, Armin 2010-09-01 Low energy electron point source (LEEPS) microscopy has the capability to record in-line holograms at very high magnifications with a fairly simple set-up. After the holograms are numerically reconstructed, structural features with the size of about 2 nm can be resolved. The achievement of an even higher resolution has been predicted. However, a number of obstacles are known to impede the realization of this goal, for example the presence of electric fields around the imaged object, electrostatic charging or radiation induced processes. This topical review gives an overview of the achievements as well as the difficulties in the efforts to shift the resolution limit of LEEPS microscopy towards the atomic level. A special emphasis is laid on the high sensitivity of low energy electrons to electrical fields, which limits the structural determination of the imaged objects. On the other hand, the investigation of the electrical field around objects of known structure is very useful for other tasks and LEEPS microscopy can be extended beyond the task of imaging. The determination of the electrical resistance of individual nanowires can be achieved by a proper analysis of the corresponding LEEPS micrographs. This conductivity imaging may be a very useful application for LEEPS microscopes. 6. Collisions of low-energy electrons with cyclohexane Energy Technology Data Exchange (ETDEWEB) Barbosa, Alessandra Souza; Bettega, Márcio H. F., E-mail: [email protected] [Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990 Curitiba, Paraná (Brazil) 2014-12-28 We report calculated cross sections for elastic scattering of low-energy electrons by cyclohexane (c-C{sub 6}H{sub 12}). We employed the Schwinger multichannel method implemented with norm-conserving pseudopotentials in the static-exchange and static-exchange plus polarization approximations, for impact energies up to 30 eV. We compare our calculated integral cross section with experimental total cross sections available in the literature. We also compare our calculated differential cross sections (DCSs) with experimental results for benzene and experimental and theoretical results for 1,4-dioxane, in order to investigate the similarities between those molecules under electron collisions. Although benzene is a cyclic six-carbon molecule, as cyclohexane, we found that the differential cross sections of the latter are more similar to those of 1,4-dioxane than those of benzene. These similarities suggest that the geometry may play an important role in the behavior of the DCSs of these molecules. Our integral cross section displays a broad structure at around 8.5 eV, in agreement with the total cross section experimental data of 8 eV and vibrational excitation data of 7.5 eV. The present integral cross section also shows the presence of a Ramsauer-Townsend minimum at around 0.12 eV. In general, our integral cross section shows a qualitative agreement with the experimental total cross section. 7. Formation and Observation of a Quasi-Two-Dimensional dxy Electron Liquid in Epitaxially Stabilized Sr(2-x)La(x)TiO4 Thin Films. Science.gov (United States) Nie, Y F; Di Sante, D; Chatterjee, S; King, P D C; Uchida, M; Ciuchi, S; Schlom, D G; Shen, K M 2015-08-28 We report the formation and observation of an electron liquid in Sr(2-x)La(x)TiO4, the quasi-two-dimensional counterpart of SrTiO3, through reactive molecular-beam epitaxy and in situ angle-resolved photoemission spectroscopy. The lowest lying states are found to be comprised of Ti 3d_{xy} orbitals, analogous to the LaAlO3/SrTiO3 interface and exhibit unusually broad features characterized by quantized energy levels and a reduced Luttinger volume. Using model calculations, we explain these characteristics through an interplay of disorder and electron-phonon coupling acting cooperatively at similar energy scales, which provides a possible mechanism for explaining the low free carrier concentrations observed at various oxide heterostructures such as the LaAlO3/SrTiO3 interface. 8. Electronic structure of the Si/GaP(110) interface Science.gov (United States) Niles, David W.; Höchst, Hartmut 1989-04-01 We present the results of an angle-resolved photoemission study of the Si/GaP(110) heterostructure. Band mapping of sputtered and annealed GaP(110) unambiguously determines the position of the valence-band maximum at Γ15 to be 1.2 eV below the Fermi level. The Fermi-level pinning position for the sputtered and annealed surface is different from that of cleaved GaP(110) and suggests the introduction of defect levels by the cleaning process. However, deposition of one monolayer (ML) Si onto GaP(110) changes the pinning position despite the defect levels. The electronic structure of the interface evolves slowly as a function of the Si-overlayer thickness, but appears to be fully developed at 20 ML. We discuss the electronic structure of the heterojunction in light of the midgap energy rule for band alignments and try to clarify why it appears to fail for this particular system. Specifically, a comparison of theoretical and experimental band structures shows that a linear extrapolation of the leading edge of an angle-resolved valence-band spectrum does not determine the GaP Γ15 valence-band maximum with the accuracy (~0.1 eV) desired for band-alignment measurements. This shortcoming conjures up questions about the validity of using the leading edge of angle-integrated spectra to determine the Γ15 valence-band maximum in GaP and about the previously reported band alignment for the Si/GaP(110) heterostructure. 9. Practical spatial resolution of electron energy loss spectroscopy in aberration corrected scanning transmission electron microscopy. Science.gov (United States) Shah, A B; Ramasse, Q M; Wen, J G; Bhattacharya, A; Zuo, J M 2011-08-01 The resolution of electron energy loss spectroscopy (EELS) is limited by delocalization of inelastic electron scattering rather than probe size in an aberration corrected scanning transmission electron microscope (STEM). In this study, we present an experimental quantification of EELS spatial resolution using chemically modulated 2×(LaMnO(3))/2×(SrTiO(3)) and 2×(SrVO(3))/2×(SrTiO(3)) superlattices by measuring the full width at half maxima (FWHM) of integrated Ti M(2,3), Ti L(2,3), V L(2,3), Mn L(2,3), La N(4,5), La N(2,3) La M(4,5) and Sr L(3) edges over the superlattices. The EELS signals recorded using large collection angles are peaked at atomic columns. The FWHM of the EELS profile, obtained by curve-fitting, reveals a systematic trend with the energy loss for the Ti, V, and Mn edges. However, the experimental FWHM of the Sr and La edges deviates significantly from the observed experimental tendency. Copyright © 2011 Elsevier Ltd. All rights reserved. 10. Electronic properties of Mn-phthalocyanine–C60 bulk heterojunctions: Combining photoemission and electron energy-loss spectroscopy International Nuclear Information System (INIS) Roth, Friedrich; Herzig, Melanie; Knupfer, Martin; Lupulescu, Cosmin; Darlatt, Erik; Gottwald, Alexander; Eberhardt, Wolfgang 2015-01-01 The electronic properties of co-evaporated mixtures (blends) of manganese phthalocyanine and the fullerene C 60 (MnPc:C 60 ) have been studied as a function of the concentration of the two constituents using two supplementary electron spectroscopic methods, photoemission spectroscopy (PES) and electron energy-loss spectroscopy (EELS) in transmission. Our PES measurements provide a detailed picture of the electronic structure measured with different excitation energies as well as different mixing ratios between MnPc and C 60 . Besides a relative energy shift, the occupied electronic states of the two materials remain essentially unchanged. The observed energy level alignment is different compared to that of the related CuPc:C 60 bulk heterojunction. Moreover, the results from our EELS investigations show that, despite the rather small interface interaction, the MnPc related electronic excitation spectrum changes significantly by admixing C 60 to MnPc thin films 11. Strongly anisotropic spin-orbit splitting in a two-dimensional electron gas DEFF Research Database (Denmark) Michiardi, Matteo; Bianchi, Marco; Dendzik, Maciej 2015-01-01 Near-surface two-dimensional electron gases on the topological insulator Bi$_2$Te$_2$Se are induced by electron doping and studied by angle-resolved photoemission spectroscopy. A pronounced spin-orbit splitting is observed for these states. The $k$-dependent splitting is strongly anisotropic... 12. Energy level alignment and electron transport through metal/organic contacts. From interfaces to molecular electronics Energy Technology Data Exchange (ETDEWEB) 2013-07-01 A new calculational approach to describing metal/organic interfaces. A valuable step towards a better understanding of molecular electronics. Nominated as an outstanding contribution by the Autonomous University of Madrid. In recent years, ever more electronic devices have started to exploit the advantages of organic semiconductors. The work reported in this thesis focuses on analyzing theoretically the energy level alignment of different metal/organic interfaces, necessary to tailor devices with good performance. Traditional methods based on density functional theory (DFT), are not appropriate for analyzing them because they underestimate the organic energy gap and fail to correctly describe the van der Waals forces. Since the size of these systems prohibits the use of more accurate methods, corrections to those DFT drawbacks are desirable. In this work a combination of a standard DFT calculation with the inclusion of the charging energy (U) of the molecule, calculated from first principles, is presented. Regarding the dispersion forces, incorrect long range interaction is substituted by a van der Waals potential. With these corrections, the C60, benzene, pentacene, TTF and TCNQ/Au(111) interfaces are analyzed, both for single molecules and for a monolayer. The results validate the induced density of interface states model. 13. Electronic emission produced by light projectiles at intermediate energies International Nuclear Information System (INIS) Bernardi, G.C. 1989-01-01 Two aspects of the electronic emission produced by light projectiles of intermediate energies have been studied experimentally. In the first place, measurements of angular distributions in the range from θ = 0 deg -50 deg induced by collisions of 50-200 keV H + incident on He have been realized. It was found that the double differential cross section of electron emission presents a structure focussed in the forward direction and which extends up to relatively large angles. Secondly, the dependence of the double differential cross section on the projectile charge was studied using H + and He 3 2+ projectiles of 50 and 100 keV/amu incident on He. Strong deviations from a constant scaling factor were found for increasing projectile charge. The double differential cross sections and the single differential cross sections as a function of the emission angle, and the ratios of the emissions induced by He 3 2+ and H + at equal incident projectile velocities are compared with the 'Continuum Distorted Wave-Eikonal Initial State' (CDW-EIS) approximation and the 'Classical Trajectory Monte Carlo' (CTMC) method. Both approximations, in which the potential of the projectile exercises a relevant role, reproduce the general aspects of the experimental results. An electron analyzer and the corresponding projectile beam line has been designed and installed; it is characterized by a series of properties which are particularly appropriate for the study of double differential electronic emission in gaseous as well as solid targets. The design permits to assure the conditions to obtain a well localized gaseous target and avoid instrumental distortions of the measured distributions. (Author) [es 14. Photoelectron spectroscopy bulk and surface electronic structures CERN Document Server Suga, Shigemasa 2014-01-01 Photoelectron spectroscopy is now becoming more and more required to investigate electronic structures of various solid materials in the bulk, on surfaces as well as at buried interfaces. The energy resolution was much improved in the last decade down to 1 meV in the low photon energy region. Now this technique is available from a few eV up to 10 keV by use of lasers, electron cyclotron resonance lamps in addition to synchrotron radiation and X-ray tubes. High resolution angle resolved photoelectron spectroscopy (ARPES) is now widely applied to band mapping of materials. It attracts a wide attention from both fundamental science and material engineering. Studies of the dynamics of excited states are feasible by time of flight spectroscopy with fully utilizing the pulse structures of synchrotron radiation as well as lasers including the free electron lasers (FEL). Spin resolved studies also made dramatic progress by using higher efficiency spin detectors and two dimensional spin detectors. Polarization depend... 15. Low-energy electron transmission through high aspect ratio Al O nanocapillaries DEFF Research Database (Denmark) Milosavljević, A.R.; Jureta, J.; Víkor, G. 2009-01-01 Electron transmission through insulating AlO nanocapillaries of different diameters (40 and 270 nm) and 15 μm length has been investigated for low-energy electrons (2-120 V). The total intensity of transmitted current weakly depends on the incident electron energy and tilt angle defined with resp......Electron transmission through insulating AlO nanocapillaries of different diameters (40 and 270 nm) and 15 μm length has been investigated for low-energy electrons (2-120 V). The total intensity of transmitted current weakly depends on the incident electron energy and tilt angle defined... 16. The application analysis of high energy electron accelerator in food irradiation processing International Nuclear Information System (INIS) Deng Wenmin; Chen Hao; Feng Lei; Zhang Yaqun; Chen Xun; Li Wenjun; Xiang Chengfen; Pei Ying; Wang Zhidong 2012-01-01 Irradiation technology of high energy electron accelerator has been highly concerned in food processing industry with its fast development, especially in the field of food irradiation processing. In this paper, equipment and research situation of high energy electron accelerator were collected, meanwhile, the similarities and differences between high energy electron beam and 60 Co γ-rays were discussed. In order to provide more references of high energy electron beam irradiation, the usages of high energy electron in food irradiation processing was prospected. These information would promote the development of domestic food irradiation industry and give a useful message to irradiation enterprises and researchers. (authors) 17. Energy dissipation from a correlated system driven out of equilibrium. Science.gov (United States) Rameau, J D; Freutel, S; Kemper, A F; Sentef, M A; Freericks, J K; Avigo, I; Ligges, M; Rettig, L; Yoshida, Y; Eisaki, H; Schneeloch, J; Zhong, R D; Xu, Z J; Gu, G D; Johnson, P D; Bovensiepen, U 2016-12-20 In complex materials various interactions have important roles in determining electronic properties. Angle-resolved photoelectron spectroscopy (ARPES) is used to study these processes by resolving the complex single-particle self-energy and quantifying how quantum interactions modify bare electronic states. However, ambiguities in the measurement of the real part of the self-energy and an intrinsic inability to disentangle various contributions to the imaginary part of the self-energy can leave the implications of such measurements open to debate. Here we employ a combined theoretical and experimental treatment of femtosecond time-resolved ARPES (tr-ARPES) show how population dynamics measured using tr-ARPES can be used to separate electron-boson interactions from electron-electron interactions. We demonstrate a quantitative analysis of a well-defined electron-boson interaction in the unoccupied spectrum of the cuprate Bi 2 Sr 2 CaCu 2 O 8+x characterized by an excited population decay time that maps directly to a discrete component of the equilibrium self-energy not readily isolated by static ARPES experiments. 18. Control of runaway electron energy using externally injected whistler waves Science.gov (United States) Guo, Zehua; McDevitt, Christopher J.; Tang, Xian-Zhu 2018-03-01 One way of mitigating runaway damage of the plasma-facing components in a tokamak fusion reactor is by limiting the runaway electron energy under a few MeV, while not necessarily reducing the runaway current appreciably. Here, we describe a physics mechanism by which such momentum space engineering of the runaway distribution can be facilitated by externally injected high-frequency electromagnetic waves such as whistler waves. The drastic impact that wave-induced scattering can have on the runaway energy distribution is fundamentally the result of its ability to control the runaway vortex in the momentum space. The runaway vortex, which is a local circulation of runaways in momentum space, is the outcome of the competition between Coulomb collisions, synchrotron radiation damping, and runaway acceleration by the parallel electric field. By introducing a wave that resonantly interacts with runaways in a particular range of energies which is mildly relativistic, the enhanced scattering would reshape the vortex by cutting off the part that is highly relativistic. The efficiency of resonant scattering accentuates the requirement that the wave amplitude can be small so the power requirement from external wave injection is practical for the mitigation scheme. 19. A Flexible Power Electronics Configuration for Coupling Renewable Energy Sources Directory of Open Access Journals (Sweden) Mattia Filippini 2015-05-01 Full Text Available A combination of series, parallel and multilevel power electronics has been investigated as a potential interface for two different types of renewable energy sources and in order to reach higher power levels. Renewable energy sources are typically dispersed in a territory, and sources, like wind and solar, allow small to medium-scale generation of electricity. The configuration investigated in this article aims at adapting the coupling solution to the specific generation characteristics of the renewable energy source to make it fit the electrical network. The configuration consists of a combination of three-phase multilevel converters and single-phase inverters, which are designed to provide flexibility, high power quality and high efficiency. A detailed analysis and simulation is performed to identify the properties in conjunction with the electrical grid requirements and the potential challenges encountered during operation. An optimized operation example of wind generation combined with solar PV generation is presented to exemplify the flexibility and benefits of the proposed configuration. 20. Electron-Nuclear Energy Sharing in Above-Threshold Multiphoton Dissociative Ionization of H2 DEFF Research Database (Denmark) Wu, J.; Kunitski, M.; Pitzer, M. 2013-01-01 We report experimental observation of the energy sharing between electron and nuclei in above-threshold multiphoton dissociative ionization of H2 by strong laser fields. The absorbed photon energy is shared between the ejected electron and nuclei in a correlated fashion, resulting in multiple...... diagonal lines in their joint energy spectrum governed by the energy conservation of all fragment particles.... 1. Experimental measurement of the electron energy distribution function in the radio frequency electron cyclotron resonance inductive discharge International Nuclear Information System (INIS) Chung, ChinWook; Kim, S.S.; Chang, H.Y. 2004-01-01 Recently, the existence of electron cyclotron resonance (ECR) in a weakly magnetized inductively coupled plasma (MICP) has been evidenced [ChinWook Chung et al., Phys. Rev. Lett. 80, 095002 (2002)]. The distinctive feature of the ECR effect in the MICP is efficacious heating of low-energy electrons. In the present paper, electron heating characteristics in the MICP have been investigated by observing electron energy distribution function dependencies on various external parameters such as gas pressure, driving frequency, and rf power (electron density). It is found that the ECR effect on electron heating becomes enhanced with decreasing pressure or increasing driving frequency. The ECR heating becomes weak at high rf power due to the electron-electron collisions 2. Methods for measurement of electron emission yield under low energy electron-irradiation by collector method and Kelvin probe method Energy Technology Data Exchange (ETDEWEB) Tondu, Thomas; Belhaj, Mohamed; Inguimbert, Virginie [Onera, DESP, 2 Avenue Edouard Belin, 31400 Toulouse (France); Onera, DESP, 2 Avenue Edouard Belin, 31400 Toulouse, France and Fondation STAE, 4 allee Emile Monso, BP 84234-31432, Toulouse Cedex 4 (France); Onera, DESP, 2 Avenue Edouard Belin, 31400 Toulouse (France) 2010-09-15 Secondary electron emission yield of gold under electron impact at normal incidence below 50 eV was investigated by the classical collector method and by the Kelvin probe method. The authors show that biasing a collector to ensure secondary electron collection while keeping the target grounded can lead to primary electron beam perturbations. Thus reliable secondary electron emission yield at low primary electron energy cannot be obtained with a biased collector. The authors present two collector-free methods based on current measurement and on electron pulse surface potential buildup (Kelvin probe method). These methods are consistent, but at very low energy, measurements become sensitive to the earth magnetic field (below 10 eV). For gold, the authors can extrapolate total emission yield at 0 eV to 0.5, while a total electron emission yield of 1 is obtained at 40{+-}1 eV. 3. Methods for measurement of electron emission yield under low energy electron-irradiation by collector method and Kelvin probe method International Nuclear Information System (INIS) Tondu, Thomas; Belhaj, Mohamed; Inguimbert, Virginie 2010-01-01 Secondary electron emission yield of gold under electron impact at normal incidence below 50 eV was investigated by the classical collector method and by the Kelvin probe method. The authors show that biasing a collector to ensure secondary electron collection while keeping the target grounded can lead to primary electron beam perturbations. Thus reliable secondary electron emission yield at low primary electron energy cannot be obtained with a biased collector. The authors present two collector-free methods based on current measurement and on electron pulse surface potential buildup (Kelvin probe method). These methods are consistent, but at very low energy, measurements become sensitive to the earth magnetic field (below 10 eV). For gold, the authors can extrapolate total emission yield at 0 eV to 0.5, while a total electron emission yield of 1 is obtained at 40±1 eV. 4. Precessed electron beam electron energy loss spectroscopy of graphene: Beyond channelling effects International Nuclear Information System (INIS) Yedra, Ll.; Estradé, S.; Torruella, P.; Eljarrat, A.; Peiró, F.; Darbal, A. D.; Weiss, J. K. 2014-01-01 The effects of beam precession on the Electron Energy Loss Spectroscopy (EELS) signal of the carbon K edge in a 2 monolayer graphene sheet are studied. In a previous work, we demonstrated the use of precession to compensate for the channeling-induced reduction of EELS signal when in zone axis. In the case of graphene, no enhancement of EELS signal is found in the usual experimental conditions, as graphene is not thick enough to present channeling effects. Interestingly, though it is found that precession makes it possible to increase the collection angle, and, thus, the overall signal, without a loss of signal-to-background ratio 5. Electrostatic electron cyclotron waves generated by low-energy electron beams Czech Academy of Sciences Publication Activity Database Menietti, J. D.; Santolík, Ondřej; Scudder, J. D.; Pickett, J. S.; Gurnett, D. A. 2002-01-01 Roč. 107, A10, 1285 (2002), s. SMP 8-1-8-11, doi: 10.1029/2001JA009223 ISSN 0148-0227 R&D Projects: GA ČR GA205/01/1064 Grant - others:NASA(US) NAG5-7943; NASA(US) NAG5-9561; NASA(US) NAG5-8119 Institutional research plan: CEZ:AV0Z3042911; CEZ:MSM 113200004 Keywords : low-energy electron beams * cyclotron frequency Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 2.245, year: 2002 6. Progresses in low energy electron microscopy and photoemission electron microscopy studies (LEEM and PEEM) International Nuclear Information System (INIS) Koshikawa, Takanori; Yasue, Tsuneo; Kobayashi, Keisuke; Kinoshita, Toyohiko; Ono, Kanta 2008-02-01 Photon factory workshop on low energy electron microscopy (LEEM) and photoemission electron microscopy (PEEM) studies was held on October 12-13, 2005. The workshop had 18 presentations and 8 contributions to the poster session with 62 attendees. The workshop started with an invitation presentation about nano-imaging and nano-spectroscopy by photoemission electron microscope using synchrotron radiation x-rays. Next two reports were about antiferromagnetic domain structure observations of a NiO(100) surface using a combined method of PEEM and soft x-ray linear dichroism. Recent development of spin SEM (scanning electron microscope) and the observation of magnetic domains of La 1.36 Sr 1.64 Mn 2 O 7 were reported. A new method for observing magnetic domain structures with SEM was developed in which the image is the result of spin polarization of secondary electrons. This method is called spin SEM. A lecture about observation of ultra-high speed phenomena by PEEM and the invitation presentation about spin dynamics in nano-scale magnetic materials attracted much attention. Structural studies of surfaces by LEEM and PEEM were actively discussed. Summaries about the measurements of Au-Si alloy island at atomic steps on Si(111), fabrication of Ga nano-dots in SiO 2 , growth of pentacene films on thin bismuth film and graphite, the surface phase transition on metal surfaces of In/Cu(001) and Sn/Cu(001), and Cu thin film growth on W(110) were also compiled in this report. Many contributions in this report were resulted from the experiments by LEEM and PEEM using SPring-8 synchrotron radiations. (Y.K.) 7. A facility for the analysis of the electronic structures of solids and their surfaces by synchrotron radiation photoelectron spectroscopy Science.gov (United States) Hoesch, M.; Kim, T. K.; Dudin, P.; Wang, H.; Scott, S.; Harris, P.; Patel, S.; Matthews, M.; Hawkins, D.; Alcock, S. G.; Richter, T.; Mudd, J. J.; Basham, M.; Pratt, L.; Leicester, P.; Longhi, E. C.; Tamai, A.; Baumberger, F. 2017-01-01 A synchrotron radiation beamline in the photon energy range of 18-240 eV and an electron spectroscopy end station have been constructed at the 3 GeV Diamond Light Source storage ring. The instrument features a variable polarisation undulator, a high resolution monochromator, a re-focussing system to form a beam spot of 50 × 50 μm2, and an end station for angle-resolved photoelectron spectroscopy (ARPES) including a 6-degrees-of-freedom cryogenic sample manipulator. The beamline design and its performance allow for a highly productive and precise use of the ARPES technique at an energy resolution of 10-15 meV for fast k-space mapping studies with a photon flux up to 2 ṡ 1013 ph/s and well below 3 meV for high resolution spectra. 8. A facility for the analysis of the electronic structures of solids and their surfaces by synchrotron radiation photoelectron spectroscopy. Science.gov (United States) Hoesch, M; Kim, T K; Dudin, P; Wang, H; Scott, S; Harris, P; Patel, S; Matthews, M; Hawkins, D; Alcock, S G; Richter, T; Mudd, J J; Basham, M; Pratt, L; Leicester, P; Longhi, E C; Tamai, A; Baumberger, F 2017-01-01 A synchrotron radiation beamline in the photon energy range of 18-240 eV and an electron spectroscopy end station have been constructed at the 3 GeV Diamond Light Source storage ring. The instrument features a variable polarisation undulator, a high resolution monochromator, a re-focussing system to form a beam spot of 50 × 50 μm 2 , and an end station for angle-resolved photoelectron spectroscopy (ARPES) including a 6-degrees-of-freedom cryogenic sample manipulator. The beamline design and its performance allow for a highly productive and precise use of the ARPES technique at an energy resolution of 10-15 meV for fast k-space mapping studies with a photon flux up to 2 ⋅ 10 13 ph/s and well below 3 meV for high resolution spectra. 9. Simulation of off-energy electron background in DELPHI CERN Document Server Falk, E; Von Holtey, Georg 1997-01-01 Monte Carlo simulations of off-energy electron background in the DELPHI luminometer STIC are reported. The study simulates the running conditions at 68 GeV with and without bunch trains. The electrostatic separators, which create the vertical separation bumps for the the bunch trains, cause a high concentration of background in the vertical plane. The simulations are compared to LEP data taken under similar running conditions. A comparison between the simulated running conditions at 68 GeV and those of the new LEP2 beam optics at 80.5 GeV is made. Moreover, the study investigates background components entering STIC elsewhere that through the front of the detector, and a significant portion is found to enter either from the back or from below. Possible improvements of the background situation are also discussed. 10. Electronic Instrumentations for High Energy Particle Physics and Neutrino Physics CERN Document Server AUTHOR\|(INSPIRE)INSPIRE-00452332 The present dissertation describes design, qualification and operation of several electronic instrumentations for High Energy Particle Physics experiments (LHCb) and Neutrino Physics experiments (CUORE and CUPID). Starting from 2019, the LHCb experiment at the LHC accelerator will be upgraded to operate at higher luminosity and several of its detectors will be redesigned. The RICH detector will require a completely new optoelectronic readout system. The development of such system has already reached an advanced phase, and several tests at particle beam facilities allowed to qualify the performance of the entire system. In order to achieve a higher stability and a better power supply regulation for the front-end chip, a rad-hard low dropout linear regulator, named ALDO, has been developed. Design strategies, performance tests and results from the irradiation campaign are presented. In the Neutrino Physics field, large-scale bolometric detectors, like those adopted by CUORE and its future upgrade CUPID, offer u... 11. New directions in low energy electron molecule collision calculations International Nuclear Information System (INIS) Burke, P.G.; Noble, C.J. 1982-01-01 New theoretical and computational methods for studying low energy electron molecule collisions are discussed. Having considered the fixed-nuclei approximation and the form of the expansion of the total collision wavefunction, the various approximations which have been made are examined, including the static plus model exchange approximation, the static exchange approximation and the close coupling approximation, particular attention being paid to methods of including the molecular charge polarisation. Various ways which have been developed to solve the resultant equations are discussed and it is found that there is increasing emphasis being given to methods which combine the advantages of discrete multi-centre analytic bases with single centre numerical bases. (U.K.) 12. Absorptive form factors for high-energy electron diffraction International Nuclear Information System (INIS) Bird, D.M.; King, Q.A. 1990-01-01 The thermal diffuse scattering contribution to the absorptive potential in high-energy electron diffraction is calculated in the form of an absorptive contribution to the atomic form factor. To do this, the Einstein model of lattice vibrations is used, with isotropic Debye-Waller factors. The absorptive form factors are calculated as a function of scattering vector s and temperature factor M on a grid which enables polynomial interpolation of the results to be accurate to better than 2% for much of the ranges 0≤Ms 2 ≤6 and 0≤M≤2 A 2 . The computed values, together with an interpolation routine, have been incorporated into a Fortran subroutine which calculates both the real and absorptive form factors for 54 atomic species. (orig.) 13. Spectral representations of the electron energy loss in composite media International Nuclear Information System (INIS) Fuchs, R.; Barrera, R.G.; Carrillo, J.L. 1996-01-01 Using a recently developed theory for the inverse longitudinal nonlocal dielectric response for a granular composite [R. G. Barrera and R. Fuchs, Phys. Rev. B 52, 3256 (1995)], we find an effective local dielectric response from the condition that it must give the same electron energy-loss probability density as the actual nonlocal response. This local response is expressed as a spectral representation: a sum of terms with simple poles corresponding to the excitation of bulk and interfacial modes. Taking as a guideline the condition that the strength and location of the poles must satisfy sum rules, a single-surface-mode approximation is proposed. This single-mode approximation is tested for a random system of aluminum spheres in vacuum. copyright 1996 The American Physical Society 14. Influence of host matrices on krypton electron binding energies and KLL Auger transition energies Czech Academy of Sciences Publication Activity Database Inoyatov, A. K.; Perevoshchikov, L. L.; Kovalík, Alojz; Filosofov, D. V.; Yushkevich, Yu. V.; Ryšavý, Miloš; Lee, B. Q.; Kibédi, T.; Stuchbery, A. E.; Zhdanov, V. S. 2014-01-01 Roč. 197, DEC (2014), s. 64-71 ISSN 0368-2048 R&D Projects: GA ČR(CZ) GAP203/12/1896; GA MŠk LG14004 Institutional support: RVO:61389005 Keywords : Kr-83 * Rb-83 * Sr-83 * electron binding energy * KLL transitions * natural atomic level width * multiconfiguration Dirac-Fock calculations Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.436, year: 2014 15. Reflection High Energy Electron Diffraction Studies of Interface Formation. Science.gov (United States) Pukite, Paul 1988-12-01 The epitaxial growth of semiconductors, such as GaAs, by the technique of molecular beam epitaxy (MBE) has led to many improvements in device performance and capabilities. One important system is the epitaxial growth of GaAs on Si. This holds great promise for integrating optical and electronic devices on the same chip. The key to achieving this is to grow high quality GaAs layers on Si substrates. In this investigation, single-crystal GaAs was grown on Si and Ge substrates by MBE. The growth of the epitaxial layers was investigated in situ with reflection high-energy electron diffraction (RHEED). Important in this heteroepitaxial system is that two possible GaAs crystal orientations can be obtained. By using a theory of kinematic electron diffraction developed in the course of this work, the mechanisms and growth conditions which choose between the two GaAs orientations have been determined for the first time. A further result is that the epitaxial growth processes are anisotropic on the two orientations. This leads to different crystalline qualities dependent on the orientation. To understand this in more detail, the crystal growth process was formulated mathematically. By incorporating the concepts of anisotropic diffusion and adsorption into a nonlinear differential equation, the time-dependent growth and RHEED behavior has been calculated and compared to experiment. The experimental observations of RHEED intensity oscillations and two-dimensional clustering are in excellent agreement with the diffraction and growth theories. It is concluded that surface steps play a vital role in the crystal growth and interface formation processes reported in this study. 16. Electron energy-loss and soft X-ray emission spectroscopy of electronic structure of MgB4 Science.gov (United States) Sato, Yohei; Saito, Taiki; Tsuchiya, Kohei; Terauchi, Masami; Saito, Hiroki; Takeda, Masatoshi 2017-09-01 The electronic structure of MgB4, with the characteristic crystal structure comprising one-dimensional pentagonal B6 cluster chain, was investigated using electron energy-loss spectroscopy and soft X-ray emission spectroscopy based on transmission electron microscopy. The dielectric function and density of state of unoccupied and occupied states were clarified experimentally for the first time. Although theoretical calculations has predicted MgB4 to be a semiconductor, the electron energy-loss spectrum in this study show a plasmon peak at 0.4 eV, which might be due to carrier electrons. Theoretical calculations suggested that the electronic states near the Fermi energy are localized along the one dimensional B6 cluster chain. Therefore, one-dimensional electric conductivity is expected. 17. Ab initio electronic band structure study of III-VI layered semiconductors Science.gov (United States) Olguín, Daniel; Rubio-Ponce, Alberto; Cantarero, Andrés 2013-08-01 We present a total energy study of the electronic properties of the rhombohedral γ-InSe, hexagonal ɛ-GaSe, and monoclinic GaTe layered compounds. The calculations have been done using the full potential linear augmented plane wave method, including spin-orbit interaction. The calculated valence bands of the three compounds compare well with angle resolved photoemission measurements and a discussion of the small discrepancies found has been given. The present calculations are also compared with recent and previous band structure calculations available in the literature for the three compounds. Finally, in order to improve the calculated band gap value we have used the recently proposed modified Becke-Johnson correction for the exchange-correlation potential. 18. Probe method of measuring the electron energy distribution in plasmas International Nuclear Information System (INIS) Amemiya, Hiroshi 1984-01-01 The function for the velocity distribution of electrons in plasma in a basic function associated with various phenomena. The probe method gives the distribution by a simple technique to insert a micro-electrode into plasma, and has good spatial resolution. It is specifically useful for weakly ionized, low temperature plasma. The purpose of this paper is to assist experimenters so that they can easily use this method for various phenomena by starting at its basic principle and explaining the scope of application and actual measuring techniques. The scope of application is considered by dividing it into the problems of sheath thickness, collision effect, the energy distribution of beam, the influence of probe end, probe surface phenomenon, magnetized plasma, the measurement of high energy tail, etc. For sheath thickness, it is accepted if the difference between sheath radius and probe radius is shorter than mean free path, and this is a measure for the application limit. The probe method is applicable as far as the beam density is far smaller than plasma density, and the symmetry of positive ion sheath is not disturbed. The surface area of a counter electrode should be 10 4 .Rc/lambda times or more of the probe surface area, where Rc is the radius of a counter electrode. The differentiation method of the probe characteristics includes A.C. method, high speed sweep measurement or digital method, and some applications are described. (Wakatsuki, Y.) 19. High-Resolution Measurements of Low-Energy Conversion Electrons CERN Multimedia Gizon, A; Putaux, J 2002-01-01 Measurements of low-energy internal conversion electrons have been performed with high energy resolution in some N = 105 odd and odd-odd nuclei using a semi-circular spectrograph associated to a specific tape transport system. These experiments aimed to answer the following questions~: \\begin{itemize} \\item Do M3 isomeric transitions exist in $^{183}$Pt and $^{181}$Os, isotones of $^{184}$Au~? \\item Are the neutron configurations proposed to describe the isomeric and ground states of $^{184}$Au right or wrong~? \\item Does it exist an isomeric state in $^{182}$Ir, isotone of $^{181}$Os, $^{183}$Pt and $^{184}$Au~? \\item What are the spin and parity values of the excited states of $^{182}$Ir~? \\end{itemize} In $^{183}$Pt, the 35.0 keV M3 isomeric transition has been clearly observed and the reduced transition probability has been determined. The deduced hindrance factor is close to that observed in the neighbouring odd-odd $^{184}$Au nucleus. This confirms the neutron configurations previously proposed for the ... 20. Conductive Elastomers for Stretchable Electronics, Sensors and Energy Harvesters Directory of Open Access Journals (Sweden) Jin-Seo Noh 2016-04-01 Full Text Available There have been a wide variety of efforts to develop conductive elastomers that satisfy both mechanical stretchability and electrical conductivity, as a response to growing demands on stretchable and wearable devices. This article reviews the important progress in conductive elastomers made in three application fields of stretchable technology: stretchable electronics, stretchable sensors, and stretchable energy harvesters. Diverse combinations of insulating elastomers and non-stretchable conductive materials have been studied to realize optimal conductive elastomers. It is noted that similar material combinations and similar structures have often been employed in different fields of application. In terms of stretchability, cyclic operation, and overall performance, fields such as stretchable conductors and stretchable strain/pressure sensors have achieved great advancement, whereas other fields like stretchable memories and stretchable thermoelectric energy harvesting are in their infancy. It is worth mentioning that there are still obstacles to overcome for the further progress of stretchable technology in the respective fields, which include the simplification of material combination and device structure, securement of reproducibility and reliability, and the establishment of easy fabrication techniques. Through this review article, both the progress and obstacles associated with the respective stretchable technologies will be understood more clearly. 1. Energy spectrum of Compton scattering of laser photons on relativistic electrons International Nuclear Information System (INIS) Ando, Hiroaki; Yoneda, Yasuharu 1976-01-01 The high energy photons in gamma-ray region are obtainable by the Compton scattering of laser photons on relativistic electrons. But the motion of the electrons in the storage ring is not necessarily uniform. In the study of the uneven effect, the energy distribution of scattered photons is derived from the assumed momentum distribution of incident electrons. It is generally impossible to derive the momentum distribution of incident electrons from the energy spectrum of scattered photons. The additional conditions which make this possible in a special case are considered. A calculational method is examined for deriving the energy spectrum of scattered photons from the assumed momentum distribution of incident electrons. (Mori, K.) 2. Radiosensitivity of chlorella after medium energy accelerated electron irradiation; Radiosensibilite des chlorelles aux electrons acceleres de moyenne energie Energy Technology Data Exchange (ETDEWEB) Roux, J.C. [commissariat a L' Energie Atomique, Grenoble (France). Centre d' Etudes Nucleaires 1966-06-01 The survival curves (capability of multiplication) of chlorella pyrenoidosa after irradiations can be used for soft electrons (0.65 and 1 MeV), hence penetrating into only 2 to 4 millimeters of water: the algae are laying on porous membranes and the doses are calculated from the power of the electron beam measured by the electric current on a metallic target or by Fricke's dosimetry. With these techniques, it is showed and discussed the part of anoxia in the radioprotection (magnitude or reduction of the dose calculated from the slope of survival curves: 2.5 ) that is more important than the restoration studied by the fractionation of the dose. The 0.65 and 1 MeV electrons have a biologic effect lesser than 180 keV X-rays (RBE - relative biological efficiency - calculated on the slope of survival curves is 0.92 in aerated irradiation, 0.56 in the deoxygenated irradiation). (author) [French] Les courbes de survie clonale (capacite de multiplication) de chlorella pyrenoidosa apres irradiation sont realisables meme avec des electrons peu energetiques (0.65 et 1 MeV), donc peu penetrants, par l'irradiation d'algues deposees sur membrane filtrante et grace au calcul de la dose a partir de l'energie du faisceau mesure par le courant que celui-ci cree dans une cible metallique ou par dosimetrie de Fricke. Par ces techniques, on a montre et discute le role de l'anoxie dans la radioprotection des chlorelles (facteur de reduction de la dose calcule sur la pente des courbes de survie de 2.5) qui est plus important que le pouvoir de restauration etudie par le fractionnement de la dose. Les electrons utilises ont un effet biologique moins grand que les rayons X de 180 keV (l'efficacite biologique relative - EBR - calculee sur la pente des courbes de survie est de 0.9 en presence d'air, 0.6 en presence d'azote) 3. Excitation and dissociation of molecules by low-energy (0-15 eV) electrons International Nuclear Information System (INIS) Verhaart, G.J. 1980-01-01 The author deals with excitation and dissociation processes which result from the interaction between low-energy (0.15 eV) electrons and molecules. Low-energy electron-impact spectroscopy is used to gain a better knowledge of the electronic structure of halomethanes, ethylene and some of its halogen substituted derivatives, and some more complex organic molecules. (Auth.) 4. Electron energy loss spectroscopy of YBa sub 2 Cu sub 3 O sub 7-x Energy Technology Data Exchange (ETDEWEB) Richter, A.; Mahmoud, S.; Kleint, C.; Ritschel, M. (Inst. fuer Werkstoffphysik und Schichttechnology, Dresden (Germany) Fachbereich Physik, Univ. Leipzig (Germany)) 1991-01-01 Electronic excitations of Y-Ba-Cu-O polycrystalline material in superconducting form have been investigated by electron energy loss spectroscopy in reflection. The data obtained confirm recent band structure models for this material. Low electron energy losses correspond to energy levels close to the Fermi energy with an upper and lower Hubbard subband and an anionic O 2p band in the middle. Loss peaks due to interband transitions, plasmon excitations, and core electron excitations have been observed, the origin of which is interpreted by a schematic energy level diagram. (orig.). 5. Energy dependence of ulrathin LiF-dosemeters for high energy electrons and high energy X-radiation International Nuclear Information System (INIS) Kupfer, T. 1977-02-01 The energy dependence of ultrathin LiF-dosemeters for high energy electrons (5-40 MeV) and high energy X-radiation (6 MV, 42 MV) is experimentally determined. The experimental values are compared to values calculted earlier by other authors. The influence of the thickness of the dosemeters have been considered by comparison of experimental values for 0.03 mm thick dosemeters and theoretical values for 0.13 mm and 0.38 mm thick ones. Also different commersially available dosemeters have been compared by experiments. It is difficult to draw any other conclutions about the energy dependence than that the variation of the relative responce is within +- 3 percent (2S). However the results seems to be sulficient for clinical applications 6. Introduction to electronics and applications in high energy physics CERN Multimedia CERN. Geneva 2004-01-01 Electronics in HEP experiments: specificities and evolution The Art of Electronics: is there something beyond Ohm's law? Basic building blocks of Analog electronics: quickly understanding a schematic Charge preamps, current preamps and future preamps, shaping and the rest Electronics noise: fundamental and practical Evolution of technology: ASICs, FPGAs... 7. Energy Dependence of Near-relativistic Electron Spectrum at ... the Relativistic Electron Dropouts (REDs) and the Relativistic Electron Enhancements. (REEs) observed at the geosynchronous altitudes. The sudden drop in the relativistic electron flux often by two orders of magnitude is called RED which is usually pre- ceded by the gradual enhancement in the relativistic electron fluxes, ... 8. Energy efficient hotspot-targeted embedded liquid cooling of electronics International Nuclear Information System (INIS) Sharma, Chander Shekhar; Tiwari, Manish K.; Zimmermann, Severin; Brunschwiler, Thomas; Schlottig, Gerd; Michel, Bruno; Poulikakos, Dimos 2015-01-01 Highlights: • We present a novel concept for hotspot-targeted, energy efficient ELC for electronic chips. • Microchannel throttling zones distribute flow optimally without any external control. • Design is optimized for highly non-uniform multicore chip heat flux maps. • Optimized design minimizes chip temperature non-uniformity. • This is achieved with pumping power consumption less than 1% of total chip power. - Abstract: Large data centers today already account for nearly 1.31% of total electricity consumption with cooling responsible for roughly 33% of that energy consumption. This energy intensive cooling problem is exacerbated by the presence of hotspots in multicore microprocessors due to excess coolant flow requirement for thermal management. Here we present a novel liquid-cooling concept, for targeted, energy efficient cooling of hotspots through passively optimized microchannel structures etched into the backside of a chip (embedded liquid cooling or ELC architecture). We adopt an experimentally validated and computationally efficient modeling approach to predict the performance of our hotspot-targeted ELC design. The design is optimized for exemplar non-uniform chip power maps using Response Surface Methodology (RSM). For industrially acceptable limits of approximately 0.4 bar (40 kPa) on pressure drop and one percent of total chip power on pumping power, the optimized designs are computationally evaluated against a base, standard ELC design with uniform channel widths and uniform flow distribution. For an average steady-state heat flux of 150 W/cm 2 in core areas (hotspots) and 20 W/cm 2 over remaining chip area (background), the optimized design reduces the maximum chip temperature non-uniformity by 61% to 3.7 °C. For a higher average, steady-state hotspot heat flux of 300 W/cm 2 , the maximum temperature non-uniformity is reduced by 54% to 8.7 °C. It is shown that the base design requires a prohibitively high level of pumping power (about 9. Modeling the high-energy electronic state manifold of adenine: Calibration for nonlinear electronic spectroscopy Energy Technology Data Exchange (ETDEWEB) Nenov, Artur, E-mail: [email protected]; Giussani, Angelo; Segarra-Martí, Javier; Jaiswal, Vishal K. [Dipartimento di Chimica “G. Ciamician,” Università di Bologna, Via Selmi 2, IT-40126 Bologna (Italy); Rivalta, Ivan [Université de Lyon, CNRS, Institut de Chimie de Lyon, École Normale Supérieure de Lyon, 46 Allée d’Italie, F-69364 Lyon Cedex 07 (France); Cerullo, Giulio [Dipartimento di Fisica, Politecnico di Milano, IFN-CNR, Piazza Leonardo Da Vinci 32, IT-20133 Milano (Italy); Mukamel, Shaul [Department of Chemistry, University of California, Irvine, California 92697-2025 (United States); Garavelli, Marco, E-mail: [email protected], E-mail: [email protected] [Dipartimento di Chimica “G. Ciamician,” Università di Bologna, Via Selmi 2, IT-40126 Bologna (Italy); Université de Lyon, CNRS, Institut de Chimie de Lyon, École Normale Supérieure de Lyon, 46 Allée d’Italie, F-69364 Lyon Cedex 07 (France) 2015-06-07 Pump-probe electronic spectroscopy using femtosecond laser pulses has evolved into a standard tool for tracking ultrafast excited state dynamics. Its two-dimensional (2D) counterpart is becoming an increasingly available and promising technique for resolving many of the limitations of pump-probe caused by spectral congestion. The ability to simulate pump-probe and 2D spectra from ab initio computations would allow one to link mechanistic observables like molecular motions and the making/breaking of chemical bonds to experimental observables like excited state lifetimes and quantum yields. From a theoretical standpoint, the characterization of the electronic transitions in the visible (Vis)/ultraviolet (UV), which are excited via the interaction of a molecular system with the incoming pump/probe pulses, translates into the determination of a computationally challenging number of excited states (going over 100) even for small/medium sized systems. A protocol is therefore required to evaluate the fluctuations of spectral properties like transition energies and dipole moments as a function of the computational parameters and to estimate the effect of these fluctuations on the transient spectral appearance. In the present contribution such a protocol is presented within the framework of complete and restricted active space self-consistent field theory and its second-order perturbation theory extensions. The electronic excited states of adenine have been carefully characterized through a previously presented computational recipe [Nenov et al., Comput. Theor. Chem. 1040–1041, 295-303 (2014)]. A wise reduction of the level of theory has then been performed in order to obtain a computationally less demanding approach that is still able to reproduce the characteristic features of the reference data. Foreseeing the potentiality of 2D electronic spectroscopy to track polynucleotide ground and excited state dynamics, and in particular its expected ability to provide 10. Modeling the high-energy electronic state manifold of adenine: Calibration for nonlinear electronic spectroscopy Science.gov (United States) Nenov, Artur; Giussani, Angelo; Segarra-Martí, Javier; Jaiswal, Vishal K.; Rivalta, Ivan; Cerullo, Giulio; Mukamel, Shaul; Garavelli, Marco 2015-06-01 Pump-probe electronic spectroscopy using femtosecond laser pulses has evolved into a standard tool for tracking ultrafast excited state dynamics. Its two-dimensional (2D) counterpart is becoming an increasingly available and promising technique for resolving many of the limitations of pump-probe caused by spectral congestion. The ability to simulate pump-probe and 2D spectra from ab initio computations would allow one to link mechanistic observables like molecular motions and the making/breaking of chemical bonds to experimental observables like excited state lifetimes and quantum yields. From a theoretical standpoint, the characterization of the electronic transitions in the visible (Vis)/ultraviolet (UV), which are excited via the interaction of a molecular system with the incoming pump/probe pulses, translates into the determination of a computationally challenging number of excited states (going over 100) even for small/medium sized systems. A protocol is therefore required to evaluate the fluctuations of spectral properties like transition energies and dipole moments as a function of the computational parameters and to estimate the effect of these fluctuations on the transient spectral appearance. In the present contribution such a protocol is presented within the framework of complete and restricted active space self-consistent field theory and its second-order perturbation theory extensions. The electronic excited states of adenine have been carefully characterized through a previously presented computational recipe [Nenov et al., Comput. Theor. Chem. 1040-1041, 295-303 (2014)]. A wise reduction of the level of theory has then been performed in order to obtain a computationally less demanding approach that is still able to reproduce the characteristic features of the reference data. Foreseeing the potentiality of 2D electronic spectroscopy to track polynucleotide ground and excited state dynamics, and in particular its expected ability to provide 11. Models for the transport of low energy electrons in water and the yield of hydrated electrons at early times International Nuclear Information System (INIS) Brenner, D.J.; Miller, J.H.; Ritchie, R.H.; Bichsel, H. 1985-01-01 An insulator model with four experimental energy bands was used to fit the optical properties of liquid water and to extend these data to non-zero momentum transfer. Inelastic mean free paths derived from this dielectric response function provided the basic information necessary to degrade high energy electrons to the subexcitation energy domain. Two approaches for the transport of subexcitation electrons were investigated. (i) Gas phase cross sections were used to degrade subexcitation electrons to thermal energy and the thermalization lengths were scaled to unit density. (ii) Thermalization lengths were estimated by age-diffusion theory with a stopping power deduced from the data on liquid water and transport cross sections derived from elastic scattering in water vapor. Theoretical ranges were compared to recent experimental results. A stochastic model was used to calculate the rapid diffusion and reaction of hydrated electrons with other radiolysis products. The sensitivity of the calculated yields to the model assumptions and comparison with experimental data are discussed 12. The role of low-energy (≤ 20 eV) electrons in astrochemistry Science.gov (United States) Boyer, Michael C.; Rivas, Nathalie; Tran, Audrey A.; Verish, Clarissa A.; Arumainayagam, Christopher R. 2016-10-01 UV photon-driven condensed phase cosmic ice reactions have been the main focus in understanding the extraterrestrial synthesis of complex organic molecules. Low-energy (≤ 20 eV) electron-induced reactions, on the other hand, have been largely ignored. In this article, we review studies employing surface science techniques to study low-energy electron-induced condensed phase reactions relevant to astrochemistry. In particular, we show that low-energy electron irradiation of methanol ices leads to the synthesis of many of the same complex molecules formed through UV irradiation. Moreover, our results are qualitatively consistent with the hypothesis that high-energy condensed phase radiolysis is mediated by low-energy electron-induced reactions. In addition, due to the numbers of available low-energy secondary electrons resulting from the interaction of high-energy radiation with matter as well as differences between electron- and photon-induced processes, low-energy electron-induced reactions are perhaps as, or even more, effective than photon-induced reactions in initiating condensed-phase chemical reactions in the interstellar medium. Consequently, we illustrate a need for astrochemical models to include the details of electron-induced reactions in addition to those driven by UV photons. Finally, we show that low-energy electron-induced reactions may lead to the production of unique molecular species that could serve as tracer molecules for electron-induced condensed phase reactions in the interstellar medium. 13. Three-dimensionality of the bulk electronic structure in WTe2 Science.gov (United States) Wu, Yun; Jo, Na Hyun; Mou, Daixiang; Huang, Lunan; Bud'ko, S. L.; Canfield, P. C.; Kaminski, Adam 2017-05-01 We use temperature- and field-dependent resistivity measurements (Shubnikov-de Haas quantum oscillations) and ultrahigh-resolution, tunable, vacuum ultraviolet laser-based angle-resolved photoemission spectroscopy (ARPES) to study the three-dimensionality (3D) of the bulk electronic structure in WTe 2 , a type II Weyl semimetal. The bulk Fermi surface (FS) consists of two pairs of electron pockets and two pairs of hole pockets along the X -Γ -X direction as detected by using an incident photon energy of 6.7 eV, which is consistent with the previously reported data. However, if using an incident photon energy of 6.36 eV, another pair of tiny electron pockets is detected on both sides of the Γ point, which is in agreement with the small quantum oscillation frequency peak observed in the magnetoresistance. Therefore, the bulk, 3D FS consists of three pairs of electron pockets and two pairs of hole pockets in total. With the ability of fine tuning the incident photon energy, we demonstrate the strong three-dimensionality of the bulk electronic structure in WTe 2 . The combination of resistivity and ARPES measurements reveals the complete, and consistent, picture of the bulk electronic structure of this material. 14. Electronic energy transfer through non-adiabatic vibrational-electronic resonance. II. 1D spectra for a dimer Science.gov (United States) Tiwari, Vivek; Jonas, David M. 2018-02-01 Vibrational-electronic resonance in photosynthetic pigment-protein complexes invalidates Förster's adiabatic framework for interpreting spectra and energy transfer, thus complicating determination of how the surrounding protein affects pigment properties. This paper considers the combined effects of vibrational-electronic resonance and inhomogeneous variations in the electronic excitation energies of pigments at different sites on absorption, emission, circular dichroism, and hole-burning spectra for a non-degenerate homodimer. The non-degenerate homodimer has identical pigments in different sites that generate differences in electronic energies, with parameters loosely based on bacteriochlorophyll a pigments in the Fenna-Matthews-Olson antenna protein. To explain the intensity borrowing, the excited state vibrational-electronic eigenvectors are discussed in terms of the vibrational basis localized on the individual pigments, as well as the correlated/anti-correlated vibrational basis delocalized over both pigments. Compared to those in the isolated pigment, vibrational satellites for the correlated vibration have the same frequency and precisely a factor of 2 intensity reduction through vibrational delocalization in both absorption and emission. Vibrational satellites for anti-correlated vibrations have their relaxed emission intensity reduced by over a factor 2 through vibrational and excitonic delocalization. In absorption, anti-correlated vibrational satellites borrow excitonic intensity but can be broadened away by the combination of vibronic resonance and site inhomogeneity; in parallel, their vibronically resonant excitonic partners are also broadened away. These considerations are consistent with photosynthetic antenna hole-burning spectra, where sharp vibrational and excitonic satellites are absent. Vibrational-excitonic resonance barely alters the inhomogeneously broadened linear absorption, emission, and circular dichroism spectra from those for a 15. Why do Electrons with "Anomalous Energies" appear in High-Pressure Gas Discharges? Science.gov (United States) Kozyrev, Andrey; Kozhevnikov, Vasily; Semeniuk, Natalia 2018-01-01 Experimental studies connected with runaway electron beams generation convincingly shows the existence of electrons with energies above the maximum voltage applied to the discharge gap. Such electrons are also known as electrons with "anomalous energies". We explain the presence of runaway electrons having so-called "anomalous energies" according to physical kinetics principles, namely, we describe the total ensemble of electrons with the distribution function. Its evolution obeys Boltzmann kinetic equation. The dynamics of self-consistent electromagnetic field is taken into the account by adding complete Maxwell's equation set to the resulting system of equations. The electrodynamic mechanism of the interaction of electrons with a travelling-wave electric field is analyzed in details. It is responsible for the appearance of electrons with high energies in real discharges. 16. Slow electron energy balance for hybrid models of direct-current glow discharges Science.gov (United States) Eliseev, S. I.; Bogdanov, E. A.; Kudryavtsev, A. A. 2017-09-01 In this paper, we present the formulation of slow electron energy balance for hybrid models of direct current (DC) glow discharge. Electrons originating from non-local ionization (secondary) contribute significantly to the energy balance of slow electrons. An approach towards calculating effective energy brought by a secondary electron to the group of slow electrons by means of Coulomb collisions is suggested. The value of effective energy shows a considerable dependence on external parameters of a discharge, such as gas pressure, type, and geometric parameters. The slow electron energy balance was implemented into a simple hybrid model that uses analytical formulation for the description of non-local ionization by fast electrons. Simulations of short (without positive column) DC glow discharge in argon are carried out for a range of gas pressures. Comparison with experimental data showed generally good agreement in terms of current-voltage characteristics, electron density, and electron temperature. Simulations also capture the trend of increasing electron density with decreasing pressure observed in the experiment. Analysis shows that for considered conditions, the product of maximum electron density ne and electron temperature Te in negative glow is independent of gas pressure and depends on the gas type, cathode material, and discharge current. Decreasing gas pressure reduces the heating rate of slow electrons during Coulomb collisions with secondary electrons, which leads to lower values of Te and, in turn, higher maximum ne. 17. Calcium measurements with electron probe X-ray and electron energy loss analysis International Nuclear Information System (INIS) LeFurgey, A.; Ingram, P. 1990-01-01 This paper presents a broad survey of the rationale for electron probe X-ray microanalysis (EPXMA) and the various methods for obtaining qualitative and quantitative information on the distribution and amount of elements, particularly calcium, in cryopreserved cells and tissues. Essential in an introductory consideration of microanalysis in biological cryosections is the physical basis for the instrumentation, fundamentals of X-ray spectrometry, and various analytical modes such as static probing and X-ray imaging. Some common artifacts are beam damage and contamination. Inherent pitfalls of energy dispersive X-ray systems include Si escape peaks, doublets, background, and detector calibration shifts. Quantitative calcium analysis of thin cryosections is carried out in real time using a multiple least squares fitting program on filtered X-ray spectra and normalizing the calcium peak to a portion of the continuum. Recent work includes the development of an X-ray imaging system where quantitative data can be retrieved off-line. The minimum detectable concentration of calcium in biological cryosections is approximately 300 mumole kg dry weight with a spatial resolution of approximately 100 A. The application of electron energy loss (EELS) techniques to the detection of calcium offers the potential for greater sensitivity and spatial resolution in measurement and imaging. Determination of mass thickness with EELS can facilitate accurate calculation of wet weight concentrations from frozen hydrated and freeze-dried specimens. Calcium has multiple effects on cell metabolism, membrane transport and permeability and, thus, on overall cell physiology or pathophysiology. Cells can be rapidly frozen for EPXMA during basal or altered functional conditions to delineate the location and amount of calcium within cells. 72 references 18. Evolutionary developments in x ray and electron energy loss microanalysis instrumentation for the analytical electron microscope Science.gov (United States) Zaluzec, Nester J. Developments in instrumentation for both X ray Dispersive and Electron Energy Loss Spectroscopy (XEDS/EELS) over the last ten years have given the experimentalist a greatly enhanced set of analytical tools for characterization. Microanalysts have waited for nearly two decades now in the hope of getting a true analytical microscope and the development of 300 to 400 kV instruments should have allowed us to attain this goal. Unfortunately, this has not generally been the case. While there have been some major improvements in the techniques, there has also been some devolution in the modern AEM (Analytical Electron Microscope). In XEDS, the majority of today's instruments are still plagued by the hole count effect, which was first described in detail over fifteen years ago. The magnitude of this problem can still reach the 20 percent level for medium atomic number species in a conventional off-the-shelf intermediate voltage AEM. This is an absurd situation and the manufacturers should be severely criticized. Part of the blame, however, also rests on the AEM community for not having come up with a universally agreed upon standard test procedure. Fortunately, such a test procedure is in the early stages of refinement. The proposed test specimen consists of an evaporated Cr film approx. 500 to 1000A thick supported upon a 3mm diameter Molybdenum 200 micron aperture. 19. Electrons' energy in GRB afterglows implied by radio peaks Science.gov (United States) Beniamini, Paz; van der Horst, Alexander J. 2017-12-01 Gamma-ray burst (GRB) afterglows have been observed across the electromagnetic spectrum, and physical parameters of GRB jets and their surroundings have been derived using broad-band modelling. While well-sampled light curves across the broad-band spectrum are necessary to constrain all the physical parameters, some can be strongly constrained by the right combination of just a few observables, almost independently of the other unknowns. We present a method involving the peaks of radio light curves to constrain the fraction of shock energy that resides in electrons, εe. This parameter is an important ingredient for understanding the microphysics of relativistic shocks. Based on a sample of 36 radio afterglows, we find εe has a narrow distribution centred around 0.13-0.15. Our method is suggested as a diagnostic tool for determining εe, and to help constrain the broad-band modelling of GRB afterglows. Some earlier measurements of the spreads in parameter values for εe, the kinetic energy of the shock and the density of the circumburst medium, based on broad-band modelling across the entire spectrum, are at odds with our analysis of radio peaks. This could be due to different modelling methods and assumptions, and possibly missing ingredients in past and current modelling efforts. Furthermore, we show that observations at ≳10 GHz performed 0.3-30 d after the GRB trigger are best suited for pinpointing the synchrotron peak frequency, and, consequently, εe. At the same time, observations at lower radio frequencies can pin down the synchrotron self-absorption frequency and help constrain the other physical parameters of GRB afterglows. 20. Applications of CCTO supercapacitor in energy storage and electronics Science.gov (United States) Pandey, R. K.; Stapleton, W. A.; Tate, J.; Bandyopadhyay, A. K.; Sutanto, I.; Sprissler, S.; Lin, S. 2013-06-01 Since the discovery of colossal dielectric constant in CCTO supercapacitor in 2000, development of its practical application to energy storage has been of great interest. In spite of intensive efforts, there has been thus far, no report of proven application. The object of this research is to understand the reason for this lack of success and to find ways to overcome this limitation. Reported herein is the synthesis of our research in ceramic processing of this material and its characterization, particularly with the objective of identifying potential applications. Experimental results have shown that CCTO's permittivity and loss tangent, the two most essential dielectric parameters of fundamental importance for the efficiency of a capacitor device, are intrinsically coupled. They increase or decrease in tandem. Therefore, efforts to simultaneously retain the high permittivity while minimizing the loss tangent of CCTO might not succeed unless an entirely non-typical approach is taken for processing this material. Based on the experimental results and their analysis, it has been identified that it is possible to produce CCTO bulk ceramics with conventional processes having properties that can be exploited for fabricating an efficient energy storage device (EDS). We have additionally identified that CCTO can be used for the development of efficient solid state capacitors of Class II type comparable to the widely used barium titanate (BT) capacitors. Based on high temperature studies of the resistivity and the Seebeck coefficient it is found that CCTO is a wide bandgap n-type semiconductor material which could be used for high temperature electronics. The temperature dependence of the linear thermal expansion of CCTO shows the presence of possible phase changes at 220 and 770 °C the origin of which remains unexplained.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8243895769119263, "perplexity": 3977.1861674677816}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794870771.86/warc/CC-MAIN-20180528024807-20180528044807-00067.warc.gz"}
http://magazine.freepchelp.uk/how-to-return-command-prompt-to-the-power-user-menu-in-windows-10-creators-update/	How to return Command Prompt to the Power User menu in Windows 10 Creators Update 0 408 How do you get the Command Prompt back on the Power User menu? With the Creators Update came a few changes to the Windows 10 Power User menu (accessed by right-clicking the Start menu or using the Windows key + X keyboard shortcut), namely the removal of the Command Prompt and Command Prompt (Admin) options, which allowed users to quickly open a new window. What’s the difference between PowerShell and Command Prompt? Command Prompt is something that is familiar to plenty of Windows users. It is based on the same DOS commands that have been used on DOS systems forever, and therefore it is limited in what it can do, especially for system administrators and advanced users. However, for most Windows users, Command Prompt is all that they’ll ever need. Windows PowerShell, on the other hand, is designed for more advanced uses, like registry editing. PowerShell uses “cmdlets,” which are similar to regular command-line commands. These cmdlets, however, can provide an output that is piped into the input of another cmdlet, essentially letting a string of commands manipulate the same data. The result is both a command-line shell and a scripting language. How to replace PowerShell with Command Prompt If PowerShell doesn’t seem like something you’ll be working with, but you do use Command Prompt to quickly check your IP or perform other tasks, you can get Command Prompt back on the Power User menu.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9218384027481079, "perplexity": 3568.4029541398636}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986675598.53/warc/CC-MAIN-20191017172920-20191017200420-00323.warc.gz"}
https://www.jiskha.com/questions/631654/For-the-sequence-an-6-5-n-1-its-first-term-is-its-second-term-is	# algebra For the sequence an=6+5*(n-1), its first term is__??__ ; its second term is__??__ ; its third term is__??__ ; its fourth term is__??__ ; its fifth term is__??_ ; its common difference d= __??__ . 1. 0 2. 0 ## Similar Questions 1. ### algebra Is the sequence an=8n-14 arithmetic? Your answer is (input yes or no)__??__ ; if your answer is yes, its first term is__??__ . its common difference is__??__ . 2. ### Math 3,5,-5... The first term in the sequence of #'s shown above is 3. Each even # term is 2 more than the previous term and each odd # term, after the first, is -1 times the previous term. For example, the second term is 3+2, and the 3. ### Algebra I am so lost on these problems. Write a geometric sequence that starts with 3 and has a common ratio of 5. What is the 23rd term in the sequence. Write an arithmetic sequence that has a common difference of 4 and the eighth term 4. ### Quick math help Find the tenth term of the sequence: -6,1,8... Is it 57? For the sequence:2,4,8,16 the value of s4 is____. Is it 8? Find the 7th term of the sequence: 1,2,4,... Is it 64? Which term of this sequence is 275? 5,10,15,... Is it 1357? 5. ### Quick Math Help Find the tenth term of the sequence: -6,1,8... Is it 57? For the sequence:2,4,8,16 the value of s4 is____. Is it 8? Find the 7th term of the sequence: 1,2,4,... Is it 64? Which term of this sequence is 275? 5,10,15,... Is it 1357? 6. ### Quick math help Find the tenth term of the sequence: -6,1,8... Is it 57? For the sequence:2,4,8,16 the value of s4 is____. Is it 8? Find the 7th term of the sequence: 1,2,4,... Is it 64? Which term of this sequence is 275? 5,10,15,... Is it 1357? 7. ### Math 1. Find the 12th term of the arithmetic sequence 2, 6, 10, … . 2. Solve for the 101st term of the sequence whose 1st term is x-y and d=2x+y-3. 3. In the sequence 2, 6, 10, … , what term has a value of 106? 8. ### math Each term in a sequence of numbers, except for the 1st term, is 2 less than the square root of the previous term.If the 3rd term of this sequence is 1, what is the first term? 9. ### math find the rule for the Nth term of the arithmetic sequence. 11/2, 25/6, 17/6, 3/2, 1/6..... If you change the denomators to 6, you should notice the numerators follow the sequence: 33,25,17,9,1,...which is an arithmetic sequence 10. ### Algebra I What is the 2011th term of the arithmetic sequence −4, −1, 2, 5, . . . , where each term after the first is 3 more than the preceding term?( remember -4 is the first term of the sequence.) (I posted this before but it was the More Similar Questions	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.942099392414093, "perplexity": 1247.50359315744}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512332.36/warc/CC-MAIN-20181019062113-20181019083613-00368.warc.gz"}
https://math.eretrandre.org/tetrationforum/showthread.php?tid=887&pid=7189	• 0 Vote(s) - 0 Average • 1 • 2 • 3 • 4 • 5 [2014] The secondary fixpoint issue. tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 06/15/2014, 06:31 PM Let exp(x) =/= x , exp(exp(x)) = x , Im(x) > 0. Thus x is a secondary fixpoint in the upper half-plane. Let y be a number in the upper half-plane such that sexp(y) = x and sexp is analytic in the upper half-plane. Then by assuming the existance of y and the validity of sexp(z+1) = exp(sexp(z)) everywhere we get : sexp(y+1) =/= sexp(y) , sexp(y+2) = sexp(y). thus for y = a + b i and R any real , we have that : sexp(R + b i) is a nonconstant analytic PERIODIC function in R. And then by analytic continuation , sexp(z) is a nonconstant analytic periodic function in the upper half-plane !! But that cannot be true !! Same applies to n-ary fixpoints !! Seems unlikely that sexp contains none of these n-ary fixpoints ?! And as for the functional equation f(x+1) = exp(f(x)) + 2pi i that is on another branch. So that does not seem to help. Where is the mistake ?? I posted this before , hoping the seeming paradox is understood now. Also note that the "paradox" is not limited to 2nd ary fixpoints , 3rd ary fixpoints etc but also V-ary fixpoints for any V > 1 ! regards tommy1729 sheldonison Long Time Fellow Posts: 640 Threads: 22 Joined: Oct 2008 06/15/2014, 08:07 PM (This post was last modified: 06/15/2014, 09:05 PM by sheldonison.) (06/15/2014, 06:31 PM)tommy1729 Wrote: .... Seems unlikely that sexp contains none of these n-ary fixpoints ?! And as for the functional equation f(x+1) = exp(f(x)) + 2pi i that is on another branch. So that does not seem to help. Conjecture: if $\text{sexp}(z)=L$, than for some positive integer n, there is a non-zero integer m such that $\text{sexp}(z-n)=L+2m\pi i$ This would apply for L equals any fixed point of exp(z) and any finite value of z. This conjecture would apply to both the Kneser solution, and the secondary fixed point solution. I think it can be proven by showing for these two solutions, that sexp(z-n)<>L for large finite values of n. - Sheldon tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 06/15/2014, 08:17 PM (06/15/2014, 08:07 PM)sheldonison Wrote: (06/15/2014, 06:31 PM)tommy1729 Wrote: .... Seems unlikely that sexp contains none of these n-ary fixpoints ?! And as for the functional equation f(x+1) = exp(f(x)) + 2pi i that is on another branch. So that does not seem to help. Conjecture: if $\text{sexp}(z)=L$, than for some positive integer n, there is a non-zero integer m such that $\text{sexp}(z-n)=L+2m\pi i$ This would apply for L equals any fixed point of exp(z). This conjecture would apply to both the Kneser solution, and the secondary fixed point solution. I think it can be proven by showing for these two solutions, that sexp(z-n)<>L as n goes to infinity. Wait a minute , we have sexp(R + oo i) = L or conj(L) for all real R and all real oo !? I thought we all agreed on that for years ? But R + oo i - n is also of the form R + oo i. ?? Now Im even more confused. Thanks for the reply though. regards tommy1729 « Next Oldest \| Next Newest » Possibly Related Threads... Thread Author Replies Views Last Post Iteration exercises: f(x)=x^2 - 0.5 ; Fixpoint-irritation... 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https://zbmath.org/?q=an:0731.20025	× ## Sur les groupes hyperboliques d’après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov).(French)Zbl 0731.20025 Progress in Mathematics, 83. Boston, MA: Birkhäuser. vii, 285 p. sFr. 68.00 (1990). [The articles of this volume will not be indexed individually.] This book consists of a number of lectures by various authors who took part in a sustained seminar on the work of M. Gromov on hyperbolic groups, semihyperbolic groups and other related topics. The basic object of study consists of a finitely generated group, $$\Gamma$$, together with a given finite set of generators, S. The “word length” metric makes $$\Gamma$$ into a metric space. Two metric spaces, X and Y, are quasi-isomorphic if there exist maps $$f:X\to Y$$ and $$g:Y\to X$$ together with $$\lambda >0$$, $$C\geq 0$$ such that $d(f(x_ 1),f(x_ 2))\leq \lambda d(x_ 1,x_ 2)+C,\quad d(g(y_ 1),g(y_ 2))\leq \lambda d(y_ 1,y_ 2)+C,$ $d(fg(y_ 1),y_ 1)\leq C\text{ and } d(gf(x_ 1),x_ 1)\leq C\text{ for all } x_ 1,x_ 2\in X,\quad y_ 1,y_ 2\in Y.$ The quasi-isomorphism class of $$\Gamma$$ is independent of the choice for S. Studying $$\Gamma$$ (and its metric) via the associated Cayley graph, Gromov’s work shows how the geometric notion of quasi- isomorphism succeeds in capturing many algebraic properties of $$\Gamma$$. For example: Theorem: (i) If $$[\Gamma:\Gamma_ 1]<\infty$$ then $$\Gamma$$ and $$\Gamma_ 1$$ are quasi-isomorphic, (ii) Let $$\Gamma_ 1,\Gamma_ 2$$ be quasi-isomorphic and torsion free. If $$\Gamma_ 1$$ is a nontrivial free product then so is $$\Gamma_ 2.$$ An example of an application of the method is the following celebrated result: Theorem: $$\Gamma$$ has polynomial word growth if and only if it contains a nilpotent subgroup of finite index. A metric space, X, with geodesics is called hyperbolic if any geodesic triangle in X satisfies the Rips condition with a positive constant. The group, $$\Gamma$$, is hyperbolic if its Cayley graph is hyperbolic. As Gromov’s results are developed it becomes clear that the class of hyperbolic groups behaves much like the class of fundamental groups of negatively curved compact Riemannian manifolds. Within its dozen chapters this volume covers many more properties and constructions than I can mention here; for example, every hyperbolic group has a unique “boundary” (which is the analogue of the boundary of the universal covering of a hyperbolic manifold). The careful treatment makes this book ideal for the newcomer to Gromov’s theory. In addition, the book concludes with a series of interesting appendices containing, inter alia, a number of new examples of hyperbolic groups. ### MSC: 20F38 Other groups related to topology or analysis 20F05 Generators, relations, and presentations of groups 20-02 Research exposition (monographs, survey articles) pertaining to group theory 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 20E07 Subgroup theorems; subgroup growth 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.889614462852478, "perplexity": 507.18536677266684}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104542759.82/warc/CC-MAIN-20220705083545-20220705113545-00519.warc.gz"}
https://eccc.weizmann.ac.il/report/2014/165/	Under the auspices of the Computational Complexity Foundation (CCF) REPORTS > DETAIL: ### Paper: TR14-165 \| 3rd December 2014 01:20 #### An Entropy Sumset Inequality and Polynomially Fast Convergence to Shannon Capacity Over All Alphabets TR14-165 Authors: Venkatesan Guruswami, Ameya Velingker Publication: 3rd December 2014 03:42 Keywords: Abstract: We prove a lower estimate on the increase in entropy when two copies of a conditional random variable $X \| Y$, with $X$ supported on $\mathbb{Z}_q=\{0,1,\dots,q-1\}$ for prime $q$, are summed modulo $q$. Specifically, given two i.i.d. copies $(X_1,Y_1)$ and $(X_2,Y_2)$ of a pair of random variables $(X,Y)$, with $X$ taking values in $\mathbb{Z}_q$, we show $H(X_1 + X_2 \mid Y_1, Y_2) - H(X\|Y) \ge \alpha(q) \cdot H(X\|Y) (1-H(X\|Y))$ for some $\alpha(q) > 0$, where $H(\cdot)$ is the normalized (by factor $\log_2 q$) entropy. In particular, if $X \| Y$ is not close to being fully random or fully deterministic and $H(X\| Y) \in (\gamma,1-\gamma)$, then the entropy of the sum increases by $\Omega_q(\gamma)$. Our motivation is an effective analysis of the finite-length behavior of polar codes, for which the linear dependence on $\gamma$ is quantitatively important. The assumption of $q$ being prime is necessary: for $X$ supported uniformly on a proper subgroup of $\mathbb{Z}_q$ we have $H(X+X)=H(X)$. For $X$ supported on infinite groups without a finite subgroup (the torsion-free case) and no conditioning, a sumset inequality for the absolute increase in (unnormalized) entropy was shown by Tao (Tao '10). We use our sumset inequality to analyze Ar\i kan's construction of polar codes and prove that for any $q$-ary source $X$, where $q$ is any fixed prime, and any $\epsilon > 0$, polar codes allow {\em efficient} data compression of $N$ i.i.d. copies of $X$ into $(H(X)+\epsilon)N$ $q$-ary symbols, {\em as soon as $N$ is polynomially large in $1/\epsilon$}. We can get capacity-achieving source codes with similar guarantees for composite alphabets, by factoring $q$ into primes and combining different polar codes for each prime in factorization. A consequence of our result for noisy channel coding is that for {\em all} discrete memoryless channels, there are explicit codes enabling reliable communication within $\epsilon > 0$ of the symmetric Shannon capacity for a block length and decoding complexity bounded by a polynomial in $1/\epsilon$. The result was previously shown for the special case of binary-input channels (Guruswami-Xia '13, Hassani-Alishahi-Urbanke '13), and this work extends the result to channels over any alphabet. ISSN 1433-8092 \| Imprint	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9423249363899231, "perplexity": 396.09841567661033}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107894890.32/warc/CC-MAIN-20201027225224-20201028015224-00333.warc.gz"}
http://math.stackexchange.com/questions/8160/uniqueness-of-length-minimizing-geodesic	# Uniqueness of length minimizing geodesic In a compact hyperbolic Riemann surface without boundary tbe length minimizing geodesic between two points $p$ and $q$ is unique. - Think about a Riemann surface of genus 2 say. This is a 2-holed doughnut. It has a curve winding about one of its holes. (Or more mathematically speaking it has an embedded circle representing a nonzero homology class.) We can deform this curve so that it is length-minimizing in its homotopy class. Then the curve becomes a geodesic $C$. Then let $p$ and $q$ be "opposite" points of $C$, that is the distance from $p$ to $q$ along $C$ is a half of the length of $C$. Then $C$ splits into two equal-length geodesics between $p$ and $q$. I suppose there may be even shorter geodesics between $p$ and $q$, but I think that choosing the homology class to minimize the length of $C$ shoudl sort that out. - I'm not a hyperbolic geometer, but I'm going to say no. Here is my reasoning: Let $C$ be your compact hyperbolic Riemann surface, so it is the quotient of its universal cover, the hyperbolic plane, by a cocompact Fuchsian group $\Gamma$. Let $\pi: \mathbb{H} \rightarrow \Gamma \backslash \mathbb{H} = C$ be the covering map. We have points $P$ and $Q$ on $C$. Fix one lift $\tilde{P}$ of $P$ and consider all possible lifts $\tilde{Q}_{\gamma}$ of $Q$: this will be a full orbit of $\Gamma$. For each $\gamma \in \Gamma$, there is a unique geodesic in $\mathbb{H}$ from $P$ to $\tilde{Q}_{\gamma}$ and its image under $\pi$ is a geodesic from $P$ to $Q$. So certainly there are lots of geodesics in question. The ones of minimal length are going to correspond to the choices of $\gamma$ such that the hyperbolic distance from $P$ to $\tilde{Q}_{\gamma}$ is minimized. But it seems pretty clear that we can choose $P$ so as to be equidistant between two such points: choose any point $Q_1$, and then choose $Q_2$ to be distinct from $Q_1$, to lie in the same $\Gamma$-orbit as $Q_1$ and to be closest (not necessarily uniquely closest!) to $Q_1$ among all such points. Let $P$ be the midpoint of the geodesic arc from $Q_1$ to $Q_2$. Then so long as $P$ is at least as far away from any other point in the $\Gamma$-orbit of $Q$ as it is from $Q_1$ and $Q_2$, on the quotient we have two length-minimizing geodesics. I am pretty sure you can arrange for this to happen with a suitable choice of $\Gamma$. For instance, if $\Gamma$ is such that the fundamental domain is a regular hyperbolic octagon with edges identified in the usual way to get a genus $2$ quotient, then I think it works to take $Q_1$ and $Q_2$ to be adjacent vertices of the octagon. See for instance the picture towards the bottom of this page: - To complement the fine answers given earlier, it could be mentioned that in the context of a hyperelliptic Riemann surface (such as any surface of genus 2, for example), the following simpler construction can be given. Among all pairs of Weierstrass points, take the pair $A,B$ of points at least distance. Then there are two minimizing segments joining $A$ and $B$ (they are switched by the hyperelliptic involution). This provides a counterexample. Note that the union of the two segments is a systolic loop. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9525379538536072, "perplexity": 97.01542156699789}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644065318.20/warc/CC-MAIN-20150827025425-00207-ip-10-171-96-226.ec2.internal.warc.gz"}
http://xianblog.wordpress.com/tag/metropolis-hastings-algorithms/	## an extension of nested sampling Posted in Books, Statistics, University life with tags , , , , , , , on December 16, 2014 by xi'an I was reading [in the Paris métro] Hastings-Metropolis algorithm on Markov chains for small-probability estimation, arXived a few weeks ago by François Bachoc, Lionel Lenôtre, and Achref Bachouch, when I came upon their first algorithm that reminded me much of nested sampling: the following was proposed by Guyader et al. in 2011, To approximate a tail probability P(H(X)>h), • start from an iid sample of size N from the reference distribution; • at each iteration m, select the point x with the smallest H(x)=ξ and replace it with a new point y simulated under the constraint H(y)≥ξ; • stop when all points in the sample are such that H(X)>h; • take $\left(1-\dfrac{1}{N}\right)^{m-1}$ as the unbiased estimator of P(H(X)>h). Hence, except for the stopping rule, this is the same implementation as nested sampling. Furthermore, Guyader et al. (2011) also take advantage of the bested sampling fact that, if direct simulation under the constraint H(y)≥ξ is infeasible, simulating via one single step of a Metropolis-Hastings algorithm is as valid as direct simulation. (I could not access the paper, but the reference list of Guyader et al. (2011) includes both original papers by John Skilling, so the connection must be made in the paper.) What I find most interesting in this algorithm is that it even achieves unbiasedness (even in the MCMC case!). ## another instance of ABC? Posted in Statistics with tags , , , , , on December 2, 2014 by xi'an “These characteristics are (1) likelihood is not available; (2) prior information is available; (3) a portion of the prior information is expressed in terms of functionals of the model that cannot be converted into an analytic prior on model parameters; (4) the model can be simulated. Our approach depends on an assumption that (5) an adequate statistical model for the data are available.” A 2009 JASA paper by Ron Gallant and Rob McCulloch, entitled “On the Determination of General Scientific Models With Application to Asset Pricing”, may have or may not have connection with ABC, to wit the above quote, but I have trouble checking whether or not this is the case. The true (scientific) model parametrised by θ is replaced with a (statistical) substitute that is available in closed form. And parametrised by g(θ). [If you can get access to the paper, I’d welcome opinions about Assumption 1 therein which states that the intractable density is equal to a closed-form density.] And the latter is over-parametrised when compared with the scientific model. As in, e.g., a N(θ,θ²) scientific model versus a N(μ,σ²) statistical model. In addition, the prior information is only available on θ. However, this does not seem to matter that much since (a) the Bayesian analysis is operated on θ only and (b) the Metropolis approach adopted by the authors involves simulating a massive number of pseudo-observations, given the current value of the parameter θ and the scientific model, so that the transform g(θ) can be estimated by maximum likelihood over the statistical model. The paper suggests using a secondary Markov chain algorithm to find this MLE. Which is claimed to be a simulated annealing resolution (p.121) although I do not see the temperature decreasing. The pseudo-model is then used in a primary MCMC step. Hence, not truly an ABC algorithm. In the same setting, ABC would use a simulated dataset the same size as the observed dataset, compute the MLEs for both and compare them. Faster if less accurate when Assumption 1 [that the statistical model holds for a restricted parametrisation] does not stand. Another interesting aspect of the paper is about creating and using a prior distribution around the manifold η=g(θ). This clearly relates to my earlier query about simulating on measure zero sets. The paper does not bring a definitive answer, as it never simulates exactly on the manifold, but this constitutes another entry on this challenging problem… ## efficient exploration of multi-modal posterior distributions Posted in Books, Statistics, University life with tags , , , , on September 1, 2014 by xi'an The title of this recent arXival had potential appeal, however the proposal ends up being rather straightforward and hence anti-climactic! The paper by Hu, Hendry and Heng proposes to run a mixture of proposals centred at the various modes of the target for an efficient exploration. This is a correct MCMC algorithm, granted!, but the requirement to know beforehand all the modes to be explored is self-defeating, since the major issue with MCMC is about modes that are omitted from the exploration and remain undetected throughout the simulation… As provided, this is a standard MCMC algorithm with no adaptive feature and I would rather suggest our population Monte Carlo version, given the available information. Another connection with population Monte Carlo is that I think the performances would improve by Rao-Blackwellising the acceptance rate, i.e. removing the conditioning on the (ancillary) component of the index. For PMC we proved that using the mixture proposal in the ratio led to an ideally minimal variance estimate and I do not see why randomising the acceptance ratio in the current case would bring any improvement. ## understanding the Hastings algorithm Posted in Books, Statistics with tags , , , , , on August 26, 2014 by xi'an David Minh and Paul Minh [who wrote a 2001 Applied Probability Models] have recently arXived a paper on “understanding the Hastings algorithm”. They revert to the form of the acceptance probability suggested by Hastings (1970): $\rho(x,y) = s(x,y) \left(1+\dfrac{\pi(x) q(y\|x)}{\pi(y) q(x\|y)}\right)^{-1}$ where s(x,y) is a symmetric function keeping the above between 0 and 1, and q is the proposal. This obviously includes the standard Metropolis-Hastings form of the ratio, as well as Barker’s (1965): $\rho(x,y) = \left(1+\dfrac{\pi(x) q(y\|x)}{\pi(y) q(x\|y)}\right)^{-1}$ which is known to be less efficient by accepting less often (see, e.g., Antonietta Mira’s PhD thesis). The authors also consider the alternative $\rho(x,y) = \min(\pi(y)/ q(y\|x),1)\,\min(q(x\|y)/\pi(x),1)$ which I had not seen earlier. It is a rather intriguing quantity in that it can be interpreted as (a) a simulation of y from the cutoff target corrected by reweighing the previous x into a simulation from q(x\|y); (b) a sequence of two acceptance-rejection steps, each concerned with a correspondence between target and proposal for x or y. There is an obvious caveat in this representation when the target is unnormalised since the ratio may then be arbitrarily small… Yet another alternative could be proposed in this framework, namely the delayed acceptance probability of our paper with Marco and Clara, one special case being $\rho(x,y) = \min(\pi_1(y)q(x\|y)/\pi_1(x) q(y\|x),1)\,\min(\pi_2(y)/\pi_1(x),1)$ where $\pi(x)\propto\pi_1(x)\pi_2(x)$ is an arbitrary decomposition of the target. An interesting remark in the paper is that any Hastings representation can alternatively be written as $\rho(x,y) = \min(\pi(y)/k(x,y)q(y\|x),1)\,\min(k(x,y)q(x\|y)/\pi(x),1)$ where k(x,y) is a (positive) symmetric function. Hence every single Metropolis-Hastings is also a delayed acceptance in the sense that it can be interpreted as a two-stage decision. The second part of the paper considers an extension of the accept-reject algorithm where a value y proposed from a density q(y) is accepted with probability $\min(\pi(y)/ Mq(y),1)$ and else the current x is repeated, where M is an arbitrary constant (incl. of course the case where it is a proper constant for the original accept-reject algorithm). Curiouser and curiouser, as Alice would say! While I think I have read some similar proposal in the past, I am a wee intrigued at the appear of using only the proposed quantity y to decide about acceptance, since it does not provide the benefit of avoiding generations that are rejected. In this sense, it appears as the opposite of our vanilla Rao-Blackwellisation. (The paper however considers the symmetric version called the independent Markovian minorizing algorithm that only depends on the current x.) In the extension to proposals that depend on the current value x, the authors establish that this Markovian AR is in fine equivalent to the generic Hastings algorithm, hence providing an interpretation of the “mysterious” s(x,y) through a local maximising “constant” M(x,y). A possibly missing section in the paper is the comparison of the alternatives, albeit the authors mention Peskun’s (1973) result that exhibits the Metropolis-Hastings form as the optimum. Posted in Mountains, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , on April 21, 2014 by xi'an As I was flying over Skye (with [maybe] a first if hazy perspective on the Cuillin ridge!) to Iceland, three long sets of replies to some of my posts appeared on the ‘Og: Thanks to them for taking the time to answer my musings… Posted in pictures, Statistics, Travel with tags , , , , , , , , , , , on April 15, 2014 by xi'an “At equilibrium, we thus should not expect gains of several orders of magnitude.” As was signaled to me several times during the MCqMC conference in Leuven, Rémi Bardenet, Arnaud Doucet and Chris Holmes (all from Oxford) just wrote a short paper for the proceedings of ICML on a way to speed up Metropolis-Hastings by reducing the number of terms one computes in the likelihood ratio involved in the acceptance probability, i.e. $\prod_{i=1}^n\frac{L(\theta^\prime\|x_i)}{L(\theta\|x_i)}.$ The observations appearing in this likelihood ratio are a random subsample from the original sample. Even though this leads to an unbiased estimator of the true log-likelihood sum, this approach is not justified on a pseudo-marginal basis à la Andrieu-Roberts (2009). (Writing this in the train back to Paris, I am not convinced this approach is in fact applicable to this proposal as the likelihood itself is not estimated in an unbiased manner…) In the paper, the quality of the approximation is evaluated by Hoeffding’s like inequalities, which serves as the basis for a stopping rule on the number of terms eventually evaluated in the random subsample. In fine, the method uses a sequential procedure to determine if enough terms are used to take the decision and the probability to take the same decision as with the whole sample is bounded from below. The sequential nature of the algorithm requires to either recompute the vector of likelihood terms for the previous value of the parameter or to store all of them for deriving the partial ratios. While the authors adress the issue of self-evaluating whether or not this complication is worth the effort, I wonder (from my train seat) why they focus so much on recovering the same decision as with the complete likelihood ratio and the same uniform. It would suffice to get the same distribution for the decision (an alternative that is easier to propose than to create of course). I also (idly) wonder if a Gibbs version would be manageable, i.e. by changing only some terms in the likelihood ratio at each iteration, in which case the method could be exact… (I found the above quote quite relevant as, in an alternative technique we are constructing with Marco Banterle, the speedup is particularly visible in the warmup stage.) Hence another direction in this recent flow of papers attempting to speed up MCMC methods against the incoming tsunami of “Big Data” problems. ## running MCMC for too long, and even longer… Posted in Books, pictures, Running, Statistics, University life with tags , , , , , , , , , , , on October 23, 2013 by xi'an Following my earlier post about the young astronomer who feared he was running his MCMC for too long, here is an update from his visit to my office this morning. This visit proved quite an instructive visit for both of us. (Disclaimer: the picture of an observatory seen from across Brunel’s suspension bridge in Bristol is as earlier completely unrelated with the young astronomer!) First, the reason why he thought MCMC was running too long was that the acceptance rate was plummeting down to zero, whatever the random walk scale. The reason for this behaviour is that he was actually running a standard simulated annealing algorithm, hence observing the stabilisation of the Markov chain in one of the (global) modes of the target function. In that sense, he was right that the MCMC was run for “too long”, as there was nothing to expect once the mode had been reached and the temperature turned down to zero. So the algorithm was working correctly. Second, the astronomy problem he considers had a rather complex likelihood, for which he substituted a distance between the (discretised) observed data and (discretised) simulated data, simulated conditional on the current parameter value. Now…does this ring a bell? If not, here is a three letter clue: ABC… Indeed, the trick he had found to get around this likelihood calculation issue was to re-invent a version of ABC-MCMC! Except that the distance was re-introduced into a regular MCMC scheme as a substitute to the log-likelihood. And compared with the distance at the previous MCMC iteration. This is quite clever, even though this substitution suffers from a normalisation issue (that I already mentioned in the post about Holmes’ and Walker’s idea to turn loss functions into pseudo likelihoods. Regular ABC does not encounter this difficult, obviously. I am still bemused by this reinvention of ABC from scratch! So we are now at a stage where my young friend will experiment with (hopefully) correct ABC steps, trying to derive the tolerance value from warmup simulations and use some of the accelerating tricks suggested by Umberto Picchini and Julie Forman to avoid simulating the characteristics of millions of stars for nothing. And we agreed to meet soon for an update. Indeed, a fairly profitable morning for both of us!	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 9, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9044318199157715, "perplexity": 899.3026134619869}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802765584.21/warc/CC-MAIN-20141217075245-00099-ip-10-231-17-201.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/3331939/an-interesting-question-about-greatest-common-divisor-gcd-of-three-positive-in/3331956	# An interesting question about greatest common divisor (gcd) of three positive integers which form a primitive Pythagorean triple Suppose $$a$$, $$b$$, and $$c$$ are three distinct integers which share no common divisor. Note that this implies that $$a$$, $$b$$, and $$c$$ are pairwise coprime. If $$a$$,$$b$$, and $$c$$ are a primitive Pythagorean triple satisfying the equation $$a^2 + b^2 = c^2$$ , is it then always true that $$\gcd ( (a+b) , (a+b-c) ) = 1?$$ Can it be proven that $$\gcd ( (a+b) , (a+b-c) ) = 1$$ invariably ? Can you find a counterexample where $$\gcd ( (a+b) , (a+b-c) ) \neq 1$$? We have that $$\gcd(a+b, a+b-c) = \gcd(a+b, -c) = \gcd(a+b, c).$$ Now suppose that $$p$$ is a prime dividing $$\gcd(a+b, c)$$. Because $$a^2 + b^2 = c^2$$, we have that $$p^2$$ also divides $$(a+b)^2 - (a^2 + b^2) = 2ab$$. In particular $$p$$ divides either $$a$$ or $$b$$ (even if $$p=2$$). But this contradicts our assumption. • You forgot to (explicitly) eliminate the possibility $\,p = 2.\ \$ Aug 23 '19 at 13:26 • @BillDubuque, I don't treat it as a special case; note that $p^2$ divides $2ab$, so even if $p=2$, that still leaves a factor of 2 for $ab$. Aug 23 '19 at 13:32 • Yes but the peculiarity for $\,p = 2\,$ deserves explicit mention (else the reader can't know whether or not there is actually a gap in the argument). I'd write "(even if $p = 2$)" Aug 23 '19 at 13:45 Hint $$\ (a\!+\!b, a\!+\!b\!-\!c)= (a\!+\!b,c)\mid (a\!+\!b,\!\!\!\overbrace{c^2}^{a^2\,+\,b^2}\!\!\!)\mid 2(a^2,b^2)\!=\!2,\,$$ but $$c$$ is odd in a PPT • See also here for a proof that $\,(a\!+\!b,\,a^2\!+\!b^2)\mid 2(a,b)^2\$ and more. Aug 23 '19 at 14:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 25, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9302220940589905, "perplexity": 165.51402585549954}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780053918.46/warc/CC-MAIN-20210916234514-20210917024514-00604.warc.gz"}
http://philpapers.org/s/Recursive%20Function	## Search results for 'Recursive Function' (try it on Scholar) 1000+ found Sort by: 1. Nigel Cutland (1980). Computability, an Introduction to Recursive Function Theory. Cambridge University Press.score: 65.0 What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). (...) My bibliography Export citation 2. H. R. Strong (1970). Construction of Models for Algebraically Generalized Recursive Function Theory. Journal of Symbolic Logic 35 (3):401-409.score: 60.0 The Uniformly Reflexive Structure was introduced by E. G. Wagner who showed that the theory of such structures generalized much of recursive function theory. In this paper Uniformly Reflexive Structures are constructed as factor algebras of Free nonassociative algebras. Wagner's question about the existence of a model with no computable splinter ("successor set") is answered in the affirmative by the construction of a model whose only computable sets are the finite sets and their complements. Finally, for each countable (...) My bibliography Export citation 3. Klaus‐Hilmar Sprenger (1997). Some Hierarchies of Primitive Recursive Functions on Term Algebras. Mathematical Logic Quarterly 43 (2):251-286.score: 51.0 No categories My bibliography Export citation 4. Alexander Kreuzer & Ulrich Kohlenbach (2009). Ramsey's Theorem for Pairs and Provably Recursive Functions. Notre Dame Journal of Formal Logic 50 (4):427-444.score: 48.0 This paper addresses the strength of Ramsey's theorem for pairs ($RT^2_2$) over a weak base theory from the perspective of 'proof mining'. Let $RT^{2-}_2$ denote Ramsey's theorem for pairs where the coloring is given by an explicit term involving only numeric variables. We add this principle to a weak base theory that includes weak König's Lemma and a substantial amount of $\Sigma^0_1$-induction (enough to prove the totality of all primitive recursive functions but not of all primitive recursive functionals). (...) My bibliography Export citation 5. Holger Petersen (1996). The Computation of Partial Recursive Word‐Functions Without Read Instructions. Mathematical Logic Quarterly 42 (1):312-318.score: 48.0 No categories My bibliography Export citation 6. R. L. Goodstein (1953). A Problem in Recursive Function Theory. Journal of Symbolic Logic 18 (3):225-232.score: 45.0 My bibliography Export citation 7. Heinrich Rolletschek (1983). Closure Properties of Almost-Finiteness Classes in Recursive Function Theory. Journal of Symbolic Logic 48 (3):756-763.score: 45.0 My bibliography Export citation 8. J. W. Addison (2004). Tarski's Theory of Definability: Common Themes in Descriptive Set Theory, Recursive Function Theory, Classical Pure Logic, and Finite-Universe Logic. Annals of Pure and Applied Logic 126 (1-3):77-92.score: 45.0 My bibliography Export citation 9. J. P. Cleave (1974). Review: Webb Miller, Recursive Function Theory and Numerical Analysis. [REVIEW] Journal of Symbolic Logic 39 (2):346-346.score: 45.0 My bibliography Export citation 10. José Félix Costa, Bruno Loff & Jerzy Mycka (2009). A Foundation for Real Recursive Function Theory. Annals of Pure and Applied Logic 160 (3):255-288.score: 45.0 My bibliography Export citation 11. Erik Ellentuck (1968). Review: John Myhill, Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 33 (4):619-620.score: 45.0 My bibliography Export citation 12. H. B. Enderton (1971). Review: Albert A. Mullin, On a Theorem Equivalent to Post's Fundamental Theorem of Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 36 (2):343-343.score: 45.0 My bibliography Export citation 13. H. B. Enderton (1987). Review: Nigel Cutland, Computability. An Introduction to Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 52 (1):292-293.score: 45.0 My bibliography Export citation 14. Gustav Hensel (1966). Review: H. B. Enderton, Hierarchies in Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 31 (2):262-263.score: 45.0 My bibliography Export citation 15. Bruno Kopp (2012). A Simple Hypothesis of Executive Function. Frontiers in Human Neuroscience 6.score: 45.0 Executive function is traditionally conceptualized as a set of abilities required to guide behavior toward goals. Here, an integrated theoretical framework for executive function is developed which has its roots in the notion of hierarchical mental models. Further following Duncan (2010a,b), executive function is construed as a hierarchical recursive system of test-operation-test-exit units (Miller, Galanter, and Pribram, 1960). Importantly, it is shown that this framework can be used to model the main regional prefrontal syndromes, which are (...) My bibliography Export citation 16. Albert A. Mullin (1963). On A Theorem Equivalent to Post's Fundamental Theorem of Recursive Function Theory. Mathematical Logic Quarterly 9 (12‐15):203-205.score: 45.0 No categories My bibliography Export citation 17. Julia Robinson (1972). Review: Martin Davis, Application of Recursive Function Theory to Number Theory. [REVIEW] Journal of Symbolic Logic 37 (3):602-602.score: 45.0 My bibliography Export citation 18. Norman Shapiro (1955). Review: J. R. Myhill, Three Contributions to Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 20 (2):176-177.score: 45.0 My bibliography Export citation 19. score: 45.0 My bibliography Export citation 20. Joseph S. Ullian (1975). Review: Ann Yasuhara, Recursive Function Theory and Logic. [REVIEW] Journal of Symbolic Logic 40 (4):619-620.score: 45.0 My bibliography Export citation 21. Paul Young (1972). Review: Manuel Blum, Recursive Function Theory and Speed of Computation. [REVIEW] Journal of Symbolic Logic 37 (1):199-199.score: 45.0 My bibliography Export citation 22. Mark Changizi (1996). Function Identification From Noisy Data with Recursive Error Bounds. Erkenntnis 45 (1):91 - 102.score: 43.0 New success criteria of inductive inference in computational learning theory are introduced which model learning total (not necessarily recursive) functions with (possibly everywhere) imprecise theories from (possibly always) inaccurate data. It is proved that for any level of error allowable by the new success criteria, there exists a class of recursive functions such that not all f are identifiable via the criterion at that level of error. Also, necessary and sufficient conditions on the error level are given for (...) No categories My bibliography Export citation 23. Luis E. Sanchis (1992). Recursive Functionals. North-Holland.score: 42.0 This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. No categories My bibliography Export citation 24. László Á Kóczy (2007). A Recursive Core for Partition Function Form Games. Theory and Decision 63 (1):41-51.score: 42.0 We present a well-defined generalisation of the core to coalitional games with externalities, where the value of a deviation is given by an endogenous response, the solution (if nonempty: the core) of the residual game. No categories My bibliography Export citation 25. Qing Zhou (1996). Computable Real‐Valued Functions on Recursive Open and Closed Subsets of Euclidean Space. Mathematical Logic Quarterly 42 (1):379-409.score: 42.0 No categories My bibliography Export citation 26. Paul Axt (1966). Review: Robert W. Ritchie, Classes of Recursive Functions Based on Ackermann's Function. [REVIEW] Journal of Symbolic Logic 31 (4):654-654.score: 39.0 My bibliography Export citation 27. Pavel Naumov (2005). On Modal Logics of Partial Recursive Functions. Studia Logica 81 (3):295 - 309.score: 36.0 The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established. My bibliography Export citation 28. Arnold Beckmann & Andreas Weiermann (2000). Characterizing the Elementary Recursive Functions by a Fragment of Gödel's T. Archive for Mathematical Logic 39 (7):475-491.score: 36.0 Let T be Gödel's system of primitive recursive functionals of finite type in a combinatory logic formulation. Let $T^{\star}$ be the subsystem of T in which the iterator and recursor constants are permitted only when immediately applied to type 0 arguments. By a Howard-Schütte-style argument the $T^{\star}$ -derivation lengths are classified in terms of an iterated exponential function. As a consequence a constructive strong normalization proof for $T^{\star}$ is obtained. Another consequence is that every $T^{\star}$ -representable number-theoretic (...) is elementary recursive. Furthermore, it is shown that, conversely, every elementary recursive function is representable in $T^{\star}$ .The expressive weakness of $T^{\star}$ compared to the full system T can be explained as follows: In contrast to $T$ , computation steps in $T^{\star}$ never increase the nesting-depth of ${\mathcal I}_\rho$ and ${\mathcal R}_\rho$ at recursion positions. (shrink) No categories My bibliography Export citation 29. score: 36.0 My bibliography Export citation 30. Ján Komara (2011). On Nested Simple Recursion. Archive for Mathematical Logic 50 (5-6):617-624.score: 36.0 We give a novel proof that primitive recursive functions are closed under nested simple recursion. This new presentation is supplied with a detailed proof which can be easily formalized in small fragments of Peano Arithmetic. No categories My bibliography Export citation 31. John N. Crossley & Michael A. E. Dummett (eds.) (1965). Formal Systems and Recursive Functions. Amsterdam, North-Holland Pub. Co..score: 35.0 No categories My bibliography Export citation 32. score: 35.0 My bibliography Export citation 33. Daniel E. Severin (2008). Unary Primitive Recursive Functions. Journal of Symbolic Logic 73 (4):1122-1138.score: 34.0 In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets. My bibliography Export citation 34. Karl-Heinz Niggl (1998). A Restricted Computation Model on Scott Domains and its Partial Primitive Recursive Functionals. Archive for Mathematical Logic 37 (7):443-481.score: 34.0 The paper builds on both a simply typed term system ${\cal PR}^\omega$ and a computation model on Scott domains via so-called parallel typed while programs (PTWP). The former provides a notion of partial primitive recursive functional on Scott domains $D_\rho$ supporting a suitable concept of parallelism. Computability on Scott domains seems to entail that Kleene's schema of higher type simultaneous course-of-values recursion (scvr) is not reducible to partial primitive recursion. So extensions ${\cal PR}^{\omega e}$ and PTWP $^e$ are studied (...) No categories My bibliography Export citation 35. Farzad Didehvar (1999). On a Class of Recursively Enumerable Sets. Mathematical Logic Quarterly 45 (4):467-470.score: 33.0 No categories My bibliography Export citation 36. Stefano Mazzanti (1997). Iterative Characterizations of Computable Unary Functions: A General Method. Mathematical Logic Quarterly 43 (1):29-38.score: 33.0 No categories My bibliography Export citation 37. Yury P. Shimansky (2004). The Concept of a Universal Learning System as a Basis for Creating a General Mathematical Theory of Learning. Minds and Machines 14 (4):453-484.score: 31.0 The number of studies related to natural and artificial mechanisms of learning rapidly increases. However, there is no general theory of learning that could provide a unifying basis for exploring different directions in this growing field. For a long time the development of such a theory has been hindered by nativists' belief that the development of a biological organism during ontogeny should be viewed as parameterization of an innate, encoded in the genome structure by an innate algorithm, and nothing essentially (...) My bibliography Export citation 38. Karl-Heinz Niggl (1997). Non-Definability of the Ackermann Function with Type 1 Partial Primitive Recursion. Archive for Mathematical Logic 37 (1):1-13.score: 31.0 The paper builds on a simply typed term system ${\cal PR}^\omega$ providing a notion of partial primitive recursive functional on arbitrary Scott domains $D_\sigma$ that includes a suitable concept of parallelism. Computability on the partial continuous functionals seems to entail that Kleene's schema of higher type simultaneous course-of-values recursion (SCVR) is not reducible to partial primitive recursion. So an extension ${\cal PR}^{\omega e}$ is studied that is closed under SCVR and yet stays within the realm of subrecursiveness. The (...) No categories My bibliography Export citation 39. G. Lee Bowie (1982). Lucas' Number is Finally Up. Journal of Philosophical Logic 11 (3):279-85.score: 30.0 My bibliography Export citation 40. Michael Rathjen (1992). A Proof-Theoretic Characterization of the Primitive Recursive Set Functions. Journal of Symbolic Logic 57 (3):954-969.score: 30.0 Let KP- be the theory resulting from Kripke-Platek set theory by restricting Foundation to Set Foundation. Let G: V → V (V:= universe of sets) be a ▵0-definable set function, i.e. there is a ▵0-formula φ(x, y) such that φ(x, G(x)) is true for all sets x, and $V \models \forall x \exists!y\varphi (x, y)$ . In this paper we shall verify (by elementary proof-theoretic methods) that the collection of set functions primitive recursive in G coincides with the (...) My bibliography Export citation 41. Cristian Calude, Gabriel Istrate & Marius Zimand (1992). Recursive Baire Classification and Speedable Functions. Mathematical Logic Quarterly 38 (1):169-178.score: 30.0 No categories My bibliography Export citation 42. Manuel L. Campagnolo & Kerry Ojakian (2008). The Elementary Computable Functions Over the Real Numbers: Applying Two New Techniques. [REVIEW] Archive for Mathematical Logic 46 (7-8):593-627.score: 30.0 The basic motivation behind this work is to tie together various computational complexity classes, whether over different domains such as the naturals or the reals, or whether defined in different manners, via function algebras (Real Recursive Functions) or via Turing Machines (Computable Analysis). We provide general tools for investigating these issues, using two techniques we call approximation and lifting. We use these methods to obtain two main theorems. First, we provide an alternative proof of the result from Campagnolo (...) No categories My bibliography Export citation 43. W. Degen (2002). Factors of Functions, AC and Recursive Analogues. Mathematical Logic Quarterly 48 (1):73-86.score: 30.0 No categories My bibliography Export citation 44. Dev K. Roy (2003). The Shortest Definition of a Number in Peano Arithmetic. Mathematical Logic Quarterly 49 (1):83-86.score: 30.0 No categories My bibliography Export citation 45. Phil Watson (1997). Embeddings in the Strong Reducibilities Between 1 and Npm. Mathematical Logic Quarterly 43 (4):559-568.score: 30.0 No categories My bibliography Export citation 46. Hermann G. W. Burchard (2005). Symbolic Languages and Natural Structures a Mathematician's Account of Empiricism. Foundations of Science 10 (2):153-245.score: 29.0 The ancient dualism of a sensible and an intelligible world important in Neoplatonic and medieval philosophy, down to Descartes and Kant, would seem to be supplanted today by a scientific view of mind-in-nature. Here, we revive the old dualism in a modified form, and describe mind as a symbolic language, founded in linguistic recursive computation according to the Church-Turing thesis, constituting a world L that serves the human organism as a map of the Universe U. This methodological distinction of (...) My bibliography Export citation 47. William R. Stirton (2012). How to Assign Ordinal Numbers to Combinatory Terms with Polymorphic Types. Archive for Mathematical Logic 51 (5-6):475-501.score: 29.0 The article investigates a system of polymorphically typed combinatory logic which is equivalent to Gödel’s T. A notion of (strong) reduction is defined over terms of this system and it is proved that the class of well-formed terms is closed under both bracket abstraction and reduction. The main new result is that the number of contractions needed to reduce a term to normal form is computed by an ε 0-recursive function. The ordinal assignments used to obtain this result (...) No categories My bibliography Export citation 48. Joachim Lambek & Philip Scott (2005). An Exactification of the Monoid of Primitive Recursive Functions. Studia Logica 81 (1):1 - 18.score: 28.0 We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents. My bibliography Export citation 49. Stanley S. Wainer (1999). Accessible Recursive Functions. Bulletin of Symbolic Logic 5 (3):367-388.score: 28.0 The class of all recursive functions fails to possess a natural hierarchical structure, generated predicatively from "within". On the other hand, many (proof-theoretically significant) sub-recursive classes do. This paper attempts to measure the limit of predicative generation in this context, by classifying and characterizing those (predictably terminating) recursive functions which can be successively defined according to an autonomy condition of the form: allow recursions only over well-orderings which have already been "coded" at previous levels. The question is: (...)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8971244096755981, "perplexity": 3080.7248726870303}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999653644/warc/CC-MAIN-20140305060733-00003-ip-10-183-142-35.ec2.internal.warc.gz"}
http://mathhelpforum.com/advanced-algebra/64545-determine-irreducible-quadratic-polynomials-print.html	• December 11th 2008, 01:02 PM mandy123 Let p be a prime. Determine the number of irreducible quadratic polynomials over Z_p (Worried) • December 11th 2008, 08:07 PM ThePerfectHacker Quote: Originally Posted by mandy123 Let p be a prime. Determine the number of irreducible quadratic polynomials over Z_p The polynomial $x^{p^2} - x$ factors into a product of monic irreducible polynomials of order dividing $2$. There are $p$ linear monic polynomials. Let $n$ be the number of monic irreducible quadradic polynomials. Then by counting degrees of polynomials in $x^{p^2} - x = \prod_{\deg p(x) \| 2}p(x)$ We see that $p + 2N = p^2 \implies N = \tfrac{1}{2}(p^2 - p)$. (This formula can be generalized to polynomials of degree $m$ by applying Mobius inversion formula) • December 12th 2008, 07:22 AM mandy123 So then what if p is not a prime, what if we are told to Determine the number of irreducible quadratic polynomials over Z_p? how would that change the answer? • December 12th 2008, 08:28 AM ThePerfectHacker Quote: Originally Posted by mandy123 So then what if p is not a prime, what if we are told to Determine the number of irreducible quadratic polynomials over Z_p? how would that change the answer? Finite fields have orders of power of primes. Thus, your question would be to count the number of irreducible quadradics over $\mathbb{F}_q$ where $q=p^n$ (a power of prime). In this case the same theorem applies i.e. $x^{q^2} - x$ factors into monic irreducible polynomials having order dividing $2$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9052216410636902, "perplexity": 344.44540149989564}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783398209.20/warc/CC-MAIN-20160624154958-00004-ip-10-164-35-72.ec2.internal.warc.gz"}
https://eprints.soton.ac.uk/259069/	The University of Southampton University of Southampton Institutional Repository A performance comparison between two design techniques for non-linear output feedback control French, M and Xie, C (2004) A performance comparison between two design techniques for non-linear output feedback control. International Journal of Control, 77 (3), 264-276. Record type: Article Abstract For a system possessing a non-linear output feedback normal form, an observer backstepping design is compared to a high gain observer design with respect to non-singular performance cost functional. If the initial error between the initial condition of the state and the initial condition of the observer is large, the high gain observer design is shown to have better performance than the observer backstepping design. An output feedback system with parametric uncertainty is then considered. It is shown that if an a priori estimate for the bound of the uncertain parameter is conservative, then an adaptive observer backstepping design has better performance than the adaptive high gain observer design. Text xiemcf_ijc2004.pdf - Other Published date: 2004 Organisations: Southampton Wireless Group Identifiers Local EPrints ID: 259069 URI: https://eprints.soton.ac.uk/id/eprint/259069 ISSN: 0020-3270 PURE UUID: e6e5b9d4-bc77-40d5-9c53-dba7ca6afb9f Catalogue record Date deposited: 11 Mar 2004 Author: M French Author: C Xie	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8454568386077881, "perplexity": 1960.1190579853035}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573124.40/warc/CC-MAIN-20190917223332-20190918005332-00171.warc.gz"}
https://www.physicsforums.com/threads/max-power-delivered-to-variable-resistor.238174/	# Max power delivered to variable resistor 1. Jun 1, 2008 ### enian 1. The problem statement, all variables and given/known data http://img126.imageshack.us/img126/6400/picex8.jpg Determine the maximum power that can be delievered to the varaible resistor R in the circuit of Fig 4.139. 2. Relevant equations 3. The attempt at a solution I am not sure how to handle this because the resistor is in that diamond structure. I need to find V thev and R thev Any advice or a hint to get started? 2. Jun 1, 2008 3. Jun 1, 2008 ### Defennder To find $$R_{th}$$, short the voltage source. That means drawing a vertical line connecting the blue nodes in your 2nd diagram. Then you must find the equivalent resistance between the red nodes. You have to redraw the circuit in order to solve it easily. Next to find $$V_{th}$$, from the original diagram find the open circuit potential difference across the red nodes with the voltage source added back in. That would be the thevenin voltage. You can use nodal analysis to solve this. I got 30V for this. Once you got both, you can use the formulae for the maximum power theorem to get the answer.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8475849628448486, "perplexity": 594.5676220320089}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280266.9/warc/CC-MAIN-20170116095120-00258-ip-10-171-10-70.ec2.internal.warc.gz"}
https://www.lmfdb.org/GaloisGroup/?n=24	## Results (1-50 of at least 5000) Next Label Name Order Parity Solvable Subfields Low Degree Siblings 24T1 $C_{24}$ $24$ $-1$ yes $C_2$, $C_3$, $C_4$, $C_6$, $C_8$, $C_{12}$ 24T2 $C_2\times C_{12}$ $24$ $1$ yes $C_2$ x 3, $C_3$, $C_4$ x 2, $C_2^2$, $C_6$ x 3, $C_4\times C_2$, $C_{12}$ x 2, $C_6\times C_2$ 24T3 $C_2^2\times C_6$ $24$ $1$ yes $C_2$ x 7, $C_3$, $C_2^2$ x 7, $C_6$ x 7, $C_2^3$, $C_6\times C_2$ x 7 24T4 $C_3\times Q_8$ $24$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $Q_8$, $C_6\times C_2$ 24T5 $C_3:Q_8$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $Q_8$, $D_6$ 24T6 $C_2\times C_3:C_4$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_4$ x 2, $C_2^2$, $S_3$, $D_{6}$ x 2, $C_4\times C_2$, $D_6$, $C_3 : C_4$ x 2 24T7 $\SL(2,3)$ $24$ $1$ yes $C_3$, $A_4$, $A_4$, $\SL(2,3)$, $A_4$ 8T12 24T8 $C_3:C_8$ $24$ $-1$ yes $C_2$, $S_3$, $C_4$, $S_3$, $C_8$, $C_3 : C_4$ 24T9 $C_2\times A_4$ $24$ $1$ yes $C_2$, $C_3$, $A_4$, $C_6$, $A_4$, $A_4\times C_2$, $A_4\times C_2$, $A_4$, $A_4\times C_2$, $A_4 \times C_2$ 6T6, 8T13, 12T6, 12T7 24T10 $S_4$ $24$ $1$ yes $C_2$, $S_3$, $S_4$, $S_3$, $S_4$, $S_4$, $S_4$, $S_4$, $S_4$ 4T5, 6T7, 6T8, 8T14, 12T8, 12T9 24T11 $C_2^2\times S_3$ $24$ $1$ yes $C_2$ x 7, $S_3$, $C_2^2$ x 7, $S_3$, $D_{6}$ x 6, $C_2^3$, $D_6$ x 3, $S_3 \times C_2^2$ x 4 12T10 x 4 24T12 $C_4\times S_3$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_4$ x 2, $C_2^2$, $S_3$, $D_{6}$ x 2, $C_4\times C_2$, $D_6$, $S_3 \times C_4$ x 2 12T11 x 2 24T13 $D_{12}$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $S_3$, $D_{6}$ x 2, $D_4$, $D_6$, $D_{12}$ x 2 12T12 x 2 24T14 $C_3:D_4$ $24$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $S_3$, $D_{6}$ x 2, $D_4$, $D_6$, $(C_6\times C_2):C_2$, $(C_6\times C_2):C_2$ 12T13, 12T15 24T15 $C_3\times D_4$ $24$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $D_{4}$ x 2, $C_6$ x 3, $D_4$, $C_6\times C_2$, $D_4 \times C_3$ x 2 12T14 x 2 24T16 $C_3\times OD_{16}$ $48$ $-1$ yes $C_2$, $C_3$, $C_4$, $C_6$, $C_8:C_2$, $C_{12}$ 24T17 $C_3\times D_4:C_2$ $48$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $Q_8:C_2$, $C_6\times C_2$ 24T17 x 2 24T18 $D_4:S_3$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $Q_8:C_2$, $D_6$ 24T18, 24T23 24T19 $D_{12}:C_2$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $Q_8:C_2$, $D_6$ 24T24 x 2 24T20 $C_3:OD_{16}$ $48$ $-1$ yes $C_2$, $S_3$, $C_4$, $S_3$, $C_8:C_2$, $C_3 : C_4$ 24T21 $\SL(2,3):C_2$ $48$ $1$ yes $C_3$, $A_4$, $A_4\times C_2$, $A_4\times C_2$ 16T60 24T22 $\GL(2,3)$ $48$ $-1$ yes $S_3$, $S_4$, $S_4$, $\textrm{GL(2,3)}$ x 2, $S_4$ 8T23 x 2, 16T66 24T23 $D_4:S_3$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8:C_2$, $S_3 \times C_2^2$ 24T18 x 2 24T24 $D_{12}:C_2$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8:C_2$, $S_3 \times C_2^2$ 24T19, 24T24 24T25 $C_2\times C_3:D_4$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $D_{6}$ x 3, $D_4\times C_2$, $S_3 \times C_2^2$, $(C_6\times C_2):C_2$ x 2 24T25, 24T45 x 2 24T26 $S_3\times Q_8$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8$, $S_3 \times C_2^2$ 24T26 24T27 $C_2\times C_4\times S_3$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_4$ x 2, $C_2^2$, $D_{6}$ x 3, $C_4\times C_2$, $S_3 \times C_2^2$, $S_3 \times C_4$ x 2 24T27 x 3 24T28 $D_6.C_2^2$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $Q_8:C_2$, $S_3 \times C_2^2$ 24T28 x 2 24T29 $C_2\times D_{12}$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $D_{6}$ x 3, $D_4\times C_2$, $S_3 \times C_2^2$, $D_{12}$ x 2 24T29 x 3 24T30 $C_2^3\times S_3$ $48$ $1$ yes $C_2$ x 7, $S_3$, $C_2^2$ x 7, $D_{6}$ x 7, $C_2^3$, $S_3 \times C_2^2$ x 7 24T30 x 7 24T31 $C_{24}:C_2$ $48$ $-1$ yes $C_2$, $S_3$, $C_4$, $D_{6}$, $C_8:C_2$, $S_3 \times C_4$ 24T32 $C_8\times S_3$ $48$ $-1$ yes $C_2$, $S_3$, $C_4$, $D_{6}$, $C_8$, $S_3 \times C_4$ 24T32 24T33 $D_6:C_4$ $48$ $1$ yes $C_2$, $S_3$, $C_4$, $D_{4}$ x 2, $D_{6}$, $C_2^2:C_4$, $S_3 \times C_4$, $D_{12}$, $(C_6\times C_2):C_2$ 24T33 24T34 $D_{24}$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{8}$, $D_{12}$ 24T34 24T35 $C_8:S_3$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $QD_{16}$, $D_{12}$ 24T36 $Q_8:S_3$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $QD_{16}$, $(C_6\times C_2):C_2$ 24T37 $C_3:D_8$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{8}$, $(C_6\times C_2):C_2$ 24T43 24T38 $C_6\times D_4$ $48$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $D_{4}$ x 2, $C_6$ x 3, $D_4\times C_2$, $C_6\times C_2$, $D_4 \times C_3$ x 2 24T38 x 3 24T39 $C_3\times C_2^2:C_4$ $48$ $1$ yes $C_2$, $C_3$, $C_4$, $D_{4}$ x 2, $C_6$, $C_2^2:C_4$, $C_{12}$, $D_4 \times C_3$ x 2 24T39 24T40 $C_3\times D_8$ $48$ $-1$ yes $C_2$, $C_3$, $D_{4}$, $C_6$, $D_{8}$, $D_4 \times C_3$ 24T40 24T41 $C_3\times SD_{16}$ $48$ $-1$ yes $C_2$, $C_3$, $D_{4}$, $C_6$, $QD_{16}$, $D_4 \times C_3$ 24T42 $C_3:SD_{16}$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $S_3$, $QD_{16}$, $(C_6\times C_2):C_2$ 24T43 $C_3:D_8$ $48$ $-1$ yes $C_2$, $S_3$, $D_{4}$, $S_3$, $D_{8}$, $(C_6\times C_2):C_2$ 24T37 24T44 $C_6.D_4$ $48$ $1$ yes $C_2$, $S_3$, $C_4$, $D_{4}$ x 2, $S_3$, $C_2^2:C_4$, $C_3 : C_4$, $(C_6\times C_2):C_2$ x 2 24T44 24T45 $C_2\times C_3:D_4$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $D_{4}$ x 2, $S_3$, $D_{6}$ x 2, $D_4\times C_2$, $D_6$, $(C_6\times C_2):C_2$ x 2 24T25 x 2, 24T45 24T46 $C_2\times S_4$ $48$ $1$ yes $C_2$, $S_3$, $S_3$, $S_4$, $S_4$, $S_4\times C_2$ x 2, $S_4$, $C_2\times S_4$, $C_2 \times S_4$ 6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T47, 24T48 x 2 24T47 $C_2\times S_4$ $48$ $1$ yes $C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $S_4$, $S_4$, $S_4\times C_2$ x 2, $D_6$, $S_4$, $C_2\times S_4$, $C_2 \times S_4$ x 2, $C_2 \times S_4$ x 2 6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T48 x 2 24T48 $C_2\times S_4$ $48$ $1$ yes $C_2$, $S_3$, $S_4$, $D_{6}$, $S_4$, $S_4\times C_2$, $S_4\times C_2$, $S_4$, $C_2 \times S_4$, $C_2 \times S_4$ 6T11 x 2, 8T24 x 2, 12T21, 12T22, 12T23 x 2, 12T24 x 2, 16T61, 24T46, 24T47, 24T48 24T49 $C_2^2\times A_4$ $48$ $1$ yes $C_2$, $C_3$, $C_6$, $A_4$, $A_4\times C_2$ x 3, $A_4\times C_2$ x 2, $A_4 \times C_2$, $C_2^2 \times A_4$, $C_2^2 \times A_4$ x 2 12T25 x 3, 12T26 x 2, 16T58, 24T49 x 2, 24T50 24T50 $C_2^2\times A_4$ $48$ $1$ yes $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $A_4$, $A_4\times C_2$ x 3, $C_6\times C_2$, $A_4 \times C_2$ x 3, $C_2^2 \times A_4$ x 3 12T25 x 3, 12T26 x 2, 16T58, 24T49 x 3 Next Results are complete for degrees $\leq 23$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9995923638343811, "perplexity": 1166.286175142543}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141188947.19/warc/CC-MAIN-20201126200910-20201126230910-00636.warc.gz"}
https://cms.math.ca/cmb/kw/Carleman	location: Publications → journals Search results Search: All articles in the CMB digital archive with keyword Carleman Expand all Collapse all Results 1 - 3 of 3 1. CMB 2016 (vol 60 pp. 300) Gauthier, Paul M; Sharifi, Fatemeh Luzin-type Holomorphic Approximation on Closed Subsets of Open Riemann Surfaces It is known that if $E$ is a closed subset of an open Riemann surface $R$ and $f$ is a holomorphic function on a neighbourhood of $E,$ then it is usually" not possible to approximate $f$ uniformly by functions holomorphic on all of $R.$ We show, however, that for every open Riemann surface $R$ and every closed subset $E\subset R,$ there is closed subset $F\subset E,$ which approximates $E$ extremely well, such that every function holomorphic on $F$ can be approximated much better than uniformly by functions holomorphic on $R$. Keywords:Carleman approximation, tangential approximation, Myrberg surfaceCategories:30E15, 30F99 2. CMB 2015 (vol 59 pp. 87) Gauthier, Paul M.; Kienzle, Julie Approximation of a Function and its Derivatives by Entire Functions A simple proof is given for the fact that, for $m$ a non-negative integer, a function $f\in C^{(m)}(\mathbb{R}),$ and an arbitrary positive continuous function $\epsilon,$ there is an entire function $g,$ such that $\|g^{(i)}(x)-f^{(i)}(x)\|\lt \epsilon(x),$ for all $x\in\mathbb{R}$ and for each $i=0,1\dots,m.$ We also consider the situation, where $\mathbb{R}$ is replaced by an open interval. Keywords:Carleman theoremCategory:30E10 3. CMB 2002 (vol 45 pp. 80) Gauthier, P. M.; Zeron, E. S. Approximation On Arcs and Dendrites Going to Infinity in $\C^n$ On a locally rectifiable arc going to infinity, each continuous function can be approximated by entire functions. Keywords:tangential approximation, CarlemanCategories:32E30, 32E25 top of page \| contact us \| privacy \| site map \|	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9779304265975952, "perplexity": 682.599740893522}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320841.35/warc/CC-MAIN-20170626170406-20170626190406-00329.warc.gz"}
https://dept.atmos.ucla.edu/mchekroun/publications/girsanov-approach-slow-parameterizing-manifolds-presence-noise	# A Girsanov approach to slow parameterizing manifolds in the presence of noise ### Citation: Chekroun, Mickaël D., Jeroen S.W. Lamb, Christian J. Pangerl, and Martin Rasmussen. Submitted. “A Girsanov approach to slow parameterizing manifolds in the presence of noise”. chekroun_al19girsanov.pdf 3.92 MB ### Abstract: We consider a three-dimensional slow-fast system with quadratic nonlinearity and additive noise. The associated deterministic system of this stochastic differential equation (SDE) exhibits a periodic orbit and a slow manifold. The deterministic slow manifold can be viewed as an approximate parameterization of the fast variable of the SDE in terms of the slow variables. In other words the fast variable of the slow-fast system is approximately "slaved" to the slow variables via the slow manifold. We exploit this fact to obtain a two dimensional reduced model for the original stochastic system, which results in the Hopf-normal form with additive noise. Both, the original as well as the reduced system admit ergodic invariant measures describing their respective long-time behaviour. We will show that for a suitable metric on a subset of the space of all probability measures on phase space, the discrepancy between the marginals along the radial component of both invariant measures can be upper bounded by a constant and a quantity describing the quality of the parameterization. An important technical tool we use to arrive at this result is Girsanov's theorem, which allows us to modify the SDEs in question in a way that preserves transition probabilities. This approach is then also applied to reduced systems obtained through stochastic parameterizing manifolds, which can be viewed as generalized notions of deterministic slow manifolds.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8362785577774048, "perplexity": 370.36868910832374}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875142603.80/warc/CC-MAIN-20200217145609-20200217175609-00342.warc.gz"}
http://mathhelpforum.com/advanced-statistics/16566-error-analysis.html	# Math Help - Error Analysis 1. ## Error Analysis So im doing a little project, and I have various tolerances for various parts. All these tolerances add up, and if the values are too large, what my machine is trying to do won't work. I know one way to analyze this is simple to take the greatest error and add it, but the chances that each error will contribute is maximum amount to the total error is unlikely. Is there any way to add this up and do some standard deviation stuff or anything so that I get a distribution of how likely the sum of all these errors is going to get? I can easily just take the standard deviation of all the individual errors, but I'm not sure what that tells me in this case, My experiance with statics is rather limited, and consists mostly of my knowledge from grading curves, so sorry if this post makes no sense at all. I'd appreciate any help or links to any wikipedia articles or whatnot that may be able to help me. 2. Originally Posted by modain So im doing a little project, and I have various tolerances for various parts. All these tolerances add up, and if the values are too large, what my machine is trying to do won't work. I know one way to analyze this is simple to take the greatest error and add it, but the chances that each error will contribute is maximum amount to the total error is unlikely. Is there any way to add this up and do some standard deviation stuff or anything so that I get a distribution of how likely the sum of all these errors is going to get? I can easily just take the standard deviation of all the individual errors, but I'm not sure what that tells me in this case, My experiance with statics is rather limited, and consists mostly of my knowledge from grading curves, so sorry if this post makes no sense at all. I'd appreciate any help or links to any wikipedia articles or whatnot that may be able to help me. If you have a sum of errors $\epsilon_i,\ i=1, .., n$ each with standard deviation $\sigma_i,\ i=1, .., n$ and assuming they are independent the sd of the sum is $\sqrt{\sum_{i=1}^n \sigma_i^2}$. RonL 3. Originally Posted by modain So im doing a little project, and I have various tolerances for various parts. All these tolerances add up, and if the values are too large, what my machine is trying to do won't work. I know one way to analyze this is simple to take the greatest error and add it, but the chances that each error will contribute is maximum amount to the total error is unlikely. Is there any way to add this up and do some standard deviation stuff or anything so that I get a distribution of how likely the sum of all these errors is going to get? I can easily just take the standard deviation of all the individual errors, but I'm not sure what that tells me in this case, My experiance with statics is rather limited, and consists mostly of my knowledge from grading curves, so sorry if this post makes no sense at all. I'd appreciate any help or links to any wikipedia articles or whatnot that may be able to help me. Perhaps you mean the technique of Propagation of Errors. I didn't find any great articles on the web, but here's one that at least gives the general derivation. -Dan 4. Originally Posted by CaptainBlack If you have a sum of errors $\epsilon_i,\ i=1, .., n$ each with standard deviation $\sigma_i,\ i=1, .., n$ and assuming they are independent the sd of the sum is $\sqrt{\sum_{i=1}^n \sigma_i^2}$. RonL Hmm this is probably what I'm looking for. The thing is though, that don't know the standard deviation of each individual error. Is there any good guesses I can make, or is that something that is really dependant on what the piece of machinery is? 5. Originally Posted by topsquark Perhaps you mean the technique of Propagation of Errors. I didn't find any great articles on the web, but here's one that at least gives the general derivation. -Dan I read over that as well, and it doesn't make that much sense to me. Why would the total error be the square root of the sum of the squares of the individual errors? It seem like when taking a worst case scenario situation, the error can be more than just that square root sum of the squares. 6. Originally Posted by modain I read over that as well, and it doesn't make that much sense to me. Why would the total error be the square root of the sum of the squares of the individual errors? It seem like when taking a worst case scenario situation, the error can be more than just that square root sum of the squares. It's simply one way to put together a set of errors in measurements of a calculated value to get the error in the calculated value. Stats isn't my forte, so I don't know if there are better ways to do this or not. -Dan 7. Originally Posted by modain Hmm this is probably what I'm looking for. The thing is though, that don't know the standard deviation of each individual error. Is there any good guesses I can make, or is that something that is really dependant on what the piece of machinery is? It does depend on the machinery, so there is nothing we can tell you. However if you know what the machinery is and the nature of the errors in what it does you should be able to estimate the standard deviations. In fact in your original post you talk about adding the greatest errors, if you have these you may be in luck. It is often the case that you can treat the SD as 1/3 of the maximum error (at least for a first guess) RonL 8. Thanks a lot to both of you. I think I figured out the stuff from that article, and it makes more sense now, especially when I assume that the error is 3 times the STD. I've found various sources saying that the min/max error is usually a multiple of the STD, but they say anything from 1/3 to 1/1. I've been playing around with the STD being different fractions of the min/max errors and although the results vary, I now understand the concept and with a little more research, I should be well on my way. Thanks.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8590088486671448, "perplexity": 208.4048812628247}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997903265.4/warc/CC-MAIN-20140722025823-00189-ip-10-33-131-23.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/313148/finding-context-sensitive-grammar-for-a-given-language	# Finding context-sensitive grammar for a given language I was wondering, in my other topic, how to find grammar for: $\left\{ a^n b^n c^n: n\ge 1 \right\}$ when I found this. Context-sensitive grammars is completely new topic for me and I don't understand few things. Firstly: why is it OK? I think I get basic intuition behind this approach - we generate as many $a$ as we need and simultaneously same number of $B, \ C$ - space for the letters $b, \ c$. Then we use some kind of bubble sort to swap all adjacent $CB$ to get string in form: $a...aB...BC...C$ then we will easily get desired string using few steps. But why can't we just use simply rule $CB\rightarrow BC$ and we need to do this transformation in few steps using nonterminal $H$? Second question: is order of rules in context-sensitive grammars relevant? Because when we use this grammar like that: $$S\rightarrow aSBC\rightarrow aaBCBC\rightarrow aabCBC\rightarrow aabcBC$$ then we are in dead end, but I suppose I don't understand something and everything is OK. But why? Can you explain it to me? I would be very grateful. - The use of $H$ is there to force you to finish swapping the $B$s and $C$s before converting them to $b$s and $c$s. Otherwise, you could easily generate $aabcbc$, for example.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8554401397705078, "perplexity": 191.4099761260703}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644064019.39/warc/CC-MAIN-20150827025424-00096-ip-10-171-96-226.ec2.internal.warc.gz"}
https://stats.stackexchange.com/questions/554057/is-there-a-beta-distribution-over-the-entire-real-line	# Is there a "beta distribution" over the entire real line? The malleability of the beta distribution pleases me; it can be symmetric, asymmetric, platykurtic and so on, as the following picture shows us: I thought it would be interesting to use it to model the errors in regression problems, but its support is only defined to be $$(0,1)$$ so I would like to know if there is a "beta" distribution with support $$(-\infty,\infty)$$ because a error lying on $$(0,1)$$ is such a strong assumption. • The question seems a little vague / the form of the connection of a beta to distributions on the real line is unclear, as is the proposed use of this in regression (how are you planning to implement a model with this sort of distribution - presumably a conditional distribution for the response - exactly?). There are many distribution families on the real line that have a diverse range of possible skewness and kurtosis. Which 'beta'-like properties do you (a) require, (b) would like but are not required and (c) don't care about? Would a robust regression do instead? Nov 29 '21 at 2:50 • $e_i\sim real beta$, Id like a generic distribution which can be symetric, non symetric (to both sides), exponential. I know there are an enough number of distributions for it but Im looking for a one which can deal with most of situations like gradient boosting almost always give a good cross validate score. (I used gb only as example it is not even a distribution) Nov 29 '21 at 5:29 • Can you clarify what you mean by "exponential" for something on the real line? The properties you mention seem to have nothing clearly to do with the beta - except that the beta, too, can be skewed or symmetric, but so can any number of other families of distributions, it's not specifically a property of the beta. Might the distribution of the logit of a beta variate satisfy your requirements? Nov 29 '21 at 5:32 • $real beta$ almost equal to some $exp$, with $P(real beta<0)$ near to 0, Nov 29 '21 at 6:12 • I still don't follow what you mean by that. Do you mean that the density of the tail would be close to exponential (e.g. such that as $x\to\infty$ for some $k$, $f(x).e^{kx}$ approaches a constant, and similarly on the other side, mutatis mutandis?) Or something else? Nov 29 '21 at 7:03 One way to make a "real-valued beta distribution" would be to transform the interval $$(0,1)$$ onto the real line. One way of doing that is the logistic function $$\text{logit}(x)= \log(\frac{x}{1-x})$$ known from, for example, logistic regression. So if $$X \sim \mathcal{Beta}(\alpha,\beta)$$, let $$Y=\text{logit}(X)= \log(\frac{X}{1-X}).$$ Then $$Y$$ will be a random variable with range on the full real line, with a distribution we can call logistic-Beta. By standard transformation methods we find the density function of $$Y$$ as $$f_Y(y) =\frac{e^{\alpha y}}{B(\alpha, \beta) (1+e^y)^{\alpha+\beta}}$$ where $$B$$ is the beta function. This will give a flexible family of (unimodal) distributions on the real line. In this comprehensive reference that I just found, this distribution is called the Beta-Logistic Distribution. That is a useful search term! An example is below: The same transformation could be used with mixtures of betas, for instance, to get even multi-modal distributions. In reality, this example is a special case of the log-ratio transformation used with Compositional data, see also How to perform isometric log-ratio transformation. Transforming a beta random variable to the positive line (in a specific way) only gives the beta prime distribution, a recent post with an example is Distribution of the exponential of an exponentially distributed random variable?. Code use for the figure is below: dlogisticBeta <- function(x, alpha, beta, log=FALSE) { stopifnot( (alpha>0)&&(beta>0) ) logans <- alphax - lbeta(alpha, beta) - (alpha + beta)log1p( exp(x)) if(log) return(logans) else return(exp(logans)) } oldpar <- par(mfrow=c(1, 2)) plot( function(x) dlogisticBeta(x, 0.5, 0.5), from=-10, to=10, col="red", main= expression(paste(alpha == 0.5,", ", beta==0.5)) ) plot( function(x) dlogisticBeta(x, 0.5, 3), from=-10, to=10, col="red", main= expression(paste(alpha == 0.5,", ", beta==3)) ) par(oldpar) • The logit of a beta is closely related to the Fisher-z distribution Nov 29 '21 at 7:00 • great approach, I dont know if that transformation is flexible as beta is but think it's pretty enough. Nov 29 '21 at 7:28 • The utility of this distribution for modelling must be much reduced by the lack of location & scale parameters; if observations are on an interval scale - consonant with a distribution having support over the real line - estimates won't be equivariant to changes of the unit of measurement. You can add them in, but then "flexibility" is coming at a standard price - four free parameters. Dec 6 '21 at 9:26 It seems to me the convex shape the beta distribution can take is a result of the bounded sample space. If we move to a sample space that is bounded on one side then we are dealing with distributions like gamma, Weibull, etc. If we move to an unbounded sample space then we of course have the normal distribution. All of these distributions, including the beta and scaled beta, can be used in regression via generalized linear models. Rather than developed around an "error term" these models are typically developed by expressing a parameter in the likelihood or probability distribution in terms of a linear predictor. You could re-parameterize a model in terms of its mean or median and express this in terms of a linear predictor. • If you get beta support unbounded that will diverge. Nov 29 '21 at 1:17 • I agree. That is why the normal distribution is often used for an unbounded parameter space. Nov 29 '21 at 2:01 • but normal distribution is very simple and always symmetric regardless what its parameters are I'd like to know some 'adaptative' distribution as the beta is but real valuated. Nov 29 '21 at 3:10 • (1) Only a subset of Beta distributions has convex PDFs: namely, those with at least one parameter less than $1.$ (2) Distributions with unbounded support can have convex PDFs. The Pareto family is a well-known example. In light of these points, it is difficult to appreciate what your answer is trying to say. – whuber Nov 29 '21 at 14:45 • The support of the Pareto distribution is bounded from below similar to a gamma distribution and can certainly be used for modeling. This distribution is not precluded from my answer. I am suggesting there are lots of distributions the OP can use depending on the support needed, not necessitating transforming a beta distribution. The skewness and convex shapes of these distributions come from the support being bounded. Even if one did form a skewed theoretical continuous distribution having a support that is not bounded from above nor from below it may not have much practical value. Nov 30 '21 at 2:05 Beta regression is used to model continuous proportions; & that such observations are bounded by 0 & 1 is as reasonable an assumption as it is a strong one (if you'd call it an assumption rather than a definition). As noted in @GeoffreyJohnson's answer, it's the conditional distribution of each observation that's taken to be a beta distribution, not the error. In a typical beta regression you reparametrize the beta distribution with mean $$\mu = \frac{\alpha}{\alpha + \beta}$$ & precision $$\nu = \alpha + \beta$$; the joint density $$f_\boldsymbol{Y}$$ of $$n$$ independent observations $$\boldsymbol{y}$$ is given by $$f_\boldsymbol{Y}(\boldsymbol{y})=\prod_i^n\frac{\Gamma(\nu)}{\Gamma(\mu_i\nu)\Gamma\left[(1-\mu_i)\nu\right]} \cdot y_i^{\mu_i\nu-1}(1-y_i)^{(1-\mu_i)\nu-1}$$ The link function $$g$$ connects the predictor values $$\boldsymbol{x}_i$$ & the coefficients $$\boldsymbol\beta_i$$ to the mean for each observation $$\mu_i$$: $$g(\mu_i) = \eta(\boldsymbol{x}_i,\boldsymbol\beta_i)=\boldsymbol{x}_i^\mathrm{T}\boldsymbol{\beta}$$ The precision is common across all observations. Each row of plots below shows therefore how the distribution may be changed by changing the predictor values: Now there's evident flexibility ('malleability') there, but there are also evident constraints, among them these: • $$f_Y(y; \mu,\nu)=f_Y(1-y; 1-\mu,\nu)$$. This provides a desirable equivariance—if Dr A models the proportion of the day an animal spends asleep & Dr B the proportion it spends awake, we'd hope they'd make substantively identical inferences/predictions. • $$\operatorname{Var} Y_i =\frac{\mu_i(1-\mu_i)}{1+\nu}$$. The variance is at a maximum when $$\mu=\frac{1}{2}$$, increasing as $$\mu\rightarrow 0$$ or $$\mu\rightarrow 1$$. Qualitatively this is what you'd often expect from a continuous proportion, squashing up against the bounds. • $$\frac{\operatorname{E} (Y_i - \operatorname{E} Y_i)^3}{\left(\sqrt{\operatorname{Var} Y}\right)^3} =\frac{2(1-2\mu_i)\sqrt{1+\nu}}{(2+\nu)\sqrt{\mu(1-\mu)}}$$. The skewness is positive when $$\mu<\frac{1}{2}$$, increasing as $$\mu\rightarrow$$; it's negative when $$\mu>\frac{1}{2}$$, decreasing as $$\mu\rightarrow 1$$; & of course it's zero when $$\mu=\frac{1}{2}$$. Again, this is qualitatively what you'd often expect. The point of going into all this is first that in a sense there's no free lunch—you pay (in free parameters) for a certain amount of flexibility, & allocating it to some distributional properties means constraining others—and second that it's not at all clear what you'd want to carry over to modelling a real-valued response, beyond allowing skew & kurtosis to vary in some fashion (as @Glen_b comments).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 33, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8811497688293457, "perplexity": 610.3744654090914}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302740.94/warc/CC-MAIN-20220121071203-20220121101203-00599.warc.gz"}
https://alandavies.org/faqs/math/triganometric-identities	## The Pythagorean triganometric identity In this right triangle … Pythagoras’ Theorem states that $a^2 + b^2 = c^2$. Dividing both sides by $c^2$ then gives us $\frac{a^2}{c^2} + \frac{b^2}{c^2} = 1$. Since the definitions of $\sin\theta$ and $\cos\theta$ are, respectively, $\frac{b}{c}$ and $\frac{a}{c}$, the above identity follows immediately. Simple manipulation gives us the following additional identities … ## Double angle sum identities These follow immediately from the angle sum identities.	{"extraction_info": {"found_math": true, "script_math_tex": 7, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9925740361213684, "perplexity": 353.2984585284028}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370490497.6/warc/CC-MAIN-20200328074047-20200328104047-00363.warc.gz"}
https://math.stackexchange.com/questions/3874780/permutations-of-numbers-with-restrictions	# Permutations of numbers with restrictions In how many ways can one write the numbers $${1, 2, 3, 4, 5, 6}$$ in a row so that given any number in the row, all of its divisors (not including itself) appear to its left? I know $$1$$ has to be the first element, so we only concern ourselves with ordering the numbers $$2$$ to $$6$$. $$5$$ can be anywhere except the first position. We order $${2, 3, 4, 6}$$ then multiply that by five (for the five positions we can insert $$5$$ into afterwards). Is this correct? And can anyone help me solve the rest? I'm not quite sure how to proceed. Yes, you're on right track. We have two base cases $${2,4,6}$$ and $${2,6,4}$$ : • $${2,4,6}$$ Here $$3$$ can go in $$3$$ places. $$5$$ follows in $$5$$ spaces. • $${2,6,4}$$ Here $$3$$ can go in $$2$$ places. $$5$$ follows in $$5$$ spaces. Total ways $$= \boxed{25}$$. Let's place $$1, 2, 6$$ first which can be done in just one way. Now, $$4$$ can be placed in $$2$$ ways - i) either in between $$2, 6$$ - then $$3$$ can be placed in $$3$$ ways (before $$6$$). ii) after $$6$$ - then $$3$$ can be placed in $$2$$ ways (before $$6$$). $$5$$ can always be placed in $$5$$ ways (any place after $$1$$). So total number of ways = $$(3 + 2) \times 5 = 25$$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 35, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9643657803535461, "perplexity": 149.80622410340916}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141183514.25/warc/CC-MAIN-20201125154647-20201125184647-00682.warc.gz"}
http://physics.stackexchange.com/questions/130800/what-is-the-physical-meaning-of-commutators-in-quantum-mechanics	# What is the physical meaning of commutators in quantum mechanics? This is a question I've been asked several times by students and I tend to have a hard time phrasing it in terms they can understand. This is a natural question to ask and it is not usually well covered in textbooks, so I would like to know of various perspectives and explanations that I can use when teaching. The question comes up naturally in what is usually students' second course in quantum physics / quantum mechanics. At that stage one is fairly comfortable with the concept of wavefunctions and with the Schrödinger equation, and has had some limited exposure to operators. One common case, for example, is to explain that some operators commute and that this means the corresponding observables are 'compatible' and that there exists a mutual eigenbasis; the commutation relation is usually expressed as $[A,B]=0$ but no more is said about that object. This naturally leaves students wondering what is, exactly, the physical significance of the object $[A,B]$ itself? and this is not an easy question. I would like answers to address this directly, ideally at a variety of levels of abstraction and required background. Note also that I'm much more interested in the object $[A,B]$ itself than what the consequences and interpretations are when it is zero, as those are far easier and explored in much more depth in most resources. One reason this is a hard question (and that commutators are such confusing objects for students) is that they serve a variety of purposes, with only thin connecting threads between them (at least as seen from the bottom-up perspective). • Commutation relations are usually expressed in the form $[A,B]=0$ even though, a priori, there appears to be little motivation for the introduction of such terminology. • A lot of stock is placed behind the canonical commutation relation $[x,p]=i \hbar$, though it is not always clear what it means. (In my view, the fundamental principle that this encodes is essentially de Broglie's relation $\lambda=h/p$; this is made rigorous by the Stone-von Neumann uniqueness theorem but that's quite a bit to expect a student to grasp at a first go.) • From this there is a natural extension to the Heisenberg Uncertainty Principle, which in its general form includes a commutator (and an anticommutator, to make things worse). Canonically-conjugate pairs of observables are often introduced, and this is often aided by observations on commutators. (On the other hand, the energy-time and angle-angular momentum conjugacy relations cannot be expressed in terms of commutators, making things even fuzzier.) • Commutators are used very frequently, for example, when studying the angular momentum algebra of quantum mechanics. It is clear they play a big role in encoding symmetries in quantum mechanics but it is hardly made clear how and why, and particularly why the combination $AB-BA$ should be important for symmetry considerations. This becomes even more important in more rigorous treatments of quantum mechanics, where the specifics of the Hilbert space become less important and the algebra of observable operators takes centre stage. The commutator is the central operation of that algebra, but again it's not very clear why that combination should be special. • An analogy is occasionally made to the Poisson brackets of hamiltonian mechanics, but this hardly helps - Poisson brackets are equally mysterious. This also ties the commutator in with time evolution, both on the classical side and via the Heisenberg equation of motion. I can't think of any more at the moment but they are a huge number of opposing directions which can make everything very confusing, and there is rarely a uniting thread. So: what are commutators, exactly, and why are they so important? - – Qmechanic Aug 13 at 11:25 I am aware of this question, which asks something related but different. I am also aware of this one, which is closer to my question but it is fuzzy, unclear, and closed. – Emilio Pisanty Aug 13 at 11:27 I'll leave this old answer here. It makes the analogy to Poisson brackets of Hamiltonian mechanics precise, but, as you say, it is unlikely to satisfy someone searching for "physical significance". – ACuriousMind Aug 13 at 13:10 Maybe I'm underthinking this (certainly compared to the given answers), but exactly is wrong with "this expresses how much applying A then B is different from applying B then A"? Commutators of operators are important whenever operators don't commute. I suppose I realized this better when I learned about the commutator of covariant derivatives in GR (better known as the Riemann tensor of course). – Chris White Aug 14 at 4:31 @ChrisWhite One difference is that in GR the Riemann tensor quantifies the difference between two physically understandable and visualisable processes, namely parallel transport of a vector in different directions. In QM it is not so clear what "applying A or B" corresponds to physically. – Mark Mitchison Aug 14 at 10:23 Self adjoint operators enter QM, described in complex Hilbert spaces, through two logically distinct ways. This leads to a corresponding pair of meanings of the commutator. The former way is in common with the two other possible Hilbert space formulations (real and quaternionic one): Self-adjoint operators describe observables. Two observables can be compatible or incompatible, in the sense that they can or cannot be measured simultaneously (corresponding measurements disturb each other when looking at the outcomes). Up to some mathematical technicalities, the commutator is a measure of incompatibility, in view of the generalizations of Heisenberg principle you mention in your question. Roughly speaking, the more the commutator is different form $0$, the more the observables are mutually incompatible. (Think of inequalities like $\Delta A_\psi \Delta B_\psi \geq \frac{1}{2} \|\langle \psi \| [A,B] \psi\rangle\|$. It prevents the existence of a common eigenvector $\psi$ of $A$ and $B$ - the observables are simultaneously defined - since such an eigenvector would verify $\Delta A_\psi =\Delta B_\psi =0$.) The other way self-adjoint operators enter the formalism of QM (here real and quaternionic versions differ from the complex case) regards the mathematical description of continuous symmetries. In fact, they appear to be generators of unitary groups representing (strongly continuous) physical transformations of the physical system. Such a continuous transformation is represented by a unitary one-parameter group $\mathbb R \ni a \mapsto U_a$. A celebrated theorem by Stone indeed establishes that $U_a = e^{iaA}$ for a unique self-adjoint operator $A$ and all reals $a$. This approach to describe continuous transformations leads to the quantum version of Noether theorem just in view of the (distinct!) fact that $A$ also is an observable. The action of a symmetry group $U_a$ on an observable $B$ is made explicit by the well-known formula in Heisenberg picture: $$B_a := U^\dagger_a B U_a$$ For instance, if $U_a$ describes rotations of the angle $a$ around the $z$ axis, $B_a$ is the analog of the observable $B$ measured with physical instruments rotated of $a$ around $z$. The commutator here is a first-order evaluation of the action of the transformation on the observable $B$, since (again up to mathematical subtleties especially regarding domains): $$B_a = B -ia [A,B] +O(a^2) \:.$$ Usually, information encompassed in commutation relations is very deep. When dealing with Lie groups of symmetries, it permits to reconstruct the whole representation (there is a wonderful theory by Nelson on this fundamental topic) under some quite mild mathematical hypotheses. Therefore commutators play a crucial role in the analysis of symmetries. - "Roughly speaking, the more the commutator is different from 0, the more the observables are mutually incompatible". If this could be made more precise that would help a lot. – akrasia Aug 13 at 21:09 @akrasia I was thinking of inequalities like $\Delta A_\psi \Delta B_\psi \geq c \|\langle \psi \| [A,B] \psi\rangle\|$. It prevents the existence of a common eigenvector $\psi$ of $A$ and $B$ (the observables are simultaneously defined), since such an eigenvector would verify $\Delta A_\psi =\Delta B_\psi =0$. – Valter Moretti Aug 14 at 10:15 So conjugate variables have the maximum commutator and the maximum uncertainty product. Variables that are "less than conjugate" have a smaller commutator and smaller permissible uncertainty product. Once you understand what "conjugate" really means (both classically and in QM) you are there - at least for the most elementary application of the commutator. – akrasia Aug 14 at 12:25 @AlexeyBobrick No, I just mean that a measurement of $B$ (or $A$) is not formally represented by the action of the operator $B$ ($A$). Therefore it does not automatically follow that the formal statement $[A,B]\neq 0$ tells you something about "measuring B then A". Of course the two are connected but the relationship seems to be non-trivial. – Mark Mitchison Aug 14 at 15:28 @AlexeyBobrick Cool, I think we both agree, just wanted to be clear. Thanks :) – Mark Mitchison Aug 15 at 10:30 At a basic level : 1) if $[A,B]=0$, and if $A$ and $B$ are infinitesimal generators of a symmetry (so also conserved quantities), this means that both $A$ is invariant by $B$, and $B$ is invariant by $A$. For instance, $[H,J_z]=0$, means that the angular momentum is conserved during time evolution, and that the hamiltonian is invariant by rotation. As @Valter Moretti says, a non-null commutator $[A,B]$ measures the deviation from (both) symmetries. 2) Commutators of type $[A, B] = \pm B$, if $A$ is associated to a discrete spectrum, means that $B$ is a raising/lowering operator, with a " $A$-charge" $\pm 1$. An obvious example is $[J_z, J_\pm]= \pm J_\pm$ 3) Commutation relations of type $[\hat A, \hat B]= i \lambda$, if $\hat A$ and $\hat B$ are observables, corresponding to classical quantities $a$ and $b$, could be interpreted by considering the quantities $I = \int a \,db$ or $J = \int b \,da$. These classical quantities cannot be traduced in quantum observables, because the uncertainty on these quantities is always around $\lambda$. For instance, $[\hat x,\hat p] = i \hbar$ shows that there is no quantum observable corresponding to the action $S =\int (\vec p\,d \vec x - E\, dt)$. - I'm sorry, but this only serves to further confuse the issue. I know (and most importantly, a confused student knows) that there are those special cases where commutators are useful: usually one can state that if (some condition on the commutator $[A,B]$), then (some consequence that applies to $A$ and $B$). However, that doesn't really address what $[A,B]$ is, and it only serves to pull the object apart instead of providing a connecting thread. – Emilio Pisanty Aug 13 at 15:30 (See also a slight edit to the question.) – Emilio Pisanty Aug 13 at 15:31 @EmilioPisanty: Are you sure it is reasonable to expect there exists an answer to what is it, really? I mean, is there such an interpretation for the classical poisson bracket? – ACuriousMind Aug 13 at 15:50 @ACuriousMind No, I am not sure one can expect that. But I can hope for an answer - and if it doesn't exist, then bummer, and I'll settle for something I can tell students that won't confuse them further. – Emilio Pisanty Aug 13 at 17:02 @EmilioPisanty : Why not, so, beginning by an introduction to the Lie algebras, Lie groups, Lie brackets, and Lie derivatives ? The commutator appears naturally in all these structures. – Trimok Aug 14 at 8:30 I'd like to expand a little bit on the interpretation of commutators as a measure of disturbance (related to incompatibility, as touched on in the other answers). My interpretation of the commutator is that $[A,B]$ quantifies the extent to which the action of $B$ changes the value of the dynamical variable $A$, and vice versa. Let's assume that $A$ is a self-adjoint operator with a discrete non-degenerate spectrum of eigenvalues $\{a\}$ with associated eigenkets $\lvert a\rangle$. Then you can show that, for any operator $B$, the following decomposition exists $$B = \sum_{\Delta} B(\Delta),$$ such that $$[A,B(\Delta)] = \Delta B(\Delta),$$ where $B(\Delta)$ is defined below. Viewing the commutator $[A,.]$ as a linear operator, this has the form of an eigenvalue equation. The eigenvalues $\Delta$ are given by differences between pairs of eigenvalues of $A$, e.g. $\Delta = a'-a$. The specific form of the eigenoperators $B(\Delta)$ is $$B(\Delta) = \sum_{a} \langle a+\Delta\rvert B\lvert a\rangle \;\lvert a+\Delta\rangle\langle a\rvert.$$ This demonstrates that the $B(\Delta)$ are "ladder operators" which act to increase the value of the variable $A$ by an amount $\Delta$. The commutator thus induces a natural decomposition of $B$ into contributions that change the value of $A$ by a given amount. A simple example is the well known commutation relation between spin$-1/2$ operators: $$[\sigma^z,\sigma^x] = \mathrm{i}2\sigma^y = +2\sigma^+ - 2\sigma^-.$$ This tells you that $\sigma^x$ has two parts, which either increase or decrease the spin projection onto the $z$ axis by two "units", which in this case means $\pm 2\times\frac{\hbar}{2} = \pm \hbar$. In general, the full commutator is $$[A,B] = \sum_{\Delta} \Delta B(\Delta).$$ The $B(\Delta)$ are linearly independent$^{\ast}$, therefore the commutator vanishes only if $B(\Delta) = 0$ for all $\Delta \neq 0$, i.e. if $B$ does not change the value of $A$. If $[A,B]\neq 0$, one can get a measure of how much $B$ changes $A$ by computing the Hilbert-Schmidt norm (squared) of the commutator: $$\mathrm{Tr}\left\{[A,B]^{\dagger}[A,B]\right\} = \sum_{a,a'}(a-a')^2\lvert\langle a\rvert B \lvert a' \rangle\rvert^2.$$ This is the sum of the (squared) matrix elements of $B$ which link different eigenstates of $A$, weighted by the corresponding change in eigenvalues (squared). So this clearly quantifies the change in $A$ brought about by applying $B$. Now the not-so-obvious part: what does "changing $A$ by applying $B$" mean physically? As noted by Valter, evolution and transformations in QM are carried out formally by applying unitary operators generated by observables, not by applying the observables themselves. This relates to the above decomposition in the following way. Suppose that we take $A$ to be the Hamiltonian $H$. Then it is straightforward to show that the evolution of $B$ in the Heisenberg picture is given by $$B(t) = e^{i H t} B e^{-i H t} = \sum_{\Delta} e^{i\Delta t} B(\Delta),$$ where here $\Delta$ are the Bohr frequencies of the system under consideration. The jump operators $B(\Delta)$ can be interpreted as the Fourier components of the operator-valued function $B(t)$. In the context of perturbation theory, we often approximate the effect of unitary evolution by the application of a Hermitian operator (the perturbing Hamiltonian), in which case the interpretation of the jump operators is clear: they describe the transitions between energy eigenstates caused by the perturbation $B$. The oscillating time dependence ultimately leads to energy conservation as a frequency-matching condition. This is hardly a complete answer to the rather optimistic question of "what do commutators mean physically". However it might provide some food for thought for the curious student. $^{\ast}$This follows since the $B(\Delta)$ are orthogonal with respect to the Hilbert-Schmidt inner product: $$\mathrm{Tr}\left\{ B(\Delta)^{\dagger} B(\Delta') \right\} = \delta_{\Delta,\Delta'} \sum_a \lvert \langle a \rvert B \lvert a+\Delta \rangle \rvert^2,$$ where the Kronecker delta symbol $\delta_{\Delta,\Delta'}$ equals 1 if $\Delta = \Delta'$, and 0 otherwise. - It may be helpful to assign the students following HW problem : Suppose $A$ and $B$ be two observables i) What is the necessary condition that $A$ and $B$ can be simultaneously measured in an experiment without any uncertainty ? ii) Write down all the second degree polynomials in $A$ and $B$ which are again observables. iii) Suppose A be the Hamiltonian. Time evolve a state $\|\psi>$ for a time $t$ under $A$, and denote the state so obtained as $\|\psi(t)>$. Can we express $\displaystyle\frac{d<\psi(t)\|B\|\psi(t)>}{dt}$ as $<\psi(t)\|\mathcal{O}\|\psi(t)>$ for some observable $\mathcal{O}$ ? If yes, find $\mathcal{O}$. In this problem we may also take $A$ to be some other symmetry generator other than Hamiltonian. • When the commutator vanishes the two observables can be simultaneously measured in an experiment without uncertainty (this follows from the axioms of QM). • The expectation value of commutator $i[H,A]$ (where H is the Hamiltonian) in a state tells the time rate of change of the expectation value of $A$ in that state. More generally, the expectation value of the commutator $i[B,A]$ in a state is related to the infinitesimal change in the expectation value of $A$ in that state, under the one parameter symmetry generated by $B$. • For two given observables $A$, and $B$, their (i*) commutator $i[A,B]$ and anticommutator $\{A,B\}$ are again observables. However, the commutator appears more often in QM problems (and perhaps is more significant) than anticommutator because of the above two points. - Could you rephrase this in a way that makes the result apparent, and comment on the physics and its relation to the points I mentioned in the question? In its current form your answer forces everyone to go through the calculation. Plus, while problem-solving is a good way to learn things, handing out more homework, instead of an explanation, to a student with a genuine question is not (always) the best way to go. – Emilio Pisanty Aug 13 at 20:35 Let's start with the Schrödinger equation: $$\mathrm i\hbar\frac{\partial}{\partial t}\left\|\psi\right> = H\left\|\psi\right>$$ Since $H$ is self-adjunct, this also implies $$\mathrm -i\hbar\frac{\partial}{\partial t}\left<\psi\right\| = \left<\psi\right\|H$$ Now consider the most general quantum state, expressed by a density matrix $$\rho = \sum_k p_k\left\|\psi_k\middle>\middle<\psi_k\right\|$$ We want to know the time derivative of the density matrix. Obviously the time derivative is linear, and we can also use the product rule to obtain \begin{aligned}\frac{\partial\rho}{\partial t} &= \sum_k p_k\left(\left(\frac{\partial}{\partial t}\left\|\psi\right>\right) \left<\psi\right\| + \left\|\psi\right>\left(\frac{\partial}{\partial t}\left<\psi\right\|\right)\right)\\ &= \sum_k p_k\frac{1}{\mathrm i\hbar}\left(H\left\|\psi_k\middle>\middle<\psi_k\right\|-\left\|\psi_k\middle>\middle<\psi_k\right\|H\right)\\ &= \frac{1}{\mathrm i\hbar}(H\rho - \rho H)\\ &= \frac{1}{\mathrm i\hbar}[H,\rho] \end{aligned} So you see that here the commutator enters quite naturally. Next, consider an observable $A$, and let's look at the time dependence of its expectation value $\left<A\right>=\operatorname{tr}(A\rho)$. Using the linearity and cyclic invariance of the trace, we get \begin{aligned} \frac{\partial}{\partial t}\left<A\right> &= \frac{\partial}{\partial t}\operatorname{tr}(A\rho)\\ &= \operatorname{tr}\left(\frac{\partial A}{\partial t}\rho\right) + \operatorname{tr}\left(A\frac{\partial\rho}{\partial t}\right)\\ &= \left<\frac{\partial A}{\partial t}\right>+\frac{1}{\mathrm i\hbar}\operatorname{tr}(A[H,\rho])\\ &= \left<\frac{\partial A}{\partial t}\right>+\frac{1}{\mathrm i\hbar}\left(\operatorname{tr}(AH\rho) - \operatorname{tr}(A\rho H)\right)\\ &= \left<\frac{\partial A}{\partial t}\right>+\frac{1}{\mathrm i\hbar}\left(\operatorname{tr}(AH\rho) - \operatorname{tr}(HA\rho)\right)\\ &= \left<\frac{\partial A}{\partial t}\right>+\frac{1}{\mathrm i\hbar}\operatorname{tr}([A,H]\rho)\\ &= \left<\frac{\partial A}{\partial t}\right> + \frac{1}{\mathrm i\hbar}\left<[A,H]\right> \end{aligned} Now consider especially a conserved quantity that does not explicitly depend on time (that is, $\partial A/\partial t=0$). Of course if the quantity is conserved, it means its expectation value is conserved. The above equation then immediately gives $\left<[A,H]\right>=0$, and since this must be true for arbitrary $\rho$, we get $[A,H]=0$. That is, a conserved quantity commutes with the Hamiltonian. Note that all we've done here is shuffling around the commutator in the trace. Now let's take a closer look at the Hamiltonian. In classical mechanics, for non-relativistic problems we can write the Hamiltonian as $$H = \frac{p^2}{2m} + V(x)$$ and get the equation of motion \begin{aligned} \dot x &= \frac{\partial H}{\partial p} = \frac{p}{m}\\ \dot p &= -\frac{\partial H}{\partial x} = -V'(x) \end{aligned} Now let's try if we can get that at least on average with quantum mechanics. With the equation for averages, we have (since neither $x$ nor $p$ depend explicitly on time) \begin{aligned} \frac{\partial}{\partial t}\left<x\right> &= \frac{1}{\mathrm i\hbar}\left<[x,H]\right>\\ &= \frac{1}{\mathrm i\hbar}\frac{1}{2m}\left<[x,p^2]\right> + \frac{1}{\mathrm i\hbar}\underbrace{\left<[x,V(x)]\right>}_{=0}\\ &= \frac{1}{2m\mathrm i\hbar}\left(\left<[x,p]p\right> + \left<p[x,p]\right>\right) \stackrel{!}{=} \frac{1}{m}\left<p\right> \end{aligned} Now it is obvious that you get the right result if $[x,p]=\mathrm i\hbar$. Also, \begin{aligned} \frac{\partial}{\partial t}\left<p\right> &= \left<[p,H]\right>\\ &= \frac{1}{2m\mathrm i\hbar}\underbrace{\left<[p,p^2]\right>}_{=0} + \frac{1}{\mathrm i\hbar}\left<[p,V(x)]\right> \stackrel!= \left<-V'(x)\right> \end{aligned} It is not hard to check that this result is obtained if $p=-\mathrm i\hbar\partial/\partial x$, which also gives the commutation relation we just derived. About the connection with symmetries and uncertainty relations you've already gotten answers (and it's quite late in the night now), so I'll stop here. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9832234382629395, "perplexity": 377.6943366721543}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663612.31/warc/CC-MAIN-20140930004103-00004-ip-10-234-18-248.ec2.internal.warc.gz"}
https://www.varsitytutors.com/calculus_3-help/vector-subtraction	# Calculus 3 : Vector Subtraction ## Example Questions ← Previous 1 3 ### Example Question #1 : Vector Subtraction Find the difference Explanation: The difference of two vectors and is defined as For the two vectors The difference is ### Example Question #2 : Vector Subtraction Given the vectors find . Explanation: Given the vectors we can find the difference by subtracting component-wise ### Example Question #3 : Vector Subtraction Perform the following operation on the vectors specified below: Where Explanation: First, multiply out the vectors by their corresponding coefficients: Now we simply subtract the two vectors: ### Example Question #4 : Vector Subtraction Subtract the vectors and Explanation: Set up an expression to subtract the vectors. Be sure to make note of the sign change when subtracting the vectors. Simplify the vector. ### Example Question #5 : Vector Subtraction Find the difference, , of the two vectors. Explanation: To find the difference, , we distribute the minus sign and turn it into vector addition. The sum of two vectors is defined as The sum of two vectors is defined as As such, the difference is ### Example Question #2 : Vector Subtraction Compute the following: . Explanation: The formula for subtracting vectors is . Plugging in the values we were given, we get ### Example Question #3 : Vector Subtraction Solve: Explanation: To subtract vectors, we simply subtract their respective components: Note that our result is a vector still. ### Example Question #8 : Vector Subtraction Find the difference between and . Explanation: The formula for the difference of vectors is Using the vectors given, we get . ### Example Question #9 : Vector Subtraction Compute the following operation: . Explanation: The formula for subtracting vectors a and b is . Plugging in the values we were given, we get ### Example Question #10 : Vector Subtraction Perform the following vector operation:	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9787198305130005, "perplexity": 3273.009011386045}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607647.16/warc/CC-MAIN-20170523143045-20170523163045-00508.warc.gz"}
https://www.physicsforums.com/threads/essay-question-on-potential-electric-energy.165130/	# Essay Question on Potential Electric Energy 1. Apr 10, 2007 ### jkola07 If the electric field is 0, then is the electric potential 0? If the Electric pottential 0 then is the electric field 0? Explain why or why not. .. I rather say my idea on this topic, this my first post I am rather shy... 2. Apr 10, 2007 ### jkola07 I belive when the electrical potential is 0 that dose not necessary mean that the electrical field is 0 but if the electrical field is 0 than the electrical potential is 0, its just common sense to me I do not know how to explain can I get some help. 3. Apr 10, 2007 ### jkola07 is it because electirical potential is directly related to the electrical field...and electrical field can be in full motion meaning in full kinetic electric energy causeing there to be 0 potential??? Please help am I on the right track> 4. Apr 10, 2007 ### denverdoc First, there is not a man or woman on this forum who has not committed enormous blunders of reasoning. I myself recognize at least 3 in the past week alone, and friends suggest its closer to 30. My daughter would estimate it at 300,000 in one of her more sour moods, in other words, every breath I take is a mistake. There is one basic rule here at the Physics Forum that we adhere to. You are required to post at least some thoughts on the problem with which you would like help. It can be very simple, such as a definition of electric field and electric potential. You have already given the issue some consideration obviously. Often many seeking help have the additional disadvantage of trying to learn physics without much help from teachers or access to materials in their native language. I'm US born and have a good command of english and a better command of math, and it is still so, so hard at times. So as a way of getting your feet wet, just add a couple of thoughts about what potential is. Maybe consider what you know about gravity if you have studied this as there are many anologies. Welcome. We are here to help. Last edited: Apr 10, 2007 5. Apr 10, 2007 ### denverdoc Excellent, somewhere between my post and your first you added much more. These are very difficult questions you ask. I very much agree that one can be in an electric field and have no potential. The simple example would be a particle with no charge. Or in a situation where more than one field is present and exerting force on a particle such that net potential is zero? 6. Apr 10, 2007 ### jkola07 oh thanks...the Electrical potential energy is Kc(q^2/d) electrical field is Kc(q/d^2).. um in regard to gravitiy I suppose gravitational force and eletrical field are related....when it it comes to Gravational potential energy there is a point where it is zero is that when kinetic energy is the greatest?.. So would I compare Ep to Ef with anaolgy of a ball that is thrown up and has at a point 0 potential energy but still has force acting upon it... I'm I anywhere near the right track? 7. Apr 10, 2007 ### jkola07 oh thanks I did not see the previous post.... thanks 8. Apr 10, 2007 ### jkola07 Well can other force other than electrical alter electric potential energy? 9. Apr 10, 2007 ### denverdoc you're thinking, and thats all that matters. Sometimes people visit PF just because they have better things to do and want homework to be done or checked for them. Lets look at the gravity situation, you throw a ball up and it stops at some point, thats when the potential energy is greatest. Then during ascent is exchanges porential for kinetic energy. More what I had in mind was a particle between the moon and earth where the forces exerted exactly offset. With gravity, there is always attractive force.The conditions for electrical potential energy are wider given that it can be both attractive and repulsive. I don't wish to make this seem too complicated for now. 10. Apr 11, 2007 ### jkola07 If the electrical field is 0 then the electrical potential can be 0 this can be easily illustrated in when a particle has no charge in a electrical field. However when the electrical potentail is 0 that does not mean electrical field is 0 because there can be vaule to a electric field when Electrical potential is 0 an example of this is when more than on field is present exerting force on a partcle resulting the net potential energy to be 0 sound good? 11. Apr 11, 2007 ### christianjb Uhhh, in 1D E(x)=-d phi(x) / dx where E(x) is the field, phi(x) is the electric potential. if phi(x)=C (a constant, could be 0, doesn't have to be) E(x)=0 Similar Discussions: Essay Question on Potential Electric Energy	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.830011785030365, "perplexity": 1002.2038393283805}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917125849.25/warc/CC-MAIN-20170423031205-00479-ip-10-145-167-34.ec2.internal.warc.gz"}
http://physics.stackexchange.com/questions/29076/is-the-classical-doopler-effect-for-light-shift-1-v-c-exact-what-is-it-an	# Is the classical Doopler Effect, for light shift, $1-v/c$, exact? What is it an approximation of? Is the classical doopler effect for light shift equal to $1-v/c$ exact or an approximation of a classical formula? I know that it is an approximation of the relativistic formula, but what was the corresponding classical formula? I ask this because in Einstein's On the Electrodynamics of moving bodies he derives $\sqrt\frac{1-v/c}{1+v/c}$ and notes that it is different from the classical case. I'm not exactly sure what formula he is comparing it to. - "Is the [thing] exact or an approximation? I know that it is an approximation [...]" You might want to edit those two sentences. As it stands they're really bugging my inner editor. – dmckee May 27 '12 at 23:52 Thanks. I've edited it. – MadScientist May 28 '12 at 0:36 Classical mechanics is the approximation of relativistic mechanics when the speed involved is small compared to that of light. – C.R. May 28 '12 at 2:41 Doppler, not doopler... – WIMP May 28 '12 at 7:14 ## 1 Answer He is comparing $\sqrt{1-v\over 1+v}$ to the classical Doppler shift $(1-v)$ (where v is the velocity divided by c, since I use units where c=1). The formula you give $1-v\over 1+v$ doesn't have a classical interpretation, and Einstein reduces to Doppler's at slow speeds. - Thanks. I thought there was another, more exact, classical formula. – MadScientist May 31 '12 at 4:07 @BarryBarrett: What would it be? You can do a weird transformation of space and time in 1+1d space with right-moving light which keeps distances unstretched and keeps the speed of right-moving light constant, but this is just a mathematical trick, it has no physical significance. – Ron Maimon Jun 1 '12 at 6:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9499192833900452, "perplexity": 716.3224403949748}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368702444272/warc/CC-MAIN-20130516110724-00029-ip-10-60-113-184.ec2.internal.warc.gz"}
http://quant.stackexchange.com/tags/asset-pricing/hot	# Tag Info 13 You can forecast stock prices thru time-series models, cross-sectional, or panel models. There is considerable variation within these categories. In time-series models you would use an auto-regressive model such as an AR(1) where the independent variable is the dependent variable lagged by one period. Naturally, an AR(2) would consist of 2 lags and so on. ... 8 Two ways: Model the returns using an Ornstein-Uhlenbeck process You can control the variance of the residual noise in the process to your desired level of correlation. Conceptually you inject gaussian noise into the synthetic OU process to satisfy your requirement. For example, let's say you have time-series A which is what you are modelling. Time-series ... 7 A factor model has the form $$r_{j,t}=\sum_n \beta_{j,n} f_{n,t}+\epsilon_{j,t}$$ Where $r_{j,t}$ is the return of stock $j$ at time $t$, $\beta_{j,n}$ is the sensitivity (factor loading) of stock $j$ to factor $n$, $f_{n,t}$ is the return of factor $n$ at time $t$, and $\epsilon_{j,t}$ is the idiosyncratic non-factor return. One factor can be the constant. ... 6 If you want to learn more about price pressure, you should look after market impact of metaorders, which is a more adequate term. Because of the microstructure (i.e. the mix of orderbboks dynamics, trading rules, participants behaviours and habits, etc), the more you buy or sell, the more you influence the price an unfavorable way (for your trades). Just ... 6 Risk-free rate is that you get for letting someone else use your money in a riskless manner. Suppose we live in a world where there is no risk whatsoever. In particular, if you lend someone \$100 there is 100% certainty that he will pay you back in a year. Before the pay date, he can do whatever he wants with your$100, while you have no access to it. Even ... 5 I would reckon this to be a very hard exercise. Unless you know the inner workings of such algorithm and how the news was exactly interpreted you have no idea about what went "wrong" and on which side such opportunities reside. One thing I know for sure is that most all algos that capitalize on news capture primarily the numeric part of the news event. I ... 5 This the "Joint Hypothesis Problem". Basically, any test for abnormal returns is also implicitly a test of the model you use to define "abnormal". If you see a significant and positive $\alpha$, that could either mean that you actually are generating excess risk-adjusted returns, or it could mean that your risk model is incomplete. This is basically what ... 5 Then for each month $t$, you run a cross-section regression: $r_{i,t} = \lambda_0 + \hat{\beta}_i {\lambda}_t + \alpha_{i,t}$ Where: $\hat{\beta}_i \equiv [\beta_{i, MktRf}, \beta_{i, SMB}, \beta_{i, HML}]'$, is a vector of the coefficients estimated on the first step. What you are looking for is to estimate the vector of $\hat{\lambda}_t \equiv ... 5 The two step Fama-Macbeth regression works as follows: First, run a cross sectional regression in each period. I believe that you want to estimate risk premia for each of the Fama and French factors. Therefore you run:$$r_{i,t} = \lambda_{t,MKT} \hat{\beta}_{i,MKT}+\lambda_{t,HML} \hat{\beta}_{i,HML}+\lambda_{t,SMB} \hat{\beta}_{i,SMB}+ \alpha_{i,t} \quad ... 4 I mainly speak as market practitioner when I say that I believe in the end all models that are applied to data and real life pricing issues are discretized. Think about it, even the BS hedge argument is in the end just a "theoretical continuous time overlay" of actual discrete time steps and re-hedges. Thus some of the limiting assumptions re BS. You do not ... 4 Wilmott Forums - "How can I simulate correlated random numbers?" Generating correlated normal variates Random Correlated Series Generator (using R) All found with a Google search for "how to generate random correlated series". 4 Your equations are for cum-dividend prices, i.e. the price plus dividend today. The paper refers to ex-dividend prices. The correct two equations for investor group$a=1are \begin{align} p^1(0) =&\ \frac{3}{4} \left(\frac{1}{2}p^1(0) + \frac{1}{2}(1+p^1(1))\right) \\ p^1(1) =&\ \frac{3}{4} \left(\frac{2}{3}p^1(0) + \frac{1}{3}(1+p^1(1))\right) ... 4 Beware, oversimplification ahead! (This means that the following is technically not correct, in fact it is false! But: It gives an intuition what is going on!) If you toss a coin and calculate heads as-1$and tails as$1$you get a mean of$0$with a variance of$1$. When you add up multiple coin tosses, i.e. create a random process$dz(t)$, the mean ... 3 Portfolio returns are analyzed to account for risk factors only to determine what the risk factor contributed to the returns, was it the underlying assets or the skill of the portfolio manager. Fama French model explains the returns in terms of principal component such SMB and HML besides the market related returns from CAPM. These links have more detais ... 3 There are a few reasons to use factor models. Most importantly, stocks tend to move together. Stated alternately, the first principal component of the securities in a domestic market tends to explain a large share of the variance. If you're concerned with multiple securities (as in portfolio optimization), then you have to account for this or you will ... 3 What a great question -- it touches on many issues at the core of quantitative finance. This answer might be a lot more than you bargained for, but it's too interesting to pass up. References Mostly, this subject falls somewhere at the intersection of these three highly-interrelated topics: risk-neutral valuation, rational pricing and the fundamental ... 3 In my experience HFT has to balance the reward of any strategy with risk. In the case of a news-based trading strategy, the risk can be enormous, which means the algo will need a very high expected profit in order to trade the news. After important news events, volatility skyrockets and persists for some time (sometimes even days). If the market were able ... 3 You could create a rescaled stochastic indicator from your randomly generated, correlated series. 1) use whatever software/methodology you want to create your random series with 0.85 correlation to the original data. 2) find the maximum and minimum values of this new series and rescale the series to range between 0 and 1 using this formula; (series_value - ... 3 Let's consider a random process$X$. If$X$is an adapted process, then we know, without any uncertainty, what its value is at the present time. This idea is formalized with measure theory. For$X$to be a martingale, it needs to have the following property: at any given time, our best estimate of the value at some point in the future (i.e. forecast), is ... 3 The risk free rate is important and the reason for the inclusion and consideration of the risk free rate is that investors do not get compensated for not taking on risk. Now, we can argue whether the risk free rate truly provides risk free returns (we all should know that it does not, but ...) but it is important in the context of pricing risky assets that ... 3 Fitting Fama-French or Carhart is as simple as learning how to perform Bayesian regression. Pretty much every introductory book Bayesian estimation will cover this. There are analytic formulae under certain assumptions, but I would definitely try to learn the basics of MCMC and Gibbs sampling before trying this out in practice. Here are two papers. The book ... 3 Non overlapping periods would make for a far smaller sample 2 I have seen a technique which uses frequency domain and does pretty much what (I think) you are trying to do. The author does not give the complete details, so you might have to contact him for that, or take a look at the (free) software he has developed. Link here: ... 2 I think the market participants behavior on the micro-level is not different in principle from the behavior on the macro-level. The challenges of better news interpretation, and faster response time are very similar on all levels. There may be a little bit more trading opportunities in HFT, but building HFT strategy and infrastructure is very expensive, ... 2 If you can observe prices at a very high frequency, then "news" is defined as a lot more things than if you are observing prices at a lower frequency. So what you are calling corrections are also news for the high frequency guy because he can observe prices that fast, so do not consider these as corrections to the original news, consider this to be a ... 2 Glad you've asked :) Technically speaking, in factor model$\alpha$stays for return or risk premia, which asset pays when all factor returns are zero. Then, to answer question in more details, we have to specify, are we dealing in our model with return ($R_i$for asset$i$) or with risk premia over risk free ($R_i-R_f$). In the first case, ... 2 I can understand your concerns, but I think you are expecting too much from these theories. We cannot explain aggregate behavior from first principle based on a sound theory of individual decisions under uncertainty and I personally doubt that there will ever be such a Grand Unification in economics. Consumption-based asset pricing models are more related ... 2 Another important reason for using risk-adjusted returns is to disentangle "skill" from "risk-taking". Think of a equation for a fund's performance like:$r_{i,t}-r_f=\alpha_i+\epsilon_{i,t}$where$\alpha_i$gives you the average excess return of fund$i\$. Alpha is often interpreted as measure of a managers' skill in timing the market and selecting ... 2 A random process that is adapted to a filtration is measurable (ie X_t is F_t-measurable) but not necessarily a martingale. X_t is a martingale if E(X_t \| F_s) = X_s for s < t. 2 Pretty good explanation is in Schweser CFA Study Notes for CFA level III. Books 3 and 5, at least from 2009, if I remember right. See also Tsay R.S. Analysis of Financial Time Series (Wiley Series in Probability and Statistics). // 2010. - good example with implementation in R. 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https://etna.ricam.oeaw.ac.at/volumes/2011-2020/vol43/abstract.php?vol=43&pages=223-243	## Matrix decompositions for Tikhonov regularization Lothar Reichel and Xuebo Yu ### Abstract Tikhonov regularization is a popular method for solving linear discrete ill-posed problems with error-contaminated data. This method replaces the given linear discrete ill-posed problem by a penalized least-squares problem. The choice of the regularization matrix in the penalty term is important. We are concerned with the situation when this matrix is of fairly general form. The penalized least-squares problem can be conveniently solved with the aid of the generalized singular value decomposition, provided that the size of the problem is not too large. However, it is impractical to use this decomposition for large-scale penalized least-squares problems. This paper describes new matrix decompositions that are well suited for the solution of large-scale penalized least-square problems that arise in Tikhonov regularization with a regularization matrix of general form. Full Text (PDF) [379 KB], BibTeX ### Key words ill-posed problem, matrix decomposition, generalized Krylov method, Tikhonov regularization. ### AMS subject classifications 65F22, 65F10, 65R30 ### Links to the cited ETNA articles [14] Vol. 38 (2011), pp. 233-257 Stefan Kindermann: Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems [15] Vol. 40 (2013), pp. 58-81 Stefan Kindermann: Discretization independent convergence rates for noise level-free parameter choice rules for the regularization of ill-conditioned problems < Back	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8399835824966431, "perplexity": 1034.3381006063898}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588282.80/warc/CC-MAIN-20211028065732-20211028095732-00589.warc.gz"}
https://discoveryking.com/the-universe-before-the-big-bang-quantum-cosmology-part-1/	# The Universe Before the Big Bang: Quantum Cosmology (Part 1) ## Cosmology and String Theory: Quantum Cosmology The possible cosmological scenarios outlined in this book have been approached so far from a purely classical perspective, using concepts and ideas typical of the macroscopic world, like space, time, geometry, gravitational forces, and so on. The aim of this chapter is to introduce a possible alternative description of the cosmological evolution based on a quantum point of view, and using a framework where the Universe can be represented as a wave propagating in an abstract, multidimensional space dubbed superspace (no connection with the previously mentioned supersymmetry). A detailed and rigorous explanation of this approach would clearly require some knowledge of quantum mechanics, which is not necessarily part of the scientiﬁc background of the typical reader, and whose introduction is beyond the scope of this book. Hence, our discussion will be grossly qualitative and approximate. Nevertheless, we hope to provide the reader with an appropriate overview of the methods and goals pertaining to the ﬁeld of quantum cosmology. Amongst the motivations suggesting the use of a quantum cosmology approach within string models of the Universe, we should mention ﬁrst of all the difﬁculties we currently face when we try to give a quantitative and fully consistent description of the transition between the pre-Big-Bang and post-Big-Bang phases. Whereas the obstacles appear to be of a formal nature, they nevertheless have a physical origin. Indeed, they are rooted in the fact that the instability of the initial state (the string perturbative vacuum) yields to a phase (the pre-Big-Bang phase) in which the curvature and the strength of the gravitational force (and of all other forces) increase in an accelerated manner. Hence, in order to make a transition to the standard cosmological phase where the Universe decelerates and becomes radiation- dominated, and where all natural forces are stabilized, we need a mechanism that curbs the initial increase of both the curvature and the dilaton. Otherwise, the Universe would necessarily reach a singular state with inﬁnite curvature (like the one occurring in the standard scenario). Such a singularity would then completely detach the pre-Big-Bang phase from the current one. Without any physical connection, it would no longer make sense to relate the properties of the current Universe with those characterizing an epoch preceding the Big Bang. Furthermore, it would not be legitimate to hunt for possible experimental traces of such a primordial epoch in the cosmological backgrounds of relic radiation, as dis- cussed in previous chapters. The dynamics of a possible mechanism able to stop the in- crease of the curvature and to provide a transition from the pre- to the post-Big-Bang phase is quite complicated, as shown by all studies and computations so far performed. Actually, in addition to the above-mentioned effects, such a mechanism should be able to turn the kinetic energy associated with the geometry and the dilaton into thermal radiation. Furthermore, if the pre-Big-Bang phase is higher-dimensional, such a mechanism should be able to “freeze” the extra spatial dimensions, and possibly break the symmetries between the various forces. According to string theory, those effects can hardly take place when the curvature is small and the couplings are weak. The transition seems to require a phase where the gravitational forces are so strong that the resulting particles are themselves able to modify the geometry, yielding what are known as back-reaction effects, introducing quantum corrections into the classical equations (the quantum loop corrections introduced in Chap. 4). Moreover, when the curvature is quite high, other corrections (the so-called α� corrections, see again Chap. 4) are induced by the fact that it is no longer legitimate to approximate string behavior by point-like objects. In addition, the dilaton may start to develop a strong self-interaction, generating a large potential energy density. Taking into account all these effects, the full equations of string cosmology become so complicated that – up to now – it has been impossible not only to ﬁnd their exact solutions, but even to write them down in a closed form (apart from some special cases). However, all results obtained so far (in some particularly simple cases that we can deal with) are encouraging, since they seem to suggest that the quantum corrections just provide damping corrections to the classical, accelerated evolution, and tend to favor the transition to the phase described by the standard cosmological model. The relevance of the quantum corrections suggests that the obstacles we encounter when we attempt to describe the transition could be surmounted by abandoning the classical, geometric approach, where we follow the space-time evolution point-by-point, moment-by-moment. Since the equations describing this evolution are not fully known, in general, it could be convenient to adopt the probabilistic approach of quantum cosmology which does not re- quire full knowledge of all the intermediate evolutionary stages, but only of the initial and ﬁnal states. It is worth noticing here that, even in the cosmological frame- work based upon Einstein’s equations, there are open issues which it seems appropriate to address with quantum mechanical methods. We may recall for instance that, within the standard inﬂationary scenario, the primordial Universe approaches a state of exponential expansion and constant curvature. Such a state, described by the de Sitter geometry, cannot have lasted indeﬁnitely in the past (see Chap. 1). Hence, we cannot avoid facing the problem of how this state might have emerged. A possible solution to this problem was suggested independently during the 1980s by some Soviet cosmologists (Alexander Vilenkin, Andrei Linde, Valery Rubakov, Yakov Zeldovich, and Alexei Starobinski). Their solution relies upon the idea that the initial de Sitter state may emerge “from nothing”, i.e., it may be spontaneously produced from the vacuum thanks to an effect called quantum tunneling. The tunneling effect is a well-known process in elementary particle physics, where a particle, represented by a quantum mechanical wave, is able to overcome a potential barrier even if its energy is inadequate at the classical level. (Very naively, it is as if a cyclist, who does not have enough energy to climb a small hill, unexpectedly ﬁnds a tunnel at the bottom of the hill that allows him to get through.) In a cosmological setup, the description of the birth of the Universe in terms of the tunneling effect requires the introduction of a peculiar inﬁnite-dimensional space, the so-called superspace, whose points represent all possible geometric conﬁgurations of the Universe. For practical reasons it is possible to use a reduced space, dubbed mini-superspace, and characterized by a ﬁnite number of dimensions (associated, for instance, with the radii of a spatial section of the Universe measured along the different spatial axes). The motion of a wave from one point to another of this mini-superspace represents the transition of the Universe from one geometrical state to another, and is governed by the so-called Wheeler–DeWitt equation, named after two theoretical physicists (John Archibald Wheeler and Bryce DeWitt) who ﬁrst proposed it in the 1960s. The Wheeler–DeWitt equation is the exact analogue of the Schroedinger equation of ordinary quantum mechanics, the only difference being that its solutions, instead of describing the possible values of the position and momentum of a given physical system (for instance a particle), represent the possible geometrical states of the Universe. A Universe described by the Wheeler–DeWitt equation thus becomes a fully quantum mechanical Universe, subject to all possible quantum effects. We know, for instance, that the so-called second quantization of the Schroedinger wave function leads to the formalism of quantum ﬁeld theory, where it is possible to describe the creation and annihilation of particles. Similarly, quantization of the Wheeler–DeWitt wave function gives rise to the so-called third-quantization formalism, where it is possible to describe the creation and annihilation of universes. By an appropriate choice of initial conditions, it is possible in particular to ﬁnd solutions to the Wheeler–DeWitt equations describing the birth of our Universe as a tunneling process, thus providing a solution to the classical problem of the origin of the inﬂationary de Sitter space. One ﬁnds that if the state of the Universe after the tunneling process is described by the de Sitter geometry, and is thus characterized by a constant Λ representing the vacuum energy density, then the bigger the value of Λ, the higher the tunnelling or transition probability. In this way, the Universe is created just in the appropriate inﬂationary state, which does in- deed require a high enough value for the parameter Λ (also called the cosmological constant). Barring a number of formal and technical problems, the most unsatisfactory feature of this scenario is probably the fact that the initial conditions for the tunneling process are to be chosen ad hoc, since they are not unique. There are also arguments supporting the choice of different initial conditions (as discussed, again during the 1980s, by other theoretical physicists including James Hartle and Stephen Hawking), which lead to different scenarios. The reason for this arbitrariness (dubbed the boundary condition problem) is rooted in the fact that within standard cosmology the ﬁnal state – i.e., the cosmological conﬁguration we aim to obtain – is well known, whereas the initial state is completely unknown. Indeed, the very name of the tunneling process, “tunneling from nothing”, already automatically stresses the lack of knowledge about the initial state. The standard classical theory is not helpful at all, since it just predicts the Big Bang singularity as initial state, i.e., the state that the quantum mechanical approach would like to avoid. Within the self-dual pre-Big-Bang scenario, the situation is radically different. The initial state, assumed to be the perturbative vacuum of string theory, is completely known, fully justiﬁed, and fully appropriate to be described – in the low energy regime – by the Wheeler–DeWitt wave function. Given the initial state, the computation of the transition probability towards the ﬁnal state, i.e., the current Universe, is no longer arbitrary. It is therefore interesting to note that, by computing the probability that a transition occurs between the perturbative string vacuum and a post-Big-Bang Universe equipped with a cosmological constant, the outcome is quite similar to the result obtained in standard cosmology assuming the validity of the “tunnelling from nothing” scenario (as shown by Gabriele Veneziano, Jnan Maharana, and the present author). This could suggest that the ad hoc prescription for the boundary conditions, needed to obtain the tunnelling effect, somehow simulates the presence of the perturbative vacuum as initial state. It would then be more appropriate to talk about “tunneling from the string perturbative vacuum”, rather than “tunneling from nothing”. Figure 8.1 provides a qualitative representation of this result. There is, however, a conceptual difference between string cosmology and standard cosmology. The quantum mechanical transition from pre-Big-Bang to post-Big-Bang described by the Wheeler–DeWitt equation, in a two-dimensional mini-superspace where the coordinates are represented by the spatial radius of the Universe and the dilaton, does not correspond to a tunnelling effect, but rather to a quantum reﬂection effect. 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https://math.stackexchange.com/questions/1663331/combinatorially-equivalent-polyhedron-with-vertices-from-a-given-dense-set	# Combinatorially equivalent polyhedron with vertices from a given dense set In this question we are only interested in convex polyhedra in the Euclidean space $\mathbb R^3$. Polyhedra $P$ and $P'$ are said to be combinatorially equivalent iff there is a bijection between them (denoted here as $X\mapsto X'$) preserving the number of vertices, edges and faces and their relations (i.e. edge $E$ connects vertices $A$ and $B$ and separates faces $G$ and $H$ in $P$ iff edge $E'$ connects vertices $A'$ and $B'$ and separates faces $G'$ and $H'$ in $P'$). Note that we ignore possible chirality, and thus every polyhedron is combinatorially equivalent to its mirror image. Recall that a subset $S$ of $\mathbb R^3$ is dense iff there is a point from $S$ in every neighborhood of every point of $\mathbb R^3$. For example, the set of all points with rational coordinates is dense. Question: Is it true that for every dense subset $S$ and every polyhedron $P$ there is a combinatorially equivalent polyhedron whose all vertices belong to $S$? • It's kinda obvious for me that it is always possible to find a combinatorially equalent skeleton, but I have doubts about faces can always be made planar. – Vladimir Reshetnikov Feb 19 '16 at 19:47 • Is there some obvious counterexample that tells us, that $S = \mathbb Z^3$ doesn't work? It seems to me that it might be enough and if that's the case, your question follows from this in a straightforward fashion. – Stefan Mesken Feb 19 '16 at 19:50 • @Stefan $\mathbb Z^3$ is not dense in $\mathbb R^3$ – Vladimir Reshetnikov Feb 19 '16 at 20:11 • Sure, but it seems to me that your claim might hold for $S = \mathbb Z^3$ and if one can prove that, the result for dense subsets follows easily. – Stefan Mesken Feb 19 '16 at 23:50 • @Stefan Thanks. In your (deleted) answer you mentioned that by adding additional vertices any polyhedron can be transformed into a polyhedron with only triangular faces. You further assumed that those vertices can be safely removed later, after we "snap vertices to grid", restoring combinatorial properties of the original polyhedron. I think there is a problem with this step. If we started with a quadrilateral face, then after the transformation its 4 vertices might be not coplanar anymore, so they cannot become the vertices of a quadrilateral face in the transformed polyhedron. – Vladimir Reshetnikov Feb 21 '16 at 2:26 Your comment guided me onto the right track. Claim. There is a dense subset $S \subseteq \mathbb R^3$ that doesn't contain $4$ distinct, coplanar points. Proof. Fix a countable basis $\mathcal B = \{ O_n \mid n \in \mathbb N \}$ for the topology of $\mathbb R^3$ not containing $\emptyset$ as an element. We recursively construct a sequence $(S_n \mid n \in \mathbb N_0)$ such that for all $m,n \in \mathbb N_0$ with $m < n$ • $S_m$ is finite, • $S_m \subseteq S_n$, • if $0 < m$, then $S_m \cap O_m \neq \emptyset$, • no $3$ distinct points of $S_m$ are colinear and • no $4$ distinct points of $S_m$ are coplanar. If we manage to construct such a sequence, then $S = \bigcup \{ S_n \mid n \in \mathbb N_0 \}$ is countable, dense and doesn't contain $4$ distinct coplanar points. Towards this end let $S_0$ be any set of $4$ points that are not coplanar and such that no $3$ points of $S_0$ are colinear (e.g. $S_0 = \{(0,0,0), (1,0,0), (0,1,0), (0,0,1) \}$). Given $S_n$ let $[S_n]^3$ be the set of all subsets of $S_n$ that contain precisely $3$ distinct points. Since no $3$ points of $S_n$ are colinear, any $s \in [S_n]^3$ spans a two dimensional, affine subspace of $\mathbb R^3$ which we denote by $P_s$. Let $[S_n]^2$ be the set of all subset of $S_n$ that contain precisely $2$ distinct points. For each $s \in [S_n]^2$ let $L_s$ be the affine line spanned by $s$. Let $X = \bigcup \{ P_s \mid s \in [S_n]^3 \} \cup \bigcup \{ L_s \mid s \in [S_n]^2 \}$. Since $X$ is a finite union of sets with Lebesgue measure $0$, we know that $X$ has Lebesgue measure $0$. In particular, this yields $O_n \setminus X \neq \emptyset$. Choosing some $s_n \in O_n \setminus X$, we let $S_{n+1} = S_n \cup \{s_n\}$. $\square$ If $S$ is as in the claim, there is no polyhedra with vertices in $S$ that is combinatorially equivalent to the 'unit cube'. So your question indeed has a negative answer - contrary to my initial instinct.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9101091027259827, "perplexity": 169.66609825195408}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251678287.60/warc/CC-MAIN-20200125161753-20200125190753-00039.warc.gz"}
http://mathhelpforum.com/advanced-algebra/18497-list-two-different-matrices-s-t-2-i.html	# Math Help - List Two Different Matrices A s.t. A^2=I 1. ## List Two Different Matrices A s.t. A^2=I Hello, I am trying to determine two different matrices $A$ such that $A^2=\Bigg[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\Bigg]$. I am trying to solve this algebraically. Here is what I have attempted: 2. Originally Posted by Fourier Hello, I am trying to determine two different matrices $A$ such that $A^2=\Bigg[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\Bigg]$. I am trying to solve this algebraically. Here is what I have attempted: Set b = c = 0. Then a^2 = d^2 = 1. So I and -I fall out as 2 of 4 solutions. 3. Originally Posted by Fourier Hello, I am trying to determine two different matrices $A$ such that $A^2=\Bigg[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\Bigg]$. I am trying to solve this algebraically. Here is what I have attempted: Set $a^2=d^2=0$, then $bc=1$ so: $ A^2= \left[ \begin{array}{cc}0&x\\1/x&0 \end{array} \right]^2=I_{2x2} $ RonL 4. Hello, Fourier! You're off to a good start . . . . . $\begin{bmatrix}a & b\\c &d\end{bmatrix}\begin{bmatrix}a&b\\c&d\end{bmatrix }\;=\;\begin{bmatrix}1&0\\0&1\end{bmatrix}$ $\begin{array}{ccc}(1)\;\;a^2 + bc \:=\:1 &\qquad & (2)\;\;ab+bd \:=\:0 \\ (3)\;\;ac + cd \:=\:0 & \qquad & (4)\;\;bc+d^2\:=\:0\end{array}$ We have: . $\begin{array}{cccc}(2)\;\;ab+bd\:=\:0 & \Rightarrow & b(a+d)\:=\:0 & (5) \\ (3)\;\;ac + cd \:=\:0 & \Rightarrow & c(a+d)\:=\:0\ & (6)\end{array}$ Subtract: . $\begin{array}{c}(1)\;\;a^2+bc \:=\:1 \\ (4)\;\;bc+d^2\:=\:1\end{array} \quad\Rightarrow\quad a^2-d^2\:=\:0\quad\Rightarrow\quad d \,=\,\pm a$ If $a\!\cdot\!d \neq 0$, then (5) and (6) give us: . $b = c = 0$ And (1) and (4) give us: . $a^2 \,= \,1,\;d^2\,=\,1\quad\Rightarrow\quad a\,=\,\pm1,\;d\,=\,\pm1$ . . Two solutions: . $\begin{bmatrix}1 &0 \\0&1\end{bmatrix}$ .and . $\begin{bmatrix}\text{-}1 & 0\\0&\text{-}1\end{bmatrix}$ If $a = d = 0$, then (1) gives us: . $bc \,=\,1\quad\Rightarrow\quad c \,=\,\frac{1}{b}$ . . More solutions: . $\begin{bmatrix}0 & b \\ \frac{1}{b} & 0\end{bmatrix}$ . . . . for $b \neq 0$ . obviously. 5. Originally Posted by Soroban Hello, Fourier! You're off to a good start . . . We have: . $\begin{array}{cccc}(2)\;\;ab+bd\:=\:0 & \Rightarrow & b(a+d)\:=\:0 & (5) \\ (3)\;\;ac + cd \:=\:0 & \Rightarrow & c(a+d)\:=\:0\ & (6)\end{array}$ Subtract: . $\begin{array}{c}(1)\;\;a^2+bc \:=\:1 \\ (4)\;\;bc+d^2\:=\:1\end{array} \quad\Rightarrow\quad a^2-d^2\:=\:0\quad\Rightarrow\quad d \,=\,\pm a$ If $a\!\cdot\!d \neq 0$, then (5) and (6) give us: . $b = c = 0$ And (1) and (4) give us: . $a^2 \,= \,1,\;d^2\,=\,1\quad\Rightarrow\quad a\,=\,\pm1,\;d\,=\,\pm1$ . . Two solutions: . $\begin{bmatrix}1 &0 \\0&1\end{bmatrix}$ .and . $\begin{bmatrix}\text{-}1 & 0\\0&\text{-}1\end{bmatrix}$ If $a = d = 0$, then (1) gives us: . $bc \,=\,1\quad\Rightarrow\quad c \,=\,\frac{1}{b}$ . . More solutions: . $\begin{bmatrix}0 & b \\ \frac{1}{b} & 0\end{bmatrix}$ . . . . for $b \neq 0$ . obviously. More solutions are $\begin{bmatrix}\text{-1} &0 \\0&1\end{bmatrix}$ and $\begin{bmatrix}1 & 0\\0&\text{-}1\end{bmatrix}$ and $\begin{bmatrix}a & b \\ \frac{1-a^2}{b} & \text{-}a\end{bmatrix}$ and $\begin{bmatrix}a & \frac{1-a^2}{b} \\ b & \text{-}a\end{bmatrix}$ for $b \neq 0.$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 38, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9632229804992676, "perplexity": 501.9438376269317}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207927844.14/warc/CC-MAIN-20150521113207-00238-ip-10-180-206-219.ec2.internal.warc.gz"}
http://www.relativitybook.com/w/index.php?title=Einstein:Book_chapter_04_-_The_Galileian_System_of_Co-Ordinates&direction=next&oldid=452&printable=yes	# Einstein:Book chapter 04 - The Galileian System of Co-Ordinates (diff) ← Older revision \| Latest revision (diff) \| Newer revision → (diff) Albert Einstein: Relativity: The Special and the General Theory 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 - - 18 19 20 21 22 23 24 25 26 27 28 29 - - 30 31 32 ## 4: The Galileian System of Co-Ordinates AS is well known, the fundamental law of the mechanics of Galilei-Newton, which is known as the law of inertia, can be stated thus: A body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line. This law not only says something about the motion of the bodies, but it also indicates the reference-bodies or systems of co-ordinates, permissible in mechanics, which can be used in mechanical description. The visible fixed stars are bodies for which the law of inertia certainly holds for a high degree of approximation. Now if we use a system of co-ordinates which is rigidly attached to the earth, then, relative to this system, every fixed star describes a circle of immense radius in the course of an astronomical day, a result which is opposed to the statement of the law of inertia. So that if we adhere to this law we must refer these motions only to systems of co-ordinates relative to which the fixed stars do not move in a circle. A system of co-ordinates of which the state of motion is such that the law of inertia holds relative to it is called a "Galileian system of coordinates." The laws of the mechanics of Galilei-Newton can be regarded as valid only for a Galileian system of co-ordinates.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8689290881156921, "perplexity": 300.9677660116789}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710953.78/warc/CC-MAIN-20221204004054-20221204034054-00131.warc.gz"}
https://cstheory.stackexchange.com/questions/47965/generalisations-of-the-fundamental-theorem-of-statistical-learning-to-different	# Generalisations of the Fundamental Theorem of Statistical Learning to different tasks and losses The fundamental theorem of statistical learning gives an equivalence between uniform convergence of the empirical risk to learning in the PAC framework. I have only seen this stated in the case of binary classification with the 0-1 loss. Does a result of this form hold in more general settings? For example: margin-based classification rules, regression, multi-class classification, ...? Another statement of this question could be: under what circumstances does uniform convergence of the empirical risk imply PAC learning? (I am most interested in this direction of implication.) Please provide references if you have them. • Uniform convergence means that the Empirical Risk Minimizer is a PAC learner. – Aryeh May 3 at 17:14 • I take issue with your characterization of the "fundamental theorem of statistical learning". For classification, it states the equivalence of PAC learnability and finite VC-dimension. – Aryeh May 3 at 17:16	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8123860359191895, "perplexity": 538.1448487656504}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991252.15/warc/CC-MAIN-20210512035557-20210512065557-00518.warc.gz"}
http://mathhelpforum.com/calculus/106819-question-laplace-transform-definition.html	# Math Help - a question on Laplace Transform definition 1. ## a question on Laplace Transform definition Hi. I have this problem I am quite unsure of. For which complex values of $s$ is the Laplace Transform of $e^{-2t} cos(6t)$ defined? What I did was simplified it and had it as $\int_0^\infty e^{(-2-s)t}cos(6t) \,dt$ And from the L.T definitions, as t approaches infitinty, the function should converge to zero. So is it right by saying $-2-s < 0$ and hence $s > 2$ ? But then again, if I take the limit of $e^{(-2-s)t}cos(6t)$ it doesn't converge zero, rather it is undefined. Thanks. 2. If we apply the definition of LT is... $f(s)=\mathcal {L}\{e^{-2t}\cdot \cos 6t \} = \int_{0}^{\infty} \cos 6t \cdot e^{-(2+s)t}\cdot dt$ (1) The integral in (1) converges for $Re(s) >-2$ and that is also the domain of $f(s)$... Kind regards $\chi$ $\sigma$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9940268993377686, "perplexity": 481.13302127108176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999668190/warc/CC-MAIN-20140305060748-00043-ip-10-183-142-35.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/chain-rule.743584/	# Chain rule 1. Mar 16, 2014 ### anthonyk2013 Differentiate the following by rule y=(2x2+4x)5 Is the chain rule the right rule to use? dy/dx=dy/dudu/dx Let U=2x2+4x du/dx=4x+4 y=(u)5 → dy/du=5(u)4 dy/dx=5(u)44x+4 dy/dx=5(2x2+4x)44x+4 dy/dx= 30(2x2+4x)44x dy/dx= 30(2x216x)4 I'm wondering if I am on the right track? 2. Mar 16, 2014 ### Staff: Mentor Anthonyk, your questions should be posted in the Homework & Coursework sections (Calculus & Beyond) - not in the technical math sections. 3. Mar 16, 2014 ### anthonyk2013 ok no problem 4. Mar 16, 2014 ### Ray Vickson I hope you did not mean what you wrote, which was $$\frac{dy}{dx} = 5(x^2 + 4x)^4 4x + 4, \text{ which } = 4 +5(x^2 + 4x)^4 4x$$ I hope you meant $$\frac{dy}{dx} = 5(x^2 + 4x)^4 (4x + 4)$$ If that is what you did mean, that is what you should write; note the parentheses. 5. Mar 16, 2014 ### Staff: Mentor Use parentheses where they are needed. The right side should be 5u4 (4x + 4) That last factor should be (4x + 4) No. I can't tell what you did here. How did you get 30 at the beginning of the right side? 6. Mar 16, 2014 ### vela Staff Emeritus In addition to what Ray noted, I can't figure out what you did to get the last two lines. You need to go back and review algebra. 7. Mar 16, 2014 ### anthonyk2013 Ya sorry that is what I meant. can I simplify this further or can I leave it like that? 8. Mar 16, 2014 ### Staff: Mentor You can factor 4 out of the 4x + 4 term, and put it with the 5 factor. Otherwise, that's about all you can do. For most purposes, leaving it in factored form is preferable to multiplying everything out. 9. Mar 16, 2014 ### anthonyk2013 dy/dx=20(2x2+4x)(4x) this what you mean 10. Mar 16, 2014 ### Staff: Mentor No. Like vela said, you need to take some time to review algebra. Starting from here: dy/dx=5(2x2+4x)4 (4x+4), factor 4 out of the last expression in parentheses, and combine that 4 with the leading 5. You did this, but the problem is that 4x + 4 ≠ 4x. That seems to be what you're doing. 11. Mar 17, 2014 ### anthonyk2013 dy/dx=5+4(2x2+4x)44x dy/dx=9(2x2+4x)44x or dy/dx=10x2+20x(4x+4) Last edited: Mar 17, 2014 12. Mar 17, 2014 ### BruceW none of those. take your time, just using rules of arithmetic that you are certain about. for example, (4x+4) = 4(x+1) right? So then what does the equation look like? 13. Mar 17, 2014 ### anthonyk2013 I know this is probably very simple I just cant get it. dy/dx=5(2x2+4x)(4x+4) Do I separate it out and treat 5(2x2+4x) from (4x+4) 5(2x2+4x)4(x+1)? 14. Mar 17, 2014 ### BruceW yeah, almost. you forgot the first bit should be to the power of four. so it is 5(2x2+4x)44(x+1) And yes, it is fine to 'separate out'. In arithmetic, it is always OK to say a(bc)=abc i.e. in this case 5(2x2+4x)4(4x+4) = 5(2x2+4x)44(x+1) 15. Mar 17, 2014 ### anthonyk2013 5(2x2+4x)44(x+1) Thanks very much, frustrating that its so simple. thanks again 16. Mar 17, 2014 ### BruceW glad to have helped! yeah, I'm writing Makefiles at the moment, which should be a simple programming thing to do. But it's taking me ages! haha 17. Mar 17, 2014 ### anthonyk2013 Best of luck. 18. Mar 17, 2014 ### Staff: Mentor You are really not going to be able to do calculus unless you have good facility with algebra. You did not realize that you could combine the factors 5 and 4 to give 20. Your previous posts had several algebra errors in them. I implore you to please follow Vela's advice and review algebra. Chet 19. Mar 17, 2014 ### anthonyk2013 Thanks I have been looking over it today. It's just the work load of study, job and kids I can only do so much. I can multiply 54 to get 20. Can I do anything with what in the bracket? 20. Mar 17, 2014 ### Staff: Mentor Yes, you can factor out a 2, and, when it comes out of the bracket, it becomes 24=16, which, when multiplied by the 20 becomes 320. Chet Draft saved Draft deleted Similar Discussions: Chain rule	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8079990148544312, "perplexity": 2692.490275142593}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187826283.88/warc/CC-MAIN-20171023183146-20171023203146-00066.warc.gz"}
https://electronics.stackexchange.com/questions/584008/voltage-rms-and-voltage-spectral-density-from-adc-sample-are-not-consistent	# Voltage RMS and Voltage Spectral Density from ADC Sample are Not Consistent I have time series data from a 100 MS/s ADC, and I would like to calculate the RMS noise and the voltage spectral density (VSD), and see consistency between the two. I'm using a 16-bit ADC, and the data is in bits, so data point can be any integer in [-32768, 32767]. The noise of the ADC channel is 3.6 LSB. I calculate the VSD by taking the discrete Fourier transform (I use Fourier in Mathematica). I drop the data at frequencies above the Nyquist frequency (50 MHz), and take the magnitude of each term (because I don't care about the phase for this measurement). I normalize the data FFT by calculating the FFT of a 1 MHz sine wave with 1 LSB RMS amplitude: SQRT(2)SIN(2 PI 10^6 t), then I use the height of that peak (which ends up equal to 127.867) as a normalization factor. So if f is the FFT magnitude of the data the normalize FFT is f/127.867. I thought this normalization would take care of any factors of 2 or PI from the Mathematica Fourier function, but the VSD does not make sense. The VSD is flat, white noise; I don't sample at low enough rate to see the 1/f noise at low frequency. The noise level is 0.03 LSB. This is about 60 times larger than I expect the real VSD noise level to be, based on the 3.6 LSB RMS noise value since: (RMS noise) ~= VSD noise level * SQRT(f1-f0) = 0.03SQRT(50x10^6) = 218 LSB. I feel like I'm missing something fundamental here, but I'm not quite sure what's going wrong. Any feedback on what I do here, and how to get closer to a consistent VSD? Thank you. • Try acquiring a real signal of known amplitude with your ADC, see what it looks like and what the FFT looks like. That will detect problems with gain, calibration, etc. Aug 31, 2021 at 22:36 • What do you mean you "drop" the frequencies over the Nyquist limit? Do you have a low pass filter before the ADC? If not, the higher frequencies will appear aliased and you'll have to consider them as well. Aug 31, 2021 at 23:01 • Also how exactly are you computing the VSD from the FFT of the time series? Would you mind showing the results? Aug 31, 2021 at 23:19 Your sqrt(50M) assumes the VFD is in noise/sqrt(Hz). What normalisations has Mathematica applied? Have you told it fs = 100M so it's giving you noise/sqrt(Hz), or is it giving you noise/bin_width, which will be much higher? What's the length of your FFT? If (for instance) 10k, then your bins are 10M/10k = 1 kHz wide. This factor doesn't appear (and doesn't need to appear) in the sinewave calibration you did. What window did you use? They increase the noise bandwidth of a bin by a factor of typically 2, but can be more. Do a noise calibration, as well as a sinewave calibration, then vary the length of the FFT, and the type of window, to see what's going on. 'Ground Truth' of an FFT operation can be established with Parseval's Theorem. This basically says 'you get the same total energy for a sequence whether you add up the energy per time sample, or do a FFT and then add up the energy per frequency sample', subject to any scaling factor of N that the transform happens to do. If the noise bandwidth is your problem, I'd guess your factor of 60 times too much is consistent with an FFT length of around 4096. Am I right? • Yes it seems you are on the right track with the normalization. I do the FFT of a 32700 point time series. I drop the symmetrical data above 50 MHz, so the spectrum has 16350 points. I did not use a window, I just did the FFT on the data from the ADC which was sampling at 100 MS/s. How does a window filter come in? It looks like the correct calibration factor is SQRT(bin width in Hz length of data/2) so SQRT(10^8/32700*32700/2)=SQRT(50 MHz), which is what I'd expect.... This gets the RMS and spectrum to agree to within 10%, so I'm thinking this is correct. – Dan Sep 2, 2021 at 22:41	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8165299892425537, "perplexity": 1003.0520338982984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103669266.42/warc/CC-MAIN-20220630062154-20220630092154-00655.warc.gz"}
http://mathhelpforum.com/advanced-algebra/174193-relate-change-matrix-its-eigenvalues-vectors.html	# Math Help - Relate A Change in a Matrix to its Eigenvalues/vectors 1. ## Relate A Change in a Matrix to its Eigenvalues/vectors Given the eigenvalues and eigenvectors of a symmetric matrix A. How does changing one element of the matrix effect the eigenvalues/vectors? For example, if I add 1 or multiply by 2 the first element of the matrix, how does this change the value of the eigenvalues/vectors? 2. Let me add a little more detail: I have an arbitrarily sized nxn matrix. This matrix is symmetric and binary (only 0's and 1's). The eigenvalues and eigenvectors are known. An element is changed in this matrix. For example, a 0 turns to 1 or a 1 turns to 0. If an element off the main diagonal is changed, its symmetric counterpart changes as well. If the element is on the diagonal only 1 element is changed (bc it doesn't have a symmetric counterpart). Now, what is a function that outputs the new eigenvalues/eigenvectors after the change is made? Not necessarily, but preferably, a multivariable function of the old eigenvalues and the change that was made. I've come up with solutions to specific examples (ie, where the matrix is 3x3), but deriving a general solution is more difficult. Any help? 3. I don't think such a formula exists - at least, I've never seen one. However, you can get an idea of how sensitive the eigenvalues are to changes in the matrix by looking at this paper.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8448399305343628, "perplexity": 324.5736137991728}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701158609.98/warc/CC-MAIN-20160205193918-00305-ip-10-236-182-209.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/145607-differentiable-function.html	Math Help - differentiable function 1. differentiable function suppose that $f$ is a differentiable function with the derivative $f'(x)=(x+1)(x-2)(x+6)$. find all the critical numbers of f and determine whether each corresponds to a local maximum, a local minimum, or neither. 2. Use the first derivitive test... When is f'(x)=0? What are the signs of f'(x) in the intervals between these points, and beyond them? 3. Originally Posted by euclid2 suppose that $f$ is a differentiable function with the derivative $f'(x)=(x+1)(x-2)(x+6)$. find all the critical numbers of f and determine whether each corresponds to a local maximum, a local minimum, or neither. critical values occur where f'(x) = 0 local maximums occur at critical values where f'(x) changes sign from positive to negative. local minimums occur at critical values where f'(x) changes sign from negative to positive. 4. Euclid2, you have posted 4 questions, of the same kind, in a row where you have not shown any attempt to do them yourself. This is not a "we will do your homework for you" forum! 5. Originally Posted by HallsofIvy Euclid2, you have posted 4 questions, of the same kind, in a row where you have not shown any attempt to do them yourself. This is not a "we will do your homework for you" forum! nothing of the sort. i had 17 homework questions last night. i was unable to do 5 of them. i posted them here.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8715739846229553, "perplexity": 438.81933575740163}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422121540415.91/warc/CC-MAIN-20150124174540-00233-ip-10-180-212-252.ec2.internal.warc.gz"}
https://hpmuseum.org/forum/printthread.php?tid=8126&page=2	sqrt question - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: Not HP Calculators (/forum-7.html) +--- Forum: Not remotely HP Calculators (/forum-9.html) +--- Thread: sqrt question (/thread-8126.html) Pages: 1 2 RE: sqrt question - Claudio L. - 04-26-2017 03:08 AM (04-24-2017 09:36 PM)David Hayden Wrote: (04-09-2017 03:59 AM)Claudio L. Wrote: sqrt(1) = 1 sqrt( (-1)(-1) ) = sqrt(-1)sqrt(-1) = ii = -1 Isn't it: sqrt(1) = 1 or -1. sqrt( (-1)(-1) ) = sqrt(-1)sqrt(-1) = (+/-i)(+/-i) = -1 or 1 The fact that we usually mean "the positive answer" when we say "sqrt(x)" doesn't negate the fact that there is also a negative answer. You started reading the thread from the bottom up :-) That post was intended as proof that even when selecting always the positive root as "the one true answer", it is possible to arrive to the other root by using trivial algebraic manipulations. Otherwise, I agree with you and Han that both answers are correct and valid, one is not better than the other. RE: sqrt question - Han - 04-28-2017 06:09 PM (04-09-2017 03:59 AM)Claudio L. Wrote: (04-07-2017 10:54 PM)Han Wrote: Is this due to the sqrt() function, though? This seems like a consequence of assuming factorization properties of 1 and -1 that may not still hold true for complex numbers. The factorization properties hold true for complex numbers. The problem is more about the interaction between the sqrt() function and its argument because of mapping to the principal branch. For example: sqrt(1) = 1 sqrt( (-1)(-1) ) = sqrt(-1)sqrt(-1) = ii = -1 What happened here? we replaced 1 (in polar coordinates, its argument is zero), with two numbers with an argument of 180 degrees. The multiplication of these 2 numbers (-1) would give you an argument of 360 degrees. The convention for sqrt is to halve the argument, so the result of sqrt(1exp(i2pi)) is 1exp(ipi) = -1 while sqrt(1exp(i0)) = 1exp(i0) = 1 Now the value 1exp(i2pi) should've been reduced to 1exp(i0) prior to performing the sqrt(). However, when you distribute the sqrt doing sqrt(-1)sqrt(-1), you are not allowing that reduction to take place. Both arguments of 180 degree get halved, then added together by the multiplication resulting in 180 degree again (hence the negative result). So this is a consequence that 1 = (-1)*(-1), while mathematically true and correct, gets treated differently by the sqrt() when you split it. But there's nothing wrong, the result is correct, just that you've been pushed to the other solution. There's no way around it that I know of. It is not clear to me what you mean by the factorization holds true for complex numbers. I agree that $$\sqrt{ab} = \sqrt{a} \sqrt{b}$$ provided that $$a$$, $$b$$, and $$ab$$ are non-negative. However, I question whether the definition of $$\sqrt{x}$$ has been implicitly changed when you allow $$a$$ and $$b$$ to be negative. For complex numbers, which can be represented as $$re^{i\theta}$$, (where $$r$$ is a non-negative real number and $$-\pi < \theta \le \pi$$ ), we have the "principal root" $\sqrt{z} = \sqrt{re^{i\theta}} = \sqrt{r} e^{i\theta/2}$ The reason your example produces two outcomes is because you did not define the square root function (over the complex plane) to be one-to-one (unless you are restricting $$\theta$$ to be strictly positive and less than or equal to $$2\pi$$ ). My point here is that it is mathematically possible to define the square root function for a complex number without obtaining ambiguous results.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8385269641876221, "perplexity": 836.1559005332117}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304961.89/warc/CC-MAIN-20220126192506-20220126222506-00196.warc.gz"}
https://math.libretexts.org/Courses/East_Tennesee_State_University/Book%3A_Differential_Equations_for_Engineers_(Lebl)_Cintron_Copy/5%3A_Eigenvalue_problems/5.1%3A_Sturm-Liouville_problems	$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\\| #1 \\|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ # 5.1: Sturm-Liouville problems $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\\| #1 \\|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\\| #1 \\|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ ## 5.1.1 Boundary Value Problems In Chapter 4 we have encountered several different eigenvalue problems such as: $X''(x)+ \lambda X(x)=0$ with different boundary conditions $\begin{array}{rrl} X(0) = 0 & ~~X(L) = 0 & ~~\text{(Dirichlet), or} \\ X'(0) = 0 & ~~X'(L) = 0 & ~~\text{(Neumann), or} \\ X'(0) = 0 & ~~X(L) = 0 & ~~\text{(Mixed), or} \\ X(0) = 0 & ~~X'(L) = 0 & ~~\text{(Mixed)}, \ldots \end{array}$ For example for the insulated wire, Dirichlet conditions correspond to applying a zero temperature at the ends, Neumann means insulating the ends, etc…. Other types of endpoint conditions also arise naturally, such as the Robin boundary conditions $hX(0)-X'(0)=0\quad hX(L)+X'(L)=0,$ for some constant $$h$$. These conditions come up when the ends are immersed in some medium. Boundary problems came up in the study of the heat equation $$u_t=ku_{xx}$$ when we were trying to solve the equation by the method of separation of variables in Section 4.6. In the computation we encountered a certain eigenvalue problem and found the eigenfunctions $$X_n(x)$$. We then found the eigenfunction decomposition of the initial temperature $$f(x)=u(x,0)$$ in terms of the eigenfunctions $f(x)= \sum_{n=1}^{\infty}c_nX_n(x).$ Once we had this decomposition and found suitable $$T_n(t)$$ such that $$T_n(0)=1$$ and $$T_n(t)X(x)$$ were solutions, the solution to the original problem including the initial condition could be written as $u(x,t)= \sum_{n=1}^{\infty}c_nT_n(t)X_n(x).$ We will try to solve more general problems using this method. First, we will study second order linear equations of the form $\label{eq:6} \frac{d}{dx}\left( p(x)\frac{dy}{dx} \right)-q(x)y+\lambda r(x)y=0.$ Essentially any second order linear equation of the form $$a(x)y''+b(x)y'+c(x)y+\lambda d(x)y=0$$ can be written as $$\eqref{eq:6}$$ after multiplying by a proper factor. Example $$\PageIndex{1}$$: Sturm-Liouville Problem Put the following equation into the form $$\eqref{eq:6}$$: $x^2y''+xy'+(\lambda x^2-n^2)y=0.$ Multiply both sides by $$\frac{1}{x}$$ to obtain \begin{align}\begin{aligned} \frac{1}{x}(x^2y''+xy'+(\lambda x^2-n^2)y) &=xy''+y'+ \left( \lambda x -\frac{n^2}{x}\right)y &= \frac{d}{dx}\left( x \frac{dy}{dx} \right)-\frac{n^2}{x}y+\lambda xy=0.\end{aligned}\end{align} The Bessel equation turns up for example in the solution of the two-dimensional wave equation. If you want to see how one solves the equation, you can look at subsection 7.3.3. The so-called Sturm-Liouville problem$$^{1}$$ is to seek nontrivial solutions to \begin{align}\begin{aligned} \frac{d}{dx}\left( p(x)\frac{dy}{dx} \right)-q(x)y+\lambda r(x)y & =0,~~~~~a<x<b, \\ \alpha_1y(a)-\alpha_2y'(a) &=0, \\ \beta_1y(b)+\beta_2y'(b) &=0.\end{aligned}\end{align} In particular, we seek $$\lambda$$s that allow for nontrivial solutions. The $$\lambda$$s that admit nontrivial solutions are called the eigenvalues and the corresponding nontrivial solutions are called eigenfunctions. The constants $$\alpha_1$$ and $$\alpha_2$$ should not be both zero, same for $$\beta_1$$ and $$\beta_2$$. Theorem $$\PageIndex{1}$$ Suppose $$p(x),\: p'(x),\: q(x)$$ and $$r(x)$$ are continuous on $$[a,b]$$ and suppose $$p(x)>0$$ and $$r(x)>0$$ for all $$x$$ in $$[a,b]$$. Then the Sturm-Liouville problem (5.1.8) has an increasing sequence of eigenvalues $\lambda_1<\lambda_2<\lambda_3< \cdots$ such that $\lim_{n \rightarrow \infty} \lambda_n= +\infty$ and such that to each $$\lambda_n$$ there is (up to a constant multiple) a single eigenfunction $$y_n(x)$$. Moreover, if $$q(x) \geq 0$$ and $$\alpha_1, \alpha_2,\beta_1, \beta_2 \geq 0$$, then $$\lambda_n \geq 0$$ for all $$n$$. Problems satisfying the hypothesis of the theorem (including the "Moreover") are called regular Sturm-Liouville problems, and we will only consider such problems here. That is, a regular problem is one where $$p(x),\: p'(x),\: q(x)$$ and $$r(x)$$ are continuous, $$p(x)>0$$, $$r(x)>0$$, $$q(x) \geq 0$$, and $$\alpha_1, \alpha_2,\beta_1, \beta_2 \geq 0$$. Note: Be careful about the signs. Also be careful about the inequalities for $$r$$ and $$p$$, they must be strict for all $$x$$ in the interval $$[a,b]$$, including the endpoints! When zero is an eigenvalue, we usually start labeling the eigenvalues at $$0$$ rather than at $$1$$ for convenience. That is we label the eigenvalues $$\lambda_{0} <\lambda_{1} <\lambda_{2} <\cdots$$. Example $$\PageIndex{2}$$ The problem $$y''+ \lambda y,\: 0<x<L,\: y(0)=0$$, and $$y(L)=0$$ is a regular Sturm-Liouville problem: $$p(x)=1,\: q(x)=0,\: r(x)=1$$, and we have $$p(x)1>0$$ and $$r(x)1>0$$. We also have $$a=0$$, $$b=L$$, $$\alpha_{1}=\beta_{1}=1$$, $$\alpha_{2}=\beta_{2}=0$$. The eigenvalues are $$\lambda_n=\frac{n^2 \pi^2}{L^2}$$ and eigenfunctions are $$y_n(x)=\sin(\frac{n \pi}{L}x)$$. All eigenvalues are nonnegative as predicted by the theorem. Exercise $$\PageIndex{1}$$ Find eigenvalues and eigenfunctions for $y''+\lambda y=0,~~~~~y'(0)=0,~~~~~y'(1)=0.$ Identify the $$p,\: q,\: r,\: \alpha_j,\: \beta_j$$. Can you use the theorem to make the search for eigenvalues easier? (Hint: Consider the condition $$-y'(0)=0$$) Example $$\PageIndex{3}$$ Find eigenvalues and eigenfunctions of the problem \begin{align}\begin{aligned} y''+\lambda y &=0, & 0<x<1, \\ hy(0)-y'(0) & =0, & y'(1)=0, &\quad h>0.\end{aligned}\end{align} These equations give a regular Sturm-Liouville problem. Exercise $$\PageIndex{2}$$ Identify $$p,\: q,\: r,\: \alpha_j,\: \beta_j$$ in the example above. First note that $$\lambda \geq 0$$ by Theorem $$\PageIndex{1}$$. Therefore, the general solution (without boundary conditions) is \begin{align}\begin{aligned} & y(x) = A \cos ( \sqrt{\lambda}\, x) + B \sin ( \sqrt{\lambda}\, x) & & \qquad \text{if } \; \lambda > 0 , \\ & y(x) = A x + B & & \qquad \text{if } \; \lambda = 0 . \end{aligned}\end{align} Let us see if $$\lambda=0$$ is an eigenvalue: We must satisfy $$0=hB-A$$ and $$A=0$$, hence $$B=0$$ (as $$h>0$$), therefore, $$0$$ is not an eigenvalue (no nonzero solution, so no eigenfunction). Now let us try $$h>0$$. We plug in the boundary conditions. \begin{align}\begin{aligned} 0 &=hA- \sqrt{\lambda}B, \\ 0 &=-A\sqrt{\lambda}\sin(\sqrt{\lambda})+B\sqrt{\lambda}\cos(\sqrt{\lambda}).\end{aligned}\end{align} If $$A=0$$, then $$B=0$$ and vice-versa, hence both are nonzero. So $$B=\frac{hA}{\sqrt{\lambda}}$$, and $$0=-A \sqrt{\lambda}\sin(\sqrt{\lambda})+\frac{hA}{\sqrt{\lambda}}\sqrt{\lambda}\cos(\sqrt{\lambda})$$. As $$A \neq 0$$ we get $0=- \sqrt{\lambda}\sin(\sqrt{\lambda})+h\cos(\sqrt{\lambda}),$ or $\frac{h}{\sqrt{\lambda}}= \tan \sqrt{\lambda}.$ Now use a computer to find $$\lambda_n$$. There are tables available, though using a computer or a graphing calculator is far more convenient nowadays. Easiest method is to plot the functions $$\frac{h}{x}$$ and $$\tan(x)$$ and see for which they intersect. There is an infinite number of intersections. Denote the first intersection by $$\sqrt{\lambda_1}$$ the first intersection, by $$\sqrt{\lambda_2}$$ the second intersection, etc…. For example, when $$h=1$$, we get that $$\sqrt{\lambda_1}\approx 0.86,\: \sqrt{\lambda_2}\approx 3.43, ...$$. That is $$\lambda_1 \approx 0.74,\: \lambda_2 \approx 11.73,...$$, …. A plot for $$h=1$$ is given in Figure $$\PageIndex{1}$$. The appropriate eigenfunction (let $$A=1$$ for convenience, then $$B= \frac{h}{\sqrt{\lambda}}$$) is $y_n(x)=\cos(\sqrt{\lambda_n}x)+\frac{h}{\sqrt{\lambda_n}}\sin(\sqrt{\lambda_n}x).$ When $$h=1$$ we get (approximately) $y_1(x) \approx \cos(0.86x)+ \frac{1}{0.86} \sin(0.86x),\quad y_2(x) \approx \cos(3.43x)+ \frac{1}{3.43} \sin(3.43x),\quad ....$ Figure $$\PageIndex{1}$$: Plot of$$\frac{1}{x}$$ and $$\tan x$$. ## 5.1.2 Orthogonality We have seen the notion of orthogonality before. For example, we have shown that $$\sin(nx)$$ are orthogonal for distinct $$n$$ on $$[0, \pi]$$. For general Sturm-Liouville problems we will need a more general setup. Let $$r(x)$$ be a weight function (any function, though generally we will assume it is positive) on $$[a, b]$$. Two functions $$f(x)$$, $$g(x)$$ are said to be orthogonal with respect to the weight function $$r(x)$$ when $\int_a^bf(x)g(x)r(x)dx=0.$ In this setting, we define the inner product as $\langle f,g \rangle \overset{\rm{def}}= \int_a^bf(x)g(x)r(x)dx,$ and then say $$f$$ and $$g$$ are orthogonal whenever $$\langle f,g \rangle=0$$. The results and concepts are again analogous to finite dimensional linear algebra. The idea of the given inner product is that those $$x$$ where $$r(x)$$ is greater have more weight. Nontrivial (nonconstant) $$r(x)$$ arise naturally, for example from a change of variables. Hence, you could think of a change of variables such that $$d \xi =r(x)dx$$. Eigenfunctions of a regular Sturm–Liouville problem satisfy an orthogonality property, just like the eigenfunctions in Section 4.1. Its proof is very similar to the analogous Theorem 4.1.1. Theorem $$\PageIndex{2}$$ Suppose we have a regular Sturm-Liouville problem \begin{align}\begin{aligned} \frac{d}{dx} \left( p(x) \frac{dy}{dx} \right) -q(x)y+\lambda r(x)y &=0, \\ \alpha_1y(a)- \alpha_2y'(a) &=0, \\ \beta_1y(b)+ \beta_2y'(b) &=0.\end{aligned}\end{align} Let $$y_j$$ and $$y_k$$ be two distinct eigenfunctions for two distinct eigenvalues $$\lambda_j$$ and $$\lambda_k$$. Then $\int_a^by_j(x)y_k(x)r(x)dx=0,$ that is, $$y_j$$ and $$y_k$$ are orthogonal with respect to the weight function $$r$$. ## 5.1.3 Fredholm Alternative We also have the Fredholm alternative theorem we talked about before (Theorem 4.1.2) for all regular Sturm-Liouville problems. We state it here for completeness. Theorem $$\PageIndex{3}$$ Fredholm Alternative Suppose that we have a regular Sturm-Liouville problem. Then either \begin{align}\begin{aligned} \frac{d}{dx} \left( p(x) \frac{dy}{dx} \right) -q(x)y+\lambda r(x)y &=0, \\ \alpha_1y(a)- \alpha_2y'(a) &=0, \\ \beta_1y(b)+ \beta_2y'(b) &=0,\end{aligned}\end{align} has a nonzero solution, or \begin{align}\begin{aligned} \frac{d}{dx} \left( p(x) \frac{dy}{dx} \right) -q(x)y+\lambda r(x)y &=f(x), \\ \alpha_1y(a)- \alpha_2y'(a) &=0, \\ \beta_1y(b)+ \beta_2y'(b) &=0,\end{aligned}\end{align} has a unique solution for any $$f(x)$$ continuous on $$[a,b]$$. This theorem is used in much the same way as we did before in Section 4.4. It is used when solving more general nonhomogeneous boundary value problems. The theorem does not help us solve the problem, but it tells us when a unique solution exists, so that we know when to spend time looking for it. To solve the problem we decompose $$f(x)$$ and $$y(x)$$ in terms of the eigenfunctions of the homogeneous problem, and then solve for the coefficients of the series for $$y(x)$$. ## 5.1.4 Eigenfunction Series What we want to do with the eigenfunctions once we have them is to compute the eigenfunction decomposition of an arbitrary function $$f(x)$$. That is, we wish to write $\label{eq:26} f(x)= \sum_{n=1}^{\infty}c_ny_n(x),$ where $$y_n(x)$$ the eigenfunctions. We wish to find out if we can represent any function $$f(x)$$ in this way, and if so, we wish to calculate (and of course we would want to know if the sum converges). OK, so imagine we could write $$f(x)$$ as $$\eqref{eq:26}$$. We will assume convergence and the ability to integrate the series term by term. Because of orthogonality we have \begin{align}\begin{aligned} \langle f,y_m \rangle &= \int_a^bf(x)y_m(x)r(x)dx \\ &= \sum_{n=1}^{\infty}c_n \int_a^by_n(x)y_m(x)r(x)dx \\ &=c_m \int_a^by_m(x)y_m(x)r(x)dx= c_m \langle y_m,y_m \rangle .\end{aligned}\end{align} Hence, $\label{eq:28} c_m= \frac{\langle f,y_m \rangle}{\langle y_m,y_m \rangle}= \frac{\int_a^bf(x)y_m(x)r(x)dx}{\int_a^b(y_m(x))^2r(x)dx}.$ Note that $$y_m$$ are known up to a constant multiple, so we could have picked a scalar multiple of an eigenfunction such that $$\langle y_m,y_m \rangle=1$$ (if we had an arbitrary eigenfunction $$\tilde{y}_m$$, divide it by $$\sqrt{\langle \tilde{y}_m,\tilde{y}_m \rangle}$$). When $$\langle y_m,y_m \rangle=1$$ we have the simpler form $$c_m=\langle f,y_m \rangle$$ as we did for the Fourier series. The following theorem holds more generally, but the statement given is enough for our purposes. Theorem $$\PageIndex{4}$$ Suppose $$f$$ is a piecewise smooth continuous function on . If $$y_1,y_2, \ldots$$ are the eigenfunctions of a regular Sturm-Liouville problem, then there exist real constants $$c_1,c_2, \ldots$$ given by $$\eqref{eq:28}$$ such that $$\eqref{eq:26}$$ converges and holds for $$a<x<b$$. Example $$\PageIndex{4}$$ Take the simple Sturm-Liouville problem \begin{align}\begin{aligned} & y'' + \lambda y = 0, \quad 0 < x < \frac{\pi}{2} , \\ & y(0) =0, \quad y'(\frac{\pi}{2}) = 0 .\end{aligned}\end{align} The above is a regular problem and furthermore we know by Theorem $$\PageIndex{1}$$ that $$\lambda \geq 0$$. Suppose $$\lambda = 0$$, then the general solution is $$y(x)Ax+B$$, we plug in the initial conditions to get $$0=y(0)=B$$, and $$0=y'(\pi/2)=A$$, hence $$\lambda=0$$ is not an eigenvalue. The general solution, therefore, is $y(x)=A\cos(\sqrt{\lambda}x)+B\sin(\sqrt{\lambda}x).$ Plugging in the boundary conditions we get $$0=y(0)=A$$ and $$0=y'(\pi/2)=\sqrt{\lambda}B\cos(\sqrt{\lambda}\frac{\pi}{2})$$. $$B$$ cannot be zero and hence $$\cos(\sqrt{\lambda}\frac{\pi}{2}=0)$$. This means that $$\sqrt{\lambda}\frac{\pi}{2}$$ must be an odd integral multiple of $$\frac{\pi}{2}$$, i.e. $$(2n-1)\frac{\pi}{2}=\sqrt{\lambda_n}\frac{\pi}{2}$$. Hence $\lambda_n=(2n-1)^2.$ We can take $$B=1$$. Hence our eigenfunctions are $y_n(x)= \sin((2n-1)x).$ Finally we compute $\int_0^{\frac{\pi}{2}}(\sin((2n-1)x))^2dx=\frac{\pi}{4}.$ So any piecewise smooth function on $$[0, \pi/2]$$ can be written as $f(x)=\sum_{n=1}^{\infty}c_n\sin((2n-1)x),$ where $c_n= \frac{\langle f,y_n \rangle}{\langle y_n,y_n \rangle}= \frac{\int_0^{\frac{\pi}{2}}\sin((2n-1)x)dx}{\int_0^{\frac{\pi}{2}}(\sin((2n-1)x))^2dx}= \frac{4}{\pi} \int f(x)_{0}^{\frac{\pi}{2}}\sin((2n-1)x)dx.$ Note that the series converges to an odd $$2\pi$$-periodic (not $$\pi$$-periodic!) extension of $$f(x)$$. Exercise $$\PageIndex{3}$$ In the above example, the function is defined on $$0<x< \pi/2$$, yet the series with respect to the eigenfunctions $$\sin ((2n-1)x)$$ converges to an odd $$2\pi$$-periodic extension of $$f(x)$$. Find out how is the extension defined for $$\pi/2 <x< \pi$$. Let us compute an example. Consider $$f(x) = x$$ for $$0 < x < \frac{\pi}{2}$$. Some calculus later we find $c_n = \frac{4}{\pi} \int_0^{\frac{\pi}{2}} f(x) \,\sin \bigl( (2n-1)x \bigr) \, dx = \frac{4{(-1)}^{n+1}}{\pi {(2n-1)}^2} ,$ and so for $$x$$ in $$[0,\frac{\pi}{2}]$$, $f(x) = \sum_{n=1}^\infty \frac{4{(-1)}^{n+1}}{\pi {(2n-1)}^2} \sin \bigl( (2n-1)x \bigr) .$ This is different from the $$\pi$$-periodic regular sine series which can be computed to be $f(x)=\sum\limits_{n=1}^\infty \frac{(-1)^{n+1}}{n}\sin (2nx).$ Both sums converge are equal to $$f(x)$$ for $$0 < x < \frac{\pi}{2}$$, but the eigenfunctions involved come from different eigenvalue problems. ## Footnotes [1] Named after the French mathematicians Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 10, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9992212057113647, "perplexity": 282.82873946781797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588257.34/warc/CC-MAIN-20211028034828-20211028064828-00274.warc.gz"}
http://www.zora.uzh.ch/41719/	Quick Search: Browse by: Zurich Open Repository and Archive Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-41719 # Ferreras, I; Saha, P; Leier, D; Courbin, F; Falco, E E (2010). Constraining the low-mass end of the initial mass function with gravitational lensing. Monthly Notices of the Royal Astronomical Society, 409(1):L30-L34. PDF (Verlags-PDF) - Registered users only 1MB View at publisher Preview Accepted Version PDF 302kB ## Abstract The low-mass end of the stellar initial mass function (IMF) is constrained by focusing on the baryon-dominated central regions of strong lensing galaxies. We study in this Letter the Einstein Cross (Q2237+0305), a z = 0.04 barred galaxy whose bulge acts as lens on a background quasar. The positions of the four quasar images constrain the surface mass density on the lens plane, whereas the surface brightness (H-band HST/NICMOS imaging) along with deep spectroscopy of the lens (VLT/FORS1) allows us to constrain the stellar mass content, for a range of IMFs. We find that a classical single power law (Salpeter IMF) predicts more stellar mass than the observed lensing estimates. This result is confirmed at the 99 per cent confidence level, and is robust to systematic effects due to the choice of population synthesis models, the presence of dust or the complex disc/bulge population mix. Our non-parametric methodology is more robust than kinematic estimates, as we do not need to make any assumptions about the dynamical state of the galaxy or its decomposition into bulge and disc. Over a range of low-mass power-law slopes (with Salpeter being Γ = + 1.35) we find that at a 90 per cent confidence level, slopes Γ > 0 are ruled out. ## Citations 17 citations in Web of Science® 17 citations in Scopus®	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9397627711296082, "perplexity": 3387.407468223919}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430459748987.54/warc/CC-MAIN-20150501055548-00046-ip-10-235-10-82.ec2.internal.warc.gz"}
http://link.springer.com/article/10.1007%2Fs00411-012-0432-y	, Volume 51, Issue 4, pp 411-423, Open Access Date: 07 Aug 2012 # Effective dose conversion coefficients for radionuclides exponentially distributed in the ground ## Abstract In order to provide fundamental data required for dose evaluation due to environmental exposures, effective dose conversion coefficients, that is, the effective dose rate per unit activity per unit area, were calculated for a number of potentially important radionuclides, assuming an exponential distribution in ground, over a wide range of relaxation depths. The conversion coefficients were calculated for adults and a new-born baby on the basis of dosimetric methods that the authors and related researchers have previously developed, using Monte Carlo simulations and anthropomorphic computational phantoms. The differences in effective dose conversion coefficients due to body size between the adult and baby phantoms were found to lie within 50 %, for most cases; however, for some low energies, differences could amount to a factor of 3. The effective dose per unit source intensity per area was found to decrease by a factor of 2–5, for increasing relaxation depths from 0 to 5 g/cm2, above a source energy of 50 keV. It is also shown that implementation of the calculated coefficients into the computation of the tissue weighting factors and the adult reference computational phantoms of ICRP Publication 103 does not significantly influence the effective dose conversion coefficients of the environment. Consequently, the coefficients shown in this paper could be applied for the evaluation of effective doses, as defined according to both recommendations of ICRP Publications 103 and 60.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9190942645072937, "perplexity": 1090.6877601585984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375095677.90/warc/CC-MAIN-20150627031815-00235-ip-10-179-60-89.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/solving-a-second-order-differential-equation.144318/	# Solving a Second-Order Differential Equation 1. Nov 17, 2006 ### Saketh I've been trying to derive the period of a physical pendulum, and I ended up with a differential equation that boils down to this: $$\frac{d^2 \theta}{dt^2} = C \sin{\theta}$$ where C is some constant. With no experience in differential equations, I have no idea how to solve this. I can't find anything about how to solve this type of differential equation, so if someone could point me in the right direction, that would be helpful. Thanks! 2. Nov 17, 2006 It can't be solved nicely, which is why we usually assume the angle is small and make the approximation $\sin \theta \approx \theta$. If you want, there's a way to reduce it to finding the integral of something like $1/\sqrt{a-\cos(\theta)}[/tex], but that's not a nice integral to do (ie, you need special functions). 3. Nov 17, 2006 ### HallsofIvy That is an extremly non-linear equation and cannot be solved in any simple form. As StatusX said, for smal values of the angle, you can make the approximation [itex]sin(\theta)= \theta$ so the equation becomes $d^2\theta/dt^2= C\theta$. Another technique is called "quadrature". Since t does not appear explictly in the equation, let $\omega= d\theta/dt$. Then apply the chain rule: $d^2\theta/dt^2= d\omega/dt= d\omega/d\theta d\theta/dt= \omega d\omega/dt= Csin \theta$. That's a separable first order differential equation which can be written as $\omega d\omega= Csin(\theta)d\theta$ and can be integrated directly: $(1/2) \omega^2= -Ccos(\theta)+ D$. The rub is when you replace $\omega$ by $d/t\eta/dt$ and solve for $d\theta/dt$: $d\theta/dt= \sqrt{D -2C cos\theta}$ so $\frac{d\theta}{\sqrt{D- 2C cos(\theta}}= dt$ and the left side cannot be integrated in terms of any elementary function. (That's called an "elliptic" integral. I've seen whole book cases of tables of values.) 4. Nov 18, 2006 ### Saketh Does this mean that it is impossible to generate a theoretical formulation for pendulums that includes large-angle values? I suspected that I would have to make a small-angle assumption. If I did have $d^2\theta/dt^2= C\theta$, how would I solve that? (Sorry for my lack of experience - once again, I just need to be pointed in the right diretcion.) 5. Nov 18, 2006 ### HallsofIvy For small angles, yes. Of course, in order to get periodic solutions, C must be negative. 6. Nov 18, 2006 ### daniel_i_l what function equals itself times a constant when differentiating twice? (HINT: whats the derivative of e^x ?) 7. Nov 18, 2006 ### robphy 8. Nov 18, 2006 ### arildno You can get an approximate solution to this, to whichever degree of accuracy you desire, by perturbation theory. Alternatively, you may use numerics 9. Nov 18, 2006 ### Saketh I don't understand - how does that help me solve the differential equation? Thanks, everyone! http://scienceworld.wolfram.com/physics/Pendulum.html" [Broken] answers all of my questions. Last edited by a moderator: May 2, 2017 10. Nov 18, 2006 ### HallsofIvy I can think of 4 such (independent) functions. That's why I said " Of course, in order to get periodic solutions, C must be negative." 11. Nov 18, 2006 ### tim_lou just a curious question, has there ever been a series solution to the exact motion of undamped pendulum?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9225833415985107, "perplexity": 519.7016004828181}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583822341.72/warc/CC-MAIN-20190121233709-20190122015709-00459.warc.gz"}
https://maths.anu.edu.au/study/student-projects/energetic-particle-physics-international-thermonuclear-experimental-reactor	# Energetic Particle Physics of the International Thermonuclear Experimental Reactor (ITER) Fusion energy promises baseload electricity generation with zero greenhouse gas emissions, a virtually inexhaustible supply of fuel, and significantly reduced radioactive waste, compared to fission and coal. The International Thermonuclear Experimental Reactor (ITER), which is now under construction, is the final step towards a demonstration power plant. ITER, will explore the uncharted physics of burning plasmas, where the energy liberated from the confined products of reaction exceeds the energy invested in heating the plasma. To access burning plasmas conditions, ITER will rely critically on external heating methods such as neutral beam injection. These modify the particle distribution function from a thermal Maxwellian (Fig. a). Schematic particle distribution function with fusion product ($\alpha$) with speed $v_\alpha$, neutral beam injection energy $v_{NBI}$ and thermal speed $v_{th}$ Neutral beam injection can unequally heat directions parallel and perpendicular to the confining magnetic field, resulting in pressure anisotropy, which alters the shape of the internal magnetic fields. As the beam ions slow they can resonate with different Alfvén waves (e.g. Fig. b), the mode amplitude grows (Fig. 1c), and the driving distribution function is flattened. These Alfvén resonances, or “thermonuclear ringtones”, which can also be driven by fusion products, are a function of the magnetic geometry and density profile. The drive of multiple Alfvén resonances can lead to nonlinearly enhanced redistribution and radial transport, and thus threaten particle confinement in ITER. (b) projection of multiple mode $B_r$ wave field of a TAE, (c) nonlinear evolution of 88 coupled TAE modes for an isotropic, static plasma as a function of wave periods $\omega{t}/2\pi$. There are several potential projects in this topical area. • Parameter scans of anisotropy for different ITER scenarios. Part of A/Prof. Hole’s ITER Science Fellowship is quantifying the impact of anisotropy for different ITER scenarios, and assessing the impact of anisotropy on the MHD continuum (gap eigenmodes) and linear stability of kink modes. This project would involve familiarisation with the mathematical physics of toroidal magnetic force balance, an introduction to ITER physics scenarios, and developing a working knowledge of ANU (co)developed equilibrium and stability codes. The project is suitable for an Honours or Masters project. • Study of Compressional Alfven eigenmodes. In this project the student will explore the full spectrum of modes permitted within the generalised MHD, MISHKA-3, which comprises the Hall effect. The primary objective is an investigation of Compressional Alfven eigenmodes: these are modes whose frequency extends to the ion cyclotron frequency range and its harmonics, and are driven by velocity gradients of non-Maxwellian energetic beam ions. CAEs, for which the theory is much less developed, are of programmatic importance to fusion, and have been observed in D-T plasmas in the Joint European Torus, and spherical tokamaks. The project is suitable for a Masters or PhD project.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8001543283462524, "perplexity": 3213.8112732790473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151638.93/warc/CC-MAIN-20210725045638-20210725075638-00317.warc.gz"}
http://www.gradesaver.com/textbooks/science/chemistry/chemistry-the-central-science-13th-edition/chapter-1-introduction-matter-and-measurement-exercises-page-35/1-30b	## Chemistry: The Central Science (13th Edition) This question is, in essence, a density problem. We are given a density and a displaced volume, and we have to find the mass. The density is 4.51 g/$cm^{3}$, and the volume displaced is 125.0 mL. Since one mL=one $cm^{3}$, the volume displaced is 125 $cm^{3}$. When we substitute in our values into the density formula (density=mass/volume), and solve for mass, we get a mass of 564 grams.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9852791428565979, "perplexity": 800.191839754209}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886104681.22/warc/CC-MAIN-20170818140908-20170818160908-00440.warc.gz"}
http://www.chegg.com/homework-help/questions-and-answers/proton-moving-freely-circular-path-perpendicular-constant-magnetic-field-takes-100-956-s-c-q488665	## section 19.6 motion of a charged particle in a magnetic field A proton moving freely in a circular path perpendicular to a constant magnetic field takes 1.00 μs to complete one revolution. Determine the magnitude of the magnetic field. • We know the formula of the radius(r)of the circular path of the charged particle is r = mv / Bq ............... (1) But we know the relation between the linear speed(v) and angularspeed(ω) is v = rω Substitute this in the eq(1) we get Bq = mω B = mω / q .................. (1) Here m = mass of the proton = 1.6710-27kg q = charge of the proton = 1.610-19C T = time period = 1.0*10-6s Get homework help More than 200 experts are waiting to help you now...	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9596163630485535, "perplexity": 2132.90930534415}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368705749262/warc/CC-MAIN-20130516120229-00071-ip-10-60-113-184.ec2.internal.warc.gz"}
http://eprints.iisc.ernet.in/11073/	# Stability of the viscous flow of a polymeric fluid past a flexible surface Chokshi, Paresh and Kumaran, V (2007) Stability of the viscous flow of a polymeric fluid past a flexible surface. In: Physics of Fluids, 19 . 034102-1-034102-15. PDF Stability_of_the_viscous_flow_of.pdf Restricted to Registered users only Download (1651Kb) \| Request a copy ## Abstract The instability in plane Couette flow of a viscoelastic fluid past a deformable surface is examined using the temporal linear stability theory in the zero Reynolds number limit. The polymeric fluid is described using the Oldroyd-B model and the flexible wall is modeled as a linear viscoelastic solid surface. The analysis shows that the wall flexibility tends to reduce the decay rate of the stable discrete modes for the polymeric flow past a rigid wall, and one of the discrete modes becomes unstable when the wall deformability parameter $\Gamma=V \eta /(GR)$ exceeds a certain critical value $\Gamma_c$. Here, V is the top-plate velocity, \eta is the zero shear viscosity of the polymeric fluid, G is the shear modulus of the wall, and R is the width of the fluid layer. The analysis reveals the presence of two classes of modes, the first of which becomes unstable for perturbations with wavelength comparable to the channel width (finite wavelength modes), and the second becomes unstable for perturbations with wavelength small compared to the channel width (short wave modes). The latter class of modes are found to be absent for the highly concentrated polymer solutions with \beta\leq 0.23, where \beta is the ratio of solvent-to-solution viscosity. We have mapped out the regions in the parameter space \bar{W}-H) where the finite wavelength and short wave modes are unstable, where $\bar{W}=(\lambda G/ \eta)$, and lambda is the relaxation time of the viscoelastic fluid. Fluid elasticity is found to have a stabilizing influence on the unstable mode, such that when the shortwave instability is absent for \beta \leq 0.23, the flow becomes stable for any Weissenberg number $\bar{W}>\bar{W}_ {max}$. Here, $\bar{W}_{max}$ increases proportional to H for H\gg1. However, when the shortwave instability is present, the instability persists for \bar{W}\gg 1. The behavior of both classes of modes with respect to the parameters, like \bar{W}, H, \beta, and the ratio of solid-to-fluid viscosity $\eta_o$ , is examined. Item Type: Journal Article Copyright of this article belongs to American Institute of Physics. Division of Mechanical Sciences > Chemical Engineering 11 Oct 2007 19 Sep 2010 04:38 http://eprints.iisc.ernet.in/id/eprint/11073	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8941668272018433, "perplexity": 1061.3602935179154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246636650.1/warc/CC-MAIN-20150417045716-00273-ip-10-235-10-82.ec2.internal.warc.gz"}
https://brilliant.org/problems/freak-with-frequency-2/	# Freak with Frequency In the problem a figure is shown a figure which consist of a mass m=10 kg attached to a string on smooth table whose other end through a very tiny hole in the table is attached to a another mass M=1 kg in the shape of a block attached to a rod of length 1metre.When M is in equilibrium m is rotating on the table with a angular frequency 1radian/sec with a radius r=1metre about the hole. The rod can slide on the a set of vertical smooth parallel conducting rails fixed as shown.There exists a magnetic field B which we can change perpendicular to the plane of the rails. The rails are also attached to a inductor L=1H whose two ends are connected to a circuit given in the figure.The circuit contains another two inductors which are identical but whose inductance is unknown ,a capacitor whose capacitance is unknown and a bulb. In front of the bulb is a Frequency Detector connected to a Electric field generator which generated a uniform electric field E directly proportional to the angular frequency detected by the frequency detector.At time t=0 we release from the same height in the uniform electric field two neutral conducting metal balls. assume that the electric field exists even very below the ball. the metal balls are very small of radius r and mass m and are connected with a very light conducting inextensible thread of length b=2 metres .Initial separation of the balls is a=1meter. Initially M is in equilibrium and m is rotating no current flows anywhere . We displace the (rod and mass)M by a very small distance and release it at t=0 The bulb now is dimmest. the conducting balls attain their maximum horizontal velocity U at some time. Now we again do this experiment starting from equilibrium by changing the magnetic field so that the bulb is brightest.Now the conducting balls attain a maximum horizontal velocity V at another certain time.Find V-U $E=K\omega,K=10^{12}SIunits$ Assume$r\ll a$ $r=\frac{\varepsilon}{\pi}metres$ $B=3^{0.5}T$ at dimmest the whole experiment setup is carried out at a good distance above the ground. ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9583975672721863, "perplexity": 688.4863699835635}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281659.81/warc/CC-MAIN-20170116095121-00038-ip-10-171-10-70.ec2.internal.warc.gz"}
https://tel.archives-ouvertes.fr/tel-00212214/en/	# Etude de la structure des noyaux non liés $^{7,9}$He et $^{10}$Li Abstract : The unbound nuclei 7,9He and 10Li have been investigated via the high-energy breakup of beams of neutronrich nuclei (8He, 11Be and 14B). The decay-energy spectra were reconstructed from coincident measurements of the charged fragments (6,8He and 9Li) with a [DELTA]E-E telescope (CHARISSA) and the neutrons with the DEMON array. A theoretical approach based on the sudden approximation was used to model the reactions populating the unbound final states. The calculated decay-energy spectra were convoluted with the response function of the experimental setup using a simulation developed specifically for the present study and compared with the experimental results. The 10Li system was produced using an 11Be beam and the results confirm the continuation of the inversion of the º1s1/2 and º0p1/2 levels in the N = 7 isotopic chain. The 9He system was produced in two difierent ways with the breakup of 11Be and 14B, and was the most exotic system studied here. In this case, a structure was observed at very low decay energy which very probably corresponds to a virtual s state (as u -2-0 fm). This result suggests that the level inversion also occurs in 9He, but with a much weaker core-neutron interaction than for 10Li (as = -14 ± 2 fm). For the data acquired from the breakup of the 14B beam, the decay energy spectrum exhibits a resonance around Er = 1.2 MeV, which most probably corresponds to an excited 1/2- state in 9He. The 7He system was investigated with three different beams (8He, 11Be and 14B). No evidence for the existence of the proposed low-lying (Er » 1 MeV) spin-orbit partner (1/2-) of the ground state (3/2-) could be found. Keywords : Document type : Theses Nuclear Theory. Université de Caen, 2007. French https://tel.archives-ouvertes.fr/tel-00212214 Contributor : Sandrine Guesnon <> Submitted on : Tuesday, January 22, 2008 - 3:32:25 PM Last modification on : Wednesday, January 28, 2015 - 11:06:36 AM ### Identifiers • HAL Id : tel-00212214, version 1 ### Citation H. Al Falou. Etude de la structure des noyaux non liés $^{7,9}$He et $^{10}$Li. Nuclear Theory. Université de Caen, 2007. French. <tel-00212214> Consultation de la notice ## 134 Téléchargement du document	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.903268039226532, "perplexity": 4898.507997069946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207930109.71/warc/CC-MAIN-20150521113210-00186-ip-10-180-206-219.ec2.internal.warc.gz"}
https://budker.uni-mainz.de/?page_id=7	# CASPEr The nature of dark matter, the invisible substance that makes up over 80% of the matter in the universe, remains one of the most intriguing mysteries of modern physics. Elucidating the nature of dark matter will profoundly impact our understanding of cosmology, astrophysics, and particle physics, providing insights into the evolution of the Universe and potentially uncovering new physical laws and fundamental forces beyond the Standard Model. Most efforts to directly detect dark matter have focused on Weakly Interacting Massive Particles (WIMPs) [1], but despite considerable efforts, there have been no conclusive signs of WIMP interactions with ordinary matter. This absence of WIMPs has attracted attention to ultralight (sub-eV) bosonic fields: another class of theoretically well-motivated dark matter candidates [2]. A wide variety of theories predict new spin-0 bosons such as axions and axion-like particles (ALPs) as well as spin-1 bosons such as dark and hidden photons [3]. Axions are particularly interesting, as they also provide a solution [4] to the so-called strong CP problem – a “fine-tuning” problem where quantum chromodynamics (QCD) does not nec- essarily conserve combined charge conjugation and parity inversion (CP) symmetry, but no CP violation has been observed in experiments – that is also compatible with the Sakharov conditions [5], where CP violation in the early universe is necessary to explain the current matter-antimatter imbalance. Detection of such ultralight dark matter may be possible via interactions with standard model particles. Existing experiments involve detection of photons that would be created by the conversion of axions in strong electromagnetic fields via the inverse Primakoff effect [6–8] or dark-matter driven currents in electromagnetic systems [9]. More recently, another possibility has been proposed: dark-matter-driven spin-precession [10, 11]. The Cosmic Axion Spin Precession Experiment (CASPEr) is a multifaceted international research program using nuclear magnetic resonance (NMR) techniques to search for ultralight dark matter based on dark-matter-driven spin precession. CASPEr is naturally divided into two main research directions, based on two possible couplings to the Standard Model [11]: • CASPEr-Wind searches for spin precession induced by the coupling between ALPs and the axial nuclear current. The interaction that drives the spin precession may be visualized as shown in Fig. 1A, where the nuclear spin couples to the relative momentum of the local ALP field. • The coupling of axions to the gluon field, G, of quantum chromodynamics (QCD) is explored by CASPEr-Electric, which searches for the effect of an oscillating nuclear electric dipole moment (see Fig. 1B). In the presence of an electric field, this electric dipole moment generates a toque that drives spin precession. For both CASPEr-Wind and CASPEr-Electric, this interaction can be treated as a pseudo- magnetic field BALP that drives nuclear spin precession, analogous to the behavior of a real magnetic field. The oscillation frequency of BALP is the Compton frequency, ωALP = mALPc2/ ħ, where mALP is the mass of the particle, c is the speed of light, and \hbar is the reduced Planck constant. The amplitude of BALP is related to a coupling parameter, gaNN for the CASPEr- Wind coupling or gd for the CASPEr-Electric coupling [11]. Based on this formulation, one can design an NMR experiment where BALP serves as the driving field, as shown schematically in Fig. 1C. A sample of polarized nuclear spins has its magnetization initially oriented by a leading field, B0, which is swept from B0,min to B0,max. If the Larmor frequency – defined as ωL = γIB0, where γI is the gyromagnetic ratio of the nucleus under investigation – is equal to the frequency of the driving field BALP, the nuclear spins will precess into the transverse plane. The resulting precessing magnetization generates a magnetic field that can be measured by a suitable detector, such as a superconducting quantum interference device (SQUID) [12], a tuned LC circuit, or an atomic magnetometer [13]. This signal transduction scheme is summarized in Fig. 1D, where it should be noted that the range of masses available to the search is determined by the range of achievable B0 values, as well as the nuclear gyromagnetic ratio. Furthermore, the sensitivity of the search to small coupling parameters is limited by the magnetic sensitivity of the detector, as well as the degree of polarization of the nuclear spins. Figure 1: Overview of the Cosmic Axion Spin Precession Experiment (CASPEr). (A) The CASPEr-Wind coupling: nuclear spins precess about the relative local velocity of the dark matter field. (B) The CASPEr-E coupling: the QCD axion induces an oscillating nuclear electric dipole moment – in the presence of an electric field, this causes spin precession. (C) Schematic of the experimental configuration. A sample consisting of hyperpolarized nuclear spins is acted upon by the axion/ALP-induced effective magnetic field BALP. A tunable magnet produces a time-dependent field B0 such that when the nuclear Larmor frequency is equal to the dark matter Compton frequency, the nuclear spins will precess into the XY plane, resulting in measurable transverse magnetization. (D) The CASPEr signal transduction pathway, based on the use of polarized nuclear spins to convert the dark matter field into an observable magnetic field. Preliminary CASPEr results have been obtained in the ultralight mass regime, utilizing existing zero- to ultralow-field (ZULF) NMR instrumentation [14, 15]. Experimental efforts to detect axion-like dark matter are underway for masses corresponding to the frequency range up to 4 MHz using a scannable superconducting magnet up to 0.1 T and a detection system based on superconducting quantum interference devices (SQUIDs). We refer to these ongoing low-frequency efforts as CASPEr-Wind-LF. Figure 2: Projected reach of the first phase of CASPEr-Wind. Sensitivity of CASPEr-Wind-HF is expected to be limited by spin projection noise in the case of desired probe specifications. Higher masses, corresponding to Compton frequencies of up to hundreds of MHz, are also of substantial interest. To explore this higher-frequency region of parameter space with CASPEr-Wind-HF (see Fig. 2), alternative equipment will be required. Using a spin-polarized nuclear target containing a high density of 1H nuclei and a superconducting magnet capable of reaching 14.1 T, it is possible to reach Larmor frequencies of 600 MHz, allowing overlap with other experiments, such as the Axion Dark Matter eXperiment (ADMX) [8]. However, measurement of nuclear spin precession at these frequencies requires different detectors from those used in CASPEr-Wind-LF. The most sensitive detectors than can reasonably operate across this wide range of frequencies are tunable LC circuits, cooled to cryogenic temperatures. We are currently developing suitable hyperpolarized samples and NMR detectors. Martin Engler and Gary Centers checking that the components are precisely aligned while installing the CASPEr experiment at the University of Mainz. (Image: A. Wickenbrock / U. Mainz) ## References: [1] J. L. Feng, Annual Review of Astronomy and Astrophysics 48, 495 (2010). [2] P. W. Graham, I. G. Irastorza, S. K. Lamoreaux, A. Lindner, and K. A. van Bibber, Annual Review of Nuclear and Particle Science 65, 485 (2015). [3] L. Ackerman, M. R. Buckley, S. M. Carroll, and M. Kamionkowski, Phys. Rev. D 79, 023519 (2009). [4] R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977). [5] A. D. Sakharov, Soviet Physics Uspekhi 34, 392 (1991). [6] H. Primakoff, Phys. Rev. 81, 899 (1951). [7] P. Sikivie, Phys. Rev. Lett. 51, 1415 (1983). [8] N. Du, N. Force, R. Khatiwada, E. Lentz, R. Ottens, L. J. Rosenberg, G. Rybka, G. Carosi, N. Woollett, D. Bowring, et al. (ADMX Collaboration), Phys. Rev. Lett. 120, 151301 (2018). [9] S. Chaudhuri, P. W. Graham, K. Irwin, J. Mardon, S. Rajendran, and Y. Zhao, Phys. Rev. D 92, 075012 (2015). [10] D. Budker, P. W. Graham, M. Ledbetter, S. Rajendran, and A. O. Sushkov, Phys. Rev. X 4, 021030 (2014). [11] P. W. Graham and S. Rajendran, Phys. Rev. D 88, 035023 (2013). [12] J. Clarke and A. I. Braginski, The SQUID handbook: Applications of SQUIDs and SQUID systems (John Wiley & Sons, 2006). [13] T. Wang, D. F. J. Kimball, A. O. Sushkov, D. Aybas, J. W. Blanchard, G. Centers, S. R. O. Kelley, A. Wickenbrock, J. Fang, and D. Budker, Physics of the Dark Universe 19, 27 (2018), ISSN 2212-6864. [14] T. Wu, J. W. Blanchard, G. P. Centers, N. L. Figueroa, A. Garcon, P. W. Graham, D. F. J. Kimball, S. Rajendran, Y. V. Stadnik, A. O. Sushkov, et al., Phys. Rev. Lett. 122, 191302 (2019). [15] A. Garcon, J. W. Blanchard, G. P. Centers, N. L. Figueroa, P. W. Graham, D. F. Jackson Kimball, S. Rajendran, A. O. Sushkov, Y. V. Stadnik, A. Wickenbrock, T. Wu, and D. Budker, Sci. Adv. 5 (2019). ### Funder: DFG, Reinhart Koselleck Projects Project ID: 695405 Funded under: H2020-EU.1.1. – EXCELLENT SCIENCE – European Research Council (ERC)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8364318013191223, "perplexity": 2419.5109572408405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104248623.69/warc/CC-MAIN-20220703164826-20220703194826-00531.warc.gz"}
https://transistorized.net/post/stdal/post86.htm	homelist of postsdocs about & FAQ Small-signal and large-signal MOSFET channel resistance When running SPICE DC simulations one could often see two types of MOSFET transistor operating point parameters for the channel resistance printed by the simulator. These often have different names depending on model versions spanning a range: ron, rout, rds, rd, 1/gds – these are at first sight ambiguous and could be a source of confusion. Usually one of them is much bigger than the other. Here is actually what each of them represents. ron - this is the large-signal MOSFET channel resistance. This parameter is derived by the partial derivative of the current operating point versus a point where Vds = 0 and Ids = 0. Even if trivial, worth noting here that we calculate ron by: $$r_{on} = \left[ \frac{\partial v_{ds}}{\partial i_{ds}} \right]_{V_{gs} = \text{const}}$$ Thus, for convenience I provide here a plot where the red line shows the partial derivative of the chosen point at the I-V curve, with respect to a 0 volts 0 amps operating point – this is in fact what is referred as ron. It is sometimes called large-signal resistance and it is calculated through the slope of the line connecting (0,0) with (vds,ids). rout - this is the small-signal MOSFET channel resistance. Usually when running fixed operating point simulations we are interested in the small-signal resistance for the specific operating point. It is computed through the tangent line at (vds,ids), here is an example plot: Looked at it the other way rout is vds over ids for a single point. $$r_{out} = \left[ \frac{v_{ds}}{i_{ds}} \right]_{V_{gs} = \text{const}}$$ The small-signal output resistance is usually the one needed for evaluating impedances of current sources etc... It is worth noting that $1/g_{ds}$ is effectively equivalent to $r_{out}$ and represents the small-signal conductance of the device. Date:Fri Dec 25 12:11:32 CET 2018	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8771602511405945, "perplexity": 1220.5919379907489}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488512243.88/warc/CC-MAIN-20210622063335-20210622093335-00326.warc.gz"}
http://qed.princeton.edu/main/PlasmaWiki/Perturbation_Theory_(Quantum_Mechanics)	# Perturbation Theory (Quantum Mechanics) Only a tiny fraction of problems in quantum mechanics can be be solved analytically. When an exact solution cannot be obtained, one may seek approximate answers through a variety of means, perturbation theory being one of them. Loosely, it happens that the behavior of most quantum systems changes in a fairly regular way upon a slight modification. When a system can be described by a core part, which is to be solved exactly, or nearly so (perhaps using variational principles to determine the ground-state wavefunction), and a smaller part, called the perturbation, we can apply the methods of perturbation theory to determine in an approximate way the behavior of the perturbed system. Perturbation Theory also describes a more general mathematical framework for obtaining perturbative solutions to other types of systems. The core of perturbation theory, as applied to quantum mechanics, is present in the comparatively simple time-independent nondegenerate case. We need to be quite careful around degeneracies -- fortunately we provide a framework which largely handles this for us. There is a cost: we are now required to solve the Eigenvalue Problem directly. Time-dependent perturbation theory is even more involved, but it allows us to deal with an extraordinary variety of interesting systems (indeed, five nobel prizes have been awarded for resonance of two state systems in time dependent potentials! (I.I.Rabi on Molecular Beams and Nuclear Magnetic Resonance, Bloch and Purcell on B fields in atomic nuclei and nuclear magnetic moments; Townes, Basov, and Prochorov on masers, lasers, and quantum optics; Kastler on optical pumping; and Lauterbur and Mansfield (Medicine) for MRI). One of the most useful formulas to arise out of this topic is Fermi's Golden Rule for transition probabilities. In what follows we largely follow Sakurai, so please refer to Modern Quantum Mechanics if you're looking for a text. Consider a system describe by a Hamiltonian $\hat{H}$ which may be split like so: $\hat{H} = \hat{H}_0 + \hat{V}$ The $\|n^{(0)}\rang$. Here we omit this cumbersome notation. Where an expression is ambiguous assume dimensional consistency)</i> We wish to solve, approximately, the eigenstate problem for the full Hamiltonian. $(\hat{H}_0 + \lambda \hat{V}) \|n\rang = E_n\|n\rang$ We make use of a parameter λ, which may be 'dialed' from 0 to 1. In practically all systems there is a smooth transition between the perturbed and unperturbed system. (note: for this method to be valid, this eigenitems must be analytic in a complex plane around λ = 0) As the parameter λ increases from 0, the energy of the nth level shifts from it's unperturbed value. We define the energy shift as $\Delta_n = E_n - E_n^0$ Where we note that Δn,En are functions of the perturbation parameter λ. We rearrange the Schrödinger equation like so: $(E_n^0 - \hat{H}_0)\|n\rang = (\lambda \hat{V} - \Delta_n)\|n\rang$ We may invert the operator $\lang n^0\|$) $\lang n^0\|(E_n^0 - \hat{H}_0)\|n\rang = E_n^0 - E_n^0 = 0 = \lang n^0\|(\lambda \hat{V} - \Delta_n)\|n\rang$ We can define a complementary projection operator $\hat{\phi}_n$, to project states away from the unperturbed states. $\hat{\phi}_n \equiv 1 - \| n^0 \rang \lang n^0 \|$ The operator $\hat{\phi}_n$ to the right. The following equation is then correct in every dimension except for that in the direction of $\| n^0 \rang$ $\|n\rang != \frac{1}{E_n^0 - \hat{h}_0} \phi_n(\lambda \hat{V} - \Delta_n) \| n \rang$ We correct this by adding a term in the direction of $\| n^0 \rang$. $\|n\rang = c_n(\lambda) \| n^0 + \rang \frac{1}{E_n^0 - \hat{h}_0} \hat{\phi}_n(\lambda \hat{V} - \Delta_n) \| n \rang$ To reduce to the unperturbed equation when $c_n = \lang n^0\|n\rang$. In fact, since the equation is homogeneous cn is a free variable, and we may set cn(λ) = 1 and normalize the ket at the end of the calculation. Simplifying, we obtain the two equations which the rest of the method is based on: $1: \quad\quad \|n\rang = \| n^0 \rang + \frac{\hat{\phi}_n}{E_n^0 - \hat{h}_0}(\lambda \hat{V} - \Delta_n) \| n \rang$ and from $\lang n^0\|(\lambda \hat{V} - \Delta_n)\|n\rang = 0$, $2: \quad\quad \Delta_n = \lambda \lang n^0\|\hat{V}\|n\rang\quad{(2)}$ The basic strategy is to expand $\|n\rang$ and Δn in the powers of λ and then match the appropriate coefficients. This is a perfectly valid strategy, since the whole derivation has made no regard to the value of λ, and An Nth Degree Polynomial has N Roots. Thus $\| n \rang = \|n^0\rang + \lambda \| n^1 \rang + \lambda^2 \| n^2 \rang + \dots$ $\Delta_n = \lambda \Delta_n^1 + \lambda^2 \Delta_n^2 + \dots$ where $\| n^m \rang, \Delta_n^m$ stand for the mth order corrections. Substituting our expanded eigenstates and energy shifts into equation 2, and equating the coefficients of powers of λ yields $O(\lambda^m): \Delta_n^m = \lang n^0\|\hat{V}\|n^{m-1}\rang$ Turning our attention to an expanded equation 1, we have $\|n^0\rang + \lambda \| n^1 \rang + \lambda^2 \| n^2 \rang + \dots = \|n^0\rang + \frac{\hat{\phi}_n}{E_n^0 - \hat{h}_0}(\lambda \hat{V} - \lambda \Delta_n^1 - \lambda^2 \Delta_n^2 - \dots) \times (\|n^0\rang + \lambda \| n^1 \rang + \lambda^2 \| n^2 \rang + \dots )$ At this point the strategy becomes clear. $\Delta_n^m$ may be evaluated with only the m − 1th order eigenket. The mth order eigenket may be obtained knowing only up to the mth order energy shift. This procedure may continue for as long as is desired (in fact, it may even be possible to evaluate the sum analytically). If we write down, to second order, the explicit expansion for Δn and $\|n\rang$, we can make several interesting qualitative observations. $\Delta_n \equiv E_n - E_n^0 = \lambda \hat{V}_{nn} + \lambda^2 \sum_{k \neq n} \frac{\|\hat{V}_{nk}\|^2}{E_n^0 - E_k^0} + O(\lambda^3),$ where $V_{nk} \equiv \lang n^0\|\hat{V}\|k^0\rang \neq \lang n \| \hat{V} \| k \rang$ The matrix elements Vnk are taken with respect to the unperturbed kets. For the pertrubed ket, the expansion is $\|n^0\rang = \lambda \sum_{k \neq n} \|k^0\rang \frac{\hat{V}_{kn}}{E_n^0 - E_k^0}$ $\quad \quad + \lambda^2 \left({\sum_{k \neq n}\sum_{l \neq n} \frac{\|k^0\rang \hat{V}_{kl}\hat{V}_{ln}}{(E_n^0 - E_k^0)(E_n^0 - E_l^0)} - \sum_{k \neq n} \frac{\|k^0\rang \hat{V}_{nn}\hat{V}_{kn}}{(E_n^0 - E_k^0)^2}}\right) + O(\lambda^3)$ Examining the last equation closely, we see that the perturbation has the effect of mixing the previously unperturbed eigenkets. The second order energy shift (the second term in the second last equation) exhibits interesting behavior. The energy levels of kets which are "mixed" by $\hat{V}$ (where Vnk is positive) are repelled away from each other. This is a special case of the No-level Crossing Theorem, which states that a pair of energy levels connected by perturbation do not cross as the strength of the perturbation is varied. It is fairly easy to that the perturbation expansions will converge if $E \leq E_0$ (R. G. Newton 1982, p.233). This page was recovered in October 2009 from the Plasmagicians page on Perturbation_Theory_(Quantum_Mechanics) dated 07:24, 17 December 2006.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 33, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8979125022888184, "perplexity": 593.3541106270408}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207927767.46/warc/CC-MAIN-20150521113207-00049-ip-10-180-206-219.ec2.internal.warc.gz"}
https://infoscience.epfl.ch/record/198040	Infoscience Journal article # Evolution of two-dimensional antiferromagnetism with temperature and magnetic field in multiferroic Ba2CoGe2O7 We report on spherical neutron polarimetry and unpolarized neutron diffraction in zero magnetic field as well as flipping ratio and static magnetization measurements in high magnetic fields on the multiferroic square lattice antiferromagnet Ba2CoGe2O7. We found that in zero magnetic field the magnetic space group is Cm'm2' with sublattice magnetization parallel to the [100] axis of this orthorhombic setting. The spin canting has been found to be smaller than 0.2 degrees in the ground state. This assignment is in agreement with the field-induced changes of the magnetic domain structure below 40 mT as resolved by spherical neutron polarimetry. The magnitude of the ordered moment has been precisely determined. Above the magnetic ordering temperature short-range magnetic fluctuations are observed. Based on the high-field magnetization data, we refined the parameters of the recently proposed microscopic spin model describing the multiferroic phase of Ba2CoGe2O7.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8820484280586243, "perplexity": 1735.9009482420745}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172902.42/warc/CC-MAIN-20170219104612-00541-ip-10-171-10-108.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/stringy-corrections-to-sm-propagators.284367/	# Stringy corrections to SM propagators 1. Jan 12, 2009 ### jdstokes The main objections I've heard voiced toward string theory are (1) it's incredible diversity of vacua caused by large number of possible Calabi-Yau compactifications, and (2) it's lack of background independence. I would like to question from my naive viewpoint, whether either of these are as serious as purported. As far as I know, ST naturally incorporates gauge theories on sets of coincident D-branes. As such, it should be be possible to embed the standard model (ad hoc) into string theory on a flat Minkowski background. With particle content and spacetime background set by hand, what is stopping people from computing stringy corrections to the standard model propagators. Has this already been achieved and is it unique? If this can be done, then even though corrections are manifest only at the Planck scale, the fault appears to lie more with experimental limitations than with string theory. 2. Jan 12, 2009 ### BenTheMan The effective operators are characterized by the Planck mass, as you point out. So things are more or less completely decoupled from low energy physics---of course, this depends on what the "planck mass" means...if you have a large extra dimension, this scale can be pushed low enough to see it at LHC. About uniqueness...it depends. Because of the large number of vacua present in string theory, "uniqueness" loses most of it's meaning. In principle, because of the large freedom afforded you by the landscape, it looks like you can tune an arbitrary model to make it work. (This statement is not rigorous, and may be wrong :) ) This is what people typically mean when they say "you can embed the standard model into string theory"---as of yet, we lack an explicit stringy construction of the standard model, down to yukawa couplings, but it appears that we have enough degrees of freedom to "make it work". In particular, the mathematical structures needed to get the MSSM out of string theory definitely exist. In fact, they exist in more than one way---coincident d branes is one way, but there are also other ways to get Lie groups out, such as geometrically near singularities on a Calabi Yau, or from internal degrees of freedom in the heterotic string. Either way, the problem is that you have to compute the corrections within a specific string theory, and we're not sure which one we should be using. People have computed such corrections to some large classes of string models---typically the easiest thing to do is to figure out how the massive string states effect gauge coupling unification. These calculations are highly model dependent, and far from "unique" as different models may have very similar results. 3. Jan 14, 2009 ### jdstokes Thanks Ben, that clears it up quite nicely. 4. Jan 18, 2009 ### atyy If so, then why do Denef et al ask "After all, we believe that string/M theory has a finite number of vacua, and thus can lead to a finite number of 4d low energy theories; could we imagine showing that the data is fit by none of these theories, thus falsifying the theory?" http://arxiv.org/abs/hep-th/0701050	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8107320070266724, "perplexity": 676.8063150281321}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279169.4/warc/CC-MAIN-20170116095119-00489-ip-10-171-10-70.ec2.internal.warc.gz"}
https://www.space.com/25089-how-gravitational-waves-work-infographic.html	Einstein's general theory of relativity suggests, among other things, that masses in space distort the geometry of space-time. In addition, moving objects emit waves of gravitational radiation that carry energy away into space. Gravity is the weakest of the fundamental forces, and the effects of gravitational waves are also weak. The waves squeeze and stretch space as they pass, but the effect is sub-atomically small. The effects of gravitational waves had been observed indirectly by studying binary pulsars. These are pairs of dense neutron stars that orbit each other. As they orbit, they disturb the space-time around them. They give off energy in the form of gravitational waves. This loss of energy causes the neutron stars’ orbits to decay. The decrease in orbital speed can be detected from Earth. In 2014, the Harvard-Smithsonian Center for Astrophysics announced the first direct evidence for gravitational waves. By examining the map of Cosmic Microwave Background radiation, astronomers found a faint but distinctive curling pattern. This pattern is thought to have been generated by gravitational waves when the universe inflated a tiny fraction of a second after the Big Bang.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9301074147224426, "perplexity": 506.4113848287354}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524127095762.40/warc/CC-MAIN-20180427075937-20180427095937-00375.warc.gz"}
https://boredofstudies.org/threads/vce-maths-questions-help.361766/	# VCE Maths questions help (1 Viewer) #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 1. How to find the turning point and type of turning point in the equation y = (2/3)x^4 + 1/3 2. how to find equation of axis of symmetry of y = (2/3)x^4 + 1/3 #### InteGrand ##### Well-Known Member Joined Dec 11, 2014 Messages 6,091 Gender Male HSC N/A Re: maths questions help 1. How to find the turning point and type of turning point in the equation y = (2/3)x^4 + 1/3 2. how to find equation of axis of symmetry of y = (2/3)x^4 + 1/3 1) Turning point at 0, local minimum. 2) Axis of symmetry is the y-axis. Method used: inspection. #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help 2) My book said that the axis of symmetry is x = 0. Maybe my book's wrong? #### disturb_equilibrium ##### New Member Joined Jan 23, 2017 Messages 6 Gender Undisclosed HSC 2017 Re: maths questions help 2) My book said that the axis of symmetry is x = 0. Maybe my book's wrong? the y axis is x=0!!! #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help the y axis is x=0!!! Oh, right, I get it now, was just a bit confused before. #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help What's the difference between the turning point and the stationary point of inflection? #### Green Yoda ##### Hi Φ Moderator Joined Mar 28, 2015 Messages 2,875 Gender Male HSC 2017 Re: maths questions help What's the difference between the turning point and the stationary point of inflection? A point where a function changes from an increasing to a decreasing function or visa-versa is known as a turning point (i.e. gradient =0) However with turning points the concavity remains the same. In a stationary point of inflexion the gradient is 0 but the concavity changes, thus not changing from an increasing to a decreasing function or visa-versa. #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help A point where a function changes from an increasing to a decreasing function or visa-versa is known as a turning point (i.e. gradient =0) However with turning points the concavity remains the same. In a stationary point of inflexion the gradient is 0 but the concavity changes, thus not changing from an increasing to a decreasing function or visa-versa. So for x^2, x^4, x^6, x^8, etc, there's a turning point, and for x^3, x^5, x^7, x^9, etc there's a stationary point of inflection? #### InteGrand ##### Well-Known Member Joined Dec 11, 2014 Messages 6,091 Gender Male HSC N/A Re: maths questions help So for x^2, x^4, x^6, x^8, etc, there's a turning point, and for x^3, x^5, x^7, x^9, etc there's a stationary point of inflection? Correct! Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help How hard it to get raw 40 in vce maths methods? #### Drongoski ##### Well-Known Member Joined Feb 22, 2009 Messages 3,801 Gender Male HSC N/A Re: maths questions help How hard it to get raw 40 in vce maths methods? Very few here are familiar with the VCE. But I find the VCE Maths curriculum modern and progressive. #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help Find the values of m if (2m-3)x^2 + (5m-1)x + (3m-2) = 0 has 2 solutions #### InteGrand ##### Well-Known Member Joined Dec 11, 2014 Messages 6,091 Gender Male HSC N/A Re: maths questions help Find the values of m if (2m-3)x^2 + (5m-1)x + (3m-2) = 0 has 2 solutions $\bg_white \noindent Set the discriminant \Delta := (5m-1)^{2} -4(2m-3)(3m-2) to be greater than 0 and solve for m. In other words, solve the quadratic inequation (5m-1)^{2} -4(2m-3)(3m-2) > 0 for m.$ Remember, if the given quadratic equation has two distinct (real) solutions for x, then its discriminant must be greater than zero. #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help $\bg_white \noindent Set the discriminant \Delta := (5m-1)^{2} -4(2m-3)(3m-2) to be greater than 0 and solve for m. In other words, solve the quadratic inequation (5m-1)^{2} -4(2m-3)(3m-2) > 0 for m.$ Remember, if the given quadratic equation has two distinct (real) solutions for x, then its discriminant must be greater than zero. I ended up getting 25m^2 - 10m + 1 - 4(6m^2 - 13m + 6) = 25m^2 - 10m + 1 - 24m^2 + 52m - 24 = m^2 + 42m - 23 > 0 #### InteGrand ##### Well-Known Member Joined Dec 11, 2014 Messages 6,091 Gender Male HSC N/A Re: maths questions help I ended up getting 25m^2 - 10m + 1 - 4(6m^2 - 13m + 6) = 25m^2 - 10m + 1 - 24m^2 + 52m - 24 = m^2 + 42m - 23 > 0 $\bg_white \noindent Have you learnt how to solve quadratic inequations like this? If not, you should probably learn that first, since you need to know how to do it for this question. Basically you find the roots of the quadratic m^2 + 42m - 23, sketch the parabola, and deduce from there for which values of m the quadratic is positive.$ #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help A piece of wire 12 cm long is cut into two pieces. One piece is used to form a square shape and the other a rectangle shape in which the length is twice the width. a. If x cm is the side length of the square, write down the dimensions of the rectangle in terms of x b. formulate a rule for A, the combined area of the square and rectangle in cm^2, in terms of x. c. determine the lengths of the two pieces if the sum of the areas is to be a minimum. #### kawaiipotato ##### Well-Known Member Joined Apr 28, 2015 Messages 465 Gender Undisclosed HSC 2015 Re: maths questions help $\bg_white \noindent a. If x is the side-length of the square, then the square has perimeter P_S = 4x.Then the remaining length for the wire used for the rectangle is 12 - 4x. Let a,2a be the dimensions of the rectangle, so the perimeter of the rectangle P_R = 6a. Hence, 6a = 12-4x \implies a = \frac{12-4x}{6}. The dimensions of the rectangle are \frac{12-4x}{6} and \frac{12-4x}{3}.$ $\bg_white \noindent b. A = x^2 + \frac{12-4x}{6}\frac{12-4x}{3} = x^2 + \frac{(12-4x)^2}{18}.$ $\bg_white \noindent c. \frac{dA}{dx} = 2x - \frac{8(12-4x)}{18} \\ Let \frac{dA}{dx} = 0 for stationary points \\ 2x - \frac{8(12-4x)}{18} = 0 \implies x = \frac{3}{2}.$ $\bg_white \noindent You can show this is a minimum by taking the second derivative and showing the sign is positive for x=\frac{3}{2}.$ Last edited: #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help Is it normal to find maths hard even after tution? I'm in this scenario #### boredsatan ##### Member Joined Mar 23, 2017 Messages 564 Gender Male HSC 1998 Re: maths questions help The graph of y = x^4 - 2x - 12 has 2 x-intercepts a. construct a table of values for this polynomial rule for x = -3,-2,-1,0,1,2,3 b. Hence state an exact solution to the equation x^4 - 2x - 12 = 0 c. State an interval within which the other root of the equation lies and use the methods of bisection to obtain an estimate of this root correct to 1 decimal place I get how to do part a and b, but i'm finding part c extremely challenging and confusing.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8806735277175903, "perplexity": 2003.2866067195257}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574588.96/warc/CC-MAIN-20190921170434-20190921192434-00163.warc.gz"}
https://www.nature.com/articles/s42005-018-0097-1?error=cookies_not_supported&code=134eb649-5081-41f3-a8ac-871a103e89b1	# Tunnel spectroscopy of localised electronic states in hexagonal boron nitride ## Abstract Hexagonal boron nitride is a large band gap layered crystal, frequently incorporated in van der Waals heterostructures as an insulating or tunnel barrier. Localised states with energies within its band gap can emit visible light, relevant to applications in nanophotonics and quantum information processing. However, they also give rise to conducting channels, which can induce electrical breakdown when a large voltage is applied. Here we use gated tunnel transistors to study resonant electron tunnelling through the localised states in few atomic-layer boron nitride barriers sandwiched between two monolayer graphene electrodes. The measurements are used to determine the energy, linewidth, tunnelling transmission probability, and depth within the barrier of more than 50 distinct localised states. A three-step process of electron percolation through two spatially separated localised states is also investigated. ## Introduction Following the discovery of the remarkable electronic properties of graphene1, researchers have investigated a variety of other layered crystalline compounds that remain chemically stable even when they are disassembled into atomically thin flakes by mechanical exfoliation2,3,4. These two-dimensional crystals can be stacked to form heterostructures and functional devices5,6,7,8,9,10,11,12,13,14,15,16,17,18 held together by van der Waals (vdW) forces that preserve the structural integrity and physical properties of the component layers. Of particular significance is hexagonal boron nitride (hBN)2,19, which has a lattice constant only 1.8% larger than that of graphene. It is a large band gap material that can be used as an insulating barrier for a gating electrode, as a barrier for tunnelling electrons, or as a source of ultraviolet light2. Recent studies have demonstrated that crystals of hBN can contain strongly localised electronic states within the energy gap20,21,22,23,24,25,26,27. These states are attributed to the presence of structural defects and impurities likely to be present even in nominally pure hBN crystals. They could also be introduced unintentionally during mechanical exfoliation of hBN and/or its incorporation within a multilayer vdW heterostructure. Electronic transitions between localised states with energies within the large band gap of hBN are also of interest, because they are single quantum emitters of visible light28,29,30,31,32,33,34,35,36,37,38,39,40 and thus have potential for applications in nanophotonics, optoelectronics and quantum information processing. Recently, localised states have been shown to affect the electronic properties of spintronic41 and superconducting42 van der Waals devices. Defect-related phenomena can also impair the electrical properties of future devices based on hBN by inducing random telegraph noise and causing electrical breakdown of its insulating properties when a sufficiently strong electric field is applied43,44. In this paper, we investigate how electrons tunnel resonantly between two monolayer graphene electrodes through localised states within an hBN barrier. Our devices incorporate either one or two gate electrodes, which provide precise control of the density and chemical potentials of the carriers in the graphene layers. The measurements allow us to determine the energy and spatial position of each of the localised states. The crystalline lattices of the two monolayer graphene electrodes are misaligned by a small angle of a few degrees. This twist angle suppresses direct band-to-band resonant tunnelling where the in-plane momentum component of the tunnelling electron is conserved8,10,11,12, and helps resolve clearly the small tunnel current passing through an individual localised state. The momentum conservation rule is relaxed for the case of tunnelling through the bound states within the band gap of hBN due to their strong spatial localisation17,18. ## Results ### Resonant tunnelling through a single localised state The top left inset of Fig. 1a is a schematic diagram showing the configuration of Device 1. A few atomic layers of hBN (green) forms a tunnel barrier sandwiched between two graphene monolayers, Grb and Grt, which act as source and drain electrodes. The application of a bias voltage, Vb, between them causes a tunnel current, I, to flow through the hBN barrier. A third graphite layer (Grg), which lies on a SiO2 substrate, is separated from Grb by an insulating hBN layer. This gate electrode is used to adjust the carrier sheet density of the graphene layers by varying the gate voltage, Vg. The active area for current flow in Device 1 is ~50 μm2. Further details of the device fabrication are given in the Methods section and ref. 10. The red curve in Fig. 1a shows the I(Vb) curve at a measurement temperature, T = 1.75 K, and Vg = 0. For \|Vb\| 200 mV, the tunnel current is small, but has a step-like increase when Vb = V1 ≈ ±200 mV. The differential conductance plot, G = dI/dVb, shown in Fig. 1b, displays the increase of current at the step edge as a sharp peak. At Vg = 0, the two strong and sharp peaks at Vb ≈ ± 200 mV are accompanied by weaker features at higher \|Vb\|. We attribute each of the two strong peaks to the threshold of resonant tunnelling through the same localised state (state A) within the hBN barrier when its energy, EA, becomes aligned with one or other of the chemical potentials, μb or μt, of the bottom (b) or top (t) graphene layers. For Vb > V1, the conductance channel through the localized state remains open, see lower right inset of Fig. 1a for this general case. An increase of Vg decreases the \|Vb\| position of the two conductance peaks until at Vg = 1.7 V they merge into a single peak centred at Vb = 0, see the green and blue curves in Fig. 1a, b. Figure 2a is a colour map of G(Vb, Vg) measured for Device 1. The white curves show a series of seven G(Vb) plots at selected Vg (5 V, 3 V, …, −7 V). Close to the top of Fig. 2a, the white arrows highlight the positions of the two strong peaks in G(Vb) at Vg = 5 V. The Vb positions of the peaks are strongly dependent on Vg: over the range of Vg from +7 V through 0 to −7 V, their loci have a prominent X-shaped dependence, corresponding to the onset of electron tunnelling through state A. We reproduce these measurements accurately using the Landauer-Büttiker conductance formula45,46,47,48, combined with Fermi’s golden rule and an electrostatic model of the device, Fig. 2b. It includes the quantum capacitance of graphene that arises from its low density of states near the Dirac points. Details of the model are presented in Supplementary Notes 1 and 2, and refs. 7,9,10,11,49. The measured device characteristics are described accurately by the model. In this way, we obtain accurate values for the tunnel barrier thickness, d = 1.5 nm, and lower insulating hBN layer thickness, dg = 25 nm. The electric field, Fb, across the hBN tunnel barrier generated by the bias voltage-induced charge on the graphene layers shifts the energy level of a given localised state, A, so that its energy relative to the Dirac point of the bottom graphene layer is $$E_{\mathrm{A}} = E_{\mathrm{A}}^0 + eF_{\mathrm{b}}z_{\mathrm{A}}$$. To obtain a best fit to the data, we set the energy of the level at the flat band condition (Fb = 0) to be $$E_{\mathrm{A}}^{\mathrm{0}} = 0.11\,{\mathrm{eV}}$$; we set its location to be in the middle of the barrier so that its spatial coordinate perpendicular to the plane of the layers and relative to the position of the bottom graphene layer is zA = d/2 = 0.75 nm, see lower right inset of Fig. 1a. At low bias (Vb < V1) and low temperatures there are few electrons with sufficient energy to tunnel with energy conservation through the localised state. The bias voltage Vb is given by eVb = μb − μt − ϕb, where ϕb = eFbd and μb and μt are measured with respect to the Dirac points of the graphene electrodes. When Vb is increased, μb increases and EA decreases. When Vb = V1, EA = μb so that electrons can tunnel with energy conservation through this localised state, thus opening a conduction channel between the two graphene layers, and producing the peak in G. Similarly, for Vb < 0, tunnelling through the same impurity can be achieved when EA aligns with the chemical potential in the top layer, i.e. EA = μt + ϕb. The model provides an accurate fit to the measured data as can be seen by comparing our modelled conductance Fig. 2b with the measured data in Fig. 2a. Note the positions on the X-shaped loci at which the measured amplitude of the conductance peaks is suppressed; these are indicated by vertical white arrows in both maps. The model calculation in Fig. 2b confirms that this suppression occurs when the chemical potential in one or the other graphene electrode passes through its Dirac point where the density of states approaches zero. The good agreement between the measured and modelled zero conductance loci validates our electrostatic model. We find that the peaks in G broaden as T increases, consistent with the thermal broadening of the electron energy distribution at the chemical potentials of the two graphene layers, see Supplementary Fig. 1. By comparing our model with the data over the temperature range from 1.75 to 90 K, we estimate the full width half maximum linewidth of the state to be γ ≈ 6 meV and the lifetime ħ/γ ≈ 0.1 ps. The best fit to the data is obtained when we use a Gaussian lineshape, see Supplementary Note 2 for more details. This is consistent with studies of the lineshape of optical emission from localised states in hBN37 and corresponds to inhomogeneous broadening50 of the state. This lineshape could arise from spectral diffusion due to local electrostatic fluctuations in the vicinity of the state. A similar effect has also been reported for colour centres in diamond51,52. The peak in conductance at Vb = 0 when Vg = 1.7 V and T = 1.75 K corresponds to Gp = βe2/h, where e2/h is the quantum of conductance and the measured parameter β = 0.75. For coherent tunnelling through a localised state with a Gaussian density of states $$\beta = \sqrt {\pi {\mathrm{ln}}2} S$$, where S = 4γbγt/(γb + γt)2 ≈ 0.5 is the total transmission probability. Here, γb/ħ and γt/ħ are the electron tunnelling rates between the localised state and the b and t electrodes and γ = γb + γt48. Note that if γb = γt then S = 1; however, in contrast we find that γb ~ 0.8γ and γt ~ 0.2γ, which means that the state is somewhat more strongly coupled to the bottom layer than the top, see Supplementary Note 2 for more details. ### Sequential tunnelling through two localised states Figure 2a exhibits an additional feature in the measured G(Vb, Vg) data. This arises from a more complex tunnelling process involving state A and a nearby localised state B with spatial coordinates zB and energy EB. This process, in which a tunnelling electron makes three sequential steps, Gr → A → B → Gr, accounts for the broader peak in conductance highlighted by the loci of black dots in Fig. 2a, as explained at the end of this section. This additional contribution to the current flow is initiated when the bias and gate voltages are tuned so that states A and B are energetically aligned, EA = EB, allowing electrons to tunnel through the barrier in three steps, as shown schematically by the horizontal arrows in the top right inset of Fig. 2b. The two levels are aligned when $$E_{\mathrm{A}}^{\mathrm{0}} - E_{\mathrm{B}}^{\mathrm{0}} = eF_{\mathrm{b}}\left( {z_{\mathrm{A}} - z_{\mathrm{B}}} \right)$$. Sequential tunnelling only occurs when the energies of the levels are aligned with each other and are located between μb and μt. Therefore, the sequential tunnelling feature disappears when its locus intersects with that of the sharper conductance peak EA = μb corresponding to the onset of tunnelling through state A alone (see horizontal dashed white arrow at the top of Fig. 2a, b). The peak in conductance due to this three-step process corresponds to a step-like increase of current, which means that the current channel remains open when EB > EA. This requires an inelastic tunnelling process in which the electron loses energy as it tunnels between states A and B, see lower right inset in Fig. 2b. Such a process can occur by emission of a phonon53 or else by an electron–electron interaction process analogous to Auger scattering whereby the tunnelling electron transfers the required excess energy to a free electron in one or other of the nearby graphene electrodes. Comparison of Fig. 2a, b shows that the inclusion of this inelastic tunnelling process in our model (see Supplementary Note 3) provides an excellent fit to the data when we set the following parameters for state B: $$E_{\mathrm{B}}^{\mathrm{0}} = 0.02\,{\mathrm{eV}}$$ and zB = d. These values imply that state B is situated near to the top graphene layer. Such a state could arise from an impurity or defect close to, or within, the top graphene layer, or from a local perturbation of the electronic states of this layer due to the close proximity of state A, giving rise to a peak in the local density of electron states of the top graphene electrode at an energy EB54. Further evidence for this local enhancement is provided by the increased strength of the conductance peak associated with tunnelling through state A only at the intersection between the three and two-step processes, see the strong red contour highlighted by horizontal white arrow observed in the measured data, Fig. 2a, and confirmed in our model calculation, Fig. 2b. This observation of a three-step tunnelling transition process is of topical interest as it is an example of a percolation process, which has been recently reported in refs. 43,44. Comparison of Fig. 2a, b also shows that the model successfully predicts the larger linewidth, ΔVAB ~ 70 mV, of the 3-step tunnelling peak compared to ΔVA = 20 mV for the peak arising from tunnelling through state A only. This increased broadening arises due to the addition of the linewidths of the two states. Note that the region of suppressed conductance (dark blue) predicted by the model, and the minimum of the double peak in the measured conductance (indicated by the locus of black dots in Fig. 2a) is fully consistent with the intersection of EA with the Dirac point in the top graphene layer, leading to a suppression in the number of electrons in the graphene layer available for sequential tunnelling. ### Position and energy spectroscopy of the localised states We now consider the current–voltage characteristics of a second type of device, Device 2, which has two-independent gate electrodes. The schematic diagram in Fig. 3a shows the layer and gate configuration. For this device, we observe a larger number (~50) of conductance peaks than for Device 1. The double gate arrangement provides further control over the electrostatics of the device. It allows us to select the particular combination of μb and μt required for electron tunnelling through a given localised state, see schematic diagram in Fig. 3b. The top gate is separated from the upper graphene layer by an insulating hBN barrier layer with thickness $$d_{\mathrm{g}}^{\mathrm{t}}$$, see schematic diagram. The doped Si substrate is used as the bottom gate electrode and is insulated from the lower graphene electrode by a SiO2 surface layer and the thinner hBN bedding layer with a total thickness $$d_{\mathrm{g}}^{\mathrm{b}}$$ on which the lower graphene electrode, Grb, is mounted, see Fig. 3a. The lattices of the two monolayer graphene electrodes are misaligned by a small twist angle, θ. The active area for electron tunnelling in this device is 25 μm2. The larger number of localised states observed in Device 2 may be due in part to the more complex processing required for this heterostructure. Using a combination of conventional lock-in amplification and 4-probe DC measurements, we measured the tunnel current, I, and differential conductance with a small amplitude AC modulation voltage ΔV = 1 mV at zero DC bias (Vb = 0) over a range of $$V_{\mathrm{g}}^{\mathrm{b}}$$ and $$V_{\mathrm{g}}^{\mathrm{t}}$$. This allows us to determine spectroscopically the energies of the localised states in the hBN tunnel barrier. Figure 3c maps out the positions of the conductance peaks at zero applied bias voltage G(Vb = 0) over a wide range of $$V_{\mathrm{g}}^{\mathrm{b}}$$ and $$V_{\mathrm{g}}^{\mathrm{t}}$$. When Vb = 0, the chemical potentials in the top and bottom graphene electrodes are aligned in energy, i.e. μb = μt + ϕb. The electrostatic potential drop across the barrier, ϕb, is strongly dependent on the two gate voltages. Figure 3c reveals a broad, dark blue cross-shaped region of very low conductance G 10−6 S. In this region, the Fermi energy in either the top or bottom graphene electrodes is close to the Dirac point in that layer (i.e. either μt or μb ≈ 0), where the density of states is low. The white loci show the calculated values of $$V_{\mathrm{g}}^{\mathrm{b}}$$ and $$V_{\mathrm{g}}^{\mathrm{t}}$$ when μt = 0 and μb = 0 using the electrostatic model presented in Supplementary Note 1, with $$d_{\mathrm{g}}^{\mathrm{t}} = 21\,{\mathrm{nm}}$$, $$d_{\mathrm{g}}^{\mathrm{b}} = 310\,{\mathrm{nm}}$$ and d = 1 nm. The calculated loci show good agreement with the location of the measured conductance minima, thus confirming the accuracy of our model. Our model shows that at zero bias and zero gate voltages, the chemical potentials of the two graphene layers are within 40 ± 10 meV of their Dirac points corresponding to a hole doping level of ~2 × 1015 m−2. Figure 3c also reveals a sharp change in conductance from low to high (blue through yellow to orange) with well-defined loci, extending from J to K and from L to M in Fig. 3c. These correspond to the threshold at which electrons can tunnel directly between the two twisted graphene electrodes with conservation of momentum and energy10 (i.e. not through localised states). The threshold condition is given by μb = μt + ϕb = (ϕb ± ΔKvFħ)/2. Using our model, we determine the misalignment of the in-plane wavevector between the Dirac points of the top and bottom layers: ΔK = 8π sin(θ/2)/3a, where a is the lattice constant of graphene. This provides a measure of θ = 2° ± 0.5°. ## Discussion We now consider the sharply defined curved loci of conductance peaks observed in the blue regions of the colour map in Fig. 3c where band-to-band tunnelling is suppressed, and also those in the yellow–red regions where the conductance peaks are superimposed on the high conductance regions that arise from momentum conserving, direct band-to-band, tunnel transitions. Each locus is due to resonant tunnelling through an energy level of a localised state and occurs when μb = μt + ϕb = Ei, where Ei is the energy of the state relative to the Dirac point of the bottom graphene electrode. To analyze the data in more detail, we remap $$G\left( {V_{\mathrm{g}}^{\mathrm{t}},V_{\mathrm{g}}^{\mathrm{b}}} \right)$$ into a more useful colour plot of G(μt, μb), using our electrostatic model, see Fig. 4a. As $$E_{\mathrm{i}} = E_{\mathrm{i}}^{\mathrm{0}} + eF_{\mathrm{b}}z_{\mathrm{i}}$$, we determine both $$E_{\mathrm{i}}^{\mathrm{0}}$$ and zi for each state. When ϕb = μb − μt = 0 (shown by the black dashed line) the energy level of a given state, i, aligns with the chemical potential of the bottom graphene electrode so that $$E_{\mathrm{i}}^{\mathrm{0}} = \mu _{\mathrm{b}}$$, thus determining $$E_{\mathrm{i}}^0$$ at the point when the peak trace crosses the black dashed curve. Whereas some of the loci of the conductance peaks in Fig. 4a are distinctly curved, most of them are approximately straight lines given by the relation $$\mu _{\mathrm{b}}\left( {1 - z_{\mathrm{i}}{\mathrm{/}}d} \right) = E_{\mathrm{i}}^{\mathrm{0}} - \mu _{\mathrm{t}}z_{\mathrm{i}}{\mathrm{/}}d.$$ (1) Equation (1) and the colour map in Fig. 4a therefore allows us to determine the zi and $$E_{\mathrm{i}}^{\mathrm{0}}$$ values of each localised state from the gradient of the locus, b/t, and its position on the map. The results are shown in Fig. 4b, c. The width of each segment of the histogram in Fig. 4c indicates the accuracy, Δzi = 0.06 nm, with which the position of each localised state is determined and reflects the uncertainty in the value of t/b. The histogram gives the number distribution, Ni of states with respect to their position coordinate, zi, within the hBN barrier. Each bin of the histogram in Fig. 4c has a symbol and colour with which we label each conductance peak locus in Fig. 4a. Note that several peaks in G have the same gradient and therefore the same value of zi/d, within experimental error. For example, the peak at zi/d ≈ 0.65 with Ni = 14, includes a group of 4 conductance peaks, each labelled with a club-shape, numbered 11–14, in the lower left section of the plot and another group, clubs 5–8, in the lower right section. A second peak occurs when zi/d ≈ 0.3 (diamonds) corresponding to Ni = 13. The measurements therefore reveal that more than half of the detected states are located at or close to the two atomic layers that form the hBN barrier corresponding to zi/d ≈ 0.3 and 0.65. We also find a number of states which appear to be located interstitially e.g. the five states at zi/d ~ 0.85. Others with zi/d ≈ 0 and ≈1 appear to be located close to the two monolayer graphene electrodes, possibly due to defects in or close to their lattices. Figure 4b plots the energy, $$E_{\mathrm{i}}^{\mathrm{0}}$$, relative to the Dirac point of the bottom graphene layer at zero bias and gate voltages, and the binned position of each localised state in the barrier. To obtain the data shown in Figs. 3 and 4 we apply strong electric fields of up to a limit of ~±300 mV/nm across the barrier. This avoids the danger of electrical breakdown but limits our study to those localised states with energies, $$E_{\mathrm{i}}^0$$, in the range −0.3 to 0.3 eV. Previous studies indicate that the top of the valence band of hBN and the Dirac point of graphene are located at energies of 7.7 ± 0.5 eV55 and 4.6 ± 0.1 eV56,57 respectively, below the vacuum level. Based on these estimates, we determine that the group of localised states measured here are located in the mid-gap energy range between 2.8 ± 0.5 and 3.4 ± 0.5 eV above the valence band edge of the hBN barrier, with an average density of states of ~3 μm−2 eV−1. Our measurements indicate that the areal density of tunnel-active defects in our devices is quite small 1012 m−2, around 4 orders of magnitude smaller than the electron sheet densities in the graphene electrodes at zero bias and gate voltages. The average in-plane separation of the localised states is ~1 μm. These states are located at different depths within the thin hBN barrier layer and their energy levels appear to be distributed randomly over the energy range of ~0.6 eV that is accessible with these devices. However, the observation of the three-step electron tunnelling process requires that some localised states are in close proximity to each other, separated by ~1 nm. In summary, we have observed resonant electron tunnelling between graphene monolayers through individual localised states in the hBN tunnel barrier. Our theoretical model determines the energy, linewidth, tunnel coupling coefficients and spatial coordinate of individual localised states in the barrier region. A three-step percolative inelastic process is also observed. These results may provide useful insights into the future exploitation and control of electron tunnelling through localised states in hBN. ## Methods ### Fabrication The devices were fabricated by a conventional dry-transfer procedure, the graphene and hBN layers were mechanically exfoliated onto the Si/SiO2 substrate. Cr/Au contact pads were independently mounted on the single and bilayer graphene electrodes. Finally, the top hBN capping layer was covered by a Cr/Au layer of cross-sectional area 15 μm2; this served as a top gate electrode. 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Controlled charge trapping by molybdenum disulphide and graphene in ultrathin heterostructured memory devices. Nat. Commun. 4, 1624 (2013). 56. 56. Yu, Y.-J. et al. Tuning the graphene work function by electric field effect. Nano Lett. 9, 3430 (2009). 57. 57. Pierucci, D. et al. Van der Waals epitaxy of two-dimensional single-layer h-BN on graphite by molecular beam epitaxy: electronic properties and band structure. Appl. Phys. Lett. 112, 253102 (2018). ## Acknowledgements EU Graphene Flagship Program, European Research Council Synergy Grant Hetero2D, the Royal Society, Engineering and Physical Research Council (UK, grants EP/N007131/1 and EP/N010345/1), US Army Research Office (W911NF-16-1-0279). E.E.V. acknowledge support from Russian Science Foundation (17-12-01393), S.V.M. from NUST “MISiS” (K2-2017-009) and Yu.N.K. from RAS Presidium Program N4 (task 007-00220-18-00). M.T.G acknowledges use of HPC Hydra at Loughborough University. ## Author information The project was conceived by M.T.G., E.E.V., A.Mishchenko., A.K.G., K.S.N. and L.E. The measurements were carried out by E.E.V., D.G., A.Mishchenko., Z.W., Yu.N.K., S.V.M., O.M., A.P. and L.E. The theoretical model was devised by M.T.G., J.R.W., T.M.F., V.I.F. and L.E. The devices were fabricated by A.Misra, Y.C., M.H., and K.S.N. The hBN was prepared and supplied by K.W. and T.T.. The data were analysed by M.T.G., E.E.V., D.G., A.Mishchenko, K.S.N. and L.E. The manuscript was prepared by M.T.G., L.E. and K.S.N., with input from the other authors. Correspondence to M. T. Greenaway or L. Eaves. ## Ethics declarations ### Competing interests The authors declare no competing interests. Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ## Rights and permissions Reprints and Permissions • #### DOI https://doi.org/10.1038/s42005-018-0097-1 • ### Planar and van der Waals heterostructures for vertical tunnelling single electron transistors • Gwangwoo Kim • , Sung-Soo Kim • , Jonghyuk Jeon • , Seong In Yoon • , Seokmo Hong • , Young Jin Cho • , Abhishek Misra • , Servet Ozdemir • , Jun Yin • , Davit Ghazaryan • , Matthew Holwill • , Artem Mishchenko • , Daria V. Andreeva • , Yong-Jin Kim • , Hu Young Jeong • , A-Rang Jang • , Hyun-Jong Chung • , Andre K. Geim • , Kostya S. Novoselov • , Byeong-Hyeok Sohn • & Hyeon Suk Shin Nature Communications (2019) • ### Dry release transfer of graphene and few-layer h-BN by utilizing thermoplasticity of polypropylene carbonate • Kei Kinoshita • , Rai Moriya • , Momoko Onodera • , Yusai Wakafuji • , Satoru Masubuchi • , Kenji Watanabe • , Takashi Taniguchi • & Tomoki Machida npj 2D Materials and Applications (2019) • ### Semiconductor channel-mediated photodoping in h-BN encapsulated monolayer MoSe2 phototransistors • Jorge Quereda • , Talieh S Ghiasi • , Caspar H van der Wal • & Bart J van Wees 2D Materials (2019) • ### Tunneling in Graphene/h-BN/Graphene Heterostructures through Zero-Dimensional Levels of Defects in h-BN and Their Use as Probes to Measure the Density of States of Graphene • Yu. N. Khanin • , E. E. Vdovin • , M. V. Grigor’ev • , O. Makarovsky • , Manal Alhazmi • , S. V. Morozov • , A. Mishchenko • & K. S. Novoselov JETP Letters (2019) • ### Boron Vacancies Causing Breakdown in 2D Layered Hexagonal Boron Nitride Dielectrics • A. Ranjan • , N. Raghavan • , F. M. Puglisi • , S. Mei	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8477967977523804, "perplexity": 2512.64235739279}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986647517.11/warc/CC-MAIN-20191013195541-20191013222541-00286.warc.gz"}
https://www.nag.com/numeric/nl/nagdoc_27.2/clhtml/g02/g02dcc.html	# NAG CL Interfaceg02dcc (linregm_obs_edit) Settings help CL Name Style: ## 1Purpose g02dcc adds or deletes an observation from a general regression model fitted by g02dac. ## 2Specification #include void g02dcc (Nag_UpdateObserv update, Nag_IncludeMean mean, Integer m, const Integer sx[], double q[], Integer tdq, Integer ip, const double x[], Integer nr, Integer tdx, Integer ix, double y, const double wt[], double rss, NagError fail) The function may be called by the names: g02dcc, nag_correg_linregm_obs_edit or nag_regsn_mult_linear_addrem_obs. ## 3Description g02dac fits a general linear regression model to a dataset. You may wish to change the model by either adding or deleting an observation from the dataset. g02dcc takes the results from g02dac and makes the required changes to the vector $c$ and the upper triangular matrix $R$ produced by g02dac. The regression coefficients, standard errors and the variance-covariance matrix of the regression coefficients can be obtained from g02ddc after all required changes to the dataset have been made. g02dac performs a $QR$ decomposition on the (weighted) $X$ matrix of independent variables. To add a new observation to a model with $p$ arguments the upper triangular matrix $R$ and vector ${c}_{1}$, the first $p$ elements of $c$, are augmented by the new observation on independent variables in ${x}^{\mathrm{T}}$ and dependent variable $y$. Givens rotations are then used to restore the upper triangular form. $( R : c 1 x y ) ⟶ ( R * c 1 * y * 0 )$ To delete an observation Givens rotations are applied to give: $( R c 1 ) ⟶ ( R * c 1 * x y )$ Note: only the $R$ and upper part of the $c$ are updated, the remainder of the $Q$ matrix is unchanged. ## 4References Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore Hammarling S (1985) The singular value decomposition in multivariate statistics SIGNUM Newsl. 20(3) 2–25 ## 5Arguments 1: $\mathbf{update}$Nag_UpdateObserv Input On entry: indicates if an observation is to be added or deleted. ${\mathbf{update}}=\mathrm{Nag_ObservAdd}$ ${\mathbf{update}}=\mathrm{Nag_ObservDel}$ The observation is deleted. Constraint: ${\mathbf{update}}=\mathrm{Nag_ObservAdd}$ or $\mathrm{Nag_ObservDel}$. 2: $\mathbf{mean}$Nag_IncludeMean Input On entry: indicates if a mean has been used in the model. ${\mathbf{mean}}=\mathrm{Nag_MeanInclude}$ A mean term or intercept will have been included in the model by g02dac. ${\mathbf{mean}}=\mathrm{Nag_MeanZero}$ A model with no mean term or intercept will have been fitted by g02dac. Constraint: ${\mathbf{mean}}=\mathrm{Nag_MeanInclude}$ or $\mathrm{Nag_MeanZero}$. 3: $\mathbf{m}$Integer Input On entry: the total number of independent variables in the dataset. Constraint: ${\mathbf{m}}\ge 1$. 4: $\mathbf{sx}\left[{\mathbf{m}}\right]$const Integer Input On entry: if ${\mathbf{sx}}\left[\mathit{j}\right]$ is greater than $0$, then the value contained in ${\mathbf{x}}\left[{\mathbf{tdx}}×\left({\mathbf{ix}}-1\right)+\mathit{j}\right]$ is to be included as a value of ${x}^{\mathrm{T}}$, an observation on an independent variable, for $\mathit{j}=0,1,\dots ,m-1$. Constraint: if ${\mathbf{mean}}=\mathrm{Nag_MeanInclude}$, then exactly ${\mathbf{ip}}-1$ elements of sx must be $>0$ and if ${\mathbf{mean}}=\mathrm{Nag_MeanZero}$, then exactly ip elements of sx must be $>0$. 5: $\mathbf{q}\left[{\mathbf{ip}}×{\mathbf{tdq}}\right]$double Input/Output Note: the $\left(i,j\right)$th element of the matrix $Q$ is stored in ${\mathbf{q}}\left[\left(i-1\right)×{\mathbf{tdq}}+j-1\right]$. On entry: q must be array q as output by g02dac, g02dec, g02dfc, or a previous call to g02dcc. On exit: the first ip elements of the first column of q will contain ${c}_{1}^{}$, the upper triangular part of columns 2 to ${\mathbf{ip}}+1$ will contain ${R}^{}$, the remainder is unchanged. 6: $\mathbf{tdq}$Integer Input On entry: the stride separating matrix column elements in the array q. Constraint: ${\mathbf{tdq}}\ge {\mathbf{ip}}+1$. 7: $\mathbf{ip}$Integer Input On entry: the number of linear terms in general linear regression model (including mean if there is one). Constraint: ${\mathbf{ip}}\ge 1$. 8: $\mathbf{x}\left[{\mathbf{nr}}×{\mathbf{tdx}}\right]$const double Input On entry: the ip values for the dependent variables of the observation to be added or deleted, ${x}^{\mathrm{T}}$. The positions of the values x extracted depends on ix and tdx. 9: $\mathbf{nr}$Integer Input On entry: the number of rows of the notional two-dimensional array x. Constraint: ${\mathbf{nr}}\ge 1$. 10: $\mathbf{tdx}$Integer Input On entry: the stride separating matrix column elements in the array x. Constraint: ${\mathbf{tdx}}\ge {\mathbf{m}}$. 11: $\mathbf{ix}$Integer Input On entry: the row of the notional two-dimensional array x that contains the values for the dependent variables of the observation to be added or deleted. Constraint: $1\le {\mathbf{ix}}\le nr$. 12: $\mathbf{y}$double Input On entry: the value of the dependent variable for the observation to be added or deleted, $y$. 13: $\mathbf{wt}\left[1\right]$const double Input On entry: if the new observation is to be weighted, then wt must contain the weight to be used with the new observation. If ${\mathbf{wt}}\left[0\right]=0.0$, then the observation is not included in the model. If the new observation is to be unweighted, then wt must be supplied as NULL. Constraint: if the new observation is to be weighted ${\mathbf{wt}}\left[0\right]\ge 0.0$. 14: $\mathbf{rss}$double * Input/Output On entry: the value of the residual sums of squares for the original set of observations. Constraint: ${\mathbf{rss}}\ge 0.0$. On exit: the updated values of the residual sums of squares. Note: this will only be valid if the model is of full rank. 15: $\mathbf{fail}$NagError * Input/Output The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface). ## 6Error Indicators and Warnings NE_2_INT_ARG_GT On entry, ${\mathbf{ix}}=⟨\mathit{\text{value}}⟩$ while ${\mathbf{nr}}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy ${\mathbf{ix}}\le {\mathbf{nr}}$. NE_2_INT_ARG_LT On entry, ${\mathbf{tdq}}=⟨\mathit{\text{value}}⟩$ while ${\mathbf{ip}}+1=⟨\mathit{\text{value}}⟩$. These arguments must satisfy ${\mathbf{tdq}}\ge {\mathbf{ip}}+1$. On entry, ${\mathbf{tdx}}=⟨\mathit{\text{value}}⟩$ while ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy ${\mathbf{tdx}}\ge {\mathbf{m}}$. NE_ALLOC_FAIL Dynamic memory allocation failed. On entry, mean had an illegal value. On entry, update had an illegal value. NE_INT_ARG_LT On entry, ${\mathbf{ip}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{ip}}\ge 1$. On entry, ${\mathbf{ix}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{ix}}\ge 1$. On entry, ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{m}}\ge 1$. On entry, ${\mathbf{nr}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{nr}}\ge 1$. NE_IP_INCOMP_WITH_SX On entry, for ${\mathbf{mean}}=\mathrm{Nag_MeanInclude}$, number of nonzero values of sx must be equal to ${\mathbf{ip}}-1$: number of nonzero values of ${\mathbf{sx}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{ip}}-1=⟨\mathit{\text{value}}⟩$. On entry, for ${\mathbf{mean}}=\mathrm{Nag_MeanZero}$, number of nonzero values of sx must be equal to ip: number of nonzero values of ${\mathbf{sx}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{ip}}=⟨\mathit{\text{value}}⟩$. NE_MAT_NOT_UPD The $R$ matrix could not be updated: to, either, delete nonexistent observation, or, add an observation to $R$ matrix with zero diagonal element. NE_REAL_ARG_LT On entry, ${\mathbf{rss}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{rss}}\ge 0.0$. On entry, ${\mathbf{wt}}\left[0\right]=⟨\mathit{\text{value}}⟩$ Constraint: ${\mathbf{wt}}\left[0\right]\ge 0.0$. The rss could not be updated because the input rss was less than the calculated decrease in rss when the new observation was deleted. ## 7Accuracy Higher accuracy is achieved by updating the $R$ matrix rather than the traditional methods of updating X'X. ## 8Parallelism and Performance g02dcc is not threaded in any implementation. Care should be taken with the use of this function. 1. (a)It is possible to delete observations which were not included in the original model. 2. (b)If several additions/deletions have been performed you are advised to recompute the regression using g02dac. 3. (c)Adding or deleting observations can alter the rank of the model. Such changes will only be detected when a call to g02ddc has been made. g02ddc should also be used to compute the new residual sum of squares when the model is not of full rank. g02dcc may also be used after g02dec and g02dfc. ## 10Example A dataset consisting of 12 observations with four independent variables is read in and a general linear regression model fitted by g02dac and parameter estimates printed. The last observation is then dropped and the parameter estimates recalculated, using g02ddc, and printed. ### 10.1Program Text Program Text (g02dcce.c) ### 10.2Program Data Program Data (g02dcce.d) ### 10.3Program Results Program Results (g02dcce.r)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 97, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9610884785652161, "perplexity": 1641.8286504487767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046155458.35/warc/CC-MAIN-20210805063730-20210805093730-00040.warc.gz"}
http://cs.stackexchange.com/questions/9642/quadratic-residue-and-integer-factoring	# Quadratic residue and integer factoring I often read that deciding whether or not a number $r$ is a quadratic residue modulo $n$ is an interesting (and hard) problem from number theory (especially if $n$ is not prime). I am looking at the following special case of this problem: Let $p$ and $q$ be two different prime numbers and $n:=pq$. Given $r$ between $1$ and $n$. Decide if there exists an $x\in\mathbb{Z}/n\mathbb{Z}$ such that $x^2\equiv r\pmod{n}$. My question is: The functional version of this problem i.e. "Find such an $x$ as above" yields an randomized algorithm for integer factoring. So it is very interesting for practical reasons like "breaking RSA". Is there any such result for the decision version of this problem? If not, what are typical problems that let us think that deciding quadratic residuosity it is a hard problem? And furthermore, is the special case I'm looking at really a special case? Or can I solve the general case with an arbitrary $n$ with an oracle for the decision problem above? -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9392708539962769, "perplexity": 153.00769503354928}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246637979.29/warc/CC-MAIN-20150417045717-00141-ip-10-235-10-82.ec2.internal.warc.gz"}
https://mathoverflow.net/questions/207027/epsilon-approximations-of-set-systems-with-finite-vc-dimension	# Epsilon-approximations of set systems with finite VC-dimension ECorollary 6.9 in A Guide to NIP theories by Pierre Simon proves the following Theorem. For every positive integer $k$ and every positive real $\varepsilon$ there is an integer $n=n(k,\epsilon)$ such that any probability measure $\mu$ on a finite set system $(X,\Delta)$ with VC-dimension $\le k$ admits an $\varepsilon$-approximation of size $\le n$. Recall that a finite set system is a pair $(X,\Delta)$ where $X$ is a finite set and $\Delta\subseteq{\mathcal P}(X)$. Given a probability measure $\mu$, an $\varepsilon$-approximation is a set $B\subseteq X$ such that $$\left \| \frac{\|S \cap B\|}{\|B\|} - \mu(S) \right \| \leq \epsilon.$$ holds for every $S\in\Delta$. Question I can prove the theorem if working with multi-sets (i.e. sets whose elements are counted with some finite multiplicity). As it is stated it may not be true. Suppose $X$ contains two points of mass $p_0<p_1$ with $\varepsilon<p_0$ and $2\varepsilon<p_1-p_0$ it seems there isn't any $\varepsilon$-approximations, no matter what size. EDIT1: I just realize that the proof of the main theorem of Section 6 (the (q,q)-theorem) can be adapted to work with multi-sets. So it is not a major problem. Still, multi-sets make the proofs messier and I would like to know if they are really necessary. EDIT2: I just realize that in an earlier version of A Guide to NIP theories Corollary 6.9 was stated with $\epsilon$-net for $\epsilon$-approximation. This version is correct. If one is not interest in good bounds, one can obtain an $\epsilon$-net from a multi-set just forgetting multiplicity. In the proof of the (q,q)-theorem only $\epsilon$-nets are used. • You are right, but working with multisets is normally easier in these kinds of problems anyways. Many authors write "set" when they should have written "multiset". May 20 '15 at 1:52 The first one is finding S with measure greater than $1 - \epsilon$. Well, if the set $\{x_1,...,x_q\}$ is a multiset, then it's even easier to find a set which contains all these points. The second one is in the end, finding the $S_1',...,S_N'$. Same thing: if there are repetitions, then it's even better. I think that there's no way to avoid multisets in general (if $X$ is big enough and the measure is uniform enough, I think that with high probability you would get a set and not a multiset, but in general, that wouldn't be the case). • Btw. in version 1 of Simon's article, Corollary 6.9 was stated for $\epsilon$-nets. This was correct and sufficient for the (q,q)-theorem. May 20 '15 at 11:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9282281398773193, "perplexity": 229.218124599529}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057417.92/warc/CC-MAIN-20210923074537-20210923104537-00676.warc.gz"}
http://mathhelpforum.com/advanced-math-topics/203406-algorithm-max-cut-problem-using-matrix-decomposition.html	# Math Help - algorithm for Max Cut problem using matrix decomposition 1. ## algorithm for Max Cut problem using matrix decomposition Hi all, I am looking at the attached paper, trying to learn how to solve a Max Cut problem. The authors achieve this by decomposing the matrix in question into several cut matrices and then considering intersections of vertices represented by these matrices with the vertices in a cut. On page 7 in section 3.1 they approximate the number of elements in a specific intersections as \bar{f}_t and \bar{g}_t They claim that each of these parameters can take O(1/\epsilon^3) values where \epsilon is chosen during the matrix decomposition. Does anyone have a clue why the parameters can take O(1/\epsilon^3) values? Thanks choschech Attached Files	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8404251337051392, "perplexity": 598.3022101024727}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398447266.73/warc/CC-MAIN-20151124205407-00027-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.nickzom.org/blog/2020/04/page/3/	## How to Calculate and Solve for Pouring Speed \| Design of Gating System The image above represents pouring speed. To compute for poring speed, three essential parameters are needed and these parameters are Co-efficient for friction (μ), Acceleration due to Gravity (g) and Rated head static (Hs). The formula for calculating pouring speed: v = μ√(2gHs) Where: v = Pouring Speed μ = Co-efficient for Friction g = Acceleration due to Gravity Let’s solve an example; Find the pouring speed when the co-efficient for friction is 14, acceleration due to gravity is 9 and rated static head is 16. This implies that; μ = Co-efficient for Friction = 14 g = Acceleration due to Gravity = 9 Hs = Rated Static Head = 16 v = μ√(2gHs) v = 14 x √(2 x 9 x 16) v = 14 x √(288) v = 14 x 16.97 v = 237.58 Therefore, the pouring speed is 237.58 m/s. Calculating the Co-efficient for Friction when the Pouring Speed, the Acceleration due to Gravity and the Rated Static Head is Given. μ = v / √(2gHs) Where; μ = Co-efficient for Friction v = Pouring Speed g = Acceleration due to Gravity Let’s solve an example; Find the co-efficient for friction when the pouring speed is 24, the acceleration due to gravity is 9 and the rated static head is 11. This implies that; v = Pouring Speed = 24 g = Acceleration due to Gravity = 9 Hs = Rated Static Head = 11 μ = v / √(2gHs) μ = 24 / √(2 x 9 x 11) μ = 24 / √198 μ = 24 / 14.07 μ = 1.70 Therefore, the co-efficient for friction is 1.70. ## How to Calculate and Solve for Theoretical Density of Ceramics \| Ceramics The image above represents theoretical density of ceramics. To compute for theoretical density of ceramics, five essential parameters are needed and these parameters are Number of formula units in unit cell (n’), Sum of atomic weights of atoms (ΣAc), Sum of atomic weights of anions (ΣAA), Unit cell volume (Vcand Avogadro’s number (NA). The formula for calculating theoretical density of ceramics: ρ = n'(ΣAc + ΣAA) / VcNA Where: ρ = Theoretical Density of Ceramics n’ = Number of Formula Units in Unit Cell ΣAc = Sum of Atomic Weights of Atoms ΣAA = Sum of Atomic Weights of Anions Vc = Unit Cell Volume Let’s solve an example; Find the theoretical density of ceramics when the number of formula units in unit cell is 12, the sum of atomic weights of atoms is 8, the sum of atomic weights of anions is 10, the unit cell volume is 9 and the avogadro’s number is 6.02214e+23. This implies that; n’ = Number of Formula Units in Unit Cell = 12 ΣAc = Sum of Atomic Weights of Atoms = 8 ΣAA = Sum of Atomic Weights of Anions = 10 Vc = Unit Cell Volume = 9 NA = Avogadro’s Number = 6.02214e+23 ρ = n'(ΣAc + ΣAA) / VcNA ρ = (12)(8 + 10) / (9)(6.02214e+23) ρ = (12)(18) / (5.4199e+24) ρ = (216)/(5.4199e+24) ρ = 3.98e-23 Therefore, the theoretical density of ceramics is 3.98e-23.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8644715547561646, "perplexity": 3189.3273160270164}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655887377.70/warc/CC-MAIN-20200705152852-20200705182852-00122.warc.gz"}
https://painfulenglish.wordpress.com/2014/05/16/mathematical-english-powers/	# Mathematical English: Powers Non-native speakers often struggle when they have to speak about powers. For example, the correct expression used for $10^3$ is “ten to the power of three“, although it is common to instead use the shorter form “ten to the three“. Similarly, $x^7$ is “x to the (power of) seven“. The exponents 2 and 3 (can you think of other examples?) have special names: $x^2$ is “x squared“, $x^3$ is “x cubed“. A confusing yet common mistake is to say “ten to three” (which refers to the time of day 2:50) instead of “ten to the three“. If the exponent is negative, for example $10^{-3}$, the correct expression is “10 to the (power of) minus three“, but not “10 to the (power of) negative three“. Finally, the correct form for $e^x$ is either “exponential function of x” or, much shorter, “e to the (power of) x“.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 6, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.900592029094696, "perplexity": 1413.6569212712889}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917127681.50/warc/CC-MAIN-20170423031207-00394-ip-10-145-167-34.ec2.internal.warc.gz"}
https://brilliant.org/practice/calculating-the-potential-energy-of-a-spring-2/	× ## Potential Energy Potential energy lets us do work in the present to change things in the future. If energy is currency, then potential energy is money in the bank. # Potential Energy of Springs A spring is shortened by $$2\text{ m}$$ from its original length. If the elastic potential energy of the spring is $$10\text{ J},$$ what is the value of the spring constant? A spring hanging from the ceiling has a length of $$4\text{ m},$$ and its spring constant is $$k=20\text{ N/m}.$$ If the spring is pulled so that its length gets doubled, what is the elastic potential energy in the spring? An object attached to a spring lies on a frictionless horizontal floor. A force $$F=40\text{ N}$$ is applied on the object towards the right. If the spring constant is $$k=10\text{ N/m},$$ what is the elastic potential energy of the spring when it reaches its maximum length? In the figure above, an object of mass $$m=4\text{ kg}$$ is sliding towards a spring with a speed of $$v=6\text{ m/s}$$ on a frictionless horizontal floor. If the spring constant is $$k=1\text{ N/m},$$ what is the maximal change in the spring's length? The spring in a monster truck's suspension is shortened by $$4\text{ m}$$ from its original length. If the spring constant is $$k=2\text{ N/m},$$ what is the elastic potential energy of the spring? ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9048740267753601, "perplexity": 168.29048132013975}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698544679.86/warc/CC-MAIN-20161202170904-00297-ip-10-31-129-80.ec2.internal.warc.gz"}

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