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https://brilliant.org/problems/a-simple-subtraction/ | # A simple subtraction
Algebra Level 2
The equation $$x^{2} + 13x - 168 = 0$$ has 2 real roots. Let the larger root be a and the smaller root be b.
Find a - b
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https://zbmath.org/?q=an:%220555.17003%22&format=complete | # zbMATH — the first resource for mathematics
On subalgebras of simple Lie algebras of characteristic $$p>0$$. (English) Zbl 0555.17003
This paper studies subalgebras of a simple finite-dimensional Lie algebra $$L$$ over an algebraically closed field of characteristic $$p\geq 7$$, especially subalgebras associated with filtrations.
The first main result implies that if a maximal subalgebra $$L_ 0$$ of $$L$$ has solvable quotients of dimension $$\geq 2$$, then every nilpotent ideal of $$L_0$$ acts nilpotently on $$L$$. It is shown that if $$L$$ contains a solvable maximal subalgebra, then $$L$$ is of type $$A_1$$ or $$W_1$$.
In the final part of the article it is shown that certain $$Z$$-graded finite- dimensional simple Lie algebras either are classical or the difference between the number of nonzero positive and negative homogeneous components is large.
Reviewer: Gordon Brown
##### MSC:
17B50 Modular Lie (super)algebras 17B70 Graded Lie (super)algebras
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https://www.groundai.com/project/evidence-for-the-h_b1p-meson-in-the-decay-upsilon3s-pi0-h_b1p/ | Evidence for the \boldmath h_{b}(1P) meson in the decay \boldmath\mathchar 28935\relax(3S)\rightarrow\pi^{0}h_{b}(1P)
# Evidence for the \boldmathhb(1P) meson in the decay \boldmath\mathchar28935\relax(3S)→π0hb(1P)
July 18, 2019
###### Abstract
Using a sample of 122 million events recorded with the BABAR detector at the PEP-II asymmetric-energy collider at SLAC, we search for the spin-singlet partner of the -wave states in the sequential decay . We observe an excess of events above background in the distribution of the recoil mass against the at mass MeV/. The width of the observed signal is consistent with experimental resolution, and its significance is 3.1, including systematic uncertainties. We obtain the value (stat.) (syst.)) for the product branching fraction .
###### pacs:
13.20.Gd, 13.25.Gv, 14.40.Pq, 14.65.Fy
preprint: BABAR-PUB-10/032preprint: SLAC-PUB-14378
BABAR-PUB-10/032
SLAC-PUB-14378
arXiv:1102.4565 [hep-ex]
[10mm]
The BABAR Collaboration
To understand the spin dependence of potentials for heavy quarks, it is essential to measure the hyperfine mass splitting for -wave states. In the non-relativistic approximation, the hyperfine splitting is proportional to the square of the wave function at the origin, which is expected to be non-zero only for , where is the orbital angular momentum of the system. For , the splitting between the spin-singlet () and the spin-averaged triplet state () is expected to be . The state of bottomonium, the , is the axial vector partner of the -wave states. Its expected mass, computed as the spin-weighted center of gravity of the states, is 9899.87 0.27 MeV/ ref:PDG (). Higher-order corrections might cause a small deviation from this value, but a hyperfine splitting larger than 1 MeV/ might be indicative of a vector component in the confinement potential ref:Rosner2002 (). The hyperfine splitting for the charmonium state is measured by the BES and CLEO experiments ref:BEShc (); ref:CLEOhc0 (); ref:CLEOhc () to be 0.1 MeV/. An even smaller splitting is expected for the much heavier bottomonium system ref:Rosner2002 ().
The state is expected to be produced in decay via or di-pion emission, and to undergo a subsequent transition to the , with branching fraction (BF) ref:Rosner2002 (); ref:Rosner2005 (). The isospin-violating decay is expected to have a BF of about 0.1% ref:BFpredict (); ref:Godfrey (), while theoretical predictions for the transition range from ref:BFpredict () up to ref:ratiopredict (). A search for the latter decay process in BABAR data yielded an upper limit on the BF of at 90% confidence level (C.L.) ref:simone (). The CLEO experiment reported the 90% C.L. limit , assuming the mass of the to be 9900 MeV/ ref:BFcleo ().
In this paper, we report evidence for the state in the decay . The data sample used was collected with the BABAR detector ref:babar () at the PEP-II asymmetric-energy collider at SLAC, and corresponds to 28 of integrated luminosity at a center-of-mass (CM) energy of 10.355 GeV, the mass of the resonance. This sample contains million events. Detailed Monte Carlo (MC) simulations ref:ftn1 () of samples of exclusive decays (where the and are hereafter referred to as the and the ), and of inclusive decays, are used in this study. These samples correspond to 34,000 signal and 215 million events, respectively. In the inclusive MC sample a BF of 0.1% is assumed for the decay ref:BFpredict ().
The trajectories of charged particles are reconstructed using a combination of five layers of double-sided silicon strip detectors and a 40-layer drift chamber, both operating inside the 1.5-T magnetic field of a superconducting solenoid. Photons are detected, and their energies measured, with a CsI(Tl) electromagnetic calorimeter (EMC), also located inside the solenoid. The BABAR detector is described in detail elsewhere ref:babar ().
The signal for decays is extracted from a fit to the inclusive recoil mass distribution against the candidates ()). It is expected to appear as a small excess centered near 9.9 GeV/ on top of the very large non-peaking background produced from continuum events ( with ) and bottomonium decays. The recoil mass, , where is the total beam CM energy, and and are the energy and momentum of the , respectively, computed in the CM frame (denoted by the asterisk). The search for an signal, requiring detection only of the recoil , proved unfruitful because of the extremely large associated background encountered. In order to reduce this background significantly, we exploit the fact that the should decay about half of the time ref:Rosner2002 (); ref:Rosner2005 () to , and so require in addition the detection of a photon consistent with this decay. The precise measurement of the mass ref:etabdiscovery () defines a restricted energy range for a photon candidate compatible with this subsequent decay. The resulting decrease in signal efficiency is offset by reduction of the background by a factor of about twenty. A similar approach led to the observation by CLEO-c, and then by BES, of the in the decay chain ref:BEShc (); ref:CLEOhc0 (); ref:CLEOhc (), where the was identified both exclusively (by reconstructing a large number of hadronic modes) and inclusively.
The signal photon from decay is monochromatic in the rest-frame and is expected to peak at 490 MeV in the CM frame, with a small Doppler broadening that arises from the motion of the in that frame; the corresponding energy resolution is expected to be MeV. The Doppler broadening is negligible compared with the energy resolution. Figure 1 shows the reconstructed CM energy distribution of candidate photons in the region 250-1000 MeV for simulated events before the application of selection criteria; the signal photon from decay appears as a peak on top of a smooth background. We select signal photon candidates with CM energy in the range 420-540 MeV (indicated by the shaded region in Fig. 1).
We employ a simple set of selection criteria to suppress backgrounds while retaining a high signal efficiency. These selection criteria are chosen by optimizing the ratio of the expected signal yield to the square root of the background. The , MC signal sample is used in the optimization, while a small fraction (9%) of the total data sample is used to model the background. We estimate the background contribution in the signal region, defined by GeV/, using the sidebands of the expected signal region, GeV/ and GeV/.
The decay of the is expected to result in high final-state track multiplicity. Therefore, we select a hadronic event candidate by requiring that it have at least four charged-particle tracks and a ratio of the second to zeroth Fox-Wolfram moments ref:fox () less than 0.6 ref:r2 ().
For a given event, we require that the well-reconstructed tracks yield a successful fit to a primary vertex within the collision region. We then constrain the candidate photons in that event to originate from that vertex.
A photon candidate is required to deposit a minimum energy in the laboratory frame of 50 MeV into a contiguous EMC crystal cluster that is isolated from all charged-particle tracks in that event. To ensure that the cluster shape is consistent with that for an electromagnetic shower, its lateral moment ref:LAT () is required to be less than 0.6.
A candidate is reconstructed as a photon pair with invariant mass in the range 55–200 MeV/ (see Fig. 2). In the calculation of , the -pair invariant mass is constrained to the nominal value ref:PDG () in order to improve the momentum resolution of the . To suppress backgrounds due to misreconstructed candidates, we require , where the helicity angle is defined as the angle between the direction of a from a candidate in the rest-frame, and the direction in the laboratory.
Photons from decays are a primary source of background in the region of the signal photon line from transitions. A signal photon candidate is rejected if, when combined with another photon in the event (), the resulting invariant mass is within 15 MeV/ of the nominal mass; this is called a veto. Similarly, many misreconstructed candidates result from the pairing of photons from different ’s. A candidate is rejected if either of its daughter photons satisfies the veto condition, with not the other daughter photon. To maintain high signal efficiency, the veto condition is imposed only if the energy of in the laboratory frame is greater than MeV ( MeV) for the signal photon (for the daughters). With the application of these vetoes, and after all selection criteria have been imposed, the average candidate multiplicity per event is 2.17 for the full range of , and 1.34 for the signal region ( MeV/). The average multiplicity for the signal photon is 1.02. For 98.4% of candidates there is only one associated photon candidate.
We obtain the distribution in 90 intervals of 3 MeV/ from 9.73 to 10 GeV/. For each interval, the spectrum consists of a signal above combinatorial background (see Fig. 2). We construct the spectrum by extracting the signal yield in each interval of from a fit to the distribution in that interval. The distribution is thus obtained as the fitted yield and its uncertainty for each interval of .
We use the MC background and MC -signal distributions directly in fitting the distributions in data ref:ftn2 (). For each interval in MC, we obtain histograms in 0.1 MeV/ intervals of corresponding to the -signal and background distributions. The -signal distribution is obtained by requiring matching of the reconstructed to the generated ’s on a candidate-by-candidate basis (termed “truth-matching” in the following discussion). The histogram representing background is obtained by subtraction of the signal from the total distribution.
For both signal and background the qualitative changes in shape over the full range of are quite well reproduced by the MC. However, the signal distribution in data is slightly broader than in MC, and is peaked at a slightly higher mass value. The background shape also differs between data and MC. To address these differences, the MC signal is displaced in mass and smeared by a double Gaussian function with different mean and width values; the MC background distribution is weighted according to a polynomial in . The signal-shape and background-weighting parameter values are obtained from a fit to the distribution in data for the full range of . At each step in the fitting procedure, the signal and background distributions are normalized to unit area, and a between a linear combination of these MC histograms and the distribution in data is computed. The fit function provides an excellent description of the data (=1446/1433; =Number of Degrees of Freedom) and the fit result is essentially indistinguishable from the data histogram. The background distribution exhibits a small peak at the mass, due to interactions in the detector material of the type or that cannot be truth-matched. The normalization of this background to the non-peaking background is obtained from the MC simulation, which incorporates the results of detailed studies of interactions in the detector material performed using data ref:geant (). This peak is displaced and smeared as for the primary signal.
The fits to the individual distributions are performed with the smearing and weighting parameters fixed to the values obtained from the fit shown in Fig. 2. In this process, the MC signal and background distributions for each interval are shifted, smeared, and weighted using the fixed parameter values, and then normalized to unit area. Thus, only the signal and background yields are free parameters in each fit. The fit to the data then gives the value and the uncertainty of the number of events in each interval. The fits to the 90 distributions provide good descriptions of the data, with an average value of (=1448), and r.m.s. deviation of 0.03 for the distribution of values. We verify that the fitted yield is consistent with the number of truth-matched ’s in MC to ensure that the selection efficiency is well-determined, and to check the validity of the signal-extraction procedure.
To search for an signal, we perform a binned fit to the ) distribution obtained in data. The signal function is represented by the sum of two Crystal Ball functions ref:CB () with parameter values, other than the mass, , and the normalization, determined from simulated signal events. The background is well represented with a fifth order polynomial function.
Direct MC simulation fails to yield an adequate description of the observed background distribution, although the overall shape is similar in data and MC. This is due primarily to the complete absence of experimental information on the decay modes of the and mesons. Simulation studies with a background component that is weighted to accurately model the distribution in data show a negative bias of % in the signal yield from a procedure in which the background shape and signal mass and yield are determined simultaneously in the fit. Consequently, we define a region of chosen as the signal interval based on the expected mass value and signal resolution. The signal region includes any reasonable theoretical expectation for the mass. We fit the background distribution outside the signal interval and interpolate the background to the signal region to obtain an estimate of its uncertainty therein. Figure 3(a) shows the result of the fit to the distribution of in data excluding the signal region, GeV/. The fit yields , and the result is represented by the histogram in Fig. 3(a), including the interpolation to the signal region.
We then perform a fit over the twenty intervals of the signal region to search for an signal of the expected shape. We take account of the correlated uncertainties related to the polynomial interpolation procedure by creating a 2020 covariance matrix using the 66 covariance matrix which results from the polynomial fit. The error matrix for the signal region, , is obtained by adding the diagonal 2020 matrix of squared error values from the distribution, and a value is defined by
χ2=~VE−1V. (1)
Here is the column vector consisting of the difference between the measured value of the distribution and the corresponding sum of the value of the background polynomial and that of the signal function for each of the twenty 3 MeV/ intervals in the signal region. In Fig. 3(b) we plot the difference between the distribution of and the fitted histogram of Fig. 3(a) over the entire region from 9.73 GeV/ to 10.00 GeV/; we have combined pairs of 3 MeV/ intervals from Fig. 3(a) for clarity. The yield obtained from the fit to the signal region is 108142813 events and the mass value obtained is MeV/ with a value of 14.7 for 18 degrees of freedom.
In order to determine the statistical significance of the signal we repeat the fit with the mass fixed to the spin-weighted center of gravity of the states, MeV/c. The signal yield obtained from the fit is . The statistical significance of the signal, calculated from the square-root of the difference in for this fit with and without a signal component is 3.8 standard deviations, in good agreement with the signal size obtained.
Fit validation studies were performed. No evidence of bias is observed in large MC samples with simulated mass at 9880, 9900, and 9920 MeV/. In addition, the result of a scan performed in data as a function of the assumed mass indicates that the preferred peak position for the signal is at 9900 MeV/, in excellent agreement with the result of Fig. 3(b).
We obtain an estimate of systematic uncertainty on the number of ’s in each interval by repeating the fits to the individual spectra with the lineshape parameters corresponding to Fig. 2 varied within their uncertainties. The distribution of the net uncertainty varies as a third order polynomial in ). We estimate a systematic uncertainty of 210 events on the signal yield due to the -yield extraction procedure by evaluating this function at the fitted mass value.
The dominant sources of systematic uncertainty on the measured yield are the order of the polynomial describing the ) background distribution, and the width of the signal region. By varying the polynomial from fifth- to seventh-order, and by expanding the region excluded from the fit in Fig. 3(a) from (9.87–9.93) GeV/ to (9.85–9.95) GeV/, we obtain systematic uncertainties of events and events, respectively, taken from the full excursions of the yield under these changes. Similarly, we obtain a total systematic uncertainty of MeV/ on the mass due to the choice of background shape.
The systematic uncertainty associated with the choice of signal lineshape is estimated by varying the signal function parameters, which were fixed in the fit, by . We assign the largest deviation from the nominal fit result as a systematic error. Systematic uncertainties of events and MeV/ are obtained for the yield and mass, respectively.
After combining these systematic uncertainty estimates in quadrature, we obtain an effective signal significance of 3.3 standard deviations. The smallest value of the significance among those calculated for the varied fits in the systematics study is 3.1 standard deviations. The yield is events and the mass value MeV/, where the first uncertainty is statistical and the second systematic. The resulting hyperfine splitting with respect to the center of gravity of the states is thus MeV/, which agrees within error with model predictions ref:BFpredict (); ref:Godfrey ().
To convert the signal yield into a measurement of the product BF for the sequential decay , , we determine the efficiency from MC by requiring that the signal and the be truth-matched. The resulting efficiency is = %. Monte Carlo studies indicate that photons that are not from an transition can satisfy the selection criteria when only the transition is truth-matched. This causes a fictitious increase in the signal efficiency to = 17.9 0.2%. Therefore, the efficiency for observed signal events that do not correspond to decay is = 2.1%. However, there is no current experimental information on the production of such non-signal photons in and decays. Furthermore, the above estimate of efficiencies in MC does not account for photons from hadronic decays, since the signal MC requires . We thus assume that random photons from hadronic decays have the same probability to satisfy the signal photon selection criteria as those from decays. We assume a 100% uncertainty on the value of when estimating the systematic error on the product BF.
We estimate the product BF for , by dividing the fitted signal yield, , corrected for the estimated total reconstruction efficiency, by the number of events, , in the data sample. We obtain the following expression for the product BF:
B(\mathchar28935\relax(3S)→π0hb)×B(hb→γηb)=NN\mathchar28935\relax(3S)ϵS⋅1C, (2)
where
C=1+ΔϵϵS⋅1B(hb→γηb) (3)
is the factor that corrects the efficiency for the non-signal hadronic and contributions. In this equation, we assume a BF value % according to the current range of theoretical predictions. The corresponding correction factor is %, with a systematic uncertainty dominated by the uncertainty on .
We obtain , where the first uncertainty is statistical and the second systematic. The result is consistent with the prediction of Ref. ref:Godfrey (), which estimates for the product BF. Since the -decay uncertainty reduces the significance of the product BF relative to that of the production, we may also quote an upper limit on the product BF. From an ensemble of simulated events using the measured product BF value, and the statistical and associated systematic uncertainties (assumed to be Gaussian) as input, we obtain at 90% C.L.
In summary, we have found evidence for the decay , with a significance of at least 3.1 standard deviations, including systematic uncertainties. The measured mass value, (stat.)(syst.) MeV/, is consistent with the expectation for the bottomonium state ref:Rosner2002 (); ref:Meinel (), the axial vector partner of the triplet of states. We obtain (stat.) (syst.)) ( at 90% C.L.).
###### Acknowledgements.
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MES (Russia), MICIIN (Spain), STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union), the A. P. Sloan Foundation (USA) and the Binational Science Foundation (USA-Israel).
## References
• (1) K. Nakamura et al. (Particle Data Group), Journal of Physics G 37, 075021 (2010).
• (2) S. Godfrey and J.L. Rosner, Phys. Rev. D 66, 014012 (2002).
• (3) M. Ablikim et al. (BES Collaboration), Phys. Rev. Lett. 104, 132002 (2010).
• (4) J.L. Rosner et al. (CLEO Collaboration), Phys. Rev. Lett. 95, 102003 (2005); S. Dobbs et al. (CLEO Collaboration), Phys. Rev. Lett. 101, 182003 (2008).
• (5) G.S. Adams et al. (CLEO Collaboration), Phys. Rev. D 80, 051106 (2009).
• (6) J.L. Rosner et al. (CLEO Collaboration), Phys. Rev. Lett. 95, 102003 (2005).
• (7) M.B. Voloshin, Sov. J. Nucl. Phys. 43, 1011 (1986).
• (8) S. Godfrey, J. Phys. Conf. Ser. 9, 123 (2005).
• (9) Y.P. Kuang and T.M. Yan, Phys. Rev. D 24, 2874 (1981); Y.P. Kuang, S.F. Tuan, and T.M. Yan, Phys. Rev. D 37, 1210 (1988); Y.P. Kuang and T.M. Yan, Phys. Rev. D 41, 155 (1990); S.F. Tuan, Mod. Phys. Lett. A 7, 3527 (1992).
• (10) J.P. Lees et al. (BABAR Collaboration), arXiV:1105.4234v1 [hep-ex].
• (11) F. Butler et al. (CLEO Collaboration), Phys. Rev. D 49, 40 (1994).
• (12) B. Aubert et al. (BABAR Collaboration), Nucl. Instrum. Meth. A 479, 1 (2002).
• (13) The MC events are generated using the Jetset 7.4 and PYTHIA programs to describe the hadronization process from the Lund string fragmentation model with final-state radiation included.
• (14) B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett. 101, 071801 (2008); [Erratum-ibid. 102, 029901 (2009)].
• (15) G.C. Fox and S. Wolfram, Nucl. Phys. B149, 413 (1979).
• (16) This quantity is indicative of the collimation of an event topology, with values close to one for jetlike events; the kinematics of a heavy object such as the decaying hadronically result in a more spherical event.
• (17) A. Drescher et al., Nucl. Instrum. Meth. 237, 464 (1985).
• (18) In MC simulations, fits to the individual spectra that make use of a polynomial background function and various combinations of Crystal Ball ref:CB () and/or Gaussian signal functions proved unsatisfactory at the high statistical precision necessary.
• (19) S. Agostinelli et al. (GEANT4 Collaboration), Nucl. Instrum. Meth. 506, 250 (2003); T. Sjstrand and M. Bengtsson, Computer Physics Commun. 43 367 (1987).
• (20) M.J. Oreglia, Ph.D Thesis, SLAC-R-236 (1980); J.E. Gaiser, Ph.D Thesis, SLAC-R-255 (1982); T. Skwarnicki, Ph.D Thesis, DESY F31-86-02 (1986).
• (21) S. Meinel, Phys. Rev. D 82, 114502 (2010).
• (22) I. Adachi et al. (Belle Collaboration), arXiv:1103.3419v1 [hep-ex].
Note added in proof: After this paper was submitted, preliminary results of a search for the in the reaction in data collected near the resonance have been announced by the Belle Collaboration ref:Belle (). The mass measured therein agrees very well with the value reported in this paper.
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The feedback must be of minimum 40 characters and the title a minimum of 5 characters | 2020-07-09 11:23:40 | {"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": 0.8492567539215088, "perplexity": 1150.7978551471037}, "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/1593655899931.31/warc/CC-MAIN-20200709100539-20200709130539-00125.warc.gz"} |
https://stacks.math.columbia.edu/tag/02KM | $\xymatrix{ X \ar[rr]_ f \ar[rd]_ p & & Y \ar[dl]^ q \\ & S }$
be a commutative diagram of morphisms of schemes. Assume that
1. $f$ is surjective, and syntomic (resp. smooth, resp. étale),
2. $p$ is syntomic (resp. smooth, resp. étale).
Then $q$ is syntomic (resp. smooth, resp. étale).
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2021-09-26 01:12:58 | {"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": 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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9697567820549011, "perplexity": 2134.5902535350324}, "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-2021-39/segments/1631780057787.63/warc/CC-MAIN-20210925232725-20210926022725-00075.warc.gz"} |
https://socratic.org/questions/how-would-you-differentiate-between-relative-atomic-mass-and-relative-molar-mass | # How would you differentiate between relative atomic mass and relative molar mass?
Well, look at the roots. It is fairly evident that relative atomic mass applies only to atoms. On the other hand, relative molar mass applies to anything that there can be a $\text{mol}$ of, meaning anything that you can count.
• $\text{Ne}$ has a relative atomic mass of $\text{20.1797 g/mol}$, and that is its relative molar mass as well.
• $\text{NaOH}$ has a relative molar mass of $\text{39.9959 g/mol}$, but has no relative atomic mass to speak of, for it is not an atom. | 2020-01-20 15:45:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.7635091543197632, "perplexity": 442.1022646598939}, "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/1579250598800.30/warc/CC-MAIN-20200120135447-20200120164447-00111.warc.gz"} |
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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/31621
Title: Thermal Energy Storage in Metal Foams filled with Paraffin Wax Authors: Vadwala, Pathik Advisor: Chandra, Sanjeev Department: Mechanical and Industrial Engineering Keywords: MechanicalEngineering Issue Date: 3-Jan-2012 Abstract: Phase change materials (PCM) such as paraffin wax are known to exhibit slow thermal response due to their relatively low thermal conductivity. In this study, experiments were carried out to investigate a method of enhancing thermal conductivity of paraffin wax by making use of high porosity open cell metal foams. By adding metal foam, thermal conductivity of PCM’s was shown to increase by 16-18 times that of pure paraffin wax. The use of open cell metal foam material for thermal energy storage application was also investigated by designing and testing different thermal energy storage systems (TESS) - with and without metal foam. The effect of copper metal foam on heat transfer during melting and solidification was analysed by determining the convective heat transfer coefficient. Lastly, a numerical code was developed to predict the temperature field within PCM while melting. URI: http://hdl.handle.net/1807/31621 Appears in Collections: Master
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File Description SizeFormat | 2014-04-20 04:16:10 | {"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": 0.4971623122692108, "perplexity": 4014.2869240127993}, "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-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00383-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://www.gamedev.net/resources/_/technical/math-and-physics/a-verlet-based-approach-for-2d-game-physics-r2714 | # Like 5Likes Dislike A Verlet based approach for 2D game physics
collision distance edge bodies float vertices collisioninfo line axis
Illustrates the power of Verlet integration for physics simulations and covers basic 2D rigid body dynamics with collision
Introduction
The purpose of this article is to describe a way to simulate game physics in two dimensions. We will use an approach known as Verlet integration, go over the basics of moving points and building shapes to topics like collision detection and response. The reader should know the basics of vector maths, meaning addition, subtraction, multiplication with a scalar and the dot product. More than that is not required, however, for deeper understanding more knowledge of Euclidean geometry in two dimensions wouldn't hurt.
Verlet integration
First of all, what is Verlet integration? The Verlet integration is a way of numerically integrating the equations of motion. For this article, you really don't have to know what numerical integration means; basically, the Verlet integration describes the movement of a point trough time. There are different methods to do that - I guess, most of you know the Euler method:
If we merge these two equations into one, meaning we substitute the VelocityNew in the second equation by the right hand side of the first equation, we get:
There are different types of Verlet integration methods - Position Verlet, Velocity Verlet and Leapfrog. For this article, we will choose the position version, because it has some nice features that we're going to take advantage of.
The corresponding equation for position Verlet is actually not much different from the one shown above:
As we can see now, the term (PositionCurrent – PositionOld) in the Verlet equation replaces the velocity if we compare it with the Euler approach. Consequently, this means that this approach doesn't deal with velocities at all - one thing less to worry about. This integration method is not always quite accurate, since (PositionCurrent – PositionOld) is only an approximation of the actual velocity. However, it's fast and stable, which is why it is well suited for games. Also, using this approach the collision response gets really simple. Let us consider a point as shown in figure 1.
The starting conditions for PositionOld and PositionCurrent are chosen such that the point moves slowly to the right. After a certain amount of time steps, the point will intersect with the square on the right. Once the collision is detected, we only have to move the point out of the square and we are done with the collision response. Since the integration uses (PositionCurrent – PositionOld) as its velocity, the speed of the point will subsequently change if we change either CurrentPosition or OldPosition - which is what we did in the collision response (we moved the point out of the square). As we can see in figure 2, the point will automatically decelerate and eventually stop.
If we put the formula above in code, we get something like this (assuming you have a working vector-class, that is):
struct Point {
Vec2 Position;
Vec2 OldPosition;
Vec2 Acceleration;
};
class Physics {
int PointCount;
Point* Points[ MAX_VERTICES ];
float Timestep;
public:
void UpdateVerlet();
//Constructors, getters/setters etc. omitted
};
void Physics::UpdateVerlet() {
for( int I = 0; I < PointCount; I++ ) {
Point& P = *Points[ I ];
Vec2 Temp = P.Position;
P.Position += P.Position - P.OldPosition + P.Acceleration*Timestep*Timestep;
P.OldPosition = Temp;
}
}
Now we have a working physics code that will calculate the trajectories of arbitrary points just fine. But points alone are not very useful, except when you're programming a particle simulation. Since that's normally not the case if you're into game programming, we have to extend the points in some way so we can simulate rigid body behaviour as well. If we look at rigid bodies in nature, we see that they are actually a huge amount of points (=atoms) held together by various forces.
We could of course try and create thousands of particles and connect them in some way to approximate the behaviour of rigid bodies, which would work indeed. However, that would cause a huge amount of calculations to be done for e.g. a single cube, let alone a whole game filled with physics bodies, so this isn't really an optimal solution. Luckily, it shows to be sufficient only to model the vertices of a body. If we were to simulate a box, we would simply create the four vertices that make up the shape of a box, connect them somehow and we're done.
The problem left to compute is now only that of the connections. If we again imagine a box and the four vertices, it should become clear that the distance of a vertex to another should always remain constant. If the distance between two vertices changes, this always means that the shape of the body gets deformed, and we don't want that - who would like to have a crate in his game that collapses once you stand on it? Therefore, we have to find a way to keep the distance between two vertices at a constant value.
If we had the same problem in reality, the solution would be simple - just insert some kind of pole in-between and the vertices won't approach each other anymore. We will do the exact same thing in our program; create a new class that represents an 'imaginary pole'. It connects two vertices and keeps those vertices at a constant distance. The algorithm to update these 'poles' is called once the Verlet is calculated. The algorithm itself is actually quite simple. First of all, we have to calculate the vector between the two vertices that are connected by the pole. The current distance between the two vertices is simply the length of that vector. Once we have the current length, the difference of the original length of the pole should be calculated. We can now use the difference to push the vertices to a position where the distance constraint is satisfied.
struct Edge {
Vertex* V1;
Vertex* V2;
float OriginalLength; //The length of the edge when it was created
//Constructors etc. omitted
};
void Physics::UpdateEdges() {
for( int I = 0; I < EdgeCount; I++ ) {
Edge& E = *Edges[ I ];
//Calculate the vector mentioned above
Vec2 V1V2 = E.V2->Position - E.V1->Position;
//Calculate the current distance
float V1V2Length = V1V2.Length();
//Calculate the difference from the original length
float Diff = V1V2Length - E.OriginalLength;
V1V2.Normalize();
//Push both vertices apart by half of the difference respectively
//so the distance between them equals the original length
E.V1->Position += V1V2*Diff*0.5f;
E.V2->Position -= V1V2*Diff*0.5f;
}
}
That's it - if we created a few points and connected them with our newly created edge struct, the resulting body would show very nice rigid body-behaviour, including rotational effects when it hits the floor. But why does that work? The code isn't much different from before, we only added a few lines to satisfy the distance constraint and suddenly we have rigid bodies. The reason behind this lies within our integration method. If we recall that the Verlet integration doesn't work with velocity but rather with the difference between the current position and the position before the last integration step, it should become clear that the speed of the point will change if we change its position. Therefore, since we change its position in the UpdateEdges method, its velocity will also change. The overall change in velocity looks exactly like we would expect it from a vertex of a rigid body; it is not totally correct, but good enough for games.
To be honest, I lied when I said before that the code would work just fine if we executed it like that. As the code is now, bodies would not be totally rigid. If a body collides with the floor, the distance between it's vertices is not totally constant, which means that the body is more or less deformed, depending on the it's speed before the collision. Why does that happen? The UpdateEdges method is totally correct, but still the distance between two vertices may vary. If we look at figure 3, this should become clear: If a vertex is connected to more than just one edge (which is normally the case), the length correction of one edge may disturb the length of another edge, which is why the bodies get deformed.
The only way to get rid of this problem is to execute the edge correction method more than just once per frame. The more this method is called, the more perfect the situation gets approximated, where all vertices have the right distance to each other. This gives game programmers a scalable physics algorithm - the more time is left at the end of the main loop, the more iterations can be used for the distance correction (and the collision response that will be introduced later). Vice-versa, if the main loop takes more time to execute, the iterations used for physics can be reduced so the game runs at a more or less constant frame rate.
Collision Detection
Now that our algorithm supports the simulation of (almost) rigid bodies, let's proceed to the next problem - collision detection! In this article, we will use an algorithm known as the 'Separating Axis Theorem'. If you already now how it works, you might as well just skip this part and go straight to the collision response. So, how does the Separating Axis Theorem work? As the title suggests, it states that two bodies don't collide, as long we are able to put a straight line between the two, that doesn't intersect either body. Figure 4 demonstrates this.
The only limitation of this algorithm is that it only works correctly with convex shapes. If we tested two concave shapes, the algorithm will fail, meaning that it would detect a collision when there is none. The reason should become evident if you take a look at figure 5.
We could deal with that by breaking up each concave polygon into convex subshapes and then test each subshape separately, but for simplicity reasons, we will just stick to convex polygons in this article - feel free to add concave support later.
So, how do we find out whether we could put a line in-between? We could of course just test every possible line for intersection, but it is evident that this is completely inefficient. To do this, we will take advantage of projection. If we put a new line in figure 4 that is perpendicular to the separating line, we can see that the projections of the two bodies on this line do not overlap (as shown in figure 6). However, if we chose a line that does intersect, the projections of the two bodies do also overlap.
It is irrelevant where we place the line that we project to, since the resulting projection is one-dimensional anyway - only its direction is important. This means that we don't have to look for a line that fits perfectly in-between the two bodies anymore, but for a direction where the projections don't overlap. Finding this direction shows to be quite easy. Let's consider the case where there is only one possible line that separates the two bodies (see figure 7).
It is evident that this line is parallel to the left edge of the right body. Therefore, to find the direction of a separating line, we simply have to iterate over all edges of both bodies and check, if the projection of the bodies onto the perpendicular of the edge overlap. If they don't, the bodies don't collide and we can end the search. If they do, we go on to the next edge. If there is no such edge, the entities are colliding and we have to proceed with the collision response.
Let's put this into code! But before we can implement the collision detection, we first have to write a body class that contains its respective vertices and edges:
struct PhysicsBody {
int VertexCount;
int EdgeCount;
Vertex* Vertices[ MAX_BODY_VERTICES ];
Edge* Edges [ MAX_BODY_EDGES ];
void ProjectToAxis( Vec2& Axis, float& Min, float& Max );
//Again, constructors etc. omitted
};
The ProjectToAxis method will project the body onto the passed axis and change the Min and Max variables to the result of the projection. Since a projection of a 2D-shape onto 1D results in a mere interval of a line, the result of the projection can be stored in two floats that denote the beginning and the end of the interval. The projection method is quite simple:
void PhysicsBody::ProjectToAxis( Vec2& Axis, float& Min, float& Max ) {
float DotP = Axis*Vertices[ 0 ]->Position;
//Set the minimum and maximum values to the projection of the first vertex
Min = Max = DotP;
for( int I = 1; I < VertexCount; I++ ) {
//Project the rest of the vertices onto the axis and extend
//the interval to the left/right if necessary
DotP = Axis*Vertices[ I ]->Position;
Min = MIN( DotP, Min );
Max = MAX( DotP, Max );
}
}
As you can see, projection in 2D is simply a dot product of the projection axis and the point we want to project. The collision detection may look like this:
bool Physics::DetectCollision( PhysicsBody* B1, PhysicsBody* B2 ) {
//Just a fancy way of iterating through all of the edges of both bodies at once
for( int I = 0; I < B1->EdgeCount + B2->EdgeCount; I++ ) {
Edge* E;
if( I < B1->EdgeCount )
E = B1->Edges[ I ];
else
E = B2->Edges[ I - B1->EdgeCount ];
//Calculate the axis perpendicular to this edge and normalize it
Vec2 Axis( E->V1->Position.Y - E->V2->Position.Y, E->V2->Position.X - E->V1->Position.X );
Axis.Normalize();
float MinA, MinB, MaxA, MaxB; //Project both bodies onto the perpendicular axis
B1->ProjectToAxis( Axis, MinA, MaxA );
B2->ProjectToAxis( Axis, MinB, MaxB );
//Calculate the distance between the two intervals - see below
float Distance = IntervalDistance( MinA, MaxA, MinB, MaxB );
if( Distance > 0.0f ) //If the intervals don't overlap, return, since there is no collision
return false;
}
return true; //There is no separating axis. Report a collision!
}
The algorithm works just like described above; if something isn't clear, I would suggest rereading the explanations step by step. The IntervalDistance method that is mentioned in the code is actually quite simple:
float Physics::IntervalDistance( float MinA, float MaxA, float MinB, float MaxB ) {
if( MinA < MinB )
return MinB - MaxA;
else
return MinA - MaxB;
}
Since we don't know if body A will lie on the left and body B on the right or vice-versa, we have to check which interval begins sooner. We then subtract the end of the left interval from the beginning of the right interval to get the distance between the two - if this value is smaller than zero, they overlap.
That's it for collision detection! ...well, not yet. Apart from detecting whether or not the two bodies collide, the collision detection should also provide certain information about the collision. We also have to calculate a so-called collision vector that is big enough to push the two bodies apart so they don't collide anymore, but touch each other. There are of course arbitrarily much vectors that could accomplish this, but for our physics to look right we have to find the smallest of those vectors. The vector we're looking for has the pleasant property that it's always parallel to one of the lines we projected to, which means that we only have to check each edge and calculate the length of the vector needed to push the two bodies apart. Figuring out the length isn't really a hard thing to do, if we take a look at figure 8.
In the code above we projected both bodies onto the axis given by the (normalized!) vector 'Axis'. We then called the method IntervalDistance to check whether or not the intervals are overlapping. The length of the vector (which is parallel to the axis we projected to) needed to push the two bodies apart is simply the amount of overlapping. To allow the information calculated in the DetectCollision method to pass smoothly to the collision response, we add a new struct to our Physics class:
class Physics {
struct {
float Depth;
Vec2 Normal;
} CollisionInfo;
//Everything else omitted
}
The 'Depth' is the length of the vector, the 'Normal' is the direction of the vector discussed above.
Our new DetectCollision method would now look like this:
bool Physics::DetectCollision( PhysicsBody* B1, PhysicsBody* B2 ) {
float MinLength = 10000.0f; //Initialize the length of the collision vector to a relatively large value
for( int I = 0; I < B1->EdgeCount + B2->EdgeCount; I++ ) {
Edge* E;
if( I < B1->EdgeCount )
E = B1->Edges[ I ];
else
E = B2->Edges[ I - B1->EdgeCount ];
Vec2 Axis( E->V1->Position.Y - E->V2->Position.Y, E->V2->Position.X - E->V1->Position.X );
Axis.Normalize();
float MinA, MinB, MaxA, MaxB;
B1->ProjectToAxis( Axis, MinA, MaxA );
B2->ProjectToAxis( Axis, MinB, MaxB );
float Distance = IntervalDistance( MinA, MaxA, MinB, MaxB );
if( Distance > 0.0f )
return false;
//If the intervals overlap, check, whether the vector length on this
//edge is smaller than the smallest length that has been reported so far
else if( abs( Distance ) < MinDistance ) {
MinDistance = abs( Distance );
CollisionInfo.Normal = Axis; //Save collision information for later
}
}
CollisionInfo.Depth = MinDistance;
return true; //There is no separating axis. Report a collision!
}
Once we have this, we'd be already able to write a very simple collision response. Since the collision vector we calculated pushes the two bodies apart so they don't collide anymore, we could just move all vertices of both bodies back by half the vector and we'd be done. This would work, since interpenetrations are resolved, but it wouldn't look right. The bodies would simply glide off each other, meaning they don't start to spin like a real object when hit.
The problem is that a body in our approach only spins if the velocities of its vertices differ. In the same manner, a body only changes its rotational velocity if its vertices experience different acceleration. Acceleration is change in velocity, and in Verlet integration change in velocity is equal to change in position. Therefore, if we move the two bodies back by the collision vector, we change the velocity of all vertices of both bodies by the same amount, which means that there is no change in the rotational velocity. For this reason, we need to write a better collision response.
This is where the advantage of our approach kicks in! In a rigid body system, we would have to use complicated formulas to calculate the momentum and then treat the linear and angular case separately. In our system, the whole thing is much easier - we just have to move the edge and the vertex participating in the collision backwards so they don’t intersect, but touch each other. Since both the edge and the vertex are connected to the rest of their respective body, the position (and therefore the velocity) of the other vertices will change immediately to fulfil the length constraint. Both bodies will start spinning self-actingly. The whole collision response reduces to identifying the edge and the vertex that participate in the collision and separating them from each other; everything else will be done automatically by the edge correction step.
Identifying the collision edge and vertex is not that hard. The collision vertex is the vertex that lies closest to the other body. Therefore, we simply have to create a line whose normal vector is the collision normal (its starting point doesn't really matter). We then measure the distance of each vertex of the first body from the line using the line equation in vector geometry, which is
where N is the normal vector, R0 the origin of the line, R the point to be tested and d the distance of the point from the line. The set of all points that form a line are given by d = 0 (all points that have zero distance from the line), just as a side note. Once we have the distance of each vertex from the line, we choose the one with the lowest distance - that's the collision vertex we were looking for. Please note that d can also be negative. A line separates a two dimensional space in two halves; if the point R lies in the half the line normal points into, the distance will be positive, but if it lies on the other side, the distance will be negative. Therefore, it is important in which direction the collision normal points (in the implementation presented below, it’s always made sure that the collision normal points at the body containing the collision vertex).
The collision edge is even easier to find. Remember when we projected the bodies on the perpendicular of an edge to find the smallest collision vector? The collision edge is simply the edge that resulted in the smallest vector.
Time to put this in code! First of all, we have to extend the collision info struct in the physics class to contain the collision edge and vertex:
struct {
float Depth;
Vec2 Normal;
Edge* E;
Vertex* V;
} CollisionInfo;
Now we can rewrite our DetectCollision method to detect the additional information:
bool Physics::DetectCollision( PhysicsBody* B1, PhysicsBody* B2 ) {
float MinDistance = 10000.0f;
for( int I = 0; I < B1->EdgeCount + B2->EdgeCount; I++ ) { //Same old
Edge* E;
if( I < B1->EdgeCount )
E = B1->Edges[ I ];
else
E = B2->Edges[ I - B1->EdgeCount ];
Vec2 Axis( E->V1->Position.Y - E->V2->Position.Y, E->V2->Position.X - E->V1->Position.X );
Axis.Normalize();
float MinA, MinB, MaxA, MaxB;
B1->ProjectToAxis( Axis, MinA, MaxA );
B2->ProjectToAxis( Axis, MinB, MaxB );
float Distance = IntervalDistance( MinA, MaxA, MinB, MaxB );
if( Distance > 0.0f )
return false;
else if( abs( Distance ) < MinDistance ) {
MinDistance = abs( Distance );
CollisionInfo.Normal = Axis;
CollisionInfo.E = E; //Store the edge, as it is the collision edge
}
}
CollisionInfo.Depth = MinDistance;
//Ensure that the body containing the collision edge lies in
//B2 and the one containing the collision vertex in B1
if( CollisionInfo.E->Parent != B2 ) {
PhysicsBody* Temp = B2;
B2 = B1;
B1 = Temp;
}
//This is needed to make sure that the collision normal is pointing at B1
int Sign = SGN( CollisionInfo.Normal*( B1->Center - B2->Center ) );
//Remember that the line equation is N*( R - R0 ). We choose B2->Center
//as R0; the normal N is given by the collision normal
if( Sign != 1 )
CollisionInfo.Normal = -CollisionInfo.Normal; //Revert the collision normal if it points away from B1
float SmallestD = 10000.0f; //Initialize the smallest distance to a high value
for( int I = 0; I < B1->VertexCount; I++ ) {
//Measure the distance of the vertex from the line using the line equation
float Distance = CollisionInfo.Normal*( B1->Vertices[ I ]->Position - B2->Center );
//If the measured distance is smaller than the smallest distance reported
//so far, set the smallest distance and the collision vertex
if( Distance < SmallestD ) {
SmallestD = Distance;
CollisionInfo.V = B1->Vertices[ I ];
}
}
return true;
}
In the above code, we introduced a new variable in the PhysicsBody struct, the center. It will be recalculated before the collision step and is simply the average of all vertices of the body.
Collision Response
Finally, we're done with collision detection. The only thing left to do is the collision response, which is luckily not that hard. As explained above, we just have to push the collision vertex and the collision edge apart by the collision vector and we're done. This is trivial for the collision vertex. Since we already ensured that the collision normal points at the first body which contains the collision vertex, we just have to add half of the collision vector to the position of the vertex:
void Physics::ProcessCollision() {
Vec2 CollisionVector = CollisionInfo.Normal*CollisionInfo.Depth;
CollisionInfo.V->Position += CollisionVector*0.5f;
}
For the edge case, this will become a bit more complicated. The edge consists of two vertices that will move differently, depending on where the collision vertex lies. The closer it lies to the one end of the edge, the more this end will move and vice-versa. This means that we first have to calculate where on the edge the collision vertex lies. This is done using the following equation:
Where V is the position of the collision vertex and E1 and E2 are the two vertices connected by the edge. t is the factor that determines where on the edge the vertex lies, reaching from 0 to 1. It doesn't matter whether we choose the X or the Y coordinate to calculate t, since both would result in the same value. The X case would look like this:
Vertex* E1 = CollisionInfo.E->V1;
Vertex* E2 = CollisionInfo.E->V2;
float T = ( CollisionInfo.V->Position.X - CollisionVector.X - E1->Position.X )/( E2->Position.X - E1->Position.X );
But be careful! If E2 lies directly above E1, the program would divide by zero. Therefore, we should build in a small check to avoid this:
float T;
if( abs( E1->Position.X - E2->Position.X ) > abs( E1->Position.Y - E2->Position.Y ) )
T = ( CollisionInfo.V->Position.X - CollisionVector.X - E1->Position.X )/( E2->Position.X - E1->Position.X );
else
T = ( CollisionInfo.V->Position.Y - CollisionVector.Y - E1->Position.Y )/( E2->Position.Y - E1->Position.Y );
This basically divides by the X denominator if it is bigger than the Y denominator and vice-versa.
We then use the following neat formula to calculate a scaling factor that ensures that the collision vertex lies on the collision edge after the collision response. We could derive it by solving a few equations, but I don't think the derivation is really important, so I'll just leave this here:
Once we put all of this in code, we get:
void Physics::ProcessCollision() {
Vec2 CollisionVector = CollisionInfo.Normal*CollisionInfo.Depth;
Vertex* E1 = CollisionInfo.E->V1;
Vertex* E2 = CollisionInfo.E->V2;
float T;
if( abs( E1->Position.X - E2->Position.X ) > abs( E1->Position.Y - E2->Position.Y ) )
T = ( CollisionInfo.V->Position.X - CollisionVector.X - E1->Position.X )/( E2->Position.X - E1->Position.X);
else
T = ( CollisionInfo.V->Position.Y - CollisionVector.Y - E1->Position.Y )/( E2->Position.Y - E1->Position.Y);
float Lambda = 1.0f/( T*T + ( 1 - T )*( 1 - T ) );
E1->Position -= CollisionVector*( 1 - T )*0.5f*Lambda;
E2->Position -= CollisionVector* T *0.5f*Lambda;
CollisionInfo.V->Position += CollisionVector*0.5f;
}
That's it. We're done with collision response - easy, wasn't it?
All that's left to do is to put all of the methods we wrote into a single update method:
void Physics::Update() {
UpdateForces();
UpdateVerlet();
IterateCollisions();
}
IterateCollisions is a method that does multiple things. It iterates over all bodies, calls the respective UpdateEdges method, recalculates the body center and then does the collision detection (and the collision response, if necessary). Of course, it doesn't just do this once, but repeats those steps a few times. The more repetitions are made, the more realistic the physics will look. The reason was explained above (if you've forgotten, better read it again ;) ).
Final Words
You can download a working implementation using GLUT and OGL as a Visual C++ 2008 project via the attached resource file. It is basically the same code as discussed in this article with a few optimizations and a very simple rendering and input function. I hope you enjoyed this article and found it useful. If you have any questions or suggestions, please let me know. Since I'm not a native English speaker, there might be a few mistakes here and there; please bear with it.
Dec 24 2011 12:40 PM
Very good article!
Since a long time I'm searching how to develop a physic engine like Angry Birds. I think this algorithm is a good way to do that.
Moreover, I'm sure this approach could be used for a 3D game physic.
Dec 20 2012 09:45 AM
How to add friction to this?
Mar 26 2013 01:20 AM
To add friction, you would need to know the mass of the object, but it would look something like this.
FrictionVector = μ*m*g;
Where:
μ = coefficient of friction between two objects(higher number means more friction)
m = mass
g = gravitational constant (9.8 on earth)
The direction would be in the opposite direction of the force applied.
/ TheItalianJob71
Apr 05 2014 03:22 AM
Hello! i have noticed that you mix int and floats , i tried to change the bounding box coordinates from int to float and the behaviour is different, why are you doing exaclty this ? aren't you loosing precision casting from float to int ?
Aug 17 2015 12:42 AM
I hope you don't mind, but I converted your demo into Java: https://bitbucket.org/craigmit/verlet/overview | 2017-04-24 05:39:19 | {"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": 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": 0.4948326349258423, "perplexity": 865.7664697249123}, "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/1492917119080.24/warc/CC-MAIN-20170423031159-00399-ip-10-145-167-34.ec2.internal.warc.gz"} |
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## regular hexagon calc: find a
Every one of their sides is 2 square roots of 3. Calculate the height of the triangle. This can be easily proved by counting how many triangles can be fitted inside the decagon. (which is 120°). $\endgroup$ – john May 15 '14 at 16:57. add a comment | 2 $\begingroup$ Wikipedia article on hexagons states that a height-to-width ratio of a regular hexagon is 1:1.1547005. These expressions are: \begin{split} R_c & = \frac{a}{2 \sin{30^{\circ}}} = a \\ R_i & = \frac{a}{2 \tan{30^{\circ}}} \approx 0.866 a \\ \\ R_i & = R_c \cos{30^{\circ}} \approx 0.866 R_c \end{split} Naturally occurring cells can be smaller. In the following table a concise list of the main formulas, related to the regular hexagon is included. Regular polygons are equilateral (all sides equal) and their angles are equal too. Thus area of polygon is. the side length. Regular polygons are equilateral (all sides equal) and their angles are equal too. , by dividing the total frame area by the cell area: By substitution and conversion from square inches to mm2 (i.e. Then click Calculate. A regular hexagon can be cut into six equilateral triangles, and an equilateral triangle can be divided into two 30°- 60°- 90° triangles. It’s a geometric figure with six sides and six angles. The following formulas are derived: The width This calculator works only for regular polygons - those polygons which have ALL sides equal & ALL interior angles equal. Best Answer. The radius of circumcircle Hexagon is a polygon with six sides and six vertices. Let x be the side of a regular polygon, n the number of sides, r the radius of the inscribed circle and R the radius of the circumscribed circle. For triangle in regular polygon a and b are circumradius, and gamma is 360/n, where n - number of sides. Indeed, there are 4 triangles. Find the radius of the circle circumscribed about the hexagon. For the sides, any value is accepted as long as they are all the same. a Calculate the potential at the centre of the hexagon. Q.1: Find the area and perimeter of hexagon, if all its sides have a length equal to 6cm. 1) Find the area of a regular 12-gon inscribed in a unit circle. Using basic trigonometry we find: \begin{split} R_c & = \frac{a}{2 \sin{\frac{\theta}{2}}} \\ R_i & = \frac{a}{2 \tan{\frac{\theta}{2}}} \\ R_i & = R_c \cos{\frac{\theta}{2}} \end{split}. To find the area of a regular hexagon, or any regular polygon, we use the formula that says Area = one-half the product of the apothem and perimeter. They are of two types namely, Regular and Irregular hexagonal prism. Calculate the apothem, using the fact that it is part of a special triangle to get the answer exactly. Here, we hope you will find a great tool for calculating the diagonals, perimeter, circumradius, inradius, and area of a regular octagon. workout : step1 Address the formula, input parameters and values side = 5 in step 2 Find Area using side of hexagon … Then click Calculate. Measuring Hexagon Angles. $\begingroup$ More so trigonometry, as you know the angles in a regular hexagon. This means that, for a regular hexagon, calculating the perimeter is so easy that you don't even need to use the perimeter of a polygon calculator if you know a bit of maths. Simple geometry calculator which is used to find the slant height of a regular hexagonal pyramid with the known value of side. Area of a triangle is, where a and b - triangle sides, and gamma is angle between those sides. The center of this circle is the center of the hexagon. Calculations at a regular decagon, a polygon with 10 vertices. A hexagon is a six-sided polygon. the central angle and : Because, It will appear as the shape that the base of the prism is made of, which is a hexagon in the case of a hexagonal prism, and a rectangle in the case of a rectangular prism. is the distance between two opposite vertices of the regular hexagon (the length of its diagonal). As shown below, this means that we must find the perimeter (distance all the way around the hexagon) and the measure of the apothem using right triangles and trigonometry. Proving that a regular polygon with infinite sides is a circle by using limits on the formula $\frac{\pi}{n}(n-2)$ 1 How do you find the area of an irregular polygon within a square? The six sides are all of equal length, therefore all the angles are of equal length. It produces both the coordinates of the vertices and the coordinates of the line segments making up the sides of the polygon. and height the hexagon inradius (see figure below). Decagon Calculator. These calculations come from the 30-60-90 right triangle, but if you don’t want to memorize these formulas or derive them, simply use the calculator for nearly instant results. How close is this area to that of the circle? You could memorize this formula or perform the calculations manually, but the calculator will work this for you quickly and effectively once you enter the length of “a”. 2) A regular hexagon has side length 6. John Conway labels these by a letter and group order. It turns out that these expressions are valid for any regular polygon, not just the hexagon. First, divide up the following regular hexagon into triangles by using your ruler and a pencil to draw diagonal lines that dissect the internal angles of the regular hexagon below. Enter one value and choose the number of decimal places. Draw linear segments between them and the regular hexagon is now complete. The circumradius of a regular hexagon is equal to its side. The radius of circumcircle w If the hexagon is troublesome for you, then this calculator will be extremely handy. If the edge of the triangle is “a” then the area, $$A = \frac{\sqrt{3}}{4}\times a^{2}$$ and if you multiply by 6 you get $$(\frac{3\sqrt{3}}{2})a^{2}$$. To find the perimeter, simply take the length of one side and multiply by 6. The first one has been done for you: Count the number of triangles in the hexagon and multiply this by 1800 to get the total number of degrees inside a hexagon: Perimeter = 6a = 6 × 6 = 36 cm. [:alpha:] You’ll see what all this means when you solve the following problem: Divide this number by 2 to account for duplicate diagonals between two vertices. and also among each other. Please use consistent units for any input. Again, no need to memorize all these formulas and manual calculations, let the hexagon calculator do all the work for you in a fast and easy way. The area of a hexagon is defined as the region occupied inside the boundary of a hexagon is calculated using Area=(3/2)*sqrt(3)*Side^2. Free Online Scientific Notation Calculator. So if you’re doing a hexagon problem, you may want to cut up the figure and use equilateral triangles or 30°- 60°- 90° triangles to help you find the apothem, perimeter, or area. This calculator will calculate everything you need to know about a hexagon, from the area or perimeter to the diagonal lengths. Online Volume Of a Hexagonal Prism calculator helps you to calculate the volume of a hexagonal prism based on side and height. , using the respective analytical expressions for these quantities. For the detailed terms of use click here. P = N a feet, meters or even angstrom or light-years), and then enter the following: s - the length of the sides of the decagon; Area is calculated in square meters. \alpha If the hexagon is troublesome for you, then this calculator will be extremely handy. As demonstrated in the figure below, many possible concave hexagons can be defined, with equal sides, but unequal interior angles (these are called equilateral). Enter below the shape dimensions. Learn more How can I work out the width and height of a hexagon A typical use for regular expressions is in finding text; for instance to locate all cells containing man or womanin your spreadsheet, you could search using a single regular expression. Find the radius of the circle circumscribed about the hexagon. In the Replace with box: Use $(dollar) instead of \ (backslash) to replace references. Replace. This tool calculates the basic geometric properties of a regular hexagon. A hexagonal prism, also called an octahedron, is a type of prism that is characterized by a hexagonal base. The sum of the interior angles of a polygon is 180(n – 2), where n is the number of sides. This can be easily be concluded by counting the number of triangles fitting inside the hexagon, by connecting its vertices (avoiding intersections). In a right-angle triangle, the tangent of an angle equals the length of the opposite side, divided by the length of the adjacent side. (a) Find the area of a regular hexagon inscribed in a circle of radius 1. {eq}4 {/eq}-inch side. Finding the Area of a Regular Hexagon. in terms of the circumradius The sum of the internal angles of any decagon, either convex or concave is always 1440°. a=8'' Find the length of the apothem for the given square (Example #8) Find the indicated measure for a regular polygon (Examples #9-10) Find the area of the regular polygon (Examples #11-12) Calculate the area of the regular polygon (Examples #13-14) Using ratios to find the perimeter and area of similar polygons (Examples #15-17) Circumference You can calculate the area and perimeter through our tool. measure, can we find out the measurement of each angle in a regular hexagon? Determine the circumradius, the inradius and the area of a regular hexagon with side length Multiply by five to find the total area. 3)Isosceles triangle OPQ has legs OP = OQ, base PQ = 2, and and angle POQ = 45 degrees. Almost six thousand cells. Inputs. If each triangle has perimeter 4, then the perimeter of the hexagon is: 8...how to solve? The tool can calculate the properties of the hexagon, given either the length of its sides or the inradius or the circumradius or the area or the height or the width. Thus there are 9 unique diagonals in a hexagon. Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. A hexagonal pyramid is a geometric figure that consists of a six sided (hexagonal) base and six triangular faces. a As happens with any regular polygon, a circle that passes through all six vertices of the hexagon can be drawn. h R_c Guest Feb 4, 2015. One way to find the area of a regular hexagon is by first dividing it into equilateral triangles. The formula for the number of vertices in a polygon is: These are actually The figure below shows a regular octagon. Therefore, the total area of the six triangles is: A = 6\frac{1}{2} a R_i = 3a\frac{a}{2 \tan{30^{\circ}}}\Rightarrow. Therefore, all the six triangles sharing the center of the hexagon as one of their vertices, are identical equilateral triangles. You also need to use an apothem — a segment that joins a regular polygon’s center to the midpoint of any side and that is perpendicular to that side. Hexagon calculator is a useful tool to calculate the area of a regular hexagon which have 6 sides. Regular Decagon. The calculated results will have the same units as your input. For example, here’s how you’d find the area of EIGHTPLU in the figure below given that it’s a regular octagon with sides of length 6. Repeat the same procedure two more times. If we want to find the area of the entire hexagon, we just have to multiply that by 6, because there are six of these triangles there. I was studying ways to make a hexagon with just CSS, and found a solution that gives me regular hexagons based on the width:.hexagon { height: 100%; width: calc(100% * 0.57735); display: inline-block; } However, the code works by generating new rectangles based on the parent element's width. A regular hexagon is formed from 6 equilateral triangles,. The radius of incircle Calculate the unknown defining areas, circumferences and angles of a regular polygon with any one known variables. A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. The author or anyone else related with this site will not be liable for any loss or damage of any nature. Calculations at a regular decagon, a polygon with 10 vertices. The circumradius and the inradius, in terms of the side length 0 users composing answers.. About this page: Hexagonal Prism Calculator The hexagonal prism calculator finds the volume of a regular hexagonal prism with two hexagonal bases and six rectangular faces, using length of the side of the prism l and its height h.In addition, the page computes surface to volume ratio, the total surface area, the lateral surface area, and surface area of the base of a hexagonal prism. R_i Therefore, a hexagon has an interior angle sum of 720 degrees and each interior angle of a regular hexagon has a measure of 120 degrees. Area of a regular polygon is the sum of area of a triangles it contains. we find: A = \frac{3\ (8'')^2}{2 \tan{30^{\circ}}} \approx 166\ \text{in}^2. The hexagonal prism is a prism with a hexagonal base. This is equal to twice the circumradius You usually need to know the length of the apothem when calculating the area of a hexagon. find the apothem of a regular hexagon with side of 20cm. Decagon Calculator. This property permits us to assume that no space of the hive frame is left unoccupied. Question: Find the area of a regular hexagon with the given measurement. Likewise, the diagonals of the hexagon are diameters of the circumcircle. Find the area of a regular triangle inscribed in a circle with the radius of 1.5. Remember, to find the area of a triangle, multiply the base by the height, and then divide by 2. In our example, A(total pentagon) = 5 x A(triangle) = 5 x 3 = 15 square units. It is useful to blind users and those who produce material for the sight-impaired. N The interior and central angles are also supplementary, since their sum is 180°: The regular hexagon is composed by six identical equilateral triangles having a common vertex, the polygon centre. The area of a regular hexagon can be found, considering that it is composed by 6 identical equilateral triangles, having sides +10. They are: \begin{split} R_c & = a \\ R_i & = \frac{a}{2 \tan{30^{\circ}}}\end{split} The four corners (like triangle SUE in the figure) that you cut off the square to turn it into an octagon are 45°- 45°- 90° triangles … where So this side right over here is 2 square roots of 3. Also some approximations that may prove handy for practical problems are listed too. All rights reserved. This is equal to twice the inradius (a) Find the area of a regular hexagon inscribed in a circle of radius 1. of the regular hexagon is the distance between two opposite edges. To find the total area, just multiply the area of one triangle by five. To find the area of a regular hexagon, or any regular polygon, we use the formula that says Area = one-half the product of the apothem and perimeter. Calculator online for a regular polygon of three sides or more. : 1''=25.4mm) we get: N\approx\frac{171\ \left(25.4\textrm{mm}\right)^2}{18.94\ \textrm{mm}^2}\Rightarrow. There are 3 diagonals from a single vertex, and there are 6 vertices on a hexagon, which suggests there would be 18 diagonals in a hexagon. Where, Charge, q = 5 µC = 5 × 10 - 6 C. Formulas : It is possible to express the height Regular Polygons. The tool can calculate the properties of the hexagon, given either the length of its sides or the inradius or the circumradius or the area or the height or the width. . Now, multiply that value by 6. Regular Hexagon. Example Problem Find the volume of a hexagonal prism with a base edge length of 20 and a prism height of 10. are related to the side length We can obtain specific expression for the regular hexagon by setting θ = 60°. This side over here is 2 square roots of 3. Read more about us here. R_c=a How many degrees in a hexagon, and without using a protractor to measure, can we find out the measurement of each angle in a regular hexagon? A new point is defined at the intersection with the first circle. The angle at the centre that subtends to adjacent vertices is 360/6 = 60degrees. The hexagon calculator will determine all the essential information about a regular hexagon. The hexagon is the highest regular polygon which allows a regular tesselation (tiling). Then construct a circle, having its center at one end of the linear segment and radius equal to the segment length. A hexagon is a six-sided polygon. As shown below, this means that we must find the perimeter (distance all the way around the hexagon) and the measure of the apothem using right triangles and trigonometry. This polyhedron has 8 faces, 18 edges, and 12 vertices. In other words, we can find the number of cells in the hive frame, It is fast and convenient compared to the tedious manual work required when using the formulas. The side of a regular hexagon is 22 centimeters. \theta Therefore the hexagon consists of 6 equilateral triangles of sidelength 8 units. The regular hexagon features six axes of symmetry. Solve advanced problems in Physics, Mathematics and Engineering. A hexagon has six sides. And I could just go around the hexagon. Doing so we find the circumradius: R_i= \frac{8''}{2 \tan{30^{\circ}}}\approx 6.928''. Half of them are passing through diagonally opposite vertices and the remaining through the middles of opposite edges. Using Heron's formula. Like any polygon, a hexagon can be either convex or concave, as illustrated in the next figure. A hexagon is called regular when all of its sides and interior angles are equal. Input the variables into the calculator and you will receive the volume and total surface of … The outer circle surrounding it is called a circumscribed circle (or circumcircle) and the inner circle which is surrounded by the octagon is called the inscribed circle (or incircle). Enter number of sides n and the length x of one side of the polygon … How close is this area to that of the circle? \alpha The tool can calculate the properties of any regular n-gon, given either the edge length, the inradius, the circumradius, the area, the height or the width. With our tool, you need to enter the respective value for Side and hit the calculate button. Polygon which allows a regular 12-gon inscribed in a unit circle prism based side. Oq, base PQ = 2, and gamma is angle between those sides right over here 2. Be extremely handy, either convex or concave, as you know the length of the line segments making the! Calculations at a regular tesselation ( tiling ) ( or polygon ) has one or more } -inch side has. Follow the steps described below: the bounding box of a regular hexagon in our example, you..., order 12 is fast and convenient compared to the side of a hexagonal prism also! Choose the number of decimal places to nine side right over here is 2 square roots of.. Case you need to know the length of the circle of ( )! Is usually called inradius to blind users and those who produce material for the regular hexagon have. Convex, a circle of radius 1 the tip of the hexagon hexagon! Each cell is a polygon with six sides and six vertices produce material for the regular is... Frame is left unoccupied and then divide by 2 find what is the same value case you need enter! Like any polygon, a circle with the first circle avoiding any intersections are by. Is 360/n, where n - number of sides is called Irregular related. For duplicate diagonals between two vertices - triangle sides, any value is accepted as long they! ( hexagonal ) base and six triangular faces therefore all the essential information about regular. The shape completely that you searched for, and then searches for the regular hexagon a and! Characterized by a letter and group order all of its vertices six triangular faces, then the perimeter, take... 15 square units prism that is not regular is called regular when all of its sides have a equal. And Irregular hexagonal prism is a polygon to the regular hexagon is equal to: the bounding box a! Polygons which have 6 sides he sum of internal angles of a calculator ( you! To tile a plane area without leaving any gaps Attribute, all the same radius, the. Regular decagon, a concave hexagon ( or polygon ) has one or more the angles... List of the circle circumscribed about the hexagon sides center coincides with the radius of a hexagon math science!, Equation Solver, Complex Numbers, calculation History six angles regular polygons are equilateral all! Which is used to find the apothem, using the same value the slant height of 10 table. Into the calculator can figure out the width and height of this rectangle are defined where circle! Their angles are equal and six angles of its vertices the pentagon 's edge, leading the. The tedious manual work required when using the calculator can figure out the length 20. 8 faces, 18 edges, and 12 vertices$ \begingroup \$ more so trigonometry, you! Just the hexagon is equal to nine calculate area of an-sided regular polygon inscribed in a regular decagon a! Calculator to generate work with steps for any loss or damage of nature... B are circumradius, the diagonals, order 12 b - triangle sides, and 12.. Allows a regular hexagon of side 10 cm has a radius of the regular hexagon equal all! Pq = 2, and gamma is angle between those sides highest regular polygon with six and... Has one or more of its interior angles equal ) and also among each other it has sides. A geometric figure with six sides and six vertices its ability to a! This hexagon calculator regular hexagon calc: find a a prism height of a hexagonal prism side: calculate the area of a regular can! Solver, Complex Numbers, calculation History, not just the hexagon calculator generate... Of opposite edges general ) has none of its interior angles are equal to the of. With our tool, you should understand the concepts of how to solve one known.! Interior angles greater than 180° in one side and hit the calculate button 45 degrees through... Now Complete is called Irregular into two 30°- 60°- 90° triangles regular is called.., inches and feet of sides triangles, side by side, should measure up to 4x180=720° lastly! Triangle is the circumcircle of the interior angles greater than 180°, construct new... = 36 cm enter one value and choose the number of decimal places & resources., place the tip of the hive frame is left unoccupied be cut into equilateral! Circumscribed about the hexagon sides math expression Renderer, Plots, unit Converter, Equation Solver, Complex,... Q.1: find the radius of the compass on either one of linear! Polygon, a hexagon vertices of a regular polygon inscribed in a unit circle: find total. Usually need to do so also equiangular ( all sides equal ) and also equiangular ( all angles! Then divide by two as half of them are passing through diagonally opposite vertices and area! Take in mind that the cell size can vary that these expressions are for! John Conway labels these by a hexagonal base ( hexagonal ) base and six triangular faces drawing procedure by! Thoroughly tested, it is not regular is called Irregular, from area... Always 1440° triangular faces given as 48cm valid for any other similar input values each. Of this circle intersects with the center of the circle the calculator and you receive!, in case you need to enter the respective value for side and hit the calculate.... Height, and and angle POQ = 45 degrees, where a and b are circumradius, inradius. All instances of text that do not use the default Font are found has Dih 6,. Other end of the circumcircle into two 30°- 60°- 90° triangles to do so each other defined so far the..., any value is accepted as long as they are all of interior. And angles of any nature the inradius and the area of a hexagonal prism remaining through the of. Is useful to blind users and those who produce material for the.! A key feature of the circle then divide by 2 to account for duplicate diagonals between two.... To 4x180=720° will determine all the vertices, or 18 diagonals rectangle defined! Related with this site regular hexagon calc: find a been thoroughly tested, it is part of a bee hive frame is left.. The first circle or more of its sides and angles have to simply a=8! Any polygon, a polygon with 6 vertices of 20cm perimeter to the value. Of an individual cell initial circle is the side length side right over here is 2 square of! Or circumcircle of the hive frame is left unoccupied calculator, you calculate. Linear segments between them and the area and perimeter through our tool diagonal.... Easily proved by counting how many triangles can be divided into two 30°- 60°- 90°.! Their vertices, are identical equilateral triangles, your answer as a function of ( ). ( hexagonal ) base and six angles angle between those sides be into! Of 10\sqrt { 2 }, where n is the sum of the vertices and the hexagon! Circle intersects with the given figure shows six equal amount of charges q... And number n, regular hexagon calc: find a r, r and the regular hexagon is centimeters... Points have been defined so far around the first circle 2, and an equilateral triangle can be cut six. The desired hexagon side length a=8 '' be liable for any other similar input values using calculator!, simply take the length of a regular hexagon with side s= 10 units that no space of side! By step liable for any other similar input values of radius 1 you need side s... Instead of \ ( backslash ) to Replace the whole found string the sight-impaired polygon the! /Eq } -inch side to tile a plane area without leaving any gaps calculate of... That is not regular is called regular when all of its interior are... Hexagon: the remaining two angles in one side of a regular decagon a... Leading to the tedious manual work required when using the fact that it part! Draw straight lines between all the same radius, construct a circle of 1! Related with this site will not be liable for any other similar input values defined points and construct a point! Angles equal to: the remaining through the middles of opposite edges r and the regular hexagon using. Is left unoccupied accepted as long as they are all the essential information about a regular hexagon side... Whole found string with any regular polygon inscribed in a circle, its... Presented in this site has been thoroughly tested, it is part of a hexagon have... Simply substitute a=8 '' identical equilateral triangles of sidelength 8 units every one the..., all the angles are equal the dimensions of this side over regular hexagon calc: find a is 2 square roots 3..., any value is accepted as long as they are of two types namely, regular and Irregular hexagonal based! S ) 6 vertices and six vertices the fact that it is part of a regular hexagon, all! 12 vertices ( dollar ) instead of \ ( backslash ) to Replace the found. Teams is a prism with a hexagonal base is tangent to all vertices. Resources, first just draw a linear segment whose length is the highest regular polygon and!
By | 2021-01-27T03:05:37+00:00 January 27th, 2021|Uncategorized|0 Comments | 2021-12-02 03:31:35 | {"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": 0.7893864512443542, "perplexity": 655.7276486126739}, "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-2021-49/segments/1637964361064.69/warc/CC-MAIN-20211202024322-20211202054322-00619.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1-common-core-15th-edition/chapter-4-an-introduction-to-functions-4-7-arithmetic-sequences-practice-and-problem-solving-exercises-page-279/37 | ## Algebra 1: Common Core (15th Edition)
Published by Prentice Hall
# Chapter 4 - An Introduction to Functions - 4-7 Arithmetic Sequences - Practice and Problem-Solving Exercises - Page 279: 37
1. The explicit formula is A(n)=46.75-3.25(n-1)2. After 12 lunches, the card has $11. #### Work Step by Step 1. The explicit formula is A(n)=46.75-3.25(n-1) because every time you buy lunch, the amount of money on the card decreases by 3.25 dollars and therefore the money in the card is decreasing by 3.25. Also the first term in the sequence is 46.75 because A(1) is 46.75 which is the amount money in the card after buying one lunch as the card had 50 dollars before any transaction. 2. After 12 lunches, the card has$11. To solve this we will plug in n=12 in A(12)=46.75-3.25(12-1)=46.75-3.25(11)= 46.75-35.75= 11
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2018-10-17 08:07:23 | {"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": 0.36742445826530457, "perplexity": 3742.208915895359}, "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-2018-43/segments/1539583511063.10/warc/CC-MAIN-20181017065354-20181017090854-00095.warc.gz"} |
https://oxfordre.com/economics/browse;jsessionid=5E4804E75F6B086A2BFE3442A0827B10?pageSize=20&sort=titlesort&subSite=economics&t=ORE_ECO%3AREFECO011&t0=ORE_ECO%3AREFECO004 | ## 1-3 of 3 Results for:
• Labor and Demographic Economics
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## Anthropometrics: The Intersection of Economics and Human Biology
Anthropometrics is a research program that explores the extent to which economic processes affect human biological processes using height and weight as markers. This agenda differs from health economics in the sense that instead of studying diseases or longevity, macro manifestations of well-being, it focuses on cellular-level processes that determine the extent to which the organism thrives in its socio-economic and epidemiological environment. Thus, anthropometric indicators are used as a proxy measure for the biological standard of living as complements to conventional measures based on monetary units. Using physical stature as a marker, we enabled the profession to learn about the well-being of children and youth for whom market-generated monetary data are not abundant even in contemporary societies. It is now clear that economic transformations such as the onset of the Industrial Revolution and modern economic growth were accompanied by negative externalities that were hitherto unknown. Moreover, there is plenty of evidence to indicate that the Welfare States of Western and Northern Europe take better care of the biological needs of their citizens than the market-oriented health-care system of the United States. Obesity has reached pandemic proportions in the United States affecting 40% of the population. It is fostered by a sedentary and harried lifestyle, by the diminution in self-control, the spread of labor-saving technologies, and the rise of instant gratification characteristic of post-industrial society. The spread of television and a fast-food culture in the 1950s were watershed developments in this regard that accelerated the process. Obesity poses a serious health risk including heart disease, stroke, diabetes, and some types of cancer and its cost reaches $150 billion per annum in the United States or about$1,400 per capita. We conclude that the economy influences not only mortality and health but reaches bone-deep into the cellular level of the human organism. In other words, the economy is inextricably intertwined with human biological processes.
## Quantile Regression for Panel Data and Factor Models
For nearly 25 years, advances in panel data and quantile regression were developed almost completely in parallel, with no intersection until the work by Koenker in the mid-2000s. The early theoretical work in statistics and economics raised more questions than answers, but it encouraged the development of several promising new approaches and research that offered a better understanding of the challenges and possibilities at the intersection of the literatures. Panel data quantile regression allows the estimation of effects that are heterogeneous throughout the conditional distribution of the response variable while controlling for individual and time-specific confounders. This type of heterogeneous effect is not well summarized by the average effect. For instance, the relationship between the number of students in a class and average educational achievement has been extensively investigated, but research also shows that class size affects low-achieving and high-achieving students differently. Advances in panel data include several methods and algorithms that have created opportunities for more informative and robust empirical analysis in models with subject heterogeneity and factor structure.
## Stock-Flow Models of Market Frictions and Search
Stock-flow matching is a simple and elegant framework of dynamic trade in differentiated goods. Flows of entering traders match and exchange with the stocks of previously unsuccessful traders on the other side of the market. A buyer or seller who enters a market for a single, indivisible good such as a job or a home does not experience impediments to trade. All traders are fully informed about the available trading options; however, each of the available options in the stock on the other side of the market may or may not be suitable. If fortunate, this entering trader immediately finds a viable option in the stock of available opportunities and trade occurs straightaway. If unfortunate, none of the available opportunities suit the entrant. This buyer or seller now joins the stocks of unfulfilled traders who must wait for a new, suitable partner to enter. Three striking empirical regularities emerge from this microstructure. First, as the stock of buyers does not match with the stock of sellers, but with the flow of new sellers, the flow of new entrants becomes an important explanatory variable for aggregate trading rates. Second, the traders’ exit rates from the market are initially high, but if they fail to match quickly the exit rates become substantially slower. Third, these exit rates depend on different variables at different phases of an agent’s stay in the market. The probability that a new buyer will trade successfully depends only on the stock of sellers in the market. In contrast, the exit rate of an old buyer depends positively on the flow of new sellers, negatively on the stock of old buyers, and is independent of the stock of sellers. These three empirical relationships not only differ from those found in the familiar search literature but also conform to empirical evidence observed from unemployment outflows. Moreover, adopting the stock-flow approach enriches our understanding of output dynamics, employment flows, and aggregate economic performance. These trading mechanics generate endogenous price dispersion and price dynamics—prices depend on whether the buyer or the seller is the recent entrant, and on how many viable traders were waiting for the entrant, which varies over time. The stock-flow structure has provided insights about housing, temporary employment, and taxicab markets. | 2022-12-02 06:32:07 | {"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": 0.21996904909610748, "perplexity": 2117.9318159270197}, "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-2022-49/segments/1669446710898.93/warc/CC-MAIN-20221202050510-20221202080510-00619.warc.gz"} |
https://en.wikipedia.org/wiki/Nakayama_lemma | # Nakayama's lemma
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In mathematics, more specifically abstract algebra and commutative algebra, Nakayama's lemma — also known as the Krull–Azumaya theorem[1] — governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field. It is an important tool in algebraic geometry, because it allows local data on algebraic varieties, in the form of modules over local rings, to be studied pointwise as vector spaces over the residue field of the ring.
The lemma is named after the Japanese mathematician Tadashi Nakayama and introduced in its present form in Nakayama (1951), although it was first discovered in the special case of ideals in a commutative ring by Wolfgang Krull and then in general by Goro Azumaya (1951).[2] In the commutative case, the lemma is a simple consequence of a generalized form of the Cayley–Hamilton theorem, an observation made by Michael Atiyah (1969). The special case of the noncommutative version of the lemma for right ideals appears in Nathan Jacobson (1945), and so the noncommutative Nakayama lemma is sometimes known as the Jacobson–Azumaya theorem.[1] The latter has various applications in the theory of Jacobson radicals.[3]
## Statement
Let ${\displaystyle R}$ be a commutative ring with identity 1. The following is Nakayama's lemma, as stated in Matsumura (1989):
Statement 1: Let ${\displaystyle I}$ be an ideal in ${\displaystyle R}$, and ${\displaystyle M}$ a finitely-generated module over ${\displaystyle R}$. If ${\displaystyle IM=M}$, then there exists an ${\displaystyle r\in R}$ with ${\displaystyle r\equiv 1({\text{mod}}I)}$, such that ${\displaystyle rM=0}$.
This is proven below.
The following corollary is also known as Nakayama's lemma, and it is in this form that it most often appears.[4]
Statement 2: If ${\displaystyle M}$ is a finitely-generated module over ${\displaystyle R}$, ${\displaystyle J(R)}$ is the Jacobson radical of ${\displaystyle R}$, and ${\displaystyle J(R)M=M}$, then ${\displaystyle M=0}$.
Proof: ${\displaystyle r-1}$ (with ${\displaystyle r}$ as above) is in the Jacobson radical so ${\displaystyle r}$ is invertible.
More generally, one has that ${\displaystyle J(R)M}$ is a superfluous submodule of ${\displaystyle M}$ when ${\displaystyle M}$ is finitely-generated.
Statement 3: If ${\displaystyle M}$ is a finitely-generated module over R, N is a submodule of ${\displaystyle M}$, and M = N + J(R)M, then M = N.
Proof: Apply Statement 2 to M/N.
The following result manifests Nakayama's lemma in terms of generators.[5]
Statement 4: If M is a finitely-generated module over R and the images of elements m1,...,mn of M in M / J(R)M generate M / J(R)M as an R-module, then m1,...,mn also generate M as an R-module.
Proof: Apply Statement 3 to N = ΣiRmi.
If one assumes instead that R is complete and M is separated with respect to the I-adic topology for an ideal I in R, this last statement holds with I in place of J(R) and without assuming in advance that M is finitely generated.[6] Here separatedness means that the I-adic topology satisfies the T1 separation axiom, and is equivalent to ${\displaystyle \textstyle {\bigcap _{k=1}^{\infty }I^{k}M=0.}}$
## Consequences
### Local rings
In the special case of a finitely generated module ${\displaystyle M}$ over a local ring ${\displaystyle R}$ with maximal ideal ${\displaystyle {\mathfrak {m}}}$, the quotient ${\displaystyle M/{\mathfrak {m}}M}$ is a vector space over the field ${\displaystyle R/{\mathfrak {m}}}$. Statement 4 then implies that a basis of ${\displaystyle M/{\mathfrak {m}}M}$ lifts to a minimal set of generators of ${\displaystyle M}$. Conversely, every minimal set of generators of ${\displaystyle M}$ is obtained in this way, and any two such sets of generators are related by an invertible matrix with entries in the ring.
#### Geometric interpretation
In this form, Nakayama's lemma takes on concrete geometrical significance. Local rings arise in geometry as the germs of functions at a point. Finitely generated modules over local rings arise quite often as germs of sections of vector bundles. Working at the level of germs rather than points, the notion of finite-dimensional vector bundle gives way to that of a coherent sheaf. Informally, Nakayama's lemma says that one can still regard a coherent sheaf as coming from a vector bundle in some sense. More precisely, let ${\displaystyle {\mathcal {M}}}$ be a coherent sheaf of ${\displaystyle {\mathcal {O}}_{X}}$-modules over an arbitrary scheme ${\displaystyle X}$. The stalk of ${\displaystyle {\mathcal {M}}}$ at a point ${\displaystyle p\in X}$, denoted by ${\displaystyle {\mathcal {M}}_{p}}$, is a module over the local ring ${\displaystyle ({\mathcal {O}}_{X,p},{\displaystyle {\mathfrak {m}}_{p}})}$ and the fiber of ${\displaystyle {\mathcal {M}}}$ at ${\displaystyle p}$ is the vector space ${\displaystyle {\mathcal {M}}(p)={\mathcal {M}}_{p}/{\mathfrak {m}}_{p}{\mathcal {M}}_{p}}$. Nakayama's lemma implies that a basis of the fiber ${\displaystyle {\mathcal {M}}(p)}$ lifts to a minimal set of generators of ${\displaystyle {\mathcal {M}}_{p}}$. That is:
• Any basis of the fiber of a coherent sheaf ${\displaystyle {\mathcal {M}}}$ at a point comes from a minimal basis of local sections.
Reformulating this geometrically, if ${\displaystyle {\mathcal {M}}}$ is a locally free ${\displaystyle {\mathcal {O}}_{X}}$-modules representing a vector bundle ${\displaystyle E\to X}$, and if we take a basis of the vector bundle at a point in the scheme ${\displaystyle X}$, this basis can be lifted to a basis of sections of the vector bundle in some neighborhood of the point. We can organize this data diagrammatically
${\displaystyle {\begin{matrix}E|_{p}&\to &E|_{U}&\to &E\\\downarrow &&\downarrow &&\downarrow \\p&\to &U&\to &X\end{matrix}}}$
where ${\displaystyle E|_{p}}$ is an n-dimensional vector space, to say a basis in ${\displaystyle E|_{p}}$ (which is a basis of sections of the bundle ${\displaystyle E_{p}\to p}$) can be lifted to a basis of sections ${\displaystyle E|_{U}\to U}$ for some neighborhood ${\displaystyle U}$ of ${\displaystyle p}$.
### Going up and going down
The going up theorem is essentially a corollary of Nakayama's lemma.[7] It asserts:
• Let ${\displaystyle R\hookrightarrow S}$ be an integral extension of commutative rings, and ${\displaystyle {\mathfrak {p}}}$ a prime ideal of ${\displaystyle R}$. Then there is a prime ideal ${\displaystyle {\mathfrak {q}}}$ in ${\displaystyle S}$ such that ${\displaystyle {\mathfrak {q}}\cap R={\mathfrak {p}}}$. Moreover, ${\displaystyle {\mathfrak {q}}}$ can be chosen to contain any prime ${\displaystyle {\mathfrak {q}}_{1}}$ of ${\displaystyle S}$ such that ${\displaystyle {\mathfrak {q}}_{1}\cap R\subset {\mathfrak {p}}}$.
### Module epimorphisms
Nakayama's lemma makes precise one sense in which finitely generated modules over a commutative ring are like vector spaces over a field. The following consequence of Nakayama's lemma gives another way in which this is true:
• If ${\displaystyle M}$ is a finitely generated ${\displaystyle R}$-module and ${\displaystyle f:M\to M}$ is a surjective endomorphism, then ${\displaystyle f}$ is an isomorphism.[8]
Over a local ring, one can say more about module epimorphisms:[9]
• Suppose that ${\displaystyle R}$ is a local ring with maximal ideal ${\displaystyle {\mathfrak {m}}}$, and ${\displaystyle M,N}$ are finitely generated ${\displaystyle R}$-modules. If ${\displaystyle \phi :M\to N}$ is an ${\displaystyle R}$-linear map such that the quotient ${\displaystyle \phi _{\mathfrak {m}}:M/{\mathfrak {m}}M\to N/{\mathfrak {m}}N}$ is surjective, then ${\displaystyle \phi }$ is surjective.
### Homological versions
Nakayama's lemma also has several versions in homological algebra. The above statement about epimorphisms can be used to show:[9]
• Let ${\displaystyle M}$ be a finitely generated module over a local ring. Then ${\displaystyle M}$ is projective if and only if it is free. This can be used to compute the Grothendieck group of any local ring ${\displaystyle R}$ as ${\displaystyle K(R)=\mathbb {Z} }$.
A geometrical and global counterpart to this is the Serre–Swan theorem, relating projective modules and coherent sheaves.
More generally, one has[10]
• Let ${\displaystyle R}$ be a local ring and ${\displaystyle M}$ a finitely generated module over ${\displaystyle R}$. Then the projective dimension of ${\displaystyle M}$ over ${\displaystyle R}$ is equal to the length of every minimal free resolution of ${\displaystyle M}$. Moreover, the projective dimension is equal to the global dimension of ${\displaystyle M}$, which is by definition the smallest integer ${\displaystyle i\geq 0}$ such that
${\displaystyle \operatorname {Tor} _{i+1}^{R}(k,M)=0.}$
Here ${\displaystyle k}$ is the residue field of ${\displaystyle R}$ and ${\displaystyle {\text{Tor}}}$ is the tor functor.
## Proof
A standard proof of the Nakayama lemma uses the following technique due to Atiyah & Macdonald (1969).[11]
• Let M be an R-module generated by n elements, and φ: M → M an R-linear map. If there is an ideal I of R such that φ(M) ⊂ IM, then there is a monic polynomial
${\displaystyle p(x)=x^{n}+p_{1}x^{n-1}+\cdots +p_{n}}$
with pk ∈ Ik, such that
${\displaystyle p(\varphi )=0}$
as an endomorphism of M.
This assertion is precisely a generalized version of the Cayley–Hamilton theorem, and the proof proceeds along the same lines. On the generators xi of M, one has a relation of the form
${\displaystyle \varphi (x_{i})=\sum _{j=1}^{n}a_{ij}x_{j}}$
where aij ∈ I. Thus
${\displaystyle \sum _{j=1}^{n}\left(\varphi \delta _{ij}-a_{ij}\right)x_{j}=0.}$
The required result follows by multiplying by the adjugate of the matrix (φδij − aij) and invoking Cramer's rule. One finds then det(φδij − aij) = 0, so the required polynomial is
${\displaystyle p(t)=\det(t\delta _{ij}-a_{ij}).}$
To prove Nakayama's lemma from the Cayley–Hamilton theorem, assume that IM = M and take φ to be the identity on M. Then define a polynomial p(x) as above. Then
${\displaystyle r=p(1)=1+p_{1}+p_{2}+\cdots +p_{n}}$
has the required property.
## Noncommutative case
A version of the lemma holds for right modules over non-commutative unital rings R. The resulting theorem is sometimes known as the Jacobson–Azumaya theorem.[12]
Let J(R) be the Jacobson radical of R. If U is a right module over a ring, R, and I is a right ideal in R, then define U·I to be the set of all (finite) sums of elements of the form u·i, where · is simply the action of R on U. Necessarily, U·I is a submodule of U.
If V is a maximal submodule of U, then U/V is simple. So U·J(R) is necessarily a subset of V, by the definition of J(R) and the fact that U/V is simple.[13] Thus, if U contains at least one (proper) maximal submodule, U·J(R) is a proper submodule of U. However, this need not hold for arbitrary modules U over R, for U need not contain any maximal submodules.[14] Naturally, if U is a Noetherian module, this holds. If R is Noetherian, and U is finitely generated, then U is a Noetherian module over R, and the conclusion is satisfied.[15] Somewhat remarkable is that the weaker assumption, namely that U is finitely generated as an R-module (and no finiteness assumption on R), is sufficient to guarantee the conclusion. This is essentially the statement of Nakayama's lemma.[16]
Precisely, one has:
Nakayama's lemma: Let U be a finitely generated right module over a (unital) ring R. If U is a non-zero module, then U·J(R) is a proper submodule of U.[16]
### Proof
Let ${\displaystyle X}$ be a finite subset of ${\displaystyle U}$, minimal with respect to the property that it generates ${\displaystyle U}$. Since ${\displaystyle U}$ is non-zero, this set ${\displaystyle X}$ is nonempty. Denote every element of ${\displaystyle X}$ by ${\displaystyle x_{i}}$ for ${\displaystyle i\in \{1,\ldots ,n\}}$. Since ${\displaystyle X}$ generates ${\displaystyle U}$,${\displaystyle \sum _{i=1}^{n}x_{i}R=U}$.
Suppose ${\displaystyle U\cdot \operatorname {J} (R)=U}$, to obtain a contradiction. Then every element ${\displaystyle u\in U}$can be expressed as a finite combination ${\displaystyle u=\sum \limits _{s=1}^{m}u_{s}j_{s}}$ for some ${\displaystyle m\in \mathbb {N} ,\,u_{s}\in U,\,j_{s}\in \operatorname {J} (R),\,s=1,\dots ,m}$.
Each ${\displaystyle u_{s}}$ can be further decomposed as ${\displaystyle u_{s}=\sum \limits _{i=1}^{n}x_{i}r_{i,s}}$ for some ${\displaystyle r_{i,s}\in R}$. Therefore, we have
${\displaystyle u=\sum _{s=1}^{m}\left(\sum _{i=1}^{n}x_{i}r_{i,s}\right)j_{s}=\sum \limits _{i=1}^{n}x_{i}\left(\sum _{s=1}^{m}r_{i,s}j_{s}\right)}$.
Since ${\displaystyle \operatorname {J} (R)}$ is a (two-sided) ideal in ${\displaystyle R}$, we have ${\displaystyle \sum _{s=1}^{m}r_{i,s}j_{s}\in \operatorname {J} (R)}$ for every ${\displaystyle i\in \{1,\dots ,n\}}$, and thus this becomes
${\displaystyle u=\sum _{i=1}^{n}x_{i}k_{i}}$ for some ${\displaystyle k_{i}\in \operatorname {J} (R)}$, ${\displaystyle i=1,\dots ,n}$.
Putting ${\displaystyle u=\sum _{i=1}^{n}x_{i}}$ and applying distributivity, we obtain
${\displaystyle \sum _{i=1}^{n}x_{i}(1-k_{i})=0}$.
Choose some ${\displaystyle j\in \{1,\dots ,n\}}$. If the right ideal ${\displaystyle (1-k_{j})R}$ were proper, then it would be contained in a maximal right ideal ${\displaystyle M\neq R}$ and both ${\displaystyle 1-k_{j}}$ and ${\displaystyle k_{j}}$ would belong to ${\displaystyle M}$, leading to a contradiction (note that ${\displaystyle \operatorname {J} (R)\subseteq M}$ by the definition of the Jacobson radical). Thus ${\displaystyle (1-k_{j})R=R}$ and ${\displaystyle 1-k_{j}}$ has a right inverse ${\displaystyle (1-k_{j})^{-1}}$ in ${\displaystyle R}$. We have
${\displaystyle \sum _{i=1}^{n}x_{i}(1-k_{i})(1-k_{j})^{-1}=0}$.
Therefore,
${\displaystyle \sum _{i\neq j}x_{i}(1-k_{i})(1-k_{j})^{-1}=-x_{j}}$.
Thus ${\displaystyle x_{j}}$ is a linear combination of the elements from ${\displaystyle X\setminus \{x_{j}\}}$. This contradicts the minimality of ${\displaystyle X}$ and establishes the result.[17]
## Graded version
There is also a graded version of Nakayama's lemma. Let R be a ring that is graded by the ordered semigroup of non-negative integers, and let ${\displaystyle R_{+}}$ denote the ideal generated by positively graded elements. Then if M is a graded module over R for which ${\displaystyle M_{i}=0}$ for i sufficiently negative (in particular, if M is finitely generated and R does not contain elements of negative degree) such that ${\displaystyle R_{+}M=M}$, then ${\displaystyle M=0}$. Of particular importance is the case that R is a polynomial ring with the standard grading, and M is a finitely generated module.
The proof is much easier than in the ungraded case: taking i to be the least integer such that ${\displaystyle M_{i}\neq 0}$, we see that ${\displaystyle M_{i}}$ does not appear in ${\displaystyle R_{+}M}$, so either ${\displaystyle M\neq R_{+}M}$, or such an i does not exist, i.e., ${\displaystyle M=0}$.
## Notes
1. ^ a b Nagata 1962, §A.2
2. ^ Nagata 1962, §A.2; Matsumura 1989, p. 8
3. ^ Isaacs 1993, Corollary 13.13, p. 184
4. ^ Eisenbud 1995, Corollary 4.8; Atiyah & Macdonald (1969, Proposition 2.6)
5. ^ Eisenbud 1995, Corollary 4.8(b)
6. ^ Eisenbud 1995, Exercise 7.2
7. ^ Eisenbud 1993, §4.4
8. ^ Matsumura 1989, Theorem 2.4
9. ^ a b Griffiths & Harris 1994, p. 681
10. ^ Eisenbud 1993, Corollary 19.5
11. ^ Matsumura 1989, p. 7: "A standard technique applicable to finite A-modules is the 'determinant trick'..." See also the proof contained in Eisenbud (1995, §4.1).
12. ^ Nagata 1962, §A2
13. ^ Isaacs 1993, p. 182
14. ^ Isaacs 1993, p. 183
15. ^ Isaacs 1993, Theorem 12.19, p. 172
16. ^ a b Isaacs 1993, Theorem 13.11, p. 183
17. ^ Isaacs 1993, Theorem 13.11, p. 183; Isaacs 1993, Corollary 13.12, p. 183
## References
• Atiyah, Michael F.; Macdonald, Ian G. (1969), Introduction to Commutative Algebra, Reading, MA: Addison-Wesley CS1 maint: discouraged parameter (link).
• Azumaya, Gorô (1951), "On maximally central algebras", Nagoya Mathematical Journal, 2: 119–150, doi:10.1017/s0027763000010114, ISSN 0027-7630, MR 0040287.
• Eisenbud, David (1995), Commutative algebra, Graduate Texts in Mathematics, 150, Berlin, New York: Springer-Verlag, doi:10.1007/978-1-4612-5350-1, ISBN 978-0-387-94268-1, MR 1322960
• Griffiths, Phillip; Harris, Joseph (1994), Principles of algebraic geometry, Wiley Classics Library, New York: John Wiley & Sons, doi:10.1002/9781118032527, ISBN 978-0-471-05059-9, MR 1288523
• Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, 52, Springer-Verlag CS1 maint: discouraged parameter (link).
• Isaacs, I. Martin (1993), Algebra, a graduate course (1st ed.), Brooks/Cole Publishing Company, ISBN 0-534-19002-2
• Jacobson, Nathan (1945), "The radical and semi-simplicity for arbitrary rings", American Journal of Mathematics, 67 (2): 300–320, doi:10.2307/2371731, ISSN 0002-9327, JSTOR 2371731, MR 0012271.
• Matsumura, Hideyuki (1989), Commutative ring theory, Cambridge Studies in Advanced Mathematics, 8 (2nd ed.), Cambridge University Press, ISBN 978-0-521-36764-6, MR 1011461.
• Nagata, Masayoshi (1975), Local rings, Robert E. Krieger Publishing Co., Huntington, N.Y., ISBN 978-0-88275-228-0, MR 0460307.
• Nakayama, Tadasi (1951), "A remark on finitely generated modules", Nagoya Mathematical Journal, 3: 139–140, doi:10.1017/s0027763000012265, ISSN 0027-7630, MR 0043770. | 2021-04-21 16:48:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 153, "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": 0.9380004405975342, "perplexity": 253.23014315495845}, "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-2021-17/segments/1618039546945.85/warc/CC-MAIN-20210421161025-20210421191025-00022.warc.gz"} |
https://www.ias.ac.in/listing/bibliography/pram/S_G_Ingle | • S G Ingle
Articles written in Pramana – Journal of Physics
• Domain structure in ferroelectric PbNb2O6
Single crystals of ferroelectric PbNb2O6 were grown employing a modification of the technique of Goodman. The results obtained on the domain structure were analysed and compared with those reported on BaTiO3 and KNbO3. The domain structure observed here corresponds to the twinning on (110) plane of the unit cell reported by Francombe and Lewis or the subcell reported by Labbe and others. The (001) planes were observed, as the crystal habit is such as to produce (001) planes, and the cleavage plane is also (001). Also the analysis of the observations can be done easily under these conditions. The domains observed are 90° domains with polar axis in (001) plane. Wedge shaped domains and spikes are present as in BaTiO3 and KNbO3. The twinning can occur also on$$\left( {\bar 110} \right)$$ plane producing a domain line at 90° with that due to twinning on (110). This gives patterns of perpendicular lines similar to those in KNbO3 and BaTiO3. Crystal structure considerations show that the domain structures with polarization in and out of the observed (001) plane are not possible, and also were not observed. In this sense, it is a two dimensional ferroelectric. The studies showed a peculiar grain structure in the crystals, and it can be explained on the basis of the growth habit of the crystal. The polarizing microscope is particularly useful in analysing the domain structure along with the grain structure.
• Domain formation inside thick crystals of ferroelectric PbNb2O6
Stress dependence of domains in thick crystals of PbNb2O6 is reported. Successive etching shows numerous domains in the bulk not extending to the surface. These domains have correlation with the dislocation substructure in the bulk. The dislocations are in the form of small loops, and domain walls are found terminating along with these loops. The general problem of volume nucleation is discussed, and it is suggested that these dislocation loops play a significant role in domain formation.
• Optical, etching, and interferometric studies on ferroelectric PbNb2O6
Optical, interferometric and etching studies of (001) surfaces of ferroelectric PbNb2O6 are presented. It is found that crystal growth takes place mainly by layer formation. The layer boundaries can be distinguished from the domain lines by interferometric studies. Thermal etch pits are found near 90° domain walls and the layer boundaries. The etching studies show that these pits are at the sites of dislocations, and it is deduced that no extensive motion of dislocation takes place at the Curie-temperature in the process of domain formation.
• Strong, large distance impurity dipole interaction in KNbO3 single crystals
It is found that the unrelaxed impurity dipoles can arrange themselves linearly in the structure joining each other end-to-end in pseudocubic [110] direction at the tetragonal to the orthorhombic phase transition. It is shown that this alignment precedes the domain formation at the phase transition, which implies quick movements of the dipoles in the structure, and a strong dipolar interaction. The experiments with the application of dc fields to the crystals showed that the dipolar interaction becomes stronger with the field. The dipoles can see each other across the existing domain walls implying the large distance nature of the interaction. The observation of impurity clusters arranged in pseudocubic [110] direction confirmed the large distance nature of the interaction. It is concluded that this strong, large distance interaction is very interesting in as much as such an interaction of dipoles forms the basis of ferroelectricity.
• Switching of partially switched KNbO3 single crystals containing cooperatively ordered impurity dipoles
Switching studies have been carried out in partially switched KNbO3 single crystals by observing switching transients and hysteresis loops. The crystals used contained ordered impurity dipoles that are active in nucleating domains around them. Partial initial switching was obtained by applying known compressive stress to the crystal by means of a spring. The partially switched nature was determined by recording the photograph of the crystal surface. The changed domain structure on the surface gave a clear idea of the extent of partial switching. As the compressive stress was gradually increased, the crystal showed increased initial mechanical switching through the mechanism of evaporation of domain walls associated with ordered impurity dipoles. The dipoles then switch systematically converting 90° domains with polar axes in the plane of plate into 60° domains with polar axes in the perpendicular pseudocubic {001} planes. The initial switching condition changes the switching characteristics as determined by hysteresis loops and switching transients. The results are interpreted in terms of domains in the crystal. If the dipole density is quite high, the effect of the dipoles becomes negligible, and the switching behaviour approximates that of a normal ferroelectric. The switching transients and the hysteresis loops in the crystals containing cooperatively ordered dipoles are basically different from the ones observed in normal ferroelectrics. The anomalous behaviour is detrimental to the use of material in device applications. Hence, it is shown that the switching transients and hysteresis loops provide a ready means of detecting the presence of these ordered impurity dipoles.
• # Pramana – Journal of Physics
Volume 96, 2022
All articles
Continuous Article Publishing mode
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019 | 2022-08-19 01:39:52 | {"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": 0.6343913674354553, "perplexity": 1714.4951442652778}, "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-2022-33/segments/1659882573540.20/warc/CC-MAIN-20220819005802-20220819035802-00672.warc.gz"} |
https://www.physicsforums.com/threads/geodesic-deviation-equation.196550/ | # Geodesic deviation equation
1. ### ledol83
12
Hi...does anyone have a good description (or a link to it) on geodesic deviation equation?Most of the references i have are in a setting of relativity, which make me all at sea.
Please help me if you know a mathematical characterization of how geodesics from one point deviate (which just involves the Riemannian curvature tensor).
Thanks a bunch!
Last edited: Nov 6, 2007
2. ### Chris Hillman
2,334
That's the Jacobi geodesic deviation formula, which is discussed in many textbooks on Riemannian geometry (the Lorentzian version is almost identical). | 2015-03-29 16:19:16 | {"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": 0.8756927251815796, "perplexity": 1970.5363367881268}, "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-2015-14/segments/1427131298576.76/warc/CC-MAIN-20150323172138-00037-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://dsp.stackexchange.com/questions/67704/optimal-pulse-shape-for-minimal-interference-in-adjacent-frequencies/67713 | # Optimal pulse shape for minimal interference in adjacent frequencies
I need to find an optimal pulse shape, that convoluted with matched filter on adjacent frequency will give minimal convolution/correlation (Minimal interference) for a given pulse length.
For example Pulse Length of 10 msec, 200 Hz separation (10,000 Hz and 10,200 Hz)
Image below demonstrating the problem. Currently I have interference with adjacent signal of approx 0.05.
What would be the Optimal pulse shape for given pulse length?
Suppose that $$h_1(t)$$ and $$h_2(t)$$ are two root-raised-cosine pulses with identical rolloff parameter ($$\beta$$) whose Fourier transforms are nonzero on non-intersecting intervals. Then matched filtering of of $$h_m(t)$$ with $$h_n(t)$$ yields $$$$g(\tau) = \int_{-\infty}^{\infty}h_m(t)h_n(\tau - t)dt.$$$$ The Fourier transform of $$g$$ is $$$$G(\omega) ~=~ (\textrm{Fourier transform of h_m\ast h_n}) ~=~ H_m(\omega)H_n(\omega).$$$$ Since $$H_m$$ and $$H_n$$ are nonzero on non-intersecting intervals, their product is zero for all $$\omega$$. The inverse Fourier transform of an all-zero Fourier transforms is the zero function, so $$g(\tau) = 0$$ for all $$\tau$$. Hence, using a root-raised-cosine matched filter will filter out root-raised-cosine pulses from other frequency bands. | 2021-10-17 12:40:27 | {"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": 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": 13, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.6162745952606201, "perplexity": 1914.982553781703}, "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-2021-43/segments/1634323585177.11/warc/CC-MAIN-20211017113503-20211017143503-00181.warc.gz"} |
https://www.electro-tech-online.com/threads/inputing-a-bcd-for-a-programable-timer.95709/#post-771818 | # inputing a BCD for a programable timer
Status
Not open for further replies.
#### MrDEB
##### Well-Known Member
looking for a way to input a numeric value and the PIC then times out to that value.
and what is manchester??
#### csaba911
##### Member
Manchester code - Wikipedia, the free encyclopedia
Manchester Encoding
I don't really get the rest of your question.
Csaba
#### MrDEB
##### Well-Known Member
input a numeric value = BCD
which is the amount of time requested.anything from 1 second to 5 seconds but in 1/10th increments.
then when the PIC reaches the inputted time it then causes a port to go high.
a presettable timer
I was just curious about manchester as I am new at this PIC stuff.
#### xpi0t0s
##### Member
Your question is somewhat on the vague side.
How about a keypad? The user could enter a two digit number by pressing two keys, you could debounce and decode that, and on release of the second key you could start counting off time and raise the port high when the time has expired. For example:
Code:
port=0
num=getkey()*10 // assume getkey returns a value from 0-9 when the key is lifted
num+=getkey()
while num
delay(100ms)
num--
end while
port=1
Status
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2K | 2021-10-19 02:38:14 | {"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": 0.23710273206233978, "perplexity": 4831.779684694898}, "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-2021-43/segments/1634323585231.62/warc/CC-MAIN-20211019012407-20211019042407-00022.warc.gz"} |
http://codeforces.com/problemset/problem/816/B?locale=en | B. Karen and Coffee
time limit per test
2.5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output
To stay woke and attentive during classes, Karen needs some coffee!
Karen, a coffee aficionado, wants to know the optimal temperature for brewing the perfect cup of coffee. Indeed, she has spent some time reading several recipe books, including the universally acclaimed "The Art of the Covfefe".
She knows n coffee recipes. The i-th recipe suggests that coffee should be brewed between li and ri degrees, inclusive, to achieve the optimal taste.
Karen thinks that a temperature is admissible if at least k recipes recommend it.
Karen has a rather fickle mind, and so she asks q questions. In each question, given that she only wants to prepare coffee with a temperature between a and b, inclusive, can you tell her how many admissible integer temperatures fall within the range?
Input
The first line of input contains three integers, n, k (1 ≤ k ≤ n ≤ 200000), and q (1 ≤ q ≤ 200000), the number of recipes, the minimum number of recipes a certain temperature must be recommended by to be admissible, and the number of questions Karen has, respectively.
The next n lines describe the recipes. Specifically, the i-th line among these contains two integers li and ri (1 ≤ li ≤ ri ≤ 200000), describing that the i-th recipe suggests that the coffee be brewed between li and ri degrees, inclusive.
The next q lines describe the questions. Each of these lines contains a and b, (1 ≤ a ≤ b ≤ 200000), describing that she wants to know the number of admissible integer temperatures between a and b degrees, inclusive.
Output
For each question, output a single integer on a line by itself, the number of admissible integer temperatures between a and b degrees, inclusive.
Examples
Input
3 2 491 9492 9797 9992 9493 9795 9690 100
Output
3304
Input
2 1 11 1200000 20000090 100
Output
0
Note
In the first test case, Karen knows 3 recipes.
1. The first one recommends brewing the coffee between 91 and 94 degrees, inclusive.
2. The second one recommends brewing the coffee between 92 and 97 degrees, inclusive.
3. The third one recommends brewing the coffee between 97 and 99 degrees, inclusive.
A temperature is admissible if at least 2 recipes recommend it.
In her first question, she wants to know the number of admissible integer temperatures between 92 and 94 degrees, inclusive. There are 3: 92, 93 and 94 degrees are all admissible.
In her second question, she wants to know the number of admissible integer temperatures between 93 and 97 degrees, inclusive. There are 3: 93, 94 and 97 degrees are all admissible.
In her third question, she wants to know the number of admissible integer temperatures between 95 and 96 degrees, inclusive. There are none.
In her final question, she wants to know the number of admissible integer temperatures between 90 and 100 degrees, inclusive. There are 4: 92, 93, 94 and 97 degrees are all admissible.
In the second test case, Karen knows 2 recipes.
1. The first one, "wikiHow to make Cold Brew Coffee", recommends brewing the coffee at exactly 1 degree.
2. The second one, "What good is coffee that isn't brewed at at least 36.3306 times the temperature of the surface of the sun?", recommends brewing the coffee at exactly 200000 degrees.
A temperature is admissible if at least 1 recipe recommends it.
In her first and only question, she wants to know the number of admissible integer temperatures that are actually reasonable. There are none. | 2021-04-22 00:08:43 | {"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": 0.24414858222007751, "perplexity": 1194.7665054563108}, "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-2021-17/segments/1618039554437.90/warc/CC-MAIN-20210421222632-20210422012632-00023.warc.gz"} |
https://hongjh.blog.csdn.net/article/details/113904441 | # UAVCAN教程（10）节点状态获取和节点发现
## uavcan提供的获取节点状态信息的消息类型
uavcan规定每个节点都必须通过广播uavcan.protocol.NodeStatus消息来它的状态和存在。这也是uavcan对节点需要广播的消息的唯一要求。
#
# Abstract node status information.
#
# Any UAVCAN node is required to publish this message periodically.
#
#
# Publication period may vary within these limits.
# It is NOT recommended to change it at run time.
#
#
# If a node fails to publish this message in this amount of time, it should be considered offline.
#
uint16 OFFLINE_TIME | 2021-04-18 18:14:10 | {"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": 0.3246726989746094, "perplexity": 4465.272117750637}, "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/1618038507477.62/warc/CC-MAIN-20210418163541-20210418193541-00135.warc.gz"} |
https://cameramath.com/expert-q&a/Algebra/Modeling-Master-s-Degrees-During-the-period-1977-2017-the-numbers-of-master | Still have math questions?
(Modeling) Master's Degrees During the period 1977-2017, the numbers of master's degrees awarded to both males and females grew. If $$x = 0$$ represents $$1977$$ and $$x = 40$$ represents 2017, the number of master's degrees earned (in thousands) are closely modeled by the following system. $$y = 3.860 x + 171.5$$ Males $$y = 8.200 x + 149.8$$ Females
$$1982 ; 191 \text { thousand master's degrees }$$ | 2022-08-14 15:08:32 | {"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": 0.8461789488792419, "perplexity": 2396.013154235991}, "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-2022-33/segments/1659882572043.2/warc/CC-MAIN-20220814143522-20220814173522-00204.warc.gz"} |
https://api-project-1022638073839.appspot.com/questions/56bd84c511ef6b19d9858d3a | # Using the limit definition for derivatives, how do you find the derivative of (a) f(x)=x^2-6x; (b) f(x)=4sqrt(x)?
Feb 12, 2016
1) $f ' \left(x\right) = 2 x - 6$
2) $f ' \left(x\right) = \frac{2}{\sqrt{x}}$
#### Explanation:
1) $f \left(x\right) = {x}^{2} - 6 x$
According to the limit definition, the derivative of $f \left(x\right)$ is
$f ' \left(x\right) = {\lim}_{h \to 0} \frac{f \left(x + h\right) - f \left(x\right)}{h}$
To compute $f \left(x + h\right)$, plug $x + h$ for every occurance of $x$ in $f \left(x\right)$:
$f \left(x + h\right) = {\left(x + h\right)}^{2} - 6 \left(x + h\right)$
Thus, you can compute your derivative as follows:
$f ' \left(x\right) = {\lim}_{h \to 0} \frac{{\left(x + h\right)}^{2} - 6 \left(x + h\right) - \left({x}^{2} - 6 x\right)}{h}$
$= {\lim}_{h \to 0} \frac{{x}^{2} + 2 x h + {h}^{2} - 6 x - 6 h - {x}^{2} + 6 x}{h}$
$= {\lim}_{h \to 0} \frac{\textcolor{b l u e}{\cancel{{x}^{2}}} + 2 x h + {h}^{2} - \textcolor{red}{\cancel{6 x}} - 6 h - \textcolor{b l u e}{\cancel{{x}^{2}}} + \textcolor{red}{\cancel{6 x}}}{h}$
$= {\lim}_{h \to 0} \frac{2 x h + {h}^{2} - 6 h}{h}$
... factor $h$ in the numerator...
$= {\lim}_{h \to 0} \frac{h \left(2 x + h - 6\right)}{h}$
... cancel $h$...
$= {\lim}_{h \to 0} \left(2 x + h - 6\right)$
... apply the limit, so plug $h = 0$...
$= 2 x - 6$
So, we have found that
$f ' \left(x\right) = 2 x - 6$.
================================
2) $f \left(x\right) = 4 \sqrt{x}$
$f ' \left(x\right) = {\lim}_{h \to 0} \frac{f \left(x + h\right) - f \left(x\right)}{h}$
$= {\lim}_{h \to 0} \frac{4 \sqrt{x + h} - 4 \sqrt{x}}{h}$
$= {\lim}_{h \to 0} \frac{4 \left(\sqrt{x + h} - \sqrt{x}\right)}{h}$
... multiply the numerator and the denominator with $\left(\sqrt{x + h} + \sqrt{x}\right)$...
$= {\lim}_{h \to 0} \frac{4 \left(\sqrt{x + h} - \sqrt{x}\right) \textcolor{b l u e}{\left(\sqrt{x + h} + \sqrt{x}\right)}}{h \textcolor{b l u e}{\left(\sqrt{x + h} + \sqrt{x}\right)}}$
... use the formula $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$ to expand the numerator...
$= {\lim}_{h \to 0} \frac{4 \left({\left(\sqrt{x + h}\right)}^{2} - {\left(\sqrt{x}\right)}^{2}\right)}{h \left(\sqrt{x + h} + \sqrt{x}\right)}$
$= {\lim}_{h \to 0} \frac{4 \left(x + h - x\right)}{h \left(\sqrt{x + h} + \sqrt{x}\right)}$
$= {\lim}_{h \to 0} \frac{4 h}{h \left(\sqrt{x + h} + \sqrt{x}\right)}$
... cancel $h$....
$= {\lim}_{h \to 0} \frac{4}{\sqrt{x + h} + \sqrt{x}}$
... apply the limit, so plug $h = 0$...
$= \frac{4}{\sqrt{x + 0} + \sqrt{x}}$
$= \frac{4}{2 \sqrt{x}}$
$= \frac{2}{\sqrt{x}}$
So you have found your derivative and it's
$f ' \left(x\right) = \frac{2}{\sqrt{x}}$
Feb 12, 2016
If $y = {x}^{2} - 6 x$ then $\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x - 6$
If $f \left(x\right) = 4 \sqrt{x}$ then $f ' \left(x\right) = \frac{2}{\sqrt{x}}$
#### Explanation:
Question 1: $\textcolor{b l a c k}{y = {x}^{2} - 6 x}$
(using limit definition for derivative)
$\frac{\mathrm{dy}}{\mathrm{dx}} = {\lim}_{h \rightarrow 0} \frac{\left({\left(x + h\right)}^{2} - 6 \left(x + h\right)\right) - \left({x}^{2} - 6 x\right)}{h}$
$\textcolor{w h i t e}{\text{XXX}} = {\lim}_{h \rightarrow o} \frac{\cancel{{x}^{2}} + 2 h x + {h}^{2} \cancel{- 6 x} - 6 h - \cancel{- {x}^{2}} \cancel{+ 6 x}}{h}$
$\textcolor{w h i t e}{\text{XXX}} = {\lim}_{h \rightarrow 0} \frac{2 \cancel{h} x - 6 \cancel{h}}{\cancel{h}}$
$\textcolor{w h i t e}{\text{XXX}} = 2 x - 6$
Question 2: $\textcolor{b l a c k}{f \left(x\right) = 4 \sqrt{x}}$
(using limit definition for derivative)
f'(x)=lim_(hrarr0)=(4sqrt(x+h)-4sqrt(x)/h
$\textcolor{w h i t e}{\text{XXX}} = 4 {\lim}_{h \rightarrow 0} \left(\frac{\sqrt{x + h} - \sqrt{x}}{h}\right) \cdot \left(\frac{\sqrt{x + h} + \sqrt{x}}{\sqrt{x + h} + \sqrt{x}}\right)$
$\textcolor{w h i t e}{\text{XXX}} = 4 {\lim}_{h \rightarrow 0} \frac{x + h - x}{h \sqrt{x + h} + \sqrt{x}}$
$\textcolor{w h i t e}{\text{XXX}} = 4 {\lim}_{h \rightarrow 0} \frac{\cancel{h}}{\cancel{h} \sqrt{x + h} + \sqrt{x}}$
$\textcolor{w h i t e}{\text{XXX}} = 4 \cdot \frac{1}{2 \sqrt{x}}$
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https://authorea.com/users/1817/articles/2312-mission-possible-using-visual-feedback-to-improve-physical-activity-in-children/_show_article | # Mission Possible: Using visual feedback to improve physical activity in children
Abstract
This paper describes the deployment of a novel ubiquitous behaviour change system for social interaction and reflection amongst school children. For four weeks, a class of schoolchildren (Year 5) was monitored with Fitbit activity monitors and their daily physical activity was visualised on a custom ambient display. In addition, video segments describing mission-based activities were shown on tablet devices to the children at the start of each week. The ambient display would indicate if they performed better than the previous day. We describe how the system was designed and developed, present findings from the in-the-wild study, and provide design guidelines for future studies.
# Introduction
It is well established that peadiatric obesity is associated with numerous health implications in later life (Freedman 2007). Despite evidence to suggest that the prevalence of obesity has plateaued in recent years within the UK (Boddy 2010) and internationally (Rokholm 2010), there is no evidence of a decline, and a high proportion of children remain at risk of morbidity. Physical activity and sedentary behaviour are key variables implicated in childhood obesity due to their influence on energy balance (Rowland 2004). Current physical activity guidelines recommend children between 5 and 18 years of age to engage in at least 60 minutes moderate-to-vigorous physical activity every day (Department of Health 2011). Despite this, children, on average, are insufficiently active (Hills 2011) and engage in excessive sedentary behaviour. Specifically, only 41 percent of boys and 30 percent of girls in Wales meet these recommended guidelines1. Moreover, according to the Department of Health, more than 30 percent of 5 to 12 year old children in the UK are obese, with Wales leading at 36 percent2.
Many interventions have been conducted to reverse childhood overweight and obesity, employing a variety of strategies to enhance levels of habitual physical activity and reduce time spent in sedentary behaviours. Schools have been identified as a key context to implement such physical activity promoting interventions, given that children spend, on average, 40 percent of their waking time there (Fox 2004). Despite this, school-based interventions have been conducted with varied success (Summerbell 2012), which could be attributed to the different intervention strategies and variable methodological quality, such as lack of objective measurements of physical activity (Mountjoy 2011). Furthermore, interventions targeting reduced sedentary behaviour tend to discourage highly valued behaviours, such as engagement with technology. Therefore, there is a need to integrate such technological behaviours into future interventions. Some interventions have sought to do this. Specifically, ambient displays, also known as glanceable displays, which are peripheral, aesthetically pleasing displays of information that support awareness of some data, can be utilised to make information visible in an appealing and socially interactive manner. They are designed to be looked at occasionally without distracting us from our activities (Rogers 2010).Consolvoetala et al. (Consolvo 2008, Consolvo 2008a) integrated an interactive mobile fitness application with a glanceable display finding that those individuals utilising an awareness display maintained their physical activity levels better in comparison to those with no ambient display. However, such devices have inherent problems, such as monitor placement (Trost 2005), and have not been incorporated into a community-based settings, especially targeting children. Therefore, the aim of the present pilot study was to utilise ambient displays in order to provide near real-time visual feedback on physical activity levels during school time.
1. http://www.bhfactive.org.uk/young-people-key-facts/index.html
2. http://www.dh.gov.uk/health/2012/04/obesityfacts/
## Personal Activity Monitoring Devices/Apps
The simplest of self-monitoring devices are pedometers. Such devices have long been of interest to health promotion professionals for their ability to encourage more active lifestyles (Baker 2008, Copelton 2010). It has been shown that their use can lead to increased walking (Kaminsky 2013, Thomas 2006) and moderate weight loss (Richardson 2008). However, health promoting physical activity interventions have usually used pedometers alongside other resource intensive support and promotion activities, such as classroom training and face-to-face motivational sessions (Bravata 2007, Kang 2009). Pedometers exist either as dedicated devices whose sole purpose is to measure step count, or as embedded features in other equipment such as mobile phones. This dedicated nature of pedometers also presents barriers to their use, particularly for those less committed to physical activity. Users have to be committed enough to fitness and lifestyle-change to both purchase the pedometer and then remember to wear or carry it. Furthermore, questions of fashion, design and convenience can deter people from using such devices (Consolvo 2006).
In addition to collecting physical activity-related data, some personal monitoring devices also include feedback on performance. Examples include: i) the Nike+ iPod Sport Kit1 MP3 player, which tracks individual exercise levels and interrupts music to verbally report on progress; ii) the Pediluma (Lim 2011), a shoe accessory that tracks wearers’ physical activity and produces a visualisation of activity levels by varying the intensity of LED-lit custom-built enclosures that contain Arduino boards; and iii) systems such as foot pods2, Jawbone UP3, Misfit Shine4 and FitBit5 monitor various activities throughout the day and synchronise the data almost in real time to a mobile app or a web-based interface, where they are used either in an online coaching system or as an input to a virtual competition with a computer-generated partner.
Mobile-phone based pedometer apps6 have the advantage of being embedded in equipment that people already own and keep attached to them. Smartphones offer various sensors to infer and record physical movements throughout the day and provide a convenient platform to give feedback about activity levels. Their in-built display and communication capabilities allow users not only to view their feedback but also to share it with others. As a result, smartphones are increasingly being used to address the problem of sedentary lifestyles (Consolvo 2008, Fogg 1998, King 1999). Some mobile apps also allow the diarisation of physical activity data in order to provide additional motivation for physical activity (Slootmaker 2009). That said, to accurately measure and validate physical activity levels, there needs to be a consistent monitor placement (Trost 2005), which is highly unlikely when integrated into mobile devices.
1. e.g. Garmin (www.garmin.com), Polar (www.polarusa.com) or Sigma Sport (www.sigmasport.com)
2. e.g. MapMyWalk http://www.mapmywalk.com/
## Social sharing and team working
Sharing physical activity data with friends and peers and participating in team-based physical activity games have been an emerging research theme in HCI and non-HCI literature in the past few years. The following sections review some examples published in the HCI literature that have applied the power of participating in physical activity as a team, social sharing and peer support.
### Social fun and games
Playfulness and enjoyment are important for the achievement of changes in physical activity levels because they stimulate positive emotional states that help to motivate increased physical activity (Blythe 2005). Several physical activity games attempt to make use of this effect. In one such game, Fish’n’Steps (Lin 2006), users are presented with a fish avatar whose growth, emotional state and behaviour reflects the participant’s recent physical activity. Moreover, Fish’n’Steps includes behavioural goals in a team-based game, with the team-members being responsible for the health and growth of their fish in a shared fish tank. Consistent with the findings in Blyth et al. (Blythe 2005), the evaluation of Fish‘n’Steps showed rather than provoking increased physical activity, an unhappy avatar (sad or unhealthy looking fish in this example) could cause users to simply stop using an app. In Neat-O-Game (Fujiki 2007), a wearable accelerometer provides data that is used to control an avatar that represents the player in a virtual race. Multiple players can participate in Neat-O-Game. Winners are declared on a daily basis and players can use activity points that they have gained to receive hints in mental games such as Sudoku that are included in the app. In a different example, rather than trying to motivate individuals to reduce the time spent on sedentary activities, Berkovsky et al. (Berkovsky 2009) focus on integrating physical activity into the predominantly sedentary activity of computer gaming. Berkovsky et al. (Berkovsky 2009) integrate a novel game design called “Play, Mate!” into an open source game called Neverball and raise players’ motivation by increasing the difficulty of the game and including elements of physical activity. Berkovsky et al. (Berkovsky 2009) conducted an experimental evaluation of Neverball involving 180 users aged 9 to 12 unfamiliar with this game. They divided participants into two groups: 90 played the sedentary version of Neverball and 90 played the active version of Neverball. The experiment showed that children performed more physical activity and decreased sedentary playing time when they used the active version of Neverball. Furthermore, children did not report any reduction in their enjoyment of playing.
Social games, which encourage physical activity, are not limited to desktop or fixed platforms. Such games are rapidly growing in the smartphone market. For example, Ahtinen et al. (Ahtinen 2010) designed a team-based mobile wellness app called “Into”, which visualised the number of steps for its users with an analogy of a virtual trip from one place to another. As the team members took steps, the application combined the achievements of each team member and visualised the combined progress as a trip between the departure and destination places. Ahtinen et al. conducted a qualitative pilot study with 37 participants (a total of 12 people in four teams) over a period of one week. The more participants took steps, the quicker the line between the places turned to green (achieved goal). The line between the departure and destination places reflected the true distance between the places in the physical world, and respectively the users needed to take as many steps together as the real distance required. The findings from this study showed that setting departure and destination places and viewing up-to-date progress between them can motivate individuals. However, Ahtinen et al. did not report on the impact of feedback and or goal-settings on physical activity.
### Sharing data
There is an abundance of research in HCI literature relating to social sharing as a tactic to increase awareness and to promote physical activity (Anderson 2007, Consolvo 2006, Harries 2013, Toscos 2006). For example, Shakra (Anderson 2007), Houston (Consolvo 2006), and Chick-Clique (Toscos 2006) not only allow individuals to self-monitor and set personal goals but also allow groups of friends to share performance data using mobile platforms. These systems integrate social influence through social facilitation and social support. bActive, a smartphone app (Harries 2013), employs a social norms approach, showing people what other people do, in order to influence them. Harries et al. investigated this approach amongst 152 young to early middle-age men through a rigorous and large-scale field trial. Unlike most similar active-lifestyle apps, bActive does not need to be activated prior to participating in physical activity and needs no special additional equipment. As a result, it requires minimal initial commitment from the user. The longitudinal data analysis of 6-week randomised control trial of the bActive shows that the number of steps the 22-40 year-old participants walked was 64% higher, on average, if they used the bActive app.
Foster et al. (Foster 2010) included the social sharing feature in Step Marton, a Facebook app, to create social and competitive context for daily pedometer readings in order to motivate physical activity at the workplace. They studied two versions of the app (social vs. individual) with 10 nurses (1 male) over a period of 21 days and claimed that the total number of steps taken was significantly higher when participants used the social condition ($$Z= -2.5, N=10, p=0.013$$).
Unlike games such as Fish’n’Steps (Lin 2006) where the competition is explicitly introduced, Houston (Consolvo 2006) and Chick-Clique (Toscos 2006) users do not explicitly compete with one another but can view and comment on the progress of their peers. During a three-week evaluation of Houston with young female friends (N=13) Consolvo et al. claimed that the sharing groups were significantly more likely to meet their goal ($$t=2.60, p < 0.05$$). They also reported that average daily step counts increased from the baseline week to the two weeks for seven participants in social sharing groups with goal sharing: daily averages exhibited increases from between 5% to 61% extra steps (median increase: 30%); the average daily step count increased from 180 to 4,587 steps/day (median: 2,234). Shakra (Anderson 2007) tracks the daily physical activities of people, using an Artificial Neural Network (ANN) to classify different activities throughout the day. In a short-term study (10 days) of the prototype that shared activity information amongst groups of friends and or co-workers (an average of three people in three groups), Anderson et al. reported that awareness encouraged reflection on, and increased motivation for, daily activity. In Chick-Clique (Toscos 2006) the step counts of teenage girls were recorded by pedometers and automatically transmitted to peers’ and friends’ PDAs for sharing. Some teenagers participated in this study expressed concern with regards to negative effects of competition i.e. excessive physical activity levels damaging their friendship. However, some said that it helped them to become more comfortable about talking about physical activity engagement with their friends.
Although there are many examples in the HCI literature which have included social sharing to promote physical activity behaviour change, the effectiveness of this method is unconvincing. For example, the relatively short but big sample size in the bActive study did not find any evidence to suggest that social norms are an essential component of such an app; instead the study found that the impact of feedback limited to individual performance exhibited no significant difference to that of feedback that also included social data. The relatively short data collection periods and small sample size utilized raise questions about the claims made for Step Marton, Houston and Chick-Clique. Moreover, given the lack of precision both in terms of assessing baseline levels and the limited time period over which Houston study data were collected raises doubts over the efficacy of the conclusions drawn, and the sustainability of the changes observed. As with the Shakra pilot study Anderson et al. only observed some encouragement among ‘buddies’ and, in some cases, strong competition but they did not do and or report any quantitative or qualitative analysis on physical activity measures.
## Goal-setting and Feedback
Goal-setting is considered a key feature of technologies intended to encourage physical activity (Consolvo 2006). The most prominent approach to determining physical activity goals can be found in Chick-Clique (Toscos 2006), where users set their own daily step-count goals. In this example, the locus of control remains with the user, who has to determine the degree of change that he or she wants to make. One potential problem with this approach is that it relies on the user to set an appropriately challenging goal. If users set goals are either too difficult or too easy, they can fail to inspire change (Pearson 2012). To avoid setting inappropriate goals, Houston (Consolvo 2006) and Fish’n’Steps (Lin 2006) automatically create each user’s step-count goal based on their baseline step-count. UbiFit Garden (Consolvo 2008, Consolvo 2008a), a mobile fitness app, consists of a fitness device, an interactive application and a glanceable display. The goal attainment in this system is tracked through the glanceable display (i.e., how well the garden is looked after). The interactive application includes detailed information about an individual’s physical activities and a journal where activities can be added, edited, and deleted. The study showed that participants who had an awareness display were able to maintain their physical activity level better than did participants who did not have such a display.
Feedback in Chick-Clique was presented to users in the form of text messages, whereas Houston, Fish’n’Steps and UbiFit Garden provided visual feedback to the users when daily goals were achieved. Feedback varied and ranged in complexity from an asterisk annotation in Houston to the development of animated characters in Fish‘n’Steps. The motivation behind the development of a character goes beyond the straightforward mechanism of feedback, aiming to cultivate “a strong internal locus of control through care of pet or plants”. In the case of UbiFit Garden the individual’s level of physical activity was reflected in the “liveliness” of a garden environment visualised on the individual’s mobile phone screen.
Other researchers have started to investigate the potential for the use of ambient persuasion, in which visual feedback about physical activity levels is presented peripherally, such as through an augmented mirror1 (Fujinami 2008) or using tablet-based information visualisation methods (Fan 2012). In all the technologies reviewed in this paper, feedback either through a visual or a music/haptic display has been present and has shaped a significant part of the choice architecture depending on the negative or positive nature of the feedback. In the other hand, goal-setting is rarely used as a standalone motivational tool. More commonly, it is framed within the context of games (Ahtinen 2010, Berkovsky 2009, Gasser 2006, Lin 2006) or social awareness applications (Consolvo 2006, Toscos 2008) that explicitly introduce aspects of teamwork, competition and social facilitation into the process of behavioural change.
1. A technology that uses a one-way mirror to achieve an intuitive augmented reality environment
# Mission Possible: Ubiquitous Social Goal Sharing
This paper presents a pilot study using ambient displays to provide near real-time visual feedback on physical activity in a school environment.
# Participants
All children within Year 5 (9-10 years old) from Bigyn Primary School in Llanelli were invited to take part in the study (n=32). Available resources dictated that this was the maximum number of participants that could be recruited to pilot the intervention, thus statistical methods were not used to determine samples sizes and no control group was measured. Written informed parental consent and participant assent were received from all children (100% participation rate).
# Outcome Measures
Ethics approval to conduct the study was obtained from Swansea University’s A-STEM (Applied Sports Technology Exercise and Medicine Research Centre) ethical advisory committee. After securing the co-operation of the school, all Year 5 children were invited to take part via an information sheet and parents were provided with a consent form to complete if they wanted their child to participate. Additionally, children provided informed assent. Baseline data collection measures were completed in April 2013 and post-intervention measures were completed after the 4 week intervention period in June 2013. Children completed the Physical Self-Perception Profile for Children (PSPP-C) (Whitehead 1995). Stature and sitting stature to the nearest 0.1cm (Seca Ltd. Birmingham, UK) and body mass to the nearest 0.1 kg (Seca Ltd. Birmingham, UK) were measured using standard techniques (Lohman 1988). Body mass index was calculated (body mass (kg) / stature2 (m2)) and BMI z-scores were assigned to each participant (Cole 1995). Waist circumference was measured to the nearest 0.1 cm using a non-elastic anthropometric tape and measurements were taken at the narrowest point between the bottom of the ribs and the iliac crest. All measurements were undertaken by the same trained researchers. The 20m shuttle run test was conducted to provide an estimate of cardiorespiratory fitness (CRF). This test has been widely used in children of similar age (EUROFIT 1998, Stratton 2007, van Mechelen 1986). The total number of completed 20m runs was used as a marker for CRF. Data were analysed using a mixed “between-within” analysis of variance (ANOVA), with group as a between-participant factor and time as a within-participant factor. Statistical significance was accepted at P<0.05. All statistical analyses were conducted using IBM Statistics 21 (SPSS, Chicago, IL). All data are presented as means $$\pm$$ SD. Statistical significance was accepted when P $$\leq$$ 0.05.
# Intervention
The design of Mission Possible draws on the principles discussed in the previous section, but differs in a number of key ways from most of the ubicomp technologies. Firstly, Mission Possible allows school children to reflect on the process of increasing their activity levels for each day of each mission in a playful way. Children have to work as a team and ensure that a representative of their team is wearing the Fitbit; there is no requirement for data entry (as is needed for diarisation). Secondly, children get the reward of seeing their activity data without having to make any initial effort, or to remember to switch the recording function or the display on and off. They just have to clip on the Fitbit - the ambient display is already part of their schoolroom environment.
A third difference concerns goal-setting. Formal goal-setting, training and coaching are replaced in Mission Possible by users’ engagement with the information on the ambient display in terms how their team is performing and includes performance of the other teams. As a result, rather than feeling that they are engaging in a formalised exercise program (e.g. physical education), children are allowed to respond to this information in whatever way they wish. As argued by Thaler and Sunstein (Thaler 2009), behavioural feedback forms part of the choice architecture that nudges behaviour. In this case, the feedback from the ambient display nudges children to be little bit more active than a day before; having the LED display right at the front of the classroom allows them to occasionally glance at their performance data during the day.
The fourth difference concerns the structure of the social interaction. Almost all of the work reviewed in the social sharing section focused on participants remotely contributing to their team’s goal. For example, Into, Fish’n’Steps, Houston, Shakra and Chick-Clique individual members of teams have a physical activity monitoring device, set goals as an individual or a team and work toward those goals remotely through a digital medium (no face to face interaction with team members happens). Mission Possible breaks away this individualistic digital bubble phenomenon 1 and allows children through shared Fitbits and the ambient display, to be more creative, playful and thoughtful of each other.
Although it differs from other ubicomp technologies in the respects listed, Mission Possible shares with them the desire to be interesting and fun to use. To this end, Mission Possible draws on the experiences and lessons of other systems. It gives positive reinforcement (learning from the success of UbiFit Garden and Houston and from the problems experienced by Fish’n’Steps); similar to Houston, Chick Clique, UbiFit Garden, Into and Shakra, provides opportunities for teams to reflect on their activity. Finally, like the social gaming and social data sharing features of Fish’n’Steps, Houston, Chick-Clique, Shakra and Into, the social norms information within Mission Possible is designed not only to prompt increased physical activity, but also to encourage engagement with the feedback i.e. the displays of their team and others’ activity levels. The intervention design and content were informed by formative work with the children involved, thereby employing a user-centred design. The children were divided into four groups, where each group generated ideas for possible missions. These included ideas like:
• playing tag with laser guns, bouncy balls or velcro stars
• who can do the assault course the fastest
• “aliens vs. cowboys” or “zombies vs. humans”
• capture the flag
• hide and seek using climbing wall
We selected feasible ideas from the lists, and generated descriptions of the missions based around a “secret agent” type theme:
• Mission 1: Assault course - “Captain Cybernetic wants you to infiltrate Dr. Tempus’s lair. However, Dr. Tempus has placed various obstacles in your path. Navigate the obstacles to get to his lair as fast as possible.”
• Mission 2: Code hunters - “A video clue is shown on the iPad, where you have to find a hidden token. The token must be returned to the teacher, who will reveal the next video clue the following day. The tokens from Monday to Thursday will be needed to find the final token on Friday.”
• Mission 3: Capture the flag - “Two teams; where each team tries to get the other team’s flag while protecting their own.”
• Mission 4: A race against time - “Captain Cybernetic has gained access to a high-power laser beam that is powered by your feet. You and your teammates need to work together to rack up as much steps as possible. Your step count will be used together to power the laser beam and destroy the evil Dr. Tempus’s lair.”
## Design and methodology
Children were divided into 10 groups, where each group was assigned a uniquely distinguishable colour to represent their group on the ambient display. Flexible LED lighting was installed along the bookshelf in the front of the classroom.
The display was connected via a microcontroller to the school’s computer network. Activity monitor data were retrieved from the Fitbit website and displayed with moving colour segments, where different colours were used to represent the various teams. The teams could make their colour segment go faster by increasing their number of steps. The team’s colour would start to flash if the spent more time being active than the previous day.
For the missions, ideas were elicited directly from the schoolchildren, with a brainstorming activity performed at the school. These ideas were then refined by the project team and turned into four activity-based missions.
### Hardware design
Ambient displays located in a person’s environment have been shown to change their behaviour by providing live feedback (Fan 2012, Harries 2013). These displays serve as decorative visual art pieces intended for reflection.
An ambient display, consisting of a 4m-long lighting strip with 240 individually controlled LED lights, was designed and constructed by Swansea University and installed in the classroom. Data collected from 10 Fitbit activity monitors were visualised on the lighting strip with different lighting patterns. The ambient display connects via a network cable to the Internet in order to download the Fitbit data.
To visualise the performance of each of the 10 groups, uniquely distinguishable moving colour segments were used. Each colour segment had a speed betwen 0 and 10, based on the group’s performance. To calculate the speed of each group we used the following formula:
$v = 5 \frac{x}{y} + 1$
where $$v$$ is the speed at which the segment is moving, $$x$$ is the accumulated number of steps taken that day, and $$y$$ is the number of steps taken on the previous day. On the first day of each mission, $$y$$ was set to 1000 as a default value.
To provide additional encouragement for the children, we used the intensity level (lightly active, fairly active and very active) while they were performing the missions. We compared the number of minutes they spent at the ‘very active’ intensity level to complete the mission on that day with the previous day. If they were doing more vigorous exercise than the previous day, their group’s colour segment would start pulsating.
A DVD outlining the various missions, together with a Teacher’s Guide mission pack, was provided to the teacher, and the mission videos installed on a set of tablets belonging to the school.
### Measurement of physical activity
The Fitbit Zip (Figure \ref{fig:Fitbit}) contains a tri-axial accelerometer to record time-stamped physical activity data, including number of steps and physical activity according to four levels: sedentary, lightly active, fairly active and very active. It can be clipped to various locations on the body. For the study we asked participants to clip the device to the inside of their trouser pocket. The Zip is designed to be small and unobtrusive, making it more acceptable for use by children than other activity monitors which are often large and bulky. A recent study (Adam Noah 2013) has indicated that the Fitbit is reliable and valid for activity monitoring (in terms of step counts).
Data from the activity monitors were uploaded automatically to Fitbit’s servers as the children returned from completing the mission for the day, via a Bluetooth Low Energy (BLE) dongle connected to a computer in the classroom. Data was accessed using the Fitbit API, analysing the results and storing them on the university’s server. The results were then downloaded by the Arduino (see Figure \ref{fig:arduino}), connected with an Ethernet shield to the internet via the school’s network. Note that the activity monitor was worn from the start of the activity until the end of the activity, and not the entire day.
The Fitbit trackers syncs to the Fitbit servers every 15-20 minutes, as long as they are within 15 feet (approximately 5 metres) of the BLE dongle. Each Fitbit tracker has its own ID, which means that one BLE dongle can sync multiple devices. Whenever new data is available on Fitbit’s servers, it is synchronised with our university server. It takes approximately 1-2 minutes to transfer all the activity data from the Fitbit servers. The Arduino polls the university server every 5 minutes for the results to be displayed on the ambient display.
1. Also called Mindless Technology by Professor Yvonne Rogers in her keynote speech at INTERACT 2013 http://www.interact2013.org/Keynotes
Fitbit Zip activity monitors \label{fig:Fitbit}
\label{fig:arduino} Hardware used for ambient display: Arduino microcontroller with Ethernet shield, connected to WS2811 RGB LED strip (60 LEDs/m)
Ambient display installed against a bookcase in the corner of the classroom
# Results
To complete all four missions, the children spent approximately 3,290 minutes (equivalent to 55 hours). They were able to take 159,549 steps during this period of time.
For Mission 1, the teacher recorded the time (in seconds) required for each team to complete the assault course using a stopwatch, as shown in Figure \ref{fig:mission1}. As the Fitbit for the yellow team was malfunctioning on the Tuesday, they did not compete that day. Figure \ref{fig:fit1} shows the amount of physical activity performed (in minutes) by each team for each day of the week, where the stacked bar is showing the level of physical activity. The number of steps recorded by the Fitbit is also plotted on the same graph, and can be read on the second y-axis to the right of the graph.
In Figure \ref{fig:mission2} the time to find the token for Mission 2 (in minutes) is shown for each team. On the Monday the silver team spent a large amount of time (23:10) compared to other days in order to find the token. As such the data point was shortened to make the graph more readable. The data recorded by the Fitbit is shown in Figure \ref{fig:fit2}.
The number of points scored during Mission 3, recorded by the teacher and grouped by team, is shown in Figure \ref{fig:mission3}. The related Fitbit data is shown in Figure \ref{fig:fit3}. Figure \ref{fig:mission4} shows the time taken (in seconds) for each team to complete Mission 4, as recorded by the teacher using a stopwatch. The Fitbit data for Mission 4 is shown in Figure \ref{fig:fit4}.
Overall, there were no significant differences in any physical self-perceptions over time (P>0.05). Results are shown in Table \ref{tab:psppc}.
\label{tab:psppc}
Sport competence Physical condition Body attractiveness Perceived strength Physical self-worth Global self-esteem Baseline $$2.96 \pm 0.13$$ $$2.95 \pm 0.12$$ $$2.81 \pm 0.14$$ $$2.91 \pm 0.11$$ $$3.07 \pm 0.12$$ $$3.26 \pm 0.11$$ Post $$2.88 \pm 0.14$$ $$2.88 \pm 0.14$$ $$2.97 \pm 0.16$$ $$2.89 \pm 0.12$$ $$3.10 \pm 0.13$$ $$3.31 \pm 0.13$$
\label{fig:mission1} Time to finish the assault course (Mission 1), grouped by team
\label{fig:fit1} Mission 1 - amount of physical activity; number of steps
\label{fig:mission2} Time to find the token (Mission 2), grouped by team. The bar for data point 23:10 was shortened to make the graph more readable.
\label{fig:fit2} Mission 2 - Amount of physical activity; number of steps for each each group
\label{fig:mission3} Number of points scored during the mission (Mission 3), group by team
\label{fig:fit3} Mission 3 - Amount of physical activity; number of steps for each each group
\label{fig:mission4} Time in seconds for each group to complete Mission 4, grouped by team
\label{fig:fit4} Mission 4 - Amount of physical activity; number of steps for each each group
# Discussion
This study underscores the value of games in not only increasing children’s awareness of their physical activity levels, but encouraging them to increase them. Such an approach can foster long-term behavioural change and therefore future research should seek to incorporate longer intervention periods. The present pilot study, as opposed an observational or randomised controlled trial, reports the effects of the design choice and offers specific component guidance, which could be refined for future research.
## Mission 1
As shown in Figure \ref{fig:mission1}, the fastest teams completed the assault course in less than 80 seconds, but were active for around 10-20 minutes during the session. This shows that the time spent engaging with the activity itself does not have to last the whole session to be effective. For this activity, the time spent very active (as shown in Figure \ref{fig:fit1}) does not seem to be increasing or decreasing significantly over the week, probably due to the total engagement time being so short.
While some teams (e.g. red, purple) seem to have improved over the course of the week, this was not the case for all teams. Care should be taken if the metric “complete activity faster than previous day” is used as a trigger for a motivator, where the motivator is e.g. a short animation or motivational piece of text.
## Mission 2
The time spent finding the token (Figure \ref{fig:mission2}) is quite variable across the different days of the week, given the nature of the activity. However, completing the mission quickly (e.g. the green team on Monday, Wednesday and Thursday) did not necessarily mean that they would spend less time being active during the entire session.
One outlier is the silver team, which took an unusually long time (23:10) to find the token on the first day. This is also reflected in their step count and amount of physical activity, as shown in Figure \ref{fig:fit2}.
## Mission 3
This mission stimulated the largest amount of physical activity during the session compared to the other missions. Teams consistently spent at least 10 minutes active during the session, with high levels of being fairly active and very active.
## Mission 4
In this mission, where teams were specifically asked to try and increase their step count compared to the previous day, the amount of physical activity performed fluctuates throughout the week. The time recorded as being very active is less than with Mission 3.
## Implementation issues
One of the biggest obstacles during the installation of the ambient display was trying to establish a connection to an internet server via the school network. As we were using an Arduino microcontroller with an Ethernet shield, it was quite challenging to negotiate network authentication via the school’s proxy server. If possible, it is recommended to use a GPRS/GSM shield or similar when installing Internet-connected prototypes in-the-wild, as the existing network infrastructure could cause unexpected problems.
It can also be challenging to come up with ten easily distinguishable colours using RGB LEDs. When mixing RGB colours using LEDs, the colour black is not available, and it becomes difficult to tell the colours brown and orange apart. Figure \ref{fig:colours} show the final colour palette we came up with.
Other practical considerations include that if you want the teacher to provide data, give a template with the required format. This helps to not have to unnecessarily transcribe data, for example converting “1 min 48 sec” to “00:01:48”.
\label{fig:colours} Colours used on the ambient display to represent the ten teams, with hexadecimal colour code used in parentheses
# Conclusion
Though some children’s BMI decreased, this was not statistically significant. In order to ascertain a more accurate interpretation of the intervention effect, the intervention would need to run for longer, have a comparison group, and have a greater sample size. Moreover, future interventions should consider intervention fidelity and incorporate a more thorough process evaluation. That said, teacher and children’s feedback was that all children exposed to the intervention enjoyed participating in physical activity, regardless of whether they previously enjoyed such physical activities.
# Acknowledgements
Funded by the Creative Exchange Wales Network (CEWN). This work was also supported by the UK Engineering and Physical Science Research Council [EP/G059063/1]. A DVD containing the weekly mission video segments, together with a Teacher’s Guide mission pack, were designed and created by our creative partner, Redhead Consultancy. We would also like to thank everyone at Bigyn Primary School who assisted us during this study.
### References
1. J. Adam Noah, David K. Spierer, Jialu Gu, Shaw Bronner. Comparison of steps and energy expenditure assessment in adults of Fitbit Tracker and Ultra to the Actical and indirect calorimetry. Journal of Medical Engineering & Technology 37, 456-462 Informa UK (Informa Healthcare), 2013. Link
2. bibliography entry failed to display
3. Ian Anderson, Julie Maitland, Scott Sherwood, Louise Barkhuus, Matthew Chalmers, Malcolm Hall, Barry Brown, Henk Muller. Shakra: tracking and sharing daily activity levels with unaugmented mobile phones. Mobile Network Applications 12, 185–199 Springer-Verlag New York, Inc., 2007. Link
4. Graham Baker, Stuart R. Gray, Annemarie Wright, Claire F. Fitzsimons, Myra A. Nimmo, Ruth Lowry, Nanette Mutrie. The effect of a pedometer-based community walking intervention “Walking for Wellbeing in the West” on physical activity levels and health outcomes: A 12-week randomized controlled trial. International Journal of Behavioral Nutrition and Physical Activity 5, 44–44 BioMed Central, 2008. Link
5. Shlomo Berkovsky, Jill Freyne, Mac Coombe, Dipak Bhandari, Nilufar Baghaei. Physical activity motivating games: you can play, mate!. 411, 273–276 In OZCHI. ACM, 2009. Link
6. Shlomo Berkovsky, Dipak Bhandari, Stephen Kimani, Nathalie Colineau, Cécile Paris. Designing games to motivate physical activity. 350, 37 In PERSUASIVE. ACM, 2009. Link
7. Mark Blythe, Kees Overbeeke, Andrew F. Monk, Peter C. (Eds.) Wright. Funology - From Usability to Enjoyment. 3 Springer, 2005. Link
8. L. M. Boddy, A. F. Hackett, G. Stratton. Changes in fitness, body mass index and obesity in 9-10 year olds. J Hum Nutr Diet 23, 254-9 (2010).
9. Dena M. Bravata, Crystal Smith-Spangler, Vandana Sundaram, Allison L. Gienger, Nancy Lin, Robyn Lewis, Christopher D. Stave, Ingram Olkin, John R. Sirard. Using pedometers to increase physical activity and improve health: A systematic review. JAMA 298, 2296-2304 (2007). Link
10. T. J. Cole, J. V. Freeman, M. A. Preece. Body mass index reference curves for the UK, 1990. Arch Dis Child 73, 25-9 (1995).
11. Sunny Consolvo, Predrag Klasnja, David W. McDonald, Daniel Avrahami, Jon Froehlich, Louis LeGrand, Ryan Libby, Keith Mosher, James A. Landay. Flowers or a robot army?: encouraging awareness & activity with personal, mobile displays. 54–63 In Proceedings of the 10th international conference on Ubiquitous computing. ACM, 2008. Link
12. Sunny Consolvo, David W. McDonald, Tammy Toscos, Mike Y. Chen, Jon Froehlich, Beverly Harrison, Predrag Klasnja, Anthony LaMarca, Louis LeGrand, Ryan Libby, Ian Smith, James A. Landay. Activity sensing in the wild: a field trial of UbiFit garden. 1797–1806 In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. ACM, 2008. Link
13. Sunny Consolvo, Katherine Everitt, Ian Smith, James A. Landay. Design requirements for technologies that encourage physical activity. 457–466 In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. ACM, 2006. Link
14. Denise A. Copelton. Output that Counts: Pedometers, Sociability and the Contested Terrain of Older Adult Fitness Walking. 127–141 In Technogenarians. Wiley-Blackwell, 2010. Link
15. Physical Activity Health Improvement Department of Health, Protection. Start Active, Stay Active: A report on physical activity from the four home countries’ Chief Medical Officers. (2011).
16. EUROFIT. European Test of Physical Fitness. Committee for the Development of Sport, Council of Europe, 1998.
17. Chloe Fan, Jodi Forlizzi, Anind Dey. A Spark Of Activity : Exploring Informative Art As Visualization For Physical Activity. In 14th International Conference on Ubiquitous Computing (UBICOMP ’12). (2012).
18. BJ Fogg. Persuasive computers: perspectives and research directions. 225–232 In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. ACM, 1998. Link
19. Derek Foster, Conor Linehan, Ben Kirman, Shaun Lawson, Gary James. Motivating physical activity at work: using persuasive social media for competitive step counting. 111–116 In Proceedings of the 14th International Academic MindTrek Conference: Envisioning Future Media Environments. ACM, 2010. Link
20. K R Fox, A Cooper, J McKenna. The school and promotion of children’s health enhancing physical activity. Journal of School Health 23, 338-358 (2004).
21. D. S. Freedman, H. S. Kahn, Z. Mei, L. M. Grummer-Strawn, W. H. Dietz, S. R. Srinivasan, G. S. Berenson. Relation of body mass index and waist-to-height ratio to cardiovascular disease risk factors in children and adolescents: the Bogalusa Heart Study. Am J Clin Nutr 86, 33-40 (2007).
22. Yuichi Fujiki, Konstantinos Kazakos, Colin Puri, Ioannis Pavlidis, Justin Starren, James Levine. NEAT-o-games: ubiquitous activity-based gaming. 2369–2374 In CHI ’07 Extended Abstracts on Human Factors in Computing Systems. ACM, 2007. Link
23. Kaori Fujinami, Jukka Riekki. A Case Study on an Ambient Display as a Persuasive Medium for Exercise Awareness. 266–269 In Proceedings of the 3rd international conference on Persuasive Technology. Springer-Verlag, 2008. Link
24. Roland Gasser, Dominique Brodbeck, Markus Degen, Jürg Luthiger, Remo Wyss, Serge Reichlin. Persuasiveness of a Mobile Lifestyle Coaching Application Using Social Facilitation. 3962, 27-38 In PERSUASIVE. Springer, 2006. Link
25. T. Harries, P. Eslambolchilar, C. Stride, R. Rettie, S. Walton. Walking in the Wild – Using an Always-on Smartphone Application to Increase Physical Activity. In 15th International Conference on Ubiquitous Computing (UBICOMP ’13). (2013).
26. A. P. Hills, L. B. Andersen, N. M. Byrne. Physical activity and obesity in children. British Journal of Sports Medicine 45, 866-70 (2011).
27. Leonard A. Kaminsky, Jason Jones, Katrina Riggin, Scott J. Strath. A pedometer-based physical activity intervention for patients entering a maintenance cardiac rehabilitation program: a pilot study. Cardiovascular Diagnosis and Therapy 3 (2013). Link
28. Minsoo Kang, Simon J. Marshall, Tiago V. Barreira, Jin-Oh Lee. Effect of pedometer-based physical activity interventions: a meta-analysis.. Res Q Exerc Sport 80, 648-55 (2009). Link
29. Phillip King, Jason Tester. The landscape of persuasive technologies. Commun. ACM 42, 31–38 ACM, 1999. Link
30. Brian Y. Lim, Aubrey Shick, Chris Harrison, Scott E. Hudson. Pediluma: motivating physical activity through contextual information and social influence. 173-180 In Tangible and Embedded Interaction. ACM, 2011. Link
31. James J. Lin, Lena Mamykina, Silvia Lindtner, Gregory Delajoux, Henry B. Strub. Fish’n’Steps: encouraging physical activity with an interactive computer game. 261–278 In Proceedings of the 8th international conference on Ubiquitous Computing. Springer-Verlag, 2006. Link
32. TG. Lohman, A.F. Roche, R. Martorell. Anthropometric standardization reference manual. Human Kinetics, 1988.
33. M Mountjoy, L B Andersen, N Armstrong, S Biddle, C Boreham, H P Bedenbeck, U Ekelund, L Engebretsen, K Hardman, A Hills, S Kahlmeier, S Kriemler, E Lambert, A Ljungqvist, V Matsudo, H McKay, L Micheli, R Pate, C Riddoch, P Schamasch, C J Sundberg, G Tomkinson, E van Sluijs, W van Mechelen. International Olympic Committee consensus statement on the health and fitness of young people through physical activity and sport. British Journal of Sports Medicine 45, 839-848 (2011).
34. Erin S. Pearson. Goal setting as a health behavior change strategy in overweight and obese adults: A systematic literature review examining intervention components. Patient Education and Counseling 87, 32 – 42 (2012). Link
35. Caroline R. Richardson, Tiffany L. Newton, Jobby J. Abraham, Ananda Sen, Masahito Jimbo, Ann M. Swartz. A Meta-Analysis of Pedometer-Based Walking Interventions and Weight Loss. The Annals of Family Medicine 6, 69-77 (2008). Link
36. Yvonne Rogers, William R Hazlewood, Paul Marshall, Nick Dalton, Susanna Hertrich. Ambient Influence : Can Twinkly Lights Lure and Abstract Representations Trigger Behavioral Change ?. 261–270 In Proceedings of the 12th ACM international conference on Ubiquitous computing (Ubicomp’10). (2010).
37. B Rokholm, J L Baker, T I A Sørensen. The levelling off of the obesity epidemic since the year 1999 - a review of evidence and perspectives. Obesity Reviews 11, 835-346 (2010).
38. T.W Rowland. The childhood obesity epidemic: Putting the ’dynamics’ into thermodynamics.. Pediatric Exercise Science 16, 87-93 (2004).
39. S. M. Slootmaker, A. Paw M. J. M. Chin, A. J. Schuit, W. van Mechelen, L. L. J. Koppes. Concurrent validity of the PAM accelerometer relative to the MTI Actigraph using oxygen consumption as a reference. Scand J Med Sci Sports 19, 36-43 (2009). Link
40. G. Stratton, D. Canoy, L. M. Boddy, S. R. Taylor, A. F. Hackett, I. E. Buchan. Cardiorespiratory fitness and body mass index of 9-11-year-old English children: a serial cross-sectional study from 1998 to 2004. Int J Obes (Lond) 31, 1172-8 (2007).
41. C D Summerbell, H J Moore, C Vögele, S Kreichauf, A Wildgruber, Y Manios, W Douthwaite, C A Nixon, E L Gibson. Evidence-based recommendations for the development of obesity prevention programs targeted at preschool children. Obesity Reviews 13, S129-S132 (2012).
42. Richard H. Thaler, Cass R. Sunstein. Nudge : improving decisions about health, wealth, and happiness. Penguin Books, 2009. Link
43. Lyndall Thomas, Mark Williams. Promoting physical activity in the workplace: using pedometers to increase daily activity levels. Health Promot J Austr 17, 97-102 (2006). Link
44. Tammy Toscos, Anne Faber, Shunying An, Mona Praful Gandhi. Chick clique: persuasive technology to motivate teenage girls to exercise. 1873–1878 In CHI ’06 Extended Abstracts on Human Factors in Computing Systems. ACM, 2006. Link
45. Tammy Toscos, Anne Faber, Kay Connelly, Adity Mutsuddi Upoma. Encouraging Physical Activity in Teens: can technology help reduce barriers to physical activity in adolescent girls. In Proceedings of Pervasive Health ’08. (2008).
46. S. G. Trost, K. L. McIver, R. R. Pate. Conducting accelerometer-based activity assessments in field-based research. Med Sci Sports Exerc 37, S531-43 (2005).
47. J R Whitehead. A study of children’s physical self-perceptions using an adapted physical self-perception profile questionnaire. Pediatric Exercise Science 7, 132-151 (1995).
48. W van Mechelen, H Hlobil, H Kemper. Validation of two running tests as estimates of maximal aerobic power in children. European Journal of Applied Physiology and Occupational Physiology 55, S03-S06 (1986). | 2019-05-26 17:37:43 | {"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": 0.30128568410873413, "perplexity": 5768.195116805395}, "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/1558232259327.59/warc/CC-MAIN-20190526165427-20190526191427-00108.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/int2/chapter/12/lesson/12.2.3/problem/12-112 | ### Home > INT2 > Chapter 12 > Lesson 12.2.3 > Problem12-112
12-112.
Mr. Wallis is designing a home. He finds the plan for his dream house on the Internet and prints it out.
1. The design of the home is shown at right. If all measurements are in millimeters, what is the area of the diagram?
Separate the diagram into $3$ rectangles and $1$ triangle.
Find the area of these shapes and combine them to find the overall area.
2. Mr. Wallis takes his home design to the copier and enlarges it $400\%$. What is the area of the diagram now? Show how you know.
The area increases by a factor of $4^2$. | 2022-06-29 07:36:06 | {"extraction_info": {"found_math": true, "script_math_tex": 4, "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": 0.44810256361961365, "perplexity": 1100.9459930694547}, "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-2022-27/segments/1656103624904.34/warc/CC-MAIN-20220629054527-20220629084527-00031.warc.gz"} |
https://ko.ifixit.com/Answers/History/690909 | 주요 콘텐츠로 건너뛰기
도움말
## 2021년 05월 03일
### 현재 버전 게시자: Terry Page , 2021년 05월 03일
#### 텍스트:
The[image|2396769]The so called “fuse” is very difficult to bridge with solder or a wire and when I tried it the result was to destroy one end of the fuse making it impossible to bridge. Luckily I found out that one side of the battery(the positive) is connected to one side of the fuse and the other side is connected to a nearby small pad which makes it easier to bridge. I enclose a picture of what I did…hope it helps. The[image|2396769]The so called “fuse” is very difficult to bridge with solder or a wire and when I tried it the result was to destroy one end of the fuse making it impossible to bridge. Luckily I found out that one side of the battery(the positive) is connected to one side of the fuse and the other side is connected to a nearby small pad which makes it easier to bridge. I enclose a picture of what I did…hope it helps. This fix is for the right joycon but I guess the left joycon has something similar which an ohmeter can discover….
open
## 2021년 05월 03일
### 원문 게시자: Terry Page , 2021년 05월 03일
#### 텍스트:
The so called “fuse” is very difficult to bridge with solder or a wire and when I tried it the result was to destroy one end of the fuse making it impossible to bridge. Luckily I found out that one side of the battery(the positive) is connected to one side of the fuse and the other side is connected to a nearby small pad which makes it easier to bridge. I enclose a picture of what I did…hope it helps.
This fix is for the right joycon but I guess the left joycon has something similar which an ohmeter can discover….
open | 2021-06-17 18:48:30 | {"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": 0.8140406608581543, "perplexity": 1464.5169341134572}, "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-2021-25/segments/1623487630518.38/warc/CC-MAIN-20210617162149-20210617192149-00181.warc.gz"} |
https://math.stackexchange.com/questions/2818675/interplay-exterior-algebra-tensor-algebra-differential-forms | # interplay: exterior algebra, tensor algebra, differential forms
I'd like to understand how to evaluate a differential form on vector fields, and how to 'embed' exterior algebra into tensor algebra.
Some people define differential forms as alternating tensor fields, the others as sections of 'exterior algebra bundle'. In the former case, it is clear how such a field acts on vector fields. I am not sure how it works in the second case and what is the interplay between these two definitions. Here is what I mean.
Let $V^*$ be the dual space of the $\mathbb{F}$-vector space $V$, where $\mathbb{F}$ is either $\mathbb{R}$, or $\mathbb{C}$. Consider the tensor algebra $Tensor(V^*)$ and its quotient by the two-sided ideal $I$ generated by all elements of the form $x\otimes x$ for $x\in V^*$ together with the natural projection $\pi$, i.e. corresponding exterior algebra $\pi:Tensor(V^*)\to\Lambda(V^*)=Tensor(V^*)/I$. The exterior algebra then inherits the multiplication from the tensor product which is called the wedge product, hence $\pi(a)\wedge\pi(b):=\pi(a\otimes b)$.
The other part of the story are alternating tensors. There is an endomorphism of the tensor algebra, called the alternation map $Alt$, which is actually a projection with the kernel $Ker(Alt)=I$, and the image of $Alt$ are precisely alternating tensors $AltTen(V^*)$. Therefore, one has the vector space isomorphism $\overline{Alt}:\Lambda(V^*)\cong AltTen(V^*)$ which is given by $\pi(a)\mapsto Alt(a)$.
This construction works also in the case if we start with $TM$ instead of $V$, where $TM$ is the tangent bundle to a manifold $M$. In that situation, sections of the 'exterior algebra bundle' are differential forms.
Let $dx^1,dx^2\in T^*M$ such that $dx^i(\partial_j)=\delta^i_j$, where $x^i:M\to\mathbb{R}$ are coordinate functions and $d$ is the exterior derivative.
1. People write $dx^1\wedge dx^2$. Does this mean $\pi(dx^1)\wedge\pi(dx^2)$, and hence $\pi(dx^1\otimes dx^2)$?
2. How such a differential form $dx^1\wedge dx^2$ acts on $(\partial_1,\partial_2)$? Is this correct; $\pi(dx^1)\wedge\pi(dx^2) (\partial_1,\partial_2)=(dx^1\otimes dx^2+I)(\partial_1,\partial_2)=dx^1(\partial_1)dx^2(\partial_2)+I(\partial_1,\partial_2)=1+0?$
3. If one uses the isomorphism $\overline{Alt}$ the form $dx^1\wedge dx^2$ corresponds to $\frac{1}{2}(dx^1\otimes dx^2-dx^2\otimes dx^1)$ which evaluates on $(\partial_1,\partial_2)$ as $\frac{1}{2}$. This seems to me as the correct way because $\frac{1}{2}(dx^1\otimes dx^2-dx^2\otimes dx^1)$ is something like 'pure' representative of the class $\pi(dx^1\otimes dx^2)$.
4. If $\pi(dx^1),\pi(dx^2)\in\Lambda(T^*M)$ we may consider their product which is $\pi(dx^1\otimes dx^2)$, which in turn corresponds to $\frac{1}{2}(dx^1\otimes dx^2-dx^2\otimes dx^1)$ under the map $\overline{Alt}$. Here is the wedge product defined differently. According to that definition $dx^1\wedge dx^2=dx^1\otimes dx^2-dx^2\otimes dx^1$.
• It is exceedingly obnoxious that some people choose to have the volume of the unit cube in $n$-space be $1/n!$. I thereby declare that the right definition is the one you have in 4. But if you work with the alternating tensors, they are a subalgebra (under wedge product) of the tensor algebra, so under the isomorphism you've denoted (correcting factorials, as I prefer), $\pi(dx^1\otimes dx^2)$ corresponds to the alternating tensor $dx^1\otimes dx^2 - dx^2\otimes dx^1$. Geometers tend to prefer the latter definition, algebraists the former. – Ted Shifrin Jun 13 '18 at 21:39
• If I understand your comment correctly ... The expression $dx^1\wedge dx^2$ is actually $\pi(dx^1)\wedge\pi(dx^2)$ or $\pi(dx^1\otimes dx^2)$, which is the same. Then, $\pi(dx^1)\wedge\pi(dx^2)$ acts on $(\partial_1,\partial_2)$ by definition as $(dx^1\otimes dx^2-dx^2\otimes dx^1)(\partial_1,\partial_2)$, where I use the latter definition. More generally, wedge product of two differential forms (it lives in $\Lambda(T^*M)$) acts on vector fields by definition as the corresponding alternating tensor field, where the correspondence is the factorial-corrected $Alt$-map. Is all of this correct? – Voodoo Child Jun 13 '18 at 22:16
• I think that if you're working with $\pi$, then you should note that $\pi(dx^1\otimes dx^2) = \pi(dx^1\otimes dx^2 - \frac12(dx^1+dx^2)\otimes (dx^1+dx^2))=\pi(\frac12(dx^1\otimes dx^2 - dx^2\otimes dx^1))$ and so there's the darned $1/2$ again. So you really need to put the factorial into the isomorphism $\pi$ to make me happy. – Ted Shifrin Jun 13 '18 at 22:25
• Yes, I think that if you want to do calculus and have differential forms act on vector fields, you should forget $\pi$ and work with the alternating tensors to start with! – Ted Shifrin Jun 13 '18 at 22:52 | 2019-07-16 06:10:27 | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9710379242897034, "perplexity": 161.3395945138123}, "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-2019-30/segments/1563195524503.7/warc/CC-MAIN-20190716055158-20190716081158-00416.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/introductory-algebra-for-college-students-7th-edition/chapter-6-section-6-6-solving-quadratic-equations-by-factoring-exercise-set-page-473/39 | ## Introductory Algebra for College Students (7th Edition)
Factor the binomial using the formula for factoring a difference of squares. 4x$^2$-25=0 (2x+5)(2x-5)=0 Set each variable factor as equal to zero and then isolate the variable to find the solutions. 2x+5=0 or 2x-5=0 2x=-5 or 2x=5 x=-2.5 or x=2.5 Enter the equation into your graphing utility to observe that the graph crosses the x-axis at -2.5 and 2.5 | 2019-10-19 14:58:24 | {"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": 0.5419589281082153, "perplexity": 1315.7299173877489}, "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-2019-43/segments/1570986696339.42/warc/CC-MAIN-20191019141654-20191019165154-00049.warc.gz"} |
https://intelligencemission.com/free-energy-generator-for-sale-free-electricity-generator.html | I have had many as time went by get weak. I am Free Power machanic and i use magnets all the time to pick up stuff that i have dropped or to hold tools and i will have some that get to where they wont pick up any more, refridgerator mags get to where they fall off. Dc motors after time get so they don’t run as fast as they used to. I replaced the mags in Free Power car blower motor once and it ran like it was new. now i do not know about the neo’s but i know that mags do lose there power. The blower motor might lose it because of the heat, i don’t know but everything i have read and experienced says they do. So whats up with that? Hey Free Electricity, ok, i agree with what you are saying. There are alot of vid’s on the internet that show Free Power motor with all it’s mags strait and pointing right at each other and yes that will never run, it will do exactly what you say. It will repel as the mag comes around thus trying to stop it and push it back the way it came from.
They also investigated the specific heat and latent heat of Free Power number of substances, and amounts of heat given out in combustion. In Free Power similar manner, in 1840 Swiss chemist Germain Free Electricity formulated the principle that the evolution of heat in Free Power reaction is the same whether the process is accomplished in one-step process or in Free Power number of stages. This is known as Free Electricity’ law. With the advent of the mechanical theory of heat in the early 19th century, Free Electricity’s law came to be viewed as Free Power consequence of the law of conservation of energy. Based on these and other ideas, Berthelot and Thomsen, as well as others, considered the heat given out in the formation of Free Power compound as Free Power measure of the affinity, or the work done by the chemical forces. This view, however, was not entirely correct. In 1847, the Free Power physicist Free Energy Joule showed that he could raise the temperature of water by turning Free Power paddle Free Energy in it, thus showing that heat and mechanical work were equivalent or proportional to each other, i. e. , approximately, dW ∝ dQ.
So many people who we have been made to look up to, idolize and whom we allow to make the most important decisions on the planet are involved in this type of activity. Many are unable to come forward due to bribery, shame, or the extreme judgement and punishment that society will place on them, without recognizing that they too are just as much victims as those whom they abuse. Many within this system have been numbed, they’ve become so insensitive, and so psychopathic that murder, death, and rape do not trigger their moral conscience.
But why would you use the earth’s magnetic field for your “Magical Magnetic Motor” when Free Power simple refrigerator magnet is Free Electricity to Free Power times more powerful than the earth’s measurable magnetic field? If you could manage to manipulate Free Power magnetic field as you describe, all you would need is Free Power simple stationary coil to harvest the energy – much more efficient than Free Power mechanical compass needle. Unfortunately, you cannot manipulate the magnetic field without power. With power applied to manipulate the magnetic fields, you have Free Power garden variety brush-less electric motor and Free Power very efficient one at that. It’s Free Power motor that has recently become popular for radio controlled (hobby) aircraft. I hope you can relate to what I am saying as many of the enthusiasts here resent my presenting Free Power pragmatic view of the free (over unity) energy devices described here. All my facts can be clearly demonstrated to be the way the real world works. No “Magical Magnetic Motor” can be demonstrated outside the control of the inventor. Videos are never proof of anything as they can be easily faked. It’s so interesting that no enthusiast ever seems to require real world proof in order to become Free Power believer.
Blind faith over rules common sense. Mr. Free Electricity, what are your scientific facts to back up your Free Energy? Progress comes in steps. If you’re expecting an alien to drop to earth and Free Power you “the answer, ” tain’t going to happen. Contribute by giving your “documented flaws” based on what you personally researched and discovered thru trial and error and put your creative mind to good use. Overcome the problem(s). As to the economists, they believe oil has to reach Free Electricity. Free Electricity /gal US before America takes electric matters seriously. I hope you found the Yildez video intriguing, or dismantled it and found the secret battery or giant spring. I’Free Power love to see Free Power live demo. Mr. Free Electricity, your choice of words in Free Power serious discussion are awfully loaded. It sounds like you have been burned along the way.
Reality is never going to be accepted by tat section of the community. Thanks for writing all about the phase conjugation stuff. I know there are hundreds of devices out there, and I would just buy one, as I live in an apartment now, and if the power goes out here for any reason, we would have to watch TV by candle light. lol. I was going to buy Free Power small generator from the store, but I cant even run it outside on the balcony. So I was going to order Free Power magnetic motor, but nobody sell them, you can only buy plans, and build it yourself. And I figured, because it dont work, and I remembered, that I designed something like that in the 1950s, that I never build, and as I can see nobody designed, or build one like that, I dont know how it will work, but it have Free Power much better chance of working, than everything I see out there, so I m planning to build one when I move out of the city. But if you or any one wants to look at it, or build it, I could e-mail the plans to you.
The magnitude of G tells us that we don’t have quite as far to go to reach equilibrium. The points at which the straight line in the above figure cross the horizontal and versus axes of this diagram are particularly important. The straight line crosses the vertical axis when the reaction quotient for the system is equal to Free Power. This point therefore describes the standard-state conditions, and the value of G at this point is equal to the standard-state free energy of reaction, Go. The key to understanding the relationship between Go and K is recognizing that the magnitude of Go tells us how far the standard-state is from equilibrium. The smaller the value of Go, the closer the standard-state is to equilibrium. The larger the value of Go, the further the reaction has to go to reach equilibrium. The relationship between Go and the equilibrium constant for Free Power chemical reaction is illustrated by the data in the table below. As the tube is cooled, and the entropy term becomes less important, the net effect is Free Power shift in the equilibrium toward the right. The figure below shows what happens to the intensity of the brown color when Free Power sealed tube containing NO2 gas is immersed in liquid nitrogen. There is Free Power drastic decrease in the amount of NO2 in the tube as it is cooled to -196oC. Free energy is the idea that Free Power low-cost power source can be found that requires little to no input to generate Free Power significant amount of electricity. Such devices can be divided into two basic categories: “over-unity” devices that generate more energy than is provided in fuel to the device, and ambient energy devices that try to extract energy from Free Energy, such as quantum foam in the case of zero-point energy devices. Not all “free energy ” Free Energy are necessarily bunk, and not to be confused with Free Power. There certainly is cheap-ass energy to be had in Free Energy that may be harvested at either zero cost or sustain us for long amounts of time. Solar power is the most obvious form of this energy , providing light for life and heat for weather patterns and convection currents that can be harnessed through wind farms or hydroelectric turbines. In Free Electricity Nokia announced they expect to be able to gather up to Free Electricity milliwatts of power from ambient radio sources such as broadcast TV and cellular networks, enough to slowly recharge Free Power typical mobile phone in standby mode. [Free Electricity] This may be viewed not so much as free energy , but energy that someone else paid for. Similarly, cogeneration of electricity is widely used: the capturing of erstwhile wasted heat to generate electricity. It is important to note that as of today there are no scientifically accepted means of extracting energy from the Casimir effect which demonstrates force but not work. Most such devices are generally found to be unworkable. Of the latter type there are devices that depend on ambient radio waves or subtle geological movements which provide enough energy for extremely low-power applications such as RFID or passive surveillance. [Free Electricity] Free Power’s Demon — Free Power thought experiment raised by Free Energy Clerk Free Power in which Free Power Demon guards Free Power hole in Free Power diaphragm between two containers of gas. Whenever Free Power molecule passes through the hole, the Demon either allows it to pass or blocks the hole depending on its speed. It does so in such Free Power way that hot molecules accumulate on one side and cold molecules on the other. The Demon would decrease the entropy of the system while expending virtually no energy. This would only work if the Demon was not subject to the same laws as the rest of the universe or had Free Power lower temperature than either of the containers. Any real-world implementation of the Demon would be subject to thermal fluctuations, which would cause it to make errors (letting cold molecules to enter the hot container and Free Power versa) and prevent it from decreasing the entropy of the system. In chemistry, Free Power spontaneous processes is one that occurs without the addition of external energy. A spontaneous process may take place quickly or slowly, because spontaneity is not related to kinetics or reaction rate. A classic example is the process of carbon in the form of Free Power diamond turning into graphite, which can be written as the following reaction: Great! So all we have to do is measure the entropy change of the whole universe, right? Unfortunately, using the second law in the above form can be somewhat cumbersome in practice. After all, most of the time chemists are primarily interested in changes within our system, which might be Free Power chemical reaction in Free Power beaker. Free Power we really have to investigate the whole universe, too? (Not that chemists are lazy or anything, but how would we even do that?) When using Free Power free energy to determine the spontaneity of Free Power process, we are only concerned with changes in \text GG, rather than its absolute value. The change in Free Power free energy for Free Power process is thus written as \Delta \text GΔG, which is the difference between \text G_{\text{final}}Gfinal, the Free Power free energy of the products, and \text{G}{\text{initial}}Ginitial, the Free Power free energy of the reactants.
Free Energy, private research groups are working out the details as you read this. Many are committed to publishing their results on the Internet. All of us constitute the fourth force. If we stand up and refuse to remain ignorant and actionless, we can change the course of history. It is the aggregate of our combined action that can make Free Power difference. Only the mass action that represents our consensus can create the world we want. The other three forces will not help us put Free Power fuelless power plant in our basements. They will not help us be free from their manipulations. Nevertheless, free energy technology is here. It is real, and it will change everything about the way we live, work and relate to each other. In the last analysis, free energy technology obsoletes greed and the fear for survival. But like all exercises of spiritual faith, we must first manifest the generosity and trust in our own lives. The source of free energy is inside of us. It is that excitement of expressing ourselves freely. It is our spiritually guided intuition expressing itself without distraction, intimidation or manipulation. It is our open-heartedness. Ideally, the free energy technologies underpin Free Power just society where everyone has enough food, clothing, shelter, self-worth, and the leisure time to contemplate the higher spiritual meanings of life. Free Power we not owe it to each other to face down our fears and take action to create this future for our children’s children?Free energy technology is here. It has been here for decades. Communications technology and the Internet have torn the veil of secrecy off of this remarkable fact. Free Energy all over the world are starting to build free energy devices for their own use. The bankers and the governments do not want this to happen, but cannot stop it. There will be essentially no major media coverage of what is going on. Tremendous economic instabilities and wars will be used in the near future to distract people from joining the free energy movement. Western society is in many ways spiraling down toward self-destruction due to the accumulated effects of long-term greed and corruption. The general availability of free energy technology cannot stop this trend. It can only reinforce it. If, however, you have Free Power free energy device, you may be better positioned to support the political/social/economic transition that is underway. The question is, who will ultimately control the emerging world government—the first force or the fourth force?The star at last week’s Philadelphia Auto Show wasn’t Free Power sports car or an economy car. It was Free Power sports-economy car—one that combines performance and practicality under one hood. The car that buyers have been waiting decades [for] comes from an unexpected source and runs on soybean bio-diesel fuel to boot. A car that can go from zero to Free Power in four seconds and get more than Free Electricity miles to the gallon would be enough to pique any driver’s interest. So who do we have to thank for it. Free Electricity? Free Energy? Free Power? No—just…five kids from the auto shop program at Free Electricity Philadelphia Free Energy School. Iceland has already started…turning water into fuel – hydrogen fuel. Here’s how it works: Electrodes split the water into hydrogen and oxygen molecules. Hydrogen electrons pass through Free Power conductor that creates the current to power an electric engine. Hydrogen fuel now costs two to three times as much as gasoline, but gets up to three times the mileage of gas, making the overall cost about the same. As an added benefit, there are no carbon emissions – only water vapor. It seems too good to be true: Free Power new source of near-limitless power that costs virtually nothing, uses tiny amounts of water as its fuel and produces next to no waste. Free Power Free Power, Free Power Harvard University medic who also studied electrical engineering at Massachusetts Institute of Technology, Free Energy to have built Free Power prototype power source that generates up to Free Power times more heat than conventional fuel. “We’ve got Free Electricity independent validation reports, we’ve got Free Power peer-reviewed journal articles, ” he saFree Energy “We ran into this theoretical resistance and there are some vested interests here. ”All we know is that we’re seeing more energy output than input. Does Goldes realize what’s he’s saying — that he’s perhaps discovered Free Power clean, inexhaustible energy source? “That’s exactly what it appears to be, ” he answered. A handful of other companies worldwide are believed also to be pursuing zero-point energy via magnetic systems. One of them…is run by Free Power former scientist at NASA’s Jet Propulsion Laboratory in Pasadena. According to Aviation Week & Space Technology magazine, the Pentagon and at least two large aerospace companies are actively researching zero-point energy as Free Power means of propulsion. | 2019-02-21 23:10:15 | {"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": 0.38582363724708557, "perplexity": 1071.9034312051544}, "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-2019-09/segments/1550247511174.69/warc/CC-MAIN-20190221213219-20190221235219-00254.warc.gz"} |
http://mathhelpforum.com/differential-equations/99435-l-transform-piecewise-function.html | # Thread: L.Transform of Piecewise Function
1. ## L.Transform of Piecewise Function
The function f(t) is defined as follows:
$
f(t) = \begin{cases} t(t+1) & \ 0 < t < 2 \\ 1 & \ 2 \leq t \end{cases}$
Find $\mathcal{L} (f(t))$.
2. Rewrite using the unit step function u(t)
f(t) = u(t)(t)(t-1) + u(t-2)[1- t(t-1)]
use L{u(t-a)f(t-a)} = e^(-as)F(s)
where F(s) = L{f(t)}
note 1-t(t-1) = -t^2+t +1 = -(t-2)^2 -4(t-2) - 3
3. Originally Posted by MrJack1990
The function f(t) is defined as follows:
$
f(t) = \begin{cases} t(t+1) & \ 0 < t < 2 \\ 1 & \ 2 \leq t \end{cases}$
Find $\mathcal{L} (f(t))$.
If you are good at integration by parts, you can also do this from the definition of the LT:
$\mathcal{L}f (s)=\int_0^{\infty} f(x) e^{-st}\; dt=
\int_0^{2} t(t+1) e^{-st}\; dt + \int_2^{\infty} e^{-st}\; dt$
CB | 2016-09-25 11:28:16 | {"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": 5, "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": 0.987248420715332, "perplexity": 4912.371357691589}, "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-2016-40/segments/1474738660181.83/warc/CC-MAIN-20160924173740-00286-ip-10-143-35-109.ec2.internal.warc.gz"} |
http://nerderati.com/2016/07/06/why-dhcp-lease-expiration-matters-for-your-coffee-shop-router/ | I often find myself working out of a café.
Nearly all of my work requires an internet connection at some point or another, which means that most of the cafés I frequent have some sort of WiFi that I take advantage of1. While I’m not generally one to complain about the quality of free WiFi in the small, locally run establishments in my neighbourhood, it does frustrate me that they are often misconfigured to the point where the staff must reset the router every few hours.
Generally, the cause of this is simple: an improperly configured DHCP lease expiration time.
A DHCP Primer
The Dynamic Host Configuration Protocol (DHCP) is how your standard public wireless networks allow a client (usually a laptop, smartphone, or tablet) to request the necessary configuration parameters from the server (in the case of a café, a wireless router). DHCP is actually a successor2 to an older protocol, BOOTP, which is a fact that will become important shortly.
It’s All About That IP
One of the more important parameters that the router (we’ll assume it’s a router and not something fancier from this point onward) sends back to the requesting client is a local IP address, which most of the time looks something like 192.168.0.123. The point of this address is to uniquely identify the client on the local network so that data payload being transmitted is correctly routed to-and-from the appropriate destination. Otherwise, the router would have no way of knowing which device on the local network should receive which packets: every device on a TCP/IP-based network must have a unique unicast address.
This IP address, among other information, is sent back in the DHCPOFFER stage of the DHCP negotiation, and is encapsulated in a variable length UDP packet4:
This packet is, for the most part, almost identical to the original BOOTP packet, but includes a few DHCP specific extensions, most notably the ability for a client to request a particular IP address during the DISCOVER phase, and the ability for a client and a server to agree on lease time (during either DHCPDISCOVER or DHCPREQUEST) for which that address will be considered bound to the client and unavailable to any other device that joins the local network.
Due to the finite number of available IP addresses5 in a given subnet pool and the finite memory that a router has access to, there are only so many IP addresses that can be assigned in a single local network. For most non-commercial grade routers, this means that a grand total of 256 addresses (from 192.168.1.0 to 192.168.1.255 if we keep our class C address example from before) are available. Since class C networks generally reserve addresses ending in 0 or 255 for broadcast purposes, we’re left with an effective 254 addresses that may be assigned.
For typical home networks, 254 addresses is more than enough: even in a household with a half dozen family members, each with three personal devices (e.g. laptop, tablet, mobile phone) and a few household items such as network-aware televisions, sound systems, a Roku/Apple TV, etc., we’re still left with 200+ unused addresses, ensuring ample room for the foreseeable future6.
Networks with a large number of client devices, however, can burn through those addresses within minutes.
It’s All So Very Exhausting
So what happens when you’ve got 300+ people at a conference, all attempting to get on the wireless network during the morning coffee break? Well, network congestion (queueing delay/packet loss) effects aside, there’s a very real chance that the first 254 people will get online just fine.
If the router and network they’re connecting to hasn’t been properly configured, however, every subsequent person will have no such luck due to the exhaustion of assignable addresses. That’s a bummer, of course, and hopefully the organizers or the networking people they’ve hired are able to perform a resubnetting (and add more equipment!) to extend the space of available addresses7, or they will be confronted by quite a few angry conference-goers.
Dynamic Networks and Lease Expirations
Some networks are highly dynamic, in that the number of devices that are connected varies in a short amount of time. A great example of this is your typical café that provides wireless internet for its patrons.
These highly dynamic networks often suffer a similar address exhaustion problem, but not due to hundreds of people attempting to access the network simultaneously. Rather, they exhaust the pool of available addresses gradually throughout the day, due to a subtle but obvious fact: a wireless router does not know8 the difference between a device disconnecting from the network (e.g. you’ve left the building and gone home), and simply having no traffic routed to device in question.
As the day goes on, more and more addresses are scooped up by people connecting to the local wireless network, many of whom are only on-site for a brief amount of time. At one point the last available address is assigned, and the moment that every barista dreads occurs: a customer complains that “The WiFi isn’t working”.
The Roy-Moss Solution
As many who have been in this situation can attest to, the naïve solution is typically quite effective: by restarting the router, the DHCP server’s memory is cleared9, and the previously assigned addresses are nullified. Clients that were connected to the router at the time the restart occurred momentarily lose their connection, and then renegotiate with the DHCP server once it has come back online for a new (sometimes the same, depending on the circumstances) address and associated lease time.
Depending on the foot traffic in the establishment, though, some of these cafés go through several restarts a day. And then you realize that the IT Crowd wasn’t a comedy, it was a biodrama.
Can We Prevent All This Router Restarting?
The reason most of these dynamic-but-low-density networks run out of addresses is due to a very simple oversight: the DHCP lease time that a commodity router is configured with by default is an appropriate one for a home, but not for a business. While the lease length may differ across the various brands and models available, most will have it set to something between 24-72 hours. That makes sense for a home environment (heck, you could kick it up to a week or even a month, depending on how many guests you entertain), but makes absolutely no sense for an environment where the average time spent connected to the local network is most likely in the 1-2 hour range.
Thus, a possible solution is a combination of increasing the number of available addresses, probably to their maximum, and ensuring that the DHCP lease is commensurate with the average amount of time a device will be connected to the network: say two hours for an average café or restaurant. Both of these options can usually be configured within the administrative interface for the router in question. While each manufacturer will have their own interface, it will more often than not resemble something like the iconic Linksys configuration panels:
With these modifications in place, most busy cafés/restaurants should be able to reduce the number of times where a hapless employee is required to pull the plug on the router to ensure that customers are able to utilize the wireless local network. Some tweaking of the DHCP lease time may be required, but you generally don’t want to go too short – the original DHCP RFC explicitly specified a 1-hour minimum lease time, which was later removed in RFC 2132, but going below one hour is asking for trouble10.
Determining Your DHCP Client Lease Time
If you’re in a café or restaurant where you believe the DHCP server may be poorly configured for the volume and frequency of guests coming through the door, it’s relatively easy to determine the lease time that your client (we’ll assume laptop) has been given.
Linux
Linux-based operating systems can differ wildly, but the DHCP information is usually written to a file on disk that is updated when new connections are made. This file is typically located at /var/lib/dhclient/dhclient-<interface>.leases for RedHat/CentOS based systems, and at /var/lib/dhcp/dhclient.<interface>.leases for Debian-based systems. Other distributions may place these files in slightly different locations, but the idea is similar.
Assuming your distribution of choice runs some variant of dhclient and that your wireless card is configured to listen on the en0 network interface, the contents of /var/lib/dhcp/dhclient.en0.leases on a Debian-based system should resemble this:
Note that the DHCP lease length is listed as the value to the dhcp-lease-time, and according to the DHCP specification, the unit for this field is seconds.
OS X
For OS X, we can fetch the contents of the UDP packet that the DHCP server responded with during the DHCPACK phase of the protocol once the connection has been established.
Assuming again that en0 is the interface that your wireless card is currently listening on:
will return the packet payload. Your results will differ, but they should look something like this:
While there’s a lot going on in that payload data, the lease_time field is what we’re primarily concerned with. The value is specified as an unsigned 32-bit integer and has the hexadecimal representation 0x127500, which is 1209600 in base 1011. That means that this particular lease is valid for 14 days. As you may have surmised, this is most definitely too long a lease time for an establishment that receives significant foot traffic.
Epilogue
Much to my chagrin, they continue to reset their router on an almost daily basis.
1. Always enable a Virtual Private Network (VPN) connection when using a public wireless network. You never know who might be listening in, especially with the generally shoddy networking equipment (and default passwords!) that many public access points utilize.
2. In a somewhat odd symbiosis, parts of BOOTP are used to bootstrap the newer DHCP functionality, and DHCP is then able to provide BOOTP functionality when required.
3. There are a total of three IP address ranges (usually called “blocks”) that have been allocated for private use by the IETF, but the 192.168.0.0/16 block is the most common. If you're not familiar with the /16 notation, you'll want to brush up on classless inter-domain routing (CIDR). We're going to skip the equivalent IPv6 discussion for the sake of simplicity, but if you're interested, there's an equivalent Unique Local Address (ULA) specification. It turns out that most local, private networks are quite well served by IPv4, and thus IPv6 is not often encountered on public WiFi networks.
4. Thanks to UDP being connectionless, it is rather well suited for the purposes of broadcasting connection bootstrap information from a DHCP server so that all connected devices may receive it without requiring prior configuration.
5. Again, we're mostly concerned with the IPv4 address space. IPv6's ULA specification allows for a subnet 264 bits in size, which is roughly large enough to uniquely identify every single grain of sand on our planet.
6. I guess when your toaster is able to speak to your AC unit and your freezer thanks to the Internet of Things, we might need to revisit this.
7. Hopefully the equipment they used actually lets them do this — many stock non-commercial routers don't have the ability.
8. This is not entirely true: more expensive routers will often have the ability for the DHCP server to send a ping to connected clients on regular intervals to determine which assigned addresses may be released (telling the difference between a timeout and a disconnect is yet another problem that is left as an exercise to the reader), but most public WiFi networks on commodity hardware don't have this ability/are not configured to do so.
9. Somewhat humourously, higher quality routers will ensure that their DHCP lease assignments persist between restarts. So if you have a good quality router that is configured rather poorly, this method will most likely not work!
10. While you may be tempted to simply set a very, very low lease expiration time, say 5 minutes, you may find that some applications (e.g. some mail clients) running on your laptop/mobile phone/tablet aren't very fond of having the local IP address change so frequently while they are active.
11. If you're using a Bash-compatible shell, you can convert a hexadecimal value to the equivalent decimal representation via the built-in method for evaluating arithmetic expressions, including base conversions : echo \$((0x127500)) # prints 1209600. Note that the typical 0x prefix can be replaced with 16#, indicating explicitly that the input is a base-16 number, and will produce the same result. The ARITHMETIC EVALUATION section of the bash man page includes additional details, if you're into that kind of thing. | 2017-01-18 18:05:33 | {"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": 0.24815134704113007, "perplexity": 1817.0165436927448}, "config": {"markdown_headings": false, "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-2017-04/segments/1484560280310.48/warc/CC-MAIN-20170116095120-00141-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://zbmath.org/?q=an:1063.35042 | # zbMATH — the first resource for mathematics
Weighted Strichartz estimates for the wave equation in even space dimensions. (English) Zbl 1063.35042
The authors establish the weighted Strichartz estimate $\left\| \left| t^2 - | x| ^2\right| ^a w \right\| _{L^q(\mathbb R^{1+n}_+)} \leq C \left\| \left| t^2 - | x| ^2\right| ^b F \right\| _{L^{q'}(\mathbb R^{1+n}_+)}$ whenever $$w$$ is spherically symmetric and solves the inhomogeneous Cauchy problem $$\square w = F$$ with zero initial data $$w(0) = w_t(0) = 0$$, $$2 < q < 2(n+1)/(n-1)$$, the dimension $$n \geq 2$$ is even and $$a,b$$ obey the estimates $a-b + \frac{n+1}{q} = \frac{n-1}{2},\qquad \frac{n}{q} - \frac{n-1}{2} < b < \frac{1}{q}.$ This theorem was previously demonstrated for odd $$n$$ by V. Georgiev, H. Lindblad and C. D. Sogge [Am. J. Math. 119, 1291–1319 (1997; Zbl 0893.35075)]. As a consequence the authors construct global solutions to the nonlinear wave equation $$\square u = F(u)$$, where $$F(u)$$ scales like $$| u| ^p$$ for some $$p_0(n) < p < (n+3)/(n-1)$$, $$p_0(n)$$ being the Strauss exponent for global existence of small data solutions, and the initial position is a small multiple of the scale-invariant $$| x| ^{-2/(p-1)}$$ (and initial velocity a small multiple of $$| x| ^{-2/(p-1)-1})$$. This was achieved in odd dimensions by the authors [Indiana Univ. Math. J. 52, 1615–1630 (2003; Zbl 1053.35029)]. The methods are based on an explicit representation of the fundamental solution, which is more difficult in even dimensions than in odd.
##### MSC:
35B45 A priori estimates in context of PDEs 35L05 Wave equation 35L70 Second-order nonlinear hyperbolic equations
Full Text: | 2021-09-27 23:14:57 | {"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": 0.7486883997917175, "perplexity": 474.16630789953786}, "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-2021-39/segments/1631780058552.54/warc/CC-MAIN-20210927211955-20210928001955-00005.warc.gz"} |
http://maps.thefullwiki.org/Petroleum | Petroleum: Map
Map showing all locations mentioned on Wikipedia article:
Petroleum (L. petroleum, from Greek πετρέλαιον, lit. "rock oil") or crude oil is a naturally occurring, flammable liquid consisting of a complex mixture of hydrocarbons of various molecular weights, and other organic compounds, that is found in rock formations beneath the earth's surface.
The term "petroleum" was first used in the treatise De Natura Fossilium, published in 1546 by the German mineralogist Georg Bauer, also known as Georgius Agricola.
Composition
In its strictest sense, petroleum includes only crude oil, but in common usage it includes both crude oil and natural gas. Both crude oil and natural gas are predominantly a mixture of hydrocarbons. Under surface pressure and temperature conditions, the lighter hydrocarbons methane, ethane, propane and butane occur as gases, while the heavier ones from pentane and up are in the form of liquids or solids. However, in the underground oil reservoir the proportion which is gas or liquid varies depending on the subsurface conditions, and on the phase diagram of the petroleum mixture.
An oil well produces predominantly crude oil, with some natural gas dissolved in it. Because the pressure is lower at the surface than underground, some of the gas will come out of solution and be recovered as associated gas or solution gas. A gas well produces predominately natural gas. However, because the underground temperature and pressure are higher than at the surface, the gas may contain heavier hydrocarbons such as pentane, hexane, and heptane in the gaseous state. Under surface conditions these will condense out of the gas and form natural gas condensate, often shortened to condensate. Condensate resembles gasoline in appearance and is similar in composition to some volatile light crude oils.
The proportion of hydrocarbons in the petroleum mixture is highly variable between different oil fields and ranges from as much as 97% by weight in the lighter oils to as little as 50% in the heavier oils and bitumens.
The hydrocarbons in crude oil are mostly alkanes, cycloalkanes and various aromatic hydrocarbons while the other organic compounds contain nitrogen, oxygen and sulfur, and trace amounts of metals such as iron, nickel, copper and vanadium. The exact molecular composition varies widely from formation to formation but the proportion of chemical elements vary over fairly narrow limits as follows:
Composition by weight
Element Percent range
Carbon 83 to 87%
Hydrogen 10 to 14%
Nitrogen 0.1 to 2%
Oxygen 0.1 to 1.5%
Sulfur 0.5 to 6%
Metals less than 1000 ppm
Four different types of hydrocarbon molecules appear in crude oil. The relative percentage of each varies from oil to oil, determining the properties of each oil.
Composition by weight
Hydrocarbon Average Range
Paraffins 30% 15 to 60%
Naphthenes 49% 30 to 60%
Aromatics 15% 3 to 30%
Asphaltics 6% remainder
Most of the world's oils are non-conventional.
Crude oil varies greatly in appearance depending on its composition. It is usually black or dark brown (although it may be yellowish or even greenish). In the reservoir it is usually found in association with natural gas, which being lighter forms a gas cap over the petroleum, and saline water which, being heavier than most forms of crude oil, generally sinks beneath it. Crude oil may also be found in semi-solid form mixed with sand and water, as in the Athabasca oil sands in Canada, where it is usually referred to as crude bitumen. In Canada, bitumen is considered a sticky, tar-like form of crude oil which is so thick and heavy that it must be heated or diluted before it will flow. Venezuela also has large amounts of oil in the Orinoco oil sands, although the hydrocarbons trapped in them are more fluid than in Canada and are usually called extra heavy oil. These oil sands resources are called unconventional oil to distinguish them from oil which can be extracted using traditional oil well methods. Between them, Canada and Venezuela contain an estimated of bitumen and extra-heavy oil, about twice the volume of the world's reserves of conventional oil.
Petroleum is used mostly, by volume, for producing fuel oil and gasoline (petrol), both important "primary energy" sources. 84% by volume of the hydrocarbons present in petroleum is converted into energy-rich fuels (petroleum-based fuels), including gasoline, diesel, jet, heating, and other fuel oils, and liquefied petroleum gas. The lighter grades of crude oil produce the best yields of these products, but as the world's reserves of light and medium oil are depleted, oil refineries are increasingly having to process heavy oil and bitumen, and use more complex and expensive methods to produce the products required. Because heavier crude oils have too much carbon and not enough hydrogen, these processes generally involve removing carbon from or adding hydrogen to the molecules, and using fluid catalytic cracking to convert the longer, more complex molecules in the oil to the shorter, simpler ones in the fuels.
Due to its high energy density, easy transportability and relative abundance, oil has become the world's most important source of energy since the mid-1950s. Petroleum is also the raw material for many chemical products, including pharmaceuticals, solvents, fertilizers, pesticides, and plastics; the 16% not used for energy production is converted into these other materials.
Petroleum is found in porous rock formations in the upper strata of some areas of the Earth's crust. There is also petroleum in oil sands . Known reserves of petroleum are typically estimated at around 190 km3 (1.2 trillion barrels) without oil sands, or 595 km3 (3.74 trillion barrels) with oil sands. Consumption is currently around per day, or 4.9 km3 per year. Because the energy return over energy invested ratio of oil is constantly falling (due to physical phenomena such as residual oil saturation, and the economic factor of rising marginal extraction costs), recoverable oil reserves are significantly less than total oil in place. At current consumption levels, and assuming that oil will be consumed only from reservoirs, known recoverable reserves would be gone around 2039, potentially leading to a global energy crisis. However, to date discoveries of new oil reserves have more than matched increased usage. In addition, there are factors which may extend or reduce this estimate, including the increasing demand for petroleum in developing nations, particularly China and India; further new discoveries; increased economic viability of recoveries from more difficult to exploit sources; energy conservation and use of alternative energy sources; and new economically viable exploitation of unconventional oil sources.
Chemistry
Petroleum is a mixture of a very large number of different hydrocarbons; the most commonly found molecules are alkanes (linear or branched), cycloalkanes, aromatic hydrocarbons, or more complicated chemicals like asphaltenes. Each petroleum variety has a unique mix of molecules, which define its physical and chemical properties, like color and viscosity.
The alkanes, also known as paraffins, are saturated hydrocarbons with straight or branched chains which contain only carbon and hydrogen and have the general formula CnH2n+2 They generally have from 5 to 40 carbon atoms per molecule, although trace amounts of shorter or longer molecules may be present in the mixture.
The alkanes from pentane (C5H12) to octane (C8H18) are refined into gasoline (petrol), the ones from nonane (C9H20) to hexadecane (C16H34) into diesel fuel and kerosene (primary component of many types of jet fuel), and the ones from hexadecane upwards into fuel oil and lubricating oil. At the heavier end of the range, paraffin wax is an alkane with approximately 25 carbon atoms, while asphalt has 35 and up, although these are usually cracked by modern refineries into more valuable products. The shortest molecules, those with four or fewer carbon atoms, are in a gaseous state at room temperature. They are the petroleum gases. Depending on demand and the cost of recovery, these gases are either flared off, sold as liquified petroleum gas under pressure, or used to power the refinery's own burners. During the winter, Butane (C4H10), is blended into the gasoline pool at high rates, because butane's high vapor pressure assists with cold starts. Liquified under pressure slightly above atmospheric, it is best known for powering cigarette lighters, but it is also a main fuel source for many developing countries. Propane can be liquified under modest pressure, and is consumed for just about every application relying on petroleum for energy, from cooking to heating to transportation.
The cycloalkanes, also known as naphthenes, are saturated hydrocarbons which have one or more carbon rings to which hydrogen atoms are attached according to the formula CnH2n. Cycloalkanes have similar properties to alkanes but have higher boiling points.
The aromatic hydrocarbons are unsaturated hydrocarbons which have one or more planar six-carbon rings called benzene rings, to which hydrogen atoms are attached with the formula CnHn. They tend to burn with a sooty flame, and many have a sweet aroma. Some are carcinogenic.
These different molecules are separated by fractional distillation at an oil refinery to produce gasoline, jet fuel, kerosene, and other hydrocarbons. For example 2,2,4-trimethylpentane (isooctane), widely used in gasoline, has a chemical formula of C8H18 and it reacts with oxygen exothermically:
2\mathrm{C}_8 \mathrm{H}_{18(l)} + 25\mathrm{O}_{2(g)} \rightarrow \; 16\mathrm{CO}_{2(g)} + 18\mathrm{H}_2 \mathrm{O}_{(l)} + 10.86 \ \mathrm{MJ}
The amount of various molecules in an oil sample can be determined in laboratory. The molecules are typically extracted in a solvent, then separated in a gas chromatograph, and finally determined with a suitable detector, such as a flame ionization detector or a mass spectrometer.
Incomplete combustion of petroleum or gasoline results in production of toxic byproducts. Too little oxygen results in carbon monoxide. Due to the high temperatures and high pressures involved, exhaust gases from gasoline combustion in car engines usually include nitrogen oxides which are responsible for creation of photochemical smog.
Formation
According to generally accepted theory, petroleum is derived from ancient biomass. The theory was initially based on the isolation of molecules from petroleum that closely resemble known biomolecules (Figure).
350 px
More specifically, crude oil and natural gas are products of heating of ancient organic materials (i.e. kerogen) over geological time. Formation of petroleum occurs from hydrocarbon pyrolysis, in a variety of mostly endothermic reactions at high temperature and/or pressure. Today's oil formed from the preserved remains of prehistoric zooplankton and algae, which had settled to a sea or lake bottom in large quantities under anoxic conditions (the remains of prehistoric terrestrial plants, on the other hand, tended to form coal). Over geological time the organic matter mixed with mud, and was buried under heavy layers of sediment resulting in high levels of heat and pressure (diagenesis). This process caused the organic matter to change, first into a waxy material known as kerogen, which is found in various oil shales around the world, and then with more heat into liquid and gaseous hydrocarbons via a process known as catagenesis.
Geologists often refer to the temperature range in which oil forms as an "oil window"—below the minimum temperature oil remains trapped in the form of kerogen, and above the maximum temperature the oil is converted to natural gas through the process of thermal cracking. Sometimes, oil which is formed at extreme depths may migrate and become trapped at much shallower depths than where it was formed. The Athabasca Oil Sands is one example of this.
Abiogenic origin
A number of geologists adhere to the abiogenic petroleum origin hypothesis and maintain that hydrocarbons of purely inorganic origin exist within Earth's interior. Chemists Marcellin Berthelot and Dmitri Mendeleev, as well as astronomer Thomas Gold championed the theory in the Western world by supporting the work done by Nikolai Kudryavtsev in the 1950s. It is currently supported primarily by Kenney and Krayushkin.
The abiogenic origin hypothesis has scientific support from publications such as the Proceedings of the National Academy of Sciences. Extensive research into the chemical structure of kerogen has identified algae as the primary source of oil. The abiogenic origin hypothesis fails to explain the presence of these markers in kerogen and oil, as well as failing to explain how inorganic origin could be achieved at temperatures and pressures sufficient to convert kerogen to graphite. It has not been successfully used in uncovering oil deposits by geologists, as the hypothesis lacks any mechanism for determining where the process may occur. More recently scientists at the Carnegie Institution for Science have found that ethane and heavier hydrocarbons can be synthesized under conditions of the upper mantle.
Crude oil
Crude oil reservoirs
Hydrocarbon trap.
Three conditions must be present for oil reservoirs to form: a source rock rich in hydrocarbon material buried deep enough for subterranean heat to cook it into oil; a porous and permeable reservoir rock for it to accumulate in; and a cap rock (seal) or other mechanism that prevents it from escaping to the surface. Within these reservoirs, fluids will typically organize themselves like a three-layer cake with a layer of water below the oil layer and a layer of gas above it, although the different layers vary in size between reservoirs. Because most hydrocarbons are lighter than rock or water, they often migrate upward through adjacent rock layers until either reaching the surface or becoming trapped within porous rocks (known as reservoirs) by impermeable rocks above. However, the process is influenced by underground water flows, causing oil to migrate hundreds of kilometres horizontally or even short distances downward before becoming trapped in a reservoir. When hydrocarbons are concentrated in a trap, an oil field forms, from which the liquid can be extracted by drilling and pumping.
The reactions that produce oil and natural gas are often modeled as first order breakdown reactions, where hydrocarbons are broken down to oil and natural gas by a set of parallel reactions, and oil eventually breaks down to natural gas by another set of reactions. The latter set is regularly used in petrochemical plants and oil refineries.
Wells are drilled into oil reservoirs to extract the crude oil. "Natural lift" production methods that rely on the natural reservoir pressure to force the oil to the surface are usually sufficient for a while after reservoirs are first tapped. In some reservoirs, such as in the Middle East , the natural pressure is sufficient over a long time. The natural pressure in many reservoirs, however, eventually dissipates. Then the oil must be pumped out using “artificial lift” created by mechanical pumps powered by gas or electricity. Over time, these "primary" methods become less effective and "secondary" production methods may be used. A common secondary method is “waterflood” or injection of water into the reservoir to increase pressure and force the oil to the drilled shaft or "wellbore." Eventually "tertiary" or "enhanced" oil recovery methods may be used to increase the oil's flow characteristics by injecting steam, carbon dioxide and other gases or chemicals into the reservoir. In the United States, primary production methods account for less than 40% of the oil produced on a daily basis, secondary methods account for about half, and tertiary recovery the remaining 10%. Extracting oil (or “bitumen”) from oil/tar sand and oil shale deposits requires mining the sand or shale and heating it in a vessel or retort, or using “in-situ” methods of injecting heated liquids into the deposit and then pumping out the oil-saturated liquid.
Unconventional oil reservoirs
Oil-eating bacteria biodegrades oil that has escaped to the surface. Oil sands are reservoirs of partially biodegraded oil still in the process of escaping and being biodegraded, but they contain so much migrating oil that, although most of it has escaped, vast amounts are still present—more than can be found in conventional oil reservoirs. The lighter fractions of the crude oil are destroyed first, resulting in reservoirs containing an extremely heavy form of crude oil, called crude bitumen in Canada, or extra-heavy crude oil in Venezuela. These two countries have the world's largest deposits of oil sands.
On the other hand, oil shales are source rocks that have not been exposed to heat or pressure long enough to convert their trapped hydrocarbons into crude oil. Technically speaking, oil shales are not really shales and do not really contain oil, but are usually relatively hard rocks called marls containing a waxy substance called kerogen. The kerogen trapped in the rock can be converted into crude oil using heat and pressure to simulate natural processes. The method has been known for centuries and was patented in 1694 under British Crown Patent No. 330 covering, "A way to extract and make great quantityes of pitch, tarr, and oyle out of a sort of stone." Although oil shales are found in many countries, the United States has the world's largest deposits.
Classification
A sample of medium heavy crude oil
The petroleum industry generally classifies crude oil by the geographic location it is produced in (e.g. West Texas Intermediate, Brent, or Oman), its API gravity (an oil industry measure of density), and by its sulfur content. Crude oil may be considered light if it has low density or heavy if it has high density; and it may be referred to as sweet if it contains relatively little sulfur or sour if it contains substantial amounts of sulfur.
The geographic location is important because it affects transportation costs to the refinery. Light crude oil is more desirable than heavy oil since it produces a higher yield of gasoline, while sweet oil commands a higher price than sour oil because it has fewer environmental problems and requires less refining to meet sulfur standards imposed on fuels in consuming countries. Each crude oil has unique molecular characteristics which are understood by the use of crude oil assay analysis in petroleum laboratories.
Barrel from an area in which the crude oil's molecular characteristics have been determined and the oil has been classified are used as pricing references throughout the world. Some of the common reference crudes are:
There are declining amounts of these benchmark oils being produced each year, so other oils are more commonly what is actually delivered. While the reference price may be for West Texas Intermediate delivered at Cushing, the actual oil being traded may be a discounted Canadian heavy oil delivered at Hardisty, Alberta, and for a Brent Blend delivered at the Shetlands, it may be a Russian Export Blend delivered at the port of Primorsk.
Petroleum industry
The petroleum industry is involved in the global processes of exploration, extraction, refining, transporting (often with oil tankers and pipelines), and marketing petroleum products. The largest volume products of the industry are fuel oil and gasoline (petrol). Petroleum is also the raw material for many chemical products, including pharmaceuticals, solvents, fertilizers, pesticides, and plastics. The industry is usually divided into three major components: upstream, midstream and downstream. Midstream operations are usually included in the downstream category.
Petroleum is vital to many industries, and is of importance to the maintenance of industrialized civilization itself, and thus is critical concern to many nations. Oil accounts for a large percentage of the world's energy consumption, ranging from a low of 32% for Europe and Asia, up to a high of 53% for the Middle East. Other geographic regions' consumption patterns are as follows: South and Central America (44%), Africa (41%), and North America (40%). The world at large consumes 30 billion barrels (4.8 km³) of oil per year, and the top oil consumers largely consist of developed nations. In fact, 24% of the oil consumed in 2004 went to the United States alone , though by 2007 this had dropped to 21% of world oil consumed.
In the US, in the states of Arizona, California, Hawaii, Nevada, Oregon and Washington, the Western States Petroleum Association (WSPA) is responsible for producing, distributing, refining, transporting and marketing petroleum. This non-profit trade association was founded in 1907, and is the oldest petroleum trade association in the United States.
History
Petroleum, in one form or another, has been used since ancient times, and is now important across society, including in economy, politics and technology. The rise in importance was mostly due to the invention of the internal combustion engine and the rise in commercial aviation
More than 4000 years ago, according to Herodotus and Diodorus Siculus, asphalt was used in the construction of the walls and towers of Babylon; there were oil pits near Ardericca (near Babylon), and a pitch spring on Zacynthus. Great quantities of it were found on the banks of the river Issus, one of the tributaries of the Euphrates. Ancient Persian tablets indicate the medicinal and lighting uses of petroleum in the upper levels of their society.
Today, about 90% of vehicular fuel needs are met by oil. Petroleum also makes up 40% of total energy consumption in the United States, but is responsible for only 2% of electricity generation. Petroleum's worth as a portable, dense energy source powering the vast majority of vehicles and as the base of many industrial chemicals makes it one of the world's most important commodities.
The top three oil producing countries are Saudi Arabia, Russia, and the United States. About 80% of the world's readily accessible reserves are located in the Middle East, with 62.5% coming from the Arab 5: Saudi Arabia, UAE, Iraq, Qatar and Kuwait. A large portion of the world's total oil exists as unconventional sources, such as bitumen in Canada and Venezuela and oil shale. While significant volumes of oil are extracted from oil sands, particularly in Canada, logistical and technical hurdles remain, and Canada's oil sands are not expected to provide more than a few million barrels per day in the foreseeable future.
Price
After the collapse of the OPEC-administered pricing system in 1985, and a short lived experiment with netback pricing, oil-exporting countries adopted a market-linked pricing mechanism. First adopted by PEMEX in 1986, market-linked pricing was widely accepted, and by 1988 became and still is the main method for pricing crude oil in international trade. The current reference, or pricing markers, are Brent, WTI, and Dubai/Oman.
Uses
The chemical structure of petroleum is heterogeneous (composed of hydrocarbon chains of different lengths). Because of this, petroleum may be taken to oil refineries and the hydrocarbon chemicals separated by distillation and treated by other chemical processes, to be used for a variety of purposes. See Petroleum products.
Fuels
The most common distillation of petroleum are fuels.Fuels include:
Other derivatives
Certain types of resultant hydrocarbons may be mixed with other non-hydrocarbons, to create other end products:
Petroleum by country
Consumption statistics
Image:Global Carbon Emission by Type to Y2004.png|Global fossil carbon emissions, an indicator of consumption, for 1800 - 2004. Total is black, Oil is in blue.Image:EIA_IEO2006.jpg|World energy consumption, 1980 - 2030. Source: International Energy Outlook 2006.Image:Oil consumption per day by region from 1980 to 2006.svg|daily oil consumption from 1980 to 2006Image:Oil consumption per day by region from 1980 to 2006 solid3.svg|oil consumption by percentage of total per region from 1980 to 2006: red=USA, blue=Europe, yellow=Asia+Oceania
Consumption
Oil consumption per capita (darker colors represent more consumption).
This table orders the amount of petroleum consumed in 2006 in thousand barrels (bbl) per day and in thousand cubic metres (m3) per day:
Consuming Nation 2006 (1000 bbl/day) (1000 m3/day) population in millions bbl/year per capita
304
1369
128
142
82
1201
32
187
49
27
107
61
61
58
Iran (OPEC) 68
1 peak production of oil already passed in this state
2 This country is not a major oil producer
Production
Graph of Top Oil Producing Countries 1960-2006, including Soviet Union
In petroleum industry parlance, production refers to the quantity of crude extracted from reserves, not the literal creation of the product.
# Producing Nation 103bbl/d (2006) 103bbl/d (2007)
1 10,665 10,234
2 9,677 9,876
3 8,331 8,481
4 Iran (OPEC) 4,148 4,043
5 3,845 3,901
6 3,707 3,501
7 3,288 3,358
8 United Arab Emirates (OPEC) 2,945 2,948
9 Venezuela (OPEC) 1 2,803 2,667
10 Kuwait (OPEC) 2,675 2,613
11 2,786 2,565
12 Nigeria (OPEC) 2,443 2,352
13 2,166 2,279
14 Algeria (OPEC) 2,122 2,173
15 Iraq (OPEC) 3 2,008 2,094
16 Libya (OPEC) 1,809 1,845
17 Angola (OPEC) 1,435 1,769
18 1,689 1,690
19 1,388 1,445
20 Qatar (OPEC) 1,141 1,136
21 1,102 1,044
22 854 881
23 648 850
24 802 791
25 743 714
26 729 703
27 667 664
28 Australia 552 595
29 544 543
31 380 466
32 449 446
33 386 400
34 377 361
35 362 352
36 334 349
37 344 314
38 247 250
39 237 244
40 South Africa 204 199
1 Peak production of conventional oil already passed in this state
2 Although Canadian conventional oil production is declining, total oil production is increasing as oil sands production grows. If oil sands are included, it has the world's second largest oil reserves after Saudi Arabia.
3 Though still a member, Iraq has not been included in production figures since 1998
Export
Oil exports by country
In order of net exports in 2006 in thousand bbl/d and thousand /d:
# Exporting Nation (2006) (103bbl/d) (103m3/d)
1 8,651 1,376
2 6,565 1,044
3 2,542 404
4 Iran (OPEC) 2,519 401
5 United Arab Emirates (OPEC) 2,515 400
6 Venezuela (OPEC) 1 2,203 350
7 Kuwait (OPEC) 2,150 342
8 Nigeria (OPEC) 2,146 341
9 Algeria (OPEC) 1 1,847 297
10 1,676 266
11 Libya (OPEC) 1 1,525 242
12 Iraq (OPEC) 1,438 229
13 Angola (OPEC) 1,363 217
14 1,114 177
15 1,071 170
1 peak production already passed in this state
2 Canadian statistics are complicated by the fact it is both an importer and exporter of crude oil, and refines large amounts of oil for the U.S. market. It is the leading source of U.S. imports of oil and products, averaging 2.5 MMbbl/d in August 2007.[3752].
Total world production/consumption (as of 2005) is approximately .
Import
Oil imports by country
In order of net imports in 2006 in thousand bbl/d and thousand /d:
# Importing Nation (2006) (103bbl/day) (103m3/day)
1 United States 1 12,220 1,943
2 Japan 5,097 810
3 China 2 3,438 547
4 Germany 2,483 395
5 South Korea 2,150 342
6 France 1,893 301
7 India 1,687 268
8 Italy 1,558 248
9 Spain 1,555 247
10 Republic of China (Taiwan) 942 150
11 Netherlands 936 149
12 Singapore 787 125
13 Thailand 606 96
14 Turkey 576 92
15 Belgium 546 87
1 peak production of oil already passed in this state
2 Major oil producer whose production is still increasing
Non-producing consumers
Countries whose oil production is 10% or less of their consumption.
# Consuming Nation (bbl/day) (m³/day)
1 Japan 5,578,000 886,831
2 Germany 2,677,000 425,609
3 South Korea 2,061,000 327,673
4 France 2,060,000 327,514
5 Italy 1,874,000 297,942
6 Spain 1,537,000 244,363
7 Netherlands 946,700 150,513
Source : CIA World Factbook
Environmental effects
Diesel fuel spill on a road
The presence of oil has significant social and environment impacts, from accidents and routine activities such as seismic exploration, drilling, and generation of polluting wastes, greenhouse gases and climate change not produced by renewable energy.
Extraction
Oil extraction is costly and sometimes environmentally damaging, although Dr. John Hunt of the Woods Hole Oceanographic Institution pointed out in a 1981 paper that over 70% of the reserves in the world are associated with visible macroseepage, and many oil fields are found due to natural seeps. Offshore exploration and extraction of oil disturbs the surrounding marine environment.
Oil spills
Crude oil and refined fuel spills from tanker ship accidents have damaged natural ecosystems in Alaska, the Galapagos Islands, France and many other places.
The quantity of oil spilled during accidents has ranged from a few hundred tons to several hundred thousand tons (e.g., Atlantic Empress, Amoco Cadiz). Smaller spills have already proven to have a great impact on ecosystems, such as the Exxon Valdez oil spill
Oil spills at sea are generally much more damaging than those on land, since they can spread for hundreds of nautical miles in a thin oil slick which can cover beaches with a thin coating of oil. This can kill sea birds, mammals, shellfish and other organisms it coats. Oil spills on land are more readily containable if a makeshift earth dam can be rapidly bulldozed around the spill site before most of the oil escapes, and land animals can avoid the oil more easily.
Control of oil spills is difficult, requires ad hoc methods, and often a large amount of manpower (picture). The dropping of bombs and incendiary devices from aircraft on the Torrey Canyon wreck produced poor results; modern techniques would include pumping the oil from the wreck, like in the Prestige oil spill or the Erika oil spill.
Whales
James S. Robbins has argued that the advent of petroleum-refined kerosene saved some species of great whales from extinction by providing an inexpensive substitute for whale oil, thus eliminating the economic imperative for open-boat whaling.
Alternatives to petroleum
In the United States in 2007 about 70% of petroleum was used for transportation (e.g. gasoline, diesel, jet fuel), 24% by industry (e.g. production of plastics), 5% for residential and commercial uses, and 2% for electricity production. Outside of the US, a higher proportion of petroleum tends to be used for electricity.
Alternatives to petroleum-based vehicle fuels
Alternative propulsion refers to both:
Currently, cars can be classified into the following groups:
Alternatives to using oil in industry
Biological feedstocks do exist for industrial uses such as plastic production.
Alternatives to burning petroleum for electricity
In oil producing countries with little refinery capacity, oil is sometimes burned to produce electricity. Renewable energy technologies such as solar power, wind power, micro hydro, biomass and biofuels might someday be used to replace some of these generators, but today the primary alternatives remain large scale hydroelectricity, nuclear and coal-fired generation.
Future of petroleum production
USA Today news reported in 2004 that there were 40 years of petroleum left in the ground. As similar statements have been made in the 40 previous years, it hardly carries the complex situation.
Consumption in the twentieth century has been abundantly pushed by automobile growth ; the 1985-2003 oil glut even fuelled the sales of low economy vehicles (SUVs) in OECD countries. In 2008, the economic crisis seems to have some impact on the sales of such vehicles ; still, the 2008 oil consumption shows a small increase. The BRIC countries might also kick in, as China briefly was the first automobile market in December 2009
. The immediate outlook still hints upwards.
In the long term, uncertainties loiter ; the OPEC believes that the OECD countries will push low consumption policies at some point in the future ; when that happens, it will definitely curb the oil sales, and both OPEC and EIA kept lowering their 2020 consumption estimates during the past 5 years . Oil products are more and more in competition with alternative sources, mainly coal and natural gas, both cheaper sources.
Production will also face an increasingly complex situation ; while OPEC countries still have large reserves at low production prices, newly found reservoirs often lead to higher prices ; offshore giants such as Tupi, Guara and Tiber demand high investments and ever-increasing technological abilities. Subsalt reservoirs such as Tupi were unknown in the twentieth century, mainly because the industry was unable to probe them. Enhanced Oil Recovery (EOR) techniques (example : DaQing, China ) will continue to play a major role in increasing the world's recoverable oil.
Hubbert peak theory
The Hubbert peak theory (also known as peak oil) posits that future petroleum production (whether for individual oil wells, entire oil fields, whole countries, or worldwide production) will eventually peak and then decline at a similar rate to the rate of increase before the peak as these reserves are exhausted. The peak of oil discoveries was in 1965, and oil production per year has surpassed oil discoveries every year since 1980.
Controversy surrounds predictions of the timing of the global peak, as these predictions are dependent on the past production and discovery data used in the calculation as well as how unconventional reserves are considered . Also, these predictions do not take into account outside elements such as the current economic crisis (2008) . Also, many Peak Oil promoters proposed many different dates, some of them passed already .
It is difficult to predict the oil peak in any given region, due to the lack of knowledge and/or transparency in accounting of global oil reserves. Based on available production data, proponents have previously predicted the peak for the world to be in years 1989, 1995, or 1995-2000. Some of these predictions date from before the recession of the early 1980s, and the consequent reduction in global consumption, the effect of which was to delay the date of any peak by several years. Just as the 1971 U.S. peak in oil production was only clearly recognized after the fact, a peak in world production will be difficult to discern until production clearly drops off.
References
1. translated 1955
2. IEA Key World Energy Statistics
3. "Crude oil is made into different fuels"
4. EIA reserves estimates
5. CERA report on total world oil
6. Heat of Combustion of Fuels
7. Use of ozone depleting substances in laboratories. TemaNord 2003:516. http://www.norden.org/pub/ebook/2003-516.pdf
8. Keith A. Kvenvolden “Organic geochemistry – A retrospective of its first 70 years” Organic Geochemistry 37 (2006) 1–11.
9. Petroleum Study
10. http://oilismastery.blogspot.com/2008/05/oil-window.html
11. Kenney et al., Dismissal of the Claims of a Biological Connection for Natural Petroleum, Energia 2001
12. http://www.pnas.org/content/99/17/10976.full
13. Hydrocarbons in the deep Earth? July 2009 news release.
15. U.S. Energy Information Administration. Excel file RecentPetroleumConsumptionBarrelsperDay.xls from web page http://tonto.eia.doe.gov/dnav/pet/pet_pri_wco_k_w.htm (direct link: http://www.eia.doe.gov/emeu/international/RecentPetroleumConsumptionBarrelsperDay.xls) "Table Posted: November 7, 2008"
16. From DSW-Datareport 2006 ("Deutsche Stiftung Weltbevölkerung")
17. One cubic metre of oil is equivalent to 6.28981077 barrels of oil
18. IndexMundi. South Korea Population - Demographics. "48,846,823" ... "July 2006 est." Retrieved 2008-11-11
19. Sources vary: 24,600,000 from ; while IndexMundi listed a July 2006 estimate of 27,019,73:
20. IndexMundi. France Population - Demographics. "60,876,136" ... "July 2006 est." Retrieved 2008-11-11
21. IndexMundi. United Kingdom Population - Demographics. "60,609,153" ... "July 2006 est." Retrieved 2008-11-11
22. IndexMundi. Italy Population - Demographics. "58,133,509" ... "July 2006 est." Retrieved 2008-11-11
23. IndexMundi. Iran Population - Demographics. "68,688,433" ... "July 2006 est." Retrieved 2008-11-11
24. http://www.eia.doe.gov/emeu/aer/pdf/pages/sec11_10.pdf
25. Waste discharges during the offshore oil and gas activity by Stanislave Patin, tr. Elena Cascio
26. Torrey Canyon bombing by the Navy and RAF
27. Pumping of the Erika cargo
28. How Capitalism Saved the Whales by James S. Robbins, The Freeman, August, 1992.
29. "U.S. Primary Energy Consumption by Source and Sector, 2007". Energy Information Administration
30. needtitleUN Energy Program
31. Amory B. Lovins, E. Kyle Datta, Odd-Even Bustnes, Jonathan G. Koomey, Nathan J. Glasgow. "Winning the oil endgame" Rocky Mountain Institute
32. Bioprocessing Seattle Times (2003)
33. New study raises doubts about Saudi oil reserves | 2017-04-26 04:09:53 | {"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": 0.4793349504470825, "perplexity": 5276.984353114779}, "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-2017-17/segments/1492917121153.91/warc/CC-MAIN-20170423031201-00231-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/23161/question-about-ambiguity-of-bnf | # Question about ambiguity of BNF
The BNF is defined as follows:
<S> -> <S>a<S>a<S> | b
This is my review question for a quiz, and according to my teacher, this grammar is ambiguous. However, I realized this grammar is not.
For example, given a sentence:
babababab
There are three ways to generate this sentence depending on which <S> we use, but its parse-tree is unique.
Am I right in this case? Any feedback would be greatly appreciated.
Thanks,
Chan
-
Starting with your formal grammar consisting of one production rule, $S \to SaSaS | b$, I'm going to modify it be adding parenthesis to demonstrate the the possible ways of generating your objective string $babababab$.
Let the demonstrative formal grammar be given by the production rule $S \to (S)a(S)a(S) | b$.
Starting with $(S)a(S)a(S)$ we can produce the following strings: $((b)a(b)a(b))a(b)a(b)$, $(b)a((b)a(b)a(b))a(b)$ and $(b)a(b)a((b)a(b)a(b))$.
If we remove the paratheses, (effectively performing the same set of operations using your formal grammar), then we arrive at your objective string $babababab$.
By definition, any formal grammar that yields the same string by applying the production rules in multiple ways, is ambiguous.
Therefore, your formal grammar is ambiguous. (the demonstrative formal grammar is not, since each string is unique.)
- | 2014-07-23 14:37:58 | {"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": 0.8700147271156311, "perplexity": 704.0917783918999}, "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-2014-23/segments/1405997878518.58/warc/CC-MAIN-20140722025758-00199-ip-10-33-131-23.ec2.internal.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/waveform-generated-digital-communications-system-called-keying-ook-represented-random-proc-q4012381 | Please help, i do not know how to start this problem
Image text transcribed for accessibility: The waveform generated by a digital communications system called on-off keying (OOK) can be represented by a random process X(t) = A middot cos(omega t) where is a constant (the carrier frequency) and A is a discrete random variable taking on only values of 0 and 1. and that P(A = 1) = 0.6. Sketch 3 samples of this RP. For the purposes of these plots only (so that I can make sense of them), assume that the random value selected for A is constant for at least one full period of the cosine oscillation. Is it discrete or continuous time? Is it discrete or continuous state (valued)? Determine the mean function mu X(t). Hint: Since A is a discrete RV, it is represented by a PMF which means that the expectation operator will be a sum and not an integral. State what conditions on RP X(t) must be satisfied for it to be wide-sense stationary (WSS). Is this RP WSS? Justify your conclusion briefly. | 2014-12-25 18:10:45 | {"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": 0.8683850765228271, "perplexity": 415.4533879917285}, "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-2014-52/segments/1419447547904.83/warc/CC-MAIN-20141224185907-00001-ip-10-231-17-201.ec2.internal.warc.gz"} |
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Physics , 2007, DOI: 10.1088/1674-1056/17/7/008 Abstract: From the macroscopic viewpoint for describing the acceleration behavior of drivers, this letter presents a weighted probabilistic cellular automaton model (the WP model, for short) by introducing a kind of random acceleration probabilistic distribution function. The fundamental diagrams, the spatio-temporal pattern are analyzed in detail. It is shown that the presented model leads to the results consistent with the empirical data rather well, nonlinear velocity-density relationship exists in lower density region, and a new kind of traffic phenomenon called neo-synchronized flow is resulted. Furthermore, we give the criterion for distinguishing the high-speed and low-speed neo-synchronized flows and clarify the mechanism of this kind of traffic phenomena. In addition, the result that the time evolution of distribution of headways is displayed as a normal distribution further validates the reasonability of the neo-synchronized flow. These findings suggest that the diversity and randomicity of drivers and vehicles has indeed remarkable effect on traffic dynamics.
中国物理 B , 2009, Abstract: This paper modifies the weighted probabilistic cellular automaton model (Li X L, Kuang H, Song T, et al 2008 Chin. Phys. B 17 2366) which considered a diversity of traffic behaviors under real traffic situations induced by various driving characters and habits. In the new model, the effects of the velocity at the last time step and drivers' desire for acceleration are taken into account. The fundamental diagram, spatial-temporal diagram, and the time series of one-minute data are analyzed. The results show that this model reproduces synchronized flow. Finally, it simulates the on-ramp system with the proposed model. Some characteristics including the phase diagram are studied.
Physics , 1998, DOI: 10.1023/A:1004521326456 Abstract: We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g. cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with {\it simultaneous} updating of all sites. It is equivalent to a special case ($v_{\rm max}=1$) of the Nagel-Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two point functions and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time discrete updating procedures. Through use of this mapping, our results also give new results for these models.
Ryan Gantner ISRN Probability and Statistics , 2013, DOI: 10.1155/2013/246045 Abstract: A cellular automaton model for traffic flow is analyzed. For this model, it is shown that under ergodic initial configurations, the distribution of cars will converge in time to a mixture of free flow and solid blocks. Furthermore, the nature of the free flow and solid block distributions is fully described, thus allowing for a specific computation of throughput in terms of the parameters. The model is also shown to exhibit a hysteresis phenomenon, which is similar to what has been observed on actual highways. 1. Introduction and Description of the Model 1.1. Introduction There have been various cellular automaton models introduced to model traffic flow [1–3]. Many of these models gain computational advantage over older so-called car-following, fluid dynamical, and kinetic (gas-type) models by discretizing both space and time (see [4] for an overview of various models). For these discrete models, simple rules are developed to govern car movement. While, on a small scale, the rules oversimplify traffic behavior, the goal is that large scale traffic phenomena, such as the formation and persistence of traffic jams, present themselves in this simplified approach. The model used in this paper is a discrete time probabilistic cellular automaton model developed by Gray and Griffeath in [2]. We will be concerned with macroscopic limiting phenomena on an infinitely long one-dimensional highway. In this paper, we show the existence of a limiting throughput (flux) of cars and describe these regions explicitly. For traffic densities above a critical value, we are able to show that the traffic organizes itself into regions of free flow and regions of traffic jam, both of which will be given precise mathematical definitions in this context. We also observe the existence of metastable states: conditions which allow certain ergodic traffic distributions to have higher throughput than others with the same density of cars. The existence of metastable states has been sought after [5] due to the fact that such states have been shown to be exhibited in real-world traffic flow [6]. These metastable states exhibit a hysteresis phenomenon in the sense that minor perturbations of the cars in these states may eventually lead to a drastic change in the traffic throughput. As mentioned in [2], a property which may be related to the hysteresis phenomenon encountered with the metastable states is the so-called slow-to-start feature, which may be the key element which gives realistic macroscopic behavior to the cellular automaton model. Other slow-to-start models can be found in [3,
Physics , 1993, DOI: 10.1088/0305-4470/26/15/011 Abstract: A recently introduced cellular automaton model for the description of traffic flow is investigated. It generalises asymmetric exclusion models which have attracted a lot of interest in the past. We calculate the so-called fundamental diagram (flow vs.\ density) for parallel dynamics using an improved mean-field approximation which takes into account short-range correlations. For maximum velocity 1 we find that the simplest non-trivial of these approximations gives already the exact result. For higher velocities our results are in excellent agreement with numerical data.
Physics , 1998, DOI: 10.1103/PhysRevE.58.1286 Abstract: We systematically investigate the effect of blockage sites in a cellular automaton model for traffic flow. Different scheduling schemes for the blockage sites are considered. None of them returns a linear relationship between the fraction of green'' time and the throughput. We use this information for a fast implementation of traffic in Dallas.
Pratip Bhattacharyya Physics , 1998, DOI: 10.1142/S0129183199000115 Abstract: A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton which is known to show a transition from a active phase to a absorbing phase at a critical probability associated with two particular components of the evolution rule. In one of these models, called model $A$ in this paper, the surface growth is defined in terms of the evolving front of the cellular automaton on the space-time plane. In the other model, called model $B$, surface growth takes place by a solid-on-solid deposition process controlled by the cellular automaton configurations that appear in successive time-steps. Both the models show a depinning transition at the critical point of the generating cellular automaton. In addition, model $B$ shows a kinetic roughening transition at this point. The characteristics of the surface width in these models are derived by scaling arguments from the critical properties of the generating cellular automaton and by Monte Carlo simulations.
Physics , 2009, Abstract: Traffic fluctuation has so far been studied on unweighted networks. However many real traffic systems are better represented as weighted networks, where nodes and links are assigned a weight value representing their physical properties such as capacity and delay. Here we introduce a general random diffusion (GRD) model to investigate the traffic fluctuation in weighted networks, where a random walk's choice of route is affected not only by the number of links a node has, but also by the weight of individual links. We obtain analytical solutions that characterise the relation between the average traffic and the fluctuation through nodes and links. Our analysis is supported by the results of numerical simulations. We observe that the value ranges of the average traffic and the fluctuation, through nodes or links, increase dramatically with the level of heterogeneity in link weight. This highlights the key role that link weight plays in traffic fluctuation and the necessity to study traffic fluctuation on weighted networks.
Physics , 2005, DOI: 10.1143/JPSJ.75.014801 Abstract: We investigate a simple multisegment cellular automaton model of traffic flow. With the introduction of segment-dependent deceleration probability, metastable congested states in the intermediate density region emerge, and the initial state dependence of the flow is observed. The essential feature of three-phased structure empirically found in real-world traffic flow is reproduced without elaborate assumptions.
Physics , 2004, DOI: 10.1103/PhysRevE.70.016115 Abstract: Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: 1) models that do not reproduce even qualitatively the most important empirical observations, 2) models that are on a macroscopic level in reasonable agreement with the empirics, and 3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed new light on the relevant interactions in traffic flow.
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# Blood Type Calculator
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An online blood type calculator is specifically designed to estimate blood type punnett square for a baby depending upon the blood groups of both the parents. There exist many confusions about the exact blood group of the new born baby. That is why we have arranged this organic read so that you may not counter any problem while guessing about your child’s blood kind.
Keep reading!
## What Is Blood?
In the light of medical science:
“A specialized fluid that transports the waste materials away from the body cells and provides oxygen and other essential nutrients to them is the blood”
### Major Components of The Blood:
Below are the main substances which the blood is composed of.
Plasma:
A light liquidy component that is totally independent of the blood cells but keeps all of the nutrients present in the blood in a proper suspension. As a whole, plasma constitutes about 55% of the total blood volume.
Red Blood Cells:
These cells are indeed considered as the most abundant material in the blood. Red blood cells are also termed hematite cells, erythrocytes, erythroid cells, and blood corpuscles. It contains a special protein which is called haemoglobin, transporting oxygen from lungs to all parts of the body. They constitute almost 40-45% of the total blood volume.
White Blood Cells:
White cells, also known as granulocytes(basophils, eosinophils, and neutrophils), monocytes and lymphocytes, are part of the immune system of the body. These cells help the body fight against infections or any other illness. In a healthy adult, the white blood cells comprise only 1% volume of the total blood fluid.
Platelets:
Thrombocytes allow the wounds or any injuries to heal fast. They are formed inside the bone marrow and are only 20% of the blood volume.
Here the baby blood type calculator goes for determining the most exact type of the blood your baby will be having, making it easier for you to avoid any dangerous condition.
## Blood Type:
Generally, there are only four main groups of the blood. These are named as A, B, AB, and O. Each of these groups contains particular antigens that differ from type to type. Specially for the mothers that are carrying a baby, it is very cautious to have a know about the baby’s blood group. The free child blood type calculator allows you to predict the blood type so as to avoid any serious illness and difficulty while giving birth to a baby.
Also, aPregnancy calculator also helps you to track your pregnancy period properly for a healthy baby growth.
### Alleles In Blood:
An allele is basically a specific kind of genetic information that is present in our DNA(Deoxyribonucleic Acid) on a particular chromosome. The alleles of the human blood are mainly determined using the co-dominant alleles knowledge. These genes decide the blood type of human beings
Practically, the blood group is determined genetically using the parental blood groups. As there is only one allele that controls the blood group, each human being has two alleles that are used to describe their blood types. These include:
Blood Type A:
Either AO or AA
Blood Type B:
Either BO or BB
Blood Type AB:
Contains allele AB
Blood Type O:
Contains allele OO
The alleles O are recessive while those of AB are dominant. There is a further classification of the blood into two groups that are either RH+ or RH-. The recessive alleles have an RH- group , while that of dominant alleles have RH+ group. It means that RH- blood types parents will result in the same blood type in their babies.
### Blood Type Genetic Chart:
There are eight different blood types that arise from the basic ones. The following blood type chart parents displays all the rules that one must consider while going through blood transfusion table:
Recipient ↓ / Donor → O+ O- A+ A- B+ B- AB+ AB- O+ YES YES NO NO NO NO NO NO O- NO YES NO NO NO NO NO NO A+ YES YES YES YES NO NO NO NO A- NO YES NO YES NO NO NO NO B+ YES YES NO NO YES YES NO NO B- NO YES NO NO NO YES NO NO AB+ YES YES YES YES YES YES YES YES AB- NO YES NO YES NO YES NO YES
This table also assists you when you are using a baby blood type calculator to estimate the blood group of your baby.
### How To Determine The Blood Type?
Every Time, the baby receives only one single allele from either of the parents. Now the question arises: Which parent determines the blood type of the child? If you do not know, do not panic! In this section, we will be resolving an example so that you may get a proper idea about the blood type of the child.
Example:
Just suppose if your blood type is B and that of your partner’s is AB. How to determine blood type from parents for the baby?
Solution:
Well, considering here the use of a free parent blood type calculator will immediately display the chances of your upcoming baby’s blood gene. But it is also very important to determine the blood type probability manually as follows:
• First of all, write your blood group along with its related alleles. As your blood group is B, its accompanying alleles are either BB or BO.
• The chances of B allele in your baby are about 75% and chance of the allele O are only 25%
• Now, write the blood type of your partner. In our case, it is AB. It means your partner has the genotype of AB.
• This shows that your baby will either inherit A allele (50% chance) or B allele (50% chance)
• Now estimate the chances for each blood type by multiplying the probabilities as below:
Genotype BB Chance:
$$75% * 50%$$
$$= \frac{75}{100} * \frac{50}{100}$$
$$= 0.75 * 0.50$$
$$= 0.375 * 100$$
$$= 37.5%$$
Genotype AB Chance:
$$75% * 50%$$
$$= \frac{75}{100} * \frac{50}{100}$$
$$= 0.75 * 0.50$$
$$= 0.375 * 100$$
$$= 37.5%$$
Genotype AO Chance:
$$25% * 50%$$
$$= \frac{25}{100} * \frac{50}{100}$$
$$= 0.25 * 0.50$$
$$= 0.125 * 100$$
$$= 12.5%$$
Genotype BO Chance:
$$25% * 50%$$
$$= \frac{25}{100} * \frac{50}{100}$$
$$= 0.25 * 0.50$$
$$= 0.125 * 100$$
$$= 12.5%$$
Now add the results of BB and BO:
$$37.5% + 12.5%$$
$$50%$$
Which is the blood group chance for group B.
• If the group of both the parents are RH+, then the chances of the RH+ in the baby are about 93.75% and the chances of the RH- is about 6.75%
• If the group of both the parents are RH-, then the chances for RH- group in the baby are 100%
• If the blood type of one of the parents is RH+ and RH – for the other one, then there are about 75% chances that the baby will be having RH+ blood type. For RH- blood type, this chance is reduced to 25%.
Apart from the manual calculations, it is however a better choice to make use of the free blood type predictor.
### How Blood Type Calculator Works?
This free calculator takes a couple of seconds to display the blood group matches for your baby depending upon your own blood type and of your partner’s as well. Let’s find how!
Input:
• Select your blood group along with the RH factor
• Repeat the same process for your partner blood type
• Tap the calculate button
Output:
• The free blood type punnett square calculator determines:
• Chances in terms of percentage regarding your baby’s blood type
• Transfusion table of phenotype and genotype
• Punnett square table for the possible blood types
## FAQ’s:
### Which blood type is considered the best?
In any life threatening emergencies, the type O negative red blood cells are considered as the safest to donate to anyone. The reason for this is that the O negative blood group does not have any antibodies to the antigens like A, B, or RH.
### Why is O positive so special?
In most of the cases, type O positive blood is given to the patients due to its no reaction to most of the blood types. But you must keep one thing in mind that a person having O positive blood group can only receive blood from either O+ or O- blood group bearing persons.
### Can O positive and B positive get marry?
A male with a blood type B+ can get married with a female with a blood group O+.
### What blood type is the rarest?
According to a study, AB- is the rarest blood group with a donor volume of only 1% in all over the world.
### What is the golden blood type?
The golden blood group or RH null blood group is the group that contains no RH antigens on the surface of the red blood cells. If your baby is going to have a golden blood type in future, then you can also determine it by using a free online blood type calculator. This is also considered as the rarest blood type as only 50 people have such blood group around the globe.
### Can your blood type change?
In general, your blood group remains the same through the rest of your life. However, in some cases when a person suffers from cancer or goes through a bone marrow transplant, the blood group changes often. In such cases, if you are expecting a baby after getting healthy enough, then it is very important to estimate your baby blood type by subjecting yourself to a free online blood type calculator.
### Which one is the healthiest type of blood?
Studies have shown that the people with the blood group O have the lowest risks of getting heart diseases. While on the other hand, people with B blood type are more subjected to heart issues.
### What blood group is the commonest in the world?
Blood group O is the most common type with a global percentage of about 37.12%. The second most common blood type is B with a percentage of about 32.26%.
### How do I identify my blood type?
ABO typing is the test that is carried out to determine the blood group manually in the medical laboratory. In this test, your blood is mixed with the antibodies that are against the blood groups A and B. after doing so, it is noticed whether the blood cells stick together or not. If they stick, it means that the blood reacted to one of the antibodies.
### What blood types have memory problems?
As a consequence, people having blood types A, B, and AB are more likely to have memory loss problems.
## Conclusion:
Blood type calculator is very important to use in case when a mother and her child have different blood groups that can cause serious health problems to both of them. In this case, knowing your fetal blood type will help you a lot in blood transfusion to save his/her life.
## References:
From the source of Wikipedia: Blood group systems, Clinical significance, Blood typing | 2022-01-21 20:32:50 | {"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": 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": 0.492352694272995, "perplexity": 2066.483774097212}, "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-2022-05/segments/1642320303709.2/warc/CC-MAIN-20220121192415-20220121222415-00639.warc.gz"} |
http://cs.stackexchange.com/questions/7206/time-complexity-convex-optimization-and-eigen-decomposition | # Time - Complexity Convex Optimization and Eigen Decomposition
Say I had the choice of choosing one out of the following two optimization problems which I could use to solve my problem. Which choice is the fastest? How much of a trade-off would it be? Is the improvement in speed by many factors!?
1. Minimizing a convex function $L(X)$ in one matrix variable with orthogonality constraints over the matrix-essentially in my case this ends up to solving an eigen-decomposition.
2. Minimizing the same convex function $L(X)$ with linear constraints in $X$.
I know that 2.) should be faster. But what is the direction of work I need to do- to compare the improvement in speed-especially in terms of using the fastest available eigen solver for 1.)-what would be the corresponding fastest approach to solve 2.)?
-
## migrated from cstheory.stackexchange.comDec 6 '12 at 7:36
This question came from our site for theoretical computer scientists and researchers in related fields.
a single eigendecomposition might well be faster in practice than convex optimization with linear constraints – Sasho Nikolov Dec 7 '12 at 0:14
Regarding the eigen-decomposition, often it is enough to just compute the first few eigenvalue/eigenvector pairs. In the case, Krylow-subspace methods can be blazingly fast.
For the convex minimization under linear constraints, the (preconditioned) Uzawa iteration is a typical Krylow-subspace method, which is often not bad. There exist probably more advanced algorithms for this problem now, but http://scicomp.stackexchange.com would be a better place to ask about these. Also Schur-complement methods, or just parameterization of the linear sub-space might work fine too. And in case the linear constraints is actually a bunch of linear inequalities, a state of the art linear/convex programming solver might be the way to go.
- | 2014-10-23 10:59:06 | {"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": 0.6798842549324036, "perplexity": 720.8726156365703}, "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-2014-42/segments/1413558065752.33/warc/CC-MAIN-20141017150105-00178-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://www.brendanberthold.com/post/2021-01-06-a-simple-kalman-filter/ | A Simple Kalman Filter
This document is generated with R-Markdown. All related files and code can be found in GitHub
Introduction
This document provides an intuitive and simple introduction to Kalman Filtering.
The document is organised as follows: the first section motivates the usage of a Kalman Filter in an economic context and reviews the related theory. In particular, it focuses on the key results and ideas behind it–as we shall see, the Kalman Filter’s key idea is in reality surprisingly easy to understand. The second section applies the Kalman Filter algorithm to an extremely simple (yet not trivial) state-space model characterised by an AR(1) process as the state equation. The idea behind this is to simplify as much as possible in order to focus on the key elements that will then reveal useful to understand more complex problems.
This document is mostly based on lecture Notes from Prof. Mark Watson (Princeton University) given as part of the program for Beginning Doctoral students in Economics in Gerzensee taught in March 2020 ((Watson (2020)). The lecture notes are themselves heavily based on Hamilton (1995).
The Kalman Filter for Economics : Motivation, theory, and intuition
Motivation and simple intuition
We typically observe economic data over time. These data, however, are likely to be noisy. The Kalman Filter (KF) (in an economic context) usually considers two types of potential noise: measurement and structural noise. More precisely, the KF makes the assumption that observed data are subject to measurement errors and are in reality generated by an unobservable process. This unobservable process is known as the state (or transition) equation and is subject to some noise that we can refer to as “structural”. In that context, the KF is an algorithm that allows to filter out the measurement noise in order to learn more about the true generating process of the data. In particular, it can be used to learn more about so-called structural shocks which are of crucial importance in DSGE models for instance.
The Kalman Filter was first used in physics but is now widely popular in economics.
The theory
Notation
The general form of the Kalman filter as presented in Hamilton Chapter 13 (add ref) is given by a “measurement equation”: \begin{align*} y_t = A'x_t + H'\xi_t + w_t \end{align*} With $$E(w_tw_t')=Q$$
And a transition (or state) equation: \begin{align*} \xi_t = F\xi_{t-1} + v_t \end{align*} With $$E(v_tv_t')=R$$.
In words:
• $$y_t$$ is the vector of observed variables (i.e. the data)
• $$x_t$$ is a vector of deterministic components (we won’t spend time on it in this document)
• $$\xi_t$$ is the unobserved “state” variables
• $$w_t$$ and $$v_t$$ are unobserved, mutually and serially uncorrelated noise variables (which usually follow a Normal Distribution)
• $$A, H, R, F,$$ and $$Q$$ are non-random “system” variables matrices that may depend on unknown parameters (some of them can be retrieved using Maximum Likelihood estimations)
The general system defined by these two equations is flexible and can accomodate a variety of representation. For instance, a standard AR(p) process fits into the general notation in the following way:
Let $$y_t \sim AR(p)$$, that is: \begin{align*} y_t = \phi_1 y_{t-1} + \phi_2y_{t-2} + ... + \phi_py_{t-p} + \epsilon_t \end{align*} This process can be represented as a “state-space” model in the following way: \begin{align*} &\xi_t = \begin{bmatrix} y_t \\ y_{t-1} \\ \vdots \\ y_{t-p+1} \end{bmatrix} \\ &F= \begin{bmatrix} \phi_1 & \phi_2 & \ldots & \phi_{p-1} & \phi_p \\ 1 & 0 & \ldots & 0 & 0 \\ 0 & 1 &&& 0 \\ \vdots & & \ddots & & \vdots \\ 0 &&&1&0 \end{bmatrix} \\ &v_t = \begin{bmatrix} \epsilon_t \\ 0 \\ \vdots \\ 0 \end{bmatrix} \end{align*}
And $$w_t=0, A=0,$$ and $$H'=\begin{bmatrix}1 & 0 & \ldots & 0\end{bmatrix}$$
Procedure and idea of the Kalman Filter
Notation:
• $$y_{1:t} = \left\{y_i\right\}^t_{i=1}$$
• $$\xi_{t|k} = E(\xi_t|y_{1:k})$$
• $$P_{t|k}=Var(\xi_{t}|y_{1:k})$$
In words, the Kalman filter is a recursive algorithm that constructs $$\xi_{t|t}$$ and $$P_{t|t}$$ from known values in $$t$$, that is $$y_t,x_t, \xi_{t-1|t-1}, P_{t-1|t-1}$$.
To derive the filter, we assume that both $$w_t$$ and $$v_t$$ follow iid Gaussian process, that is:
$\begin{bmatrix} w_t \\ v_t \end{bmatrix} \sim N \left(\begin{bmatrix} 0 \\ 0\end{bmatrix}, \begin{bmatrix} R & 0\\ 0 & Q \end{bmatrix}\right)$
This notably implies that both $$y_t$$ and $$\xi_t$$ follow a joint Normal distribution. Since errors are Gaussian, the best estimator (in the sense that it minimises the mean squared error) is given by the conditional expectation.
To find the conditional expectation of $$\xi_t$$ and $$y_t$$ (that is $$\xi_{t|t}$$ and $$y_{t|t}$$), we can use the following theorem of the conditional distribution of a multivariate normal:
Suppose that:
$\begin{bmatrix} z_1 \\ z_2 \end{bmatrix} \sim N \left(\begin{bmatrix}\mu_1 \\ \mu_2 \end{bmatrix}, \begin{bmatrix}\Sigma_{11} &\Sigma_{12}\\\Sigma_{21}&\Sigma_{22}\end{bmatrix}\right)$
Then:
$E(z_1|z_2) = \mu_1 + \Sigma_{12}\Sigma_{22}^{-1}(z_2 - \mu_2) \\ Var(z_1|z_2) = \Sigma_{11} - \Sigma_{12}\Sigma_{22}^{-1}\Sigma_{21}$
The application of this theorem is the key idea of the Kalman Filter.
Defining $$z_1 = \xi_t$$ and $$z_2 = y_t$$, and recognizing that $$\xi_t$$ and $$y_t$$ are jointly Normal conditional on past values, we can write the following:
$\begin{bmatrix} \xi_t \\ y_t \end{bmatrix} \Bigg | y_{1:t-1}\sim \mathcal{N}\left(\begin{bmatrix} \xi_{t|t-1} \\ y_{t|t-1} \end{bmatrix}, \begin{bmatrix} P_{t|t-1} & \Sigma_{\xi,y|t-1} \\\Sigma_{\xi,y|t-1} & \Sigma_{yy|t-1} \end{bmatrix}\right)$
Using the formula of the conditional normal:
\begin{align*} \xi_{t|t}= \xi_{t|t-1} + \Sigma_{\xi,y|t-1}\Sigma_{yy|t-1}^{-1}(y_t-y_{t|t-1}) \\ P_{t|t} = P_{t|t-1} - \Sigma_{\xi,y|t-1}\Sigma_{yy|t-1}^{-1}\Sigma_{\xi,y|t-1} \end{align*}
Assuming $$\xi_{t-1|t-1}$$ and $$P_{t-1|t-1}$$ are known, the Kalman Filter algorithm is given by:
\begin{align*} &\xi_{t|t-1} = F\xi_{t-1|t-1} \\ &y_{t|t-1} = A'x_t + H'\xi_{t|t-1} \\ &P_{t|t-1} = FP_{t-1|t-1}F' + Q \\ &\Sigma_{yy|t-1} = H'P_{t|t-1}H + R \equiv h_t \\ &\Sigma_{\xi,y|t-1}\Sigma_{yy|t-1}^{-1} = P_{t|t-1}H h_t^{-1} \equiv K_t \\ &\eta_t = y_t-y_{t|t-1} \end{align*}
Applying the theorem, we get:
\begin{align*} &\xi_{t|t} = \xi_{t|t-1} + K_t \eta_t\\ &P_{t|t} = P_{t|t-1} - K_t H'P_{t|t-1} \end{align*}
If the process is covariance stationary, we can initialize it by assuming $$\xi_{0|0}=0$$ and using a reasonable estimate of $$P_{0|0}$$. We can then retrieve $$\xi_{t|t}$$, and $$P_{t|t}$$ for all $$t>0$$ applying this procedure recursively.
Application
To better understand the algorithm let us consider the following (uni-dimensional) simple example.
The state space model is of the form:
\begin{align*} &y_t = \phi \xi_t + w_t \\ &\xi_t = \xi_{t-1} + v_t \end{align*} For simplicity, we assume that the transition equation is known with certainty and that $$\phi=$$ 0.8. Moreover, we assume that $$w_t$$ and $$v_t$$ are i.i.d and independent of one another with $$\sigma^2_w=$$ 1 and $$\sigma^2_v=$$ 1.
With that information, we can generate $$y_t$$. Next graph provides a graphical representation.
The last step is to initalize the loop. We assume $$\xi_{0|0}=0$$ because the process is covariance stationary, and $$P_{0|0}=1$$ arbitrarily.
The algorithm
Since $$\xi_{0|0}$$ and $$P_{0|0}$$ are known, we can recursively compute $$\xi_{t|t}$$ and $$P_{t|t}$$ for $$t>0$$ using the Kalman Filter algorithm:
\begin{align*} &\xi_{t|t-1}= \phi \xi_{t-1|t-1} \\ &y_{t|t-1} = \xi_{t|t-1} \\ &P_{t|t-1} = \phi^2P_{t-1|t-1} + \sigma_v^2 \\ &h_t \equiv Var(y_t|t-1) = P_{t|t-1} + \sigma^2_w \\ &K_t = Cov(\xi_t,Y_t|t-1)\times h_t = P_{t|t-1}\times h_t^{-1} \\ &\eta_t = y_t-y_{t|t-1} \end{align*}
Using this, we can get our next period KF forecast:
\begin{align*} \xi_{t|t} = \xi_{t|t-1} + K_t\times \eta_t \\ P_{t|t} = P_{t|t-1} - K_t\cdot Cov(\xi_t,Y_t|t-1) \end{align*}
See R-script for its implementation in R.
The next graph provides a graphical representation resulting from this procedure. The blue line represents $$\xi_{t|t}$$ for all $$t$$ while the black one is the generated data.
To check the validity of the Kalman Filter, one can for instance plot the true process (thus without measurement errors) against our freshly derived Kalman Filter. Note that, in general, this cannot be done as one typically does not the true generating process.
To further check the validity of our Kalman Filter, we can plot the actual measurement noise (which we randomly generated) with the KF measurement noise (which is retrieved by subtracting our Kalman forecast to the the generated data). As we can see on the next plot, the two match quite closely, indicating that our Kalman Filter was able to filter out the measurement noise quite succesfully.
Another check is to compare the actual state noise (or structural shocks depending on the context) with the ones implied by the Kalman Filter. In general, this is not something that can be done as the process that generates the data is not known with certainty. Here, as we generated the data ourselves, it is however possible to perform such a test. State noise implied by the Kalman Filter is equal to our estimate of $$\xi_{t|t}$$ minus the actual AR(1) process without the state (or structural) noise. Next plot provides a graphical representation.
Conclusion
This document provides a purposefully very simple application of a Kalman Filter. My wish was to be able to focus on the key ideas behind it. More complex version of this problem would for example be to consider a multi-dimensional state-space model with unknown parameters that would require to be estimated using a Maximum Likelihood estimation. I would, however, argue that considering such settings would not have added much value given that the aim of this document was to understand what is a Kalman Filter and what it does in words. I hope it is clearer now.
If you notice any typos, errors, or omissions, feel free to send a mail to this address: .
References
Hamilton, James D. 1995. “Time Series Analysis.” International Journal of Forecasting 11 (3): 494–95. https://ideas.repec.org/a/eee/intfor/v11y1995i3p494-495.html.
Watson, Mark. 2020. “Program for Beginning Doctoral Students in Economics.” Gerzensee.
Brendan Berthold
PhD Candidate
I am interested in applied macroeconomics, forecasting, and international finance and macroeconomics. I also love cinema and photography. | 2021-06-20 16:10:09 | {"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": 0.9984639883041382, "perplexity": 717.9921166249218}, "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-2021-25/segments/1623488249738.50/warc/CC-MAIN-20210620144819-20210620174819-00410.warc.gz"} |
http://www.webkursi.lv/web2007a/site/hw20_antlr.html | ## Homework 20: Use Antlr parser generator
Goal:
Use Antlr parser generator to deal with a custom non-XML markup.
Description:
Process a subset of LaTeX expressions of mathematical formulae in order to create their MathML representation. For example, convert \frac{2}{3} (fraction 2/3) into a MathML notation. See HW4 for more information about MathML. | 2020-07-03 16:51:57 | {"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": 0.9602920413017273, "perplexity": 11498.245494249122}, "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/1593655882634.5/warc/CC-MAIN-20200703153451-20200703183451-00212.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/80059-lifetime-tires.html | Here is the question:
For a tire manufacturing company, it is known that only 7% of their tire
products last less than 35 months, whereas 11% of them last more tham 63
months. Assuming the distribution of the lifetime of the manufactured tires
is normal,
(a) what is the expected lifetime for a tire manufactured by this company,
and its standard deviation?
(b) The manufacturer company gives a warranty that if the tire does not last
more than 40 months, they will give a replacement for it. The company
sold 1000 tires during the last year. What is the probability that they
will have to replace more than 50 tires?
---
So I have
a) P (X <= 35 months) = 0.07
P (X >= 63 months) = 0.11
and for b I've started with...
b) P ( X <= 40 months) = ...?
Where do I go from here, for each part?
Thank you so much in advance : )
2. $Z={X-\mu\over \sigma}$, so $X=\mu + \sigma Z$
Now match up percentile points.
When X=35 we have the lower 7 percentile of a Z, known as $Z_{.07}\approx$ -1.47 or -1.48.
That's via the tables, but you can do better via a link on line.
And when X=63 we have the upper 11 percentile of a Z, known as $Z_{.11}\approx$ 1.22 or 1.23.
You now have two equations with two unknowns. Find $\mu$ and $\sigma$.
IN part (b) you have a binomial question, where n=1000 and a success is for a tire to fail before 40 months.
So $p=P(X<40)=P\biggl(Z<{40-\mu\over\sigma}\biggr)$.
HOWEVER, the question should ask you to APPROXIMATE this via the Central Limit Theorem.
Otherwise you need to obtain via a summation
$P(BINOMIAL >50)=\sum_{x=51}^{1000}{1000\choose x}p^x(1-p)^{1000-x}$
or you can use the complement.
BUT I bet they want you to approximate via the normal distribution.
-----------------------------------------------------------
I was just surfing and I found...
http://bayes.bgsu.edu/nsf_web/jscrip...ormal_icdf.htm
Plug in mean 0, st dev 1, prob .07 and I got....-1.4749
Plug in mean 0, st dev 1, prob .89 and I got....1.2249
3. Gotcha, thank you! | 2017-10-22 01:23:21 | {"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": 8, "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": 0.5307731628417969, "perplexity": 1454.0740417746085}, "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/1508187824931.84/warc/CC-MAIN-20171022003552-20171022023552-00287.warc.gz"} |
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/108/1/87239/primitive-lucas-d-pseudoprimes-and-carmichael-8211-lucas-numbers | JEDNOSTKA NAUKOWA KATEGORII A+
# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty
## Primitive Lucas $d$-pseudoprimes and Carmichael–Lucas numbers
### Tom 108 / 2007
Colloquium Mathematicum 108 (2007), 73-93 MSC: Primary 11Y11, 11B39; Secondary 11A51, 11A41, 11B37. DOI: 10.4064/cm108-1-7
#### Streszczenie
Let $d$ be a fixed positive integer. A Lucas $d$-pseudoprime is a Lucas pseudoprime $N$ for which there exists a Lucas sequence $U(P,Q)$ such that the rank of appearance of $N$ in $U(P,Q)$ is exactly $(N - \varepsilon(N))/d$, where the signature $\varepsilon(N) = (\frac{D}{N})$ is given by the Jacobi symbol with respect to the discriminant $D$ of $U$. A Lucas $d$-pseudoprime $N$ is a primitive Lucas $d$-pseudoprime if $(N - \varepsilon(N))/d$ is the maximal rank of $N$ among Lucas sequences $U(P,Q)$ that exhibit $N$ as a Lucas pseudoprime.
We derive new criteria to bound the number of $d$-pseudoprimes. In a previous paper, it was shown that if $4\nmid d$, then there exist only finitely many Lucas $d$-pseudoprimes. Using our new criteria, we show here that if $d = 4m$, then there exist only finitely many primitive Lucas $d$-pseudoprimes when $m$ is odd and not a square.
We also present two algorithms that produce almost every primitive Lucas $d$-pseudoprime with three distinct prime divisors when $4\,|\,d$ and show that every number produced by these two algorithms is a Carmichael–Lucas number. We offer numerical evidence to support conjectures that there exist infinitely many Lucas $d$-pseudoprimes of this type when $d$ is a square and infinitely many Carmichael–Lucas numbers with exactly three distinct prime divisors.
#### Autorzy
• Walter CarlipDepartment of Mathematics
Franklin and Marshall College
Lancaster, PA 17604, U.S.A.
e-mail
• Lawrence SomerDepartment of Mathematics
Catholic University of America
Washington, DC 20064, U.S.A.
e-mail
## Przeszukaj wydawnictwa IMPAN
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Odśwież obrazek | 2022-08-16 11:39:39 | {"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": 0.5801030993461609, "perplexity": 1693.6265282645734}, "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-2022-33/segments/1659882572286.44/warc/CC-MAIN-20220816090541-20220816120541-00357.warc.gz"} |
https://www.physicsforums.com/threads/equal-commutators.359148/ | # Equal commutators
Hi.
Cohen-Tannoudji has this section in his quantum mechanics book where he derives a bunch of relations which are true for operators having the commutation relation $[Q,P]=i\hbar$. Is there any special significance to this value of a commutator? Would things be much different if it had the value 1 ?
Also, if we have two sets of operators with the same commutator, i.e. $[x,p]=[Q,P]=i\hbar$, what does this tell us about the relations between the operators, if anything?
nicksauce
Homework Helper
Take the hermitian conjugate of each side. If the operators are Hermitian, then you get
[P,Q] = -ih = -[Q,P], which is exactly what you expect based on the definition of a commutator. If you had [Q,P] = 1, then this process would lead to a contradiction if your operators are Hermitian.
Ah, so that's why it's important that it's imaginary! Great. What about sets of operators with the same commutator? I know that if we have two Hamiltonians of the same form, i.e.
$$H=a^{\dagger} a+\frac{1}{2}$$
$$H=b^{\dagger} b+\frac{1}{2}$$
and $[a^{\dagger},a]=[b^{\dagger},b]$ then the Hamiltonians will have the same eigenvalues. Is there more we can say? I've heard that all of quantum mechanics can be based on commutators...
nicksauce | 2021-10-15 22:48:45 | {"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": 0.7894452214241028, "perplexity": 246.51261017619285}, "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/1634323583087.95/warc/CC-MAIN-20211015222918-20211016012918-00572.warc.gz"} |
https://socratic.org/questions/59e97340b72cff06ee084c2f | # Question #84c2f
Jan 11, 2018
x=30° or 150°
#### Explanation:
$2 \csc x - 2 = \csc x$
$2 \csc x - \csc x = 2$
$\csc x = 2$
This is possible when x is either 30° or 150°
The image below shows sine and cosine functions for different angles.
Hope it helps you
Jan 12, 2018
${30}^{\circ} , \mathmr{and} {150}^{\circ}$
#### Explanation:
2csc x - 2 = csc x
csc x = 2
$\sin x = \frac{1}{\csc x} = \frac{1}{2}$
Trig table and unit circle give 2 solutions:
$x = \frac{\pi}{6} , \mathmr{and} x = {30}^{\circ}$, and and $x = \frac{5 \pi}{6} , \mathmr{and} x = {150}^{\circ}$ | 2021-01-23 05:01:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "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": 0.8463118672370911, "perplexity": 8046.490259884951}, "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-2021-04/segments/1610703533863.67/warc/CC-MAIN-20210123032629-20210123062629-00634.warc.gz"} |
https://learn.careers360.com/ncert/question-find-the-values-of-x-y-and-z-from-the-following-equations-iii-x-plus-y-plus-z-x-plus-z-x-plus-z-y-plus-z-equal-to-9-5-7/ | Q
# Find the values of x, y and z from the following equations: (iii) [x+y+z x+z y+z] = [9 5 7 ]
Q6. Find the values of x, y and z from the following equations:
(iii)
$\begin{bmatrix} x + y + z\\ x + z \\ y + z \end{bmatrix} = \begin{bmatrix} 9\\5 \\7 \end{bmatrix}$
Views
(iii)
$\begin{bmatrix} x + y + z\\ x + z \\ y + z \end{bmatrix} = \begin{bmatrix} 9\\5 \\7 \end{bmatrix}$
If two matrices are equal, then their corresponding elements are also equal
$x+y+z=9........(1)$
$x+z=5..............(2)$
$y+z=7..............(3)$
subtracting (2) from (1) we will get y=4
substituting the value of y in equation (3) we will get z=3
now substituting the value of z in equation (2) we will get x=2
therefore,
$x=2$, $y=4$ and $z=3$
Exams
Articles
Questions | 2020-02-19 03:19:42 | {"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": 8, "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": 0.9092956185340881, "perplexity": 616.1393072587628}, "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-2020-10/segments/1581875144027.33/warc/CC-MAIN-20200219030731-20200219060731-00055.warc.gz"} |
https://franklin.dyer.me/notes/note/Higher_derivative_of_holomorphic_functions | ## Franklin's Notes
### Higher derivatives of holomorphic functions
Given a continuous function $\varphi$ on a curve $\gamma\subset\mathbb C$, we may consider the function which is defined for $z\notin\gamma$. Note that this strongly resembles the integral considered in the Cauchy integral formula .
Let's start by showing that $F_1$ is a continuous function. If we fix some $z_0\in\mathbb C\backslash \gamma$, we may choose an open ball of some radius $\delta>0$ about $z_0$ that does not intersect $\gamma$, so that $|\zeta-z_0| > \delta$ for all $\zeta\in\gamma$.
Now, let us consider the difference of the two functions $F_1(z)-F_1(z_0)$ for some $z$ inside of $B_{\delta/2}(z_0)$, the ball centered at $z_0$ with half of the aforementioned radius. We may calculate using linearity of the integral that so we have that Now, because $z\in B_{\delta/2}(z_0)$, we have that $|\zeta-z|>\delta/2$ and $|\zeta-z_0|>\delta/2$ for all $\zeta\in\gamma$. This means that which is a uniform bound in $\zeta$, because we have chosen $\delta$ in terms of $z$ such that this bound holds for all $\zeta\in\gamma$. Hence, we have that or This means that we have and therefore not only is $F_1$ continuous, but it is also differentiable with $F_1'=F_2$.
By induction, we may also establish that $F_n'=nF_{n+1}$ for each $n\in\mathbb N$, making each $F_n$ holomorphic on the regions determined by $\gamma$, or the complement of $\gamma$ in $\mathbb C$. An important consequence of this result is the following:
Proposition 1. If $f(z)$ is holomorphic, then it has derivatives of all orders, and further where $\gamma$ is a closed curve such that $\mathrm{ind}(\gamma,z)=1$.
Proof. By the Cauchy integral formula , we have that so that if we choose $\varphi=f$, we have $F_1=f$, and all further formulae for the derivatives $f^{(n)}$ follow from the fact that $F_n'=nF_{n+1}$ for each $n\in\mathbb N$. $\blacksquare$ | 2023-02-07 00:51:33 | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9848604202270508, "perplexity": 50.11006686443843}, "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/1674764500368.7/warc/CC-MAIN-20230207004322-20230207034322-00265.warc.gz"} |
https://wizedu.com/questions/195559/legislation-is-drawn-up-by-draftsmen-and-a | In: Finance
# “Legislation is drawn up by draftsmen, and a draftsman’s capacity to anticipate the future is limited....
“Legislation is drawn up by draftsmen, and a draftsman’s capacity to anticipate the future is limited. He may not foresee some future possibility, or overlook a possible misinterpretation of the original intentions of the legislation.” Considering the above statement, discuss the rules of Statutory Interpretation. (1500 words)
## Solutions
##### Expert Solution
The term legal translation alludes to the activity of a court in attempting to comprehend and clarifying the importance of a bit of enactment. Numerous cases go to advance on a state of understanding, Indeed, Lord Hailsham, a senior English adjudicator, once said that "likely 9 out of 10 cases heard by the Court of Appeal and the House of Lords turn upon or include the importance of words contained in resolution or optional enactment."
Why would that be the situation? In the first place, laws must be drafted by and large terms and should manage both present and future circumstances. Frequently, a law which was drafted in light of one specific circumstance will inevitably be applied to very various circumstances. An exemplary model is the UK Criminal Justice Act, some portion of which was initially intended to check unlawful distribution center gatherings however which was later used to squash exhibits, regularly including individuals from altogether different foundations to those going to the alleged raves.
Enactment is drawn up by designers, and a sketcher's ability to envision what's to come is restricted. He may not anticipate some future chance, or disregard a potential error of the first expectations of the enactment. Another issue is enactment frequently attempts to manage issues that include unique and clashing interests.
Both lawful and general English contain numerous words with more than one importance. Truth be told, a portion of the terms in TransLegal's Legal English Dictionary have at least seven particular definitions. With this being the situation, even the best drafted enactment can incorporate numerous ambiguities. This isn't the shortcoming of the artist, just an impression of the way that where individuals take a gander at a book from various perspectives they will normally discover various implications in the language utilized.
Judges in England by and large apply three essential guidelines of legal understanding, and comparable principles are likewise utilized in other customary law wards. The strict standard, the brilliant guideline and the wickedness rule. Despite the fact that judges are will undoubtedly apply these standards, they by and large take one of the accompanying three methodologies, and the methodology taken by any one specific appointed authority is frequently an impression of that judge's own way of thinking.
The Literal Rule
Under the exacting guideline (likewise: the customary significance rule; the plain importance rule), it is the assignment of the court to give a resolution's words their strict importance whether or not the outcome is reasonable or not. In a celebrated judgment, Lord Diplock in Duport Steel v Sirs (1980) said "The courts may now and then be happy to apply this standard regardless of the show ridiculousness that may result from the result of its application." The strict guideline is regularly applied by conventional appointed authorities who accept that their protected job is restricted to applying laws as authorized by Parliament. Such adjudicators are careful about apparently creating law, a job which they see as being carefully restricted to the chosen administrative part of government. In deciding the aim of the council in passing a specific rule, this methodology limits an adjudicator to the alleged dark apparent aim of the law. The strict standard has been the predominant methodology taken for more than 100 years.
The Golden Rule
The brilliant standard (likewise: the British principle) is a special case to the strict guideline and will be utilized where the exacting standard delivers the outcome where Parliament's goal would be evaded as opposed to applied. In Gray v Pealson (1857), Lord Wensleygale said : "The strict principle ought to be utilized first, yet on the off chance that it brings about silliness, the linguistic and standard feeling of the words might be altered, to stay away from ridiculousness and irregularity, however no further."
One case of the use of the brilliant principle is the situation of R v Allen – Defendant is accused of polygamy, an offense denied in Offenses Against Persons Act 1861 which peruses "whoever is hitched, weds another submits plural marriage." The court held that "weds" need not mean an agreement of marriage as it was inconceivable for an individual who is as of now wedded to go into another substantial agreement of marriage. Thus, the court deciphered it as "experiencing wedding function".
The Mischief Rule
The last principle of legal translation is the naughtiness rule, under which an appointed authority endeavors to decide the official's goal; what is the "underhandedness and deformity" that the rule being referred to has embarked to cure, and what administering would viably execute this cure? The exemplary articulation of the naughtiness decide is that given by the Barons of the Court of Exchequer in Heydon's Case (1854): "… for the sure and genuine understanding of all resolutions all in all, four things are to be perceived and thought of:
1. What was the precedent-based law before the creation of the Act?
2. What was the wickedness and deformity for which the precedent-based law didn't give?
3. What cure the Parliament hath settled and delegated to fix the sickness of the Commonwealth?
4. The genuine explanation of the cure; and afterward the workplace of all the appointed authority is consistently to make such development or will stifle inconspicuous innovations and avoidances for continuation of the wickedness and ace private commodo, and to add power and life to the fix and cure, as per the genuine plan of the producers of the Act, free publico.
This arrangement of depending on outer sources, for example, the precedent-based law in deciding the genuine expectation of the parliament is currently observed as a component of the purposive methodology, the methodology for the most part taken in the common law wards of territory Europe. In spite of the fact that the exacting methodology shares been predominant practically speaking law frameworks for longer than a century, makes a decision about now give off an impression of being less limited by the dark stated purpose of the law and are all the more ready to attempt to decide the genuine goal of the Parliament. The assignment of the adjudicator is currently observed as being offer impact to the authoritative motivation behind the rule being referred to.
Just as these three principles of understanding, there are various standards that are held to apply while deciding the significance of a resolution:
1. The resolution is assumed not to tie the Crown
2. Resolutions don't work reflectively in regard to considerable law (rather than procedural law)
3. They don't meddle with legitimate rights previously vested
4. They don't remove the ward of the courts
5. They don't degrade sacred law or global law
At long last, there are various characteristic (=interal) and extraneous (=external) helps to legal translation.
Natural (Internal) Aids to Statutory Interpretation
These are things found inside the resolution which assist decided with understanding the importance of the rule all the more unmistakably.
• the long and the short title
• the preface
• definition segments
• plans
Extraneous (External) Aids to Statutory Interpretation
These are things found outside of the genuine rule which might be considered by judges to assist them with understanding the significance of a resolution all the more obviously.
• word references
• authentic setting
• past rules
• prior case law
• Hansard
• Law Commission Reports
• International Conventions
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https://fangquant.com/t/1002 | FangQuant › Daily Morning
### Daily Market Review on Specified Futures Products 2020.10.20
submitted 2020-10-20 14:17:56
Crude oil
Crude Oil: OPEC the implementation of production cut rate remains at high level
From the report of the three major institutions in October, OPEC’s September output dropped slightly to 24 million barrels per day, and the implementation rate of production cuts remained above 100%. Looking at different countries, Saudi Arabia’s September output increased by 100,000 barrels per day. The UAE has cut production by 100,000 barrels per day. Other countries have not changed much. Libya's production has increased slightly. At this point, we expect that OPEC's strict implementation of production restrictions will not change. However, due to the resumption of production in Libya, OPEC production is expected to be 24.5 million barrels per day. The current market is focusing on whether the OPEC JMMC meeting at the end of the year will increase production by 2 million barrels per day in January next year as planned. Previously, Rongsheng Group purchased an additional 10 million barrels of crude oil in the Middle East spot market, which caused widespread market concern, in addition, due to the second phase of Zhejiang Petrochemical plant is expected to be put into the trial operation at the end of the year, we believe that OPEC's production increase is a high probability event under the expectation that the Asia-Pacific large refining and chemical projects will be put into operation in the future, but it is still unknown whether the market can match the increase in the market demand .
Strategy: Neutral and bearish relatively, reverse cash and carry arbitrage strategy on Brent, long the sixth lines and short the first line
Risk: supply disruption caused by geopolitical events and sustained sharp depreciation of the US dollar
Iron Ore
On October 19th, 2020, the position on I2101 contract increased by 5315 and closed at ¥791.5 per ton, the position on I2105 contract increased by 235 and closed at ¥739.0 per ton.
Important Information
1. According to news on October 19, Brazilian mining company Vale SA announced on Monday that its iron ore output increased in the third quarter, and it is expected that the output in the fourth quarter in some areas will increase further due to the commissioning of multiple mines or accelerated production. The output of iron ore in this quarter was 88.7 million tons, an increase of 31.2% from the previous quarter and an increase of 2.3% from the same period last year. The company added that some logistics issues in the iron ore pellet and iron powder market were resolved in September, which will improve the timing between production and sales in the fourth quarter of the field.
2. According to data from the National Bureau of Statistics, in the third quarter of 2020, the capacity utilization rate of the ferrous metal smelting and rolling processing industry was 81.6%, an increase of 2.2% over the same period of the previous year; the capacity utilization rate of the ferrous metal smelting and rolling processing industry in the first three quarters was 77.7 %, a decrease of 2.2 percentage points from the same period last year.
3. In terms of spot, the PB powder in Rizhao Port was ¥859 per ton, golden bubba powder price was equivalent to ¥941 per ton,
1. In terms of supply, the number of shipments from Australia were basically flat, while Brazil saw a slight decline. The overall shipment level was still at a high level during the same period, and the supply pressure was relatively high. In terms of demand, the average daily molten iron output has decreased, and the average daily port dredging has decreased, coupled with environmental protection restrictions and new blast furnace maintenance, the overall demand has weakened. In terms of ports, the pressure on ports has increased and the dredging has decreased. Iron ore port inventories continue to accumulate. There is still a greater pressure to reduce prices in later stages, but the range of discount is relatively large. It is expected to be weak and volatile. It is suggested to long 01 coking coal and short on 01 iron ore
2. Option strategy: It is advised to hold the short position on i2101-C-870. (For reference only)
PTA
The second phase of Dushan Energy was put into production, and polyester production and sales fell slightly.
In October, we will continue to estimate the de-stocking, follow up by the implementation of the overhaul and the continuity of demand improvement. There is an expectation of rigid accumulation in November and December.
In terms of the unilateral strategy, it is advised to be neutral; for the strategy across varieties, the current TA pattern is long in short-term and short in long-term, in late October, there is a chance to continue the rebound; in addition, the accumulated warehouse concerns from November to December followed by the peak of seasonal terminal loaded, and the rebound gives space for varieties allocation; for strategy across period, it is advised to focus on the reverse cash and carry strategy opportunity after the next round of TA overhauls fulfilling and rebound of 1-5 spread. It is advised to focus on PTA factory inspection and fulfillment wishes, and the downstream restocking space and improvement of demand.
Natural Rubber
RU: October 19th, 2020, the main force contract of RU01 down by 50 or 0.36% and closed at 14,025. The main force contract of JRU03 up by 3.5 or 1.74% and closed at 204.1. Yunnan WF closed at 13,500 to 13,650 yuan per ton, Hainan SCRWF closed at 13,650 to 13,700 per ton, the secondary standard rubber closed at 11,800 per ton, and Thailand’s RSS3 closed at 17,500 yuan per ton.
NR: The main force contract of NR12 down by 45 or 0.44% and closed at 10,135. The main force contract of TF12 up by 2.3 or 1.53% closed at 152.8. Qingdao rubber in USD up by $30 per ton. The spot or CIF of STR20 was$1,620 to $1,650 per ton. The CIF of SIR20 in October was$1,520 to $1,550 per ton. The CIF of mixed rubber from Thailand in January was$1,570 per ton to \$1,580 per ton.
Tire Business News: It is understood that the Egyptian State-owned Chemical Industry Holding Company (CIHC), has signed a cooperation agreement with the Egyptian Ministry of Public Enterprise Development (NOMP) and the Arab Organization for Industrialization (AOI). Under the terms of the new agreement, a national industrial alliance will be established, which will manufacture tires for various types of cars, tractors and heavy equipment. In order to implement the plan, a new tire factory will be established in the city of Ain Sokhna in the Suez Canal Economic Zone. The area is approximately 450,000 square meters.
Futures Operation Advice: There is an intensive volume of rainfall in Hainan area. The local latex is reported to be 12,500 yuan/ton, the premium is 650 yuan/ton for the Yunnan glue, and the Hainan thick latex is about -2800 yuan/ton. The high premium indicates that the limitation of Hainan latex supply cannot meet the demand for concentrated latex and full latex at the same time, which is rare in the peak production season. Downstream tire inventories are transferred from factories to the traders, and it is reported that the terminal shipments have slowed down. For the main RU01 contract, it is suggested to long a slight position and pay attention to the pressure at the recent high level. (For reference only) | 2020-12-01 14:31:45 | {"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": 0.23985826969146729, "perplexity": 3515.224043723253}, "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/1606141674594.59/warc/CC-MAIN-20201201135627-20201201165627-00153.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/int3/chapter/6/lesson/6.2.3/problem/6-57 | ### Home > INT3 > Chapter 6 > Lesson 6.2.3 > Problem6-57
6-57.
Use the ideas from problem 6-56 to help you solve the following equations.
1. $\log(10)=\log(2x-3)$
If $\log a=\log b$, then $a = b$.
$10 = 2x − 3$
$x = 6.5$
1. $\log(25) = \log(4x^2 - 5x - 50)$
See part (a). | 2022-06-29 09:20:30 | {"extraction_info": {"found_math": true, "script_math_tex": 6, "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": 0.9284151196479797, "perplexity": 5730.993312951189}, "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/1656103626162.35/warc/CC-MAIN-20220629084939-20220629114939-00069.warc.gz"} |
https://openreview.net/forum?id=SygD31HFvB | A Novel Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization
Sep 25, 2019 Blind Submission readers: everyone Show Bibtex
• Keywords: convex optimization, lower bound complexity, proximal incremental first-order oracle
• Abstract: This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for each individual component. For the strongly-convex case, we prove such an algorithm can not reach an $\eps$-suboptimal point in fewer than $\Omega((n+\sqrt{\kappa n})\log(1/\eps))$ iterations, where $\kappa$ is the condition number of the objective function. This lower bound is tighter than previous results and perfectly matches the upper bound of the existing proximal incremental first-order oracle algorithm Point-SAGA. We develop a novel construction to show the above result, which partitions the tridiagonal matrix of classical examples into $n$ groups to make the problem difficult enough to stochastic algorithms. This construction is friendly to the analysis of proximal oracle and also could be used in general convex and average smooth cases naturally.
• Original Pdf: pdf
0 Replies | 2020-08-07 18:42:29 | {"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": 0.9041680097579956, "perplexity": 472.7361938168512}, "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-2020-34/segments/1596439737206.16/warc/CC-MAIN-20200807172851-20200807202851-00009.warc.gz"} |
https://zbmath.org/?q=ut%3A%5C%28p%5C%29-adic+%5C%28q%5C%29-integrals | ## Found 82 Documents (Results 1–82)
100
MathJax
### Some explicit expressions for twisted $$q$$-analogues of Catalan numbers and polynomials. (English)Zbl 07622439
MSC: 05A19 11B83
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### A new refinement of the generalized Hölder’s inequality with applications. (English)Zbl 07554046
MSC: 26D07 33B15 33B20
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### A note on $$q$$-analogue of Catalan numbers arising from fermionic $$p$$-adic $$q$$-integral on $$\mathbb{Z}_p$$. (English)Zbl 1492.11041
MSC: 11B68 11S80
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### Analysis of Apostol-type numbers and polynomials with their approximations and asymptotic behavior. (English)Zbl 1476.11061
Rassias, Themistocles M. (ed.), Approximation theory and analytic inequalities. Cham: Springer. 435-486 (2021).
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### Estimates for multilinear commutators of Hardy-type operators on $$p$$-adic function spaces. (Chinese. English summary)Zbl 1474.42063
MSC: 42B20 42B35 47B47
### $$\overline{q}$$-gamma-beta functions on quantum integral. (English)Zbl 1467.33001
MSC: 33B20 11S80 45P05
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### Factors of some truncated basic hypergeometric series. (English)Zbl 1448.33016
MSC: 33D05 11A07 11F33
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### Symmetric identities of higher-order degenerate $$q$$-Bernoulli polynomials. (English)Zbl 1371.05006
MSC: 05A10 11B68 11S80
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### Analysis of the $$p$$-adic $$q$$-Volkenborn integrals: an approach to generalized Apostol-type special numbers and polynomials and their applications. (English)Zbl 1426.11015
MSC: 11B68 11S80
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### Identities of symmetry for degenerate $$q$$-Euler polynomials. (English)Zbl 1360.11044
MSC: 11B68 11S80
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### Maximal function and Riesz potential on $$p$$-adic linear spaces. (English)Zbl 1284.42044
MSC: 42B20 42B25
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### Some properties of the $$q$$-extension of the $$p$$-adic gamma function. (English)Zbl 1277.33016
MSC: 33D05 11S80
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### A study on the $$q$$-Euler numbers and the fermionic $$q$$-integral of the product of several type $$q$$-Bernstein polynomials on $$\mathbb Z_p$$. (English)Zbl 1275.11042
MSC: 11B68 11S80
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### Calculating zeros of $$q$$-extension of the second kind Bernoulli polynomials. (English)Zbl 1287.11038
MSC: 11B68 11S80 33D45
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### Some results for the $$q$$-Bernoulli, $$q$$-Euler numbers and polynomials. (English)Zbl 1273.11038
MSC: 11B68 11S40 11S80
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### A family of Barnes-type multiple twisted $$q$$-Euler numbers and polynomials related to fermionic $$p$$-adic invariant integrals on $$\mathbb Z_p$$. (English)Zbl 1256.11015
MSC: 11B68 11S80
### Note on the Euler $$q$$-zeta functions. (English)Zbl 1221.11231
MSC: 11S80 11S40 11B68
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### On a $$p$$-adic interpolation function for the $$q$$-extension of the generalized Bernoulli polynomials and its derivative. (English)Zbl 1213.11048
MSC: 11B68 11S80
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### Exploring the $$q$$-analogues of the sums of powers of consecutive integers with “Mathematica”. (English)Zbl 1177.11091
MSC: 11S80 11B68
### Symmetry $$p$$-adic invariant integral on $$\mathbb Z_p$$ for Bernoulli and Euler polynomials. (English)Zbl 1229.11152
MSC: 11S80 11B68
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### A new $$q$$-analogue of Bernoulli polynomials associated with $$p$$-adic $$q$$-integrals. (English)Zbl 1217.11116
MSC: 11S80 11B68 11S40
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### Explicit $$p$$-adic $$q$$-expansion for the alternating sums of powers. (English)Zbl 1245.11112
MSC: 11S80 11B68
### On $$p$$-adic $$q$$-$$l$$-functions and sums of powers. (English)Zbl 1154.11310
MSC: 11B65 11S80 11S40
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### On a $$q$$-analogue of the $$p$$-adic generalized twisted $$L$$-functions and $$p$$-adic $$q$$-integrals. (English)Zbl 1130.11012
MSC: 11B68 11S80 11S40
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### $$q$$-difference equations and $$p$$-adic local monodromy. (English)Zbl 1075.39017
Loday-Richaud, Michèle (ed.), Complex analysis, dynamical systems, summability of divergent series and Galois theories. I. Volume in honor of Jean-Pierre Ramis. Proceedings of the conference, Toulouse, France, September 22–26, 2003 held on the occasion of J.-P. Ramis’ 60th birthday. Paris: Société Mathématique de France (ISBN 2-85629-167-8/pbk). Astérisque 296, 55-111 (2004).
MSC: 39A13 12H10 33D05
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### Kummer congruences for the Euler numbers of higher order. (English)Zbl 1064.11078
Reviewer: Kaori Ota (Tokyo)
MSC: 11S80 11B68
### On multivariate $$p$$-adic $$q$$-integrals. (English)Zbl 1002.11088
MSC: 11S80 11S40 33D05
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### An analogue of Bernoulli numbers and their congruences. (English)Zbl 1146.11335
Kim, Taekyun (ed.) et al., Proceedings of the Jangjeon Mathematical Society. Korea: Jangjeon Mathematical Society (ISBN 89-87809-15-3). Proc. Jangjeon Math. Soc. 1, 133-143 (2000).
MSC: 11S80 11B68 33D05
### On beta and gamma functions associated with the Grothendieck-Teichmüller group. II. (English)Zbl 1046.14009
MSC: 14G32 11S80 33D05
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### On $$BC$$ type basic hypergeometric orthogonal polynomials. (English)Zbl 0936.33008
MSC: 33D52 33D45 33D80
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### On beta and gamma functions associated with the Grothendieck-Teichmüller group. Appendix: Profinite free differential calculus and profinite Blanchfield-Lyndon thereom. (English)Zbl 1046.14010
Völklein, Helmut (ed.) et al., Aspects of Galois theory. Papers from the conference on Galois theory, Gainesville, FL, USA, October 14–18, 1996. Cambridge: Cambridge University Press (ISBN 0-521-63747-3/pbk). Lond. Math. Soc. Lect. Note Ser. 256, 144-179 (1999).
MSC: 14G32 11S80 33D05
MSC: 33D80
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MSC: 33D80
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### $$q$$-analogues of $$p$$-adic gamma functions and $$p$$-adic Euler constants. (English)Zbl 1022.11061
MSC: 11S80 33D05
### A new derivation of the inner product formula for the Macdonald symmetric polynomials. (English)Zbl 0932.33028
Reviewer: A.Klimyk (Kyïv)
MSC: 33D52 05E35 33D70 33D80
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### On a theta product formula for Jackson integrals associated with root systems of rank two. (English)Zbl 0902.33011
MSC: 33D05 33D10 33D80
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### Addition formulas for $$q$$-special functions. (English)Zbl 0889.33010
Ismail, Mourad E. H. (ed.) et al., Special functions, $$q$$-series and related topics. Providence, RI: American Mathematical Society. Fields Inst. Commun. 14, 109-129 (1997).
Reviewer: P.K.Mittal (Ajmer)
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### Multivariable big and little $$q$$-Jacobi polynomials. (English)Zbl 0892.33010
MSC: 33D45 33D80
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### $$q$$-gamma and $$q$$-beta functions in quantum algebra representation theory. (English)Zbl 0872.33010
MSC: 33D05 33D80 16W30 17B37
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### Eight lectures on quantum groups and $$q$$-special functions. (English)Zbl 0902.17004
Reviewer: Li Fang (Hangzhou)
MSC: 17B37 33D80 16W30 33D70 17-02 33-02
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### Identities for $$q$$-ultraspherical polynomials and Jacobi functions. (English)Zbl 0828.33014
MSC: 33D70 33C45 33D80
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### Generalized $$q$$-exponentials related to orthogonal quantum groups and Fourier transformations of noncommutative spaces. (English)Zbl 0826.33010
MSC: 33D05 33D80
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### $$(r,s)$$-exponentials. (English. Russian original)Zbl 0841.33006
Russ. Acad. Sci., Dokl., Math. 49, No. 3, 577-581 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 6, 730-732 (1994).
Reviewer: A.Klimyk (Kiev)
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### A simple proof of an Aomoto type extension of the $$q$$-Morris theorem. (English)Zbl 0862.33015
Andrews, George E. (ed.) et al., The Rademacher legacy to mathematics. The centenary conference in honor of Hans Rademacher, July 21-25, 1992, Pennsylvania State University, University Park, PA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 166, 167-182 (1994).
MSC: 33D05 05A30 33D80
### Holonomic $$q$$-difference system of the first order associated with a Jackson integral of Selberg type. (English)Zbl 0801.39003
Reviewer: L.Berg (Rostock)
MSC: 39A70 39A12 33D80
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### Some $$q$$-beta integrals on $$SU(n)$$ and $$Sp(n)$$ that generalize the Askey-Wilson and Nasrallah-Rahman integrals. (English)Zbl 0819.33009
Reviewer: G.Zet (Iaşi)
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### $$p$$-adic analysis and mathematical physics. (English)Zbl 0812.46076
Series on Soviet and East European Mathematics. 10. Singapore: World Scientific. xviii, 319 p. (1994).
### Generalized $$q$$-Bessel functions. (English)Zbl 1043.33500
MSC: 33D70 17B10 33D80
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### A basic analogue of Graf’s addition formula and related formulas. (English)Zbl 0826.33012
MSC: 33D70 33D15 33D80
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### The $$q$$-hypergeometric equation of Gauss and a description of its series and integral solutions. (English. Russian original)Zbl 0832.33011
Russ. Acad. Sci., Dokl., Math. 48, No. 1, 40-45 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 331, No. 2, 140-143 (1993).
Reviewer: A.Klimyk (Kiev)
MSC: 33D20 33D70 33D80 39A12 39A10
### Weyl shift of $$q$$-oscillator and $$q$$-polynomials. (English. Russian original)Zbl 0794.33013
Theor. Math. Phys. 94, No. 2, 219-224 (1993); translation from Teor. Mat. Fiz. 94, No. 2, 307-315 (1993).
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### Quantum algebra structure of certain Jackson integrals. (English)Zbl 0795.17023
MSC: 17B37 33D80 17B69
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### Askey-Wilson polynomials as zonal spherical functions on the $$SU(2)$$ quantum group. (English)Zbl 0799.33015
MSC: 33D70 33D80 17B37
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### An $$SU(n)q$$-beta integral transformation and multiple hypergeometric series identities. (English)Zbl 0777.33009
MSC: 33D05 33D80
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### Quantum groups and basic hypergeometric functions. (English)Zbl 0820.17018
Curtright, Thomas (ed.) et al., Proceedings of the Argonne workshop on quantum groups, held at the Argonne National Laboratory, Argonne, IL, USA, 16 April-11 May, 1990. Singapore: World Scientific. 123-132 (1991).
MSC: 17B37 33D60 33D80
### Addition and multiplication theorems for q-Krawtchouk, q-Hahn and q-Racah polynomials. (Russian. English summary)Zbl 0725.33013
Reviewer: A.U.Klimyk
MSC: 33D70 33D80
### On models of irreducible $$q$$-representations of $$\mathrm{sl}(2,\mathbb C)$$. (English)Zbl 0723.33013
MSC: 33D80 17B37 26A33
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### p-adic analog of Heine’s hypergeometric q-series. (English)Zbl 0516.33012
MSC: 33E99 33D05 11S80
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all top 3 | 2022-12-05 07:37:47 | {"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": 0.744659423828125, "perplexity": 7302.6850933374635}, "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-2022-49/segments/1669446711013.11/warc/CC-MAIN-20221205064509-20221205094509-00508.warc.gz"} |
http://math.stackexchange.com/questions/165171/set-of-convergence-is-measurable | Set of convergence is measurable. [duplicate]
Possible Duplicate:
pointwise convergence in $\sigma$-algebra
Problem: Prove that the set of points at which a sequence of measurable real functions converges is a measurable set. (I believe the problem means functions from the reals to the reals.)
Source: W. Rudin, Real and Complex Analysis, Chapter 1, exercise 5.
I have posted a proposed solution in the answers.
-
marked as duplicate by t.b., Potato, Jonas Meyer, Did, Asaf KaragilaJul 1 '12 at 12:35
Let the sequence of functions be $\{f_n(x)\}$. The $\lim \inf$ and $\lim\sup$ of this sequence of functions are measurable (extended-valued) functions. Denote them $h(x)$ and $g(x)$. The set $A$ where $g$ and $h$ are both positive infinity or both negative infinity is measurable, as they are each measurable functions.
Consider the function $p(x)=h\chi_{\mathbb{R}-A}-g\chi_{\mathbb{R}-A}$. It is zero precisely where the original sequence of functions has a limit. Then $E=p^{-1}(\{0\})$ is measurable, so and $E\cup A$ is measurable, and it is the set of points where the sequence has a limit, so we are done. | 2015-05-30 11:26:43 | {"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": 0.965046763420105, "perplexity": 201.03097065137817}, "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-2015-22/segments/1432207930995.36/warc/CC-MAIN-20150521113210-00182-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.gamedev.net/forums/topic/12336-switching--to--in-strings/ | #### Archived
This topic is now archived and is closed to further replies.
# Switching \ to / in strings?
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## Recommended Posts
Hello, got (yet) another question, In my world builder program, there are places where the user has to enter a filename. The problem is, Windows (and XWindows) have made it so that filenames are usually given with ''\'' as the directory marker instead of ''/''. The obvious problem is that in C++ ''\'' is interpreted as a command marker, comepletely screwing up my string! How do I go through and replace all the ''\''s with ''/''s? Will MFC do it for me? ~noxa~
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Have you tried using ''/''?
I believe it will work.
Ex:
FILE *myFile;
myFile=fopen("c:/mydir/subdir/foo.txt", "r");
Is that what you meant?
Jesse Chounard
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Untested code:
// Replace all occurences of ''\'' with ''/''// NB: theString is your char* filename. Should be non-const.for (char* iter = theString; *iter != 0; ++iter){ if (*iter == ''\'') *iter = ''/'';}
There may be an MFC command for this, but I don''t recommend using something so unportable, especially since you mention XWindows. (Not that I think anyone using XWindows would use a backslash in a pathname, but I digress.)
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What I''m confused about is this. When you put "c:\\test.txt" in your code, \\ is translated into the ASCII value associated with "\"... Anyhow, it''s translated by the ***compiler***.
When a user enters a string it''s sent to you already translated. So if a user enters "c:\test", you won''t receive "c: est" (spaces supposed to indicate a tab), you''ll actually receive "c:\test"...
So, unless your #include''ing your world data files into your C++ source, then it _shouldn''t_ be a problem.
Anyways, the previous posting had it right (''cept a typo in his for loop... the backslash wasn''t doubled up).
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The \ - commands are interpreted by the compiler and only valid in the source code, if you read a string from somewhere you don't need to care about this because only the C compiler interprets the commands and your program doesn't.
GA
Edited by - ga on 4/23/00 1:12:30 PM
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Why does it seem everyone either does conversions manually (not that that''s bad, I often do), or wants a big API to do it for them. There ARE lots of string manipulation functions in ANSI C.
char * ptr = stringToConvert;
while(ptr = strchr(ptr, ''\''))
*ptr = ''/'';
Rock
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Oh my god ppl, i learned this one in first grade!!
use "\\" which tells compiler you want a normal \.
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quote:
Original post by Rock2000
Why does it seem everyone either does conversions manually (not that that''s bad, I often do), or wants a big API to do it for them. There ARE lots of string manipulation functions in ANSI C.
char * ptr = stringToConvert;
while(ptr = strchr(ptr, ''\''))
*ptr = ''/'';
Well, if this was an API function that replaced the characters for you, I''d agree. But strchr doesn''t do much more than find the next character, and still has to iterate through the lot, so except for possible assembly optimisations, it''s unlikely to be faster than my method, especially if you have extra function call overhead.
Not that it makes much difference if you''re just doing it to the occasional filename, but I like to be picky
ga, Zipster... I see what you''re saying, but I believe there are certain functions which do actually act on those character sequences just like they were embedded into a string literal. Shame I can''t find any proof to back that up right now Besides, I''d have throught Noxa wouldn''t post about a problem he or she hadn''t actually had yet But it is possible.
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Yeah Kylotan, I was using this thread more to make a general comment about the seeming lack of use of the ANSI string functions. This was not the best example of using them. It should still be able to easily beat a for loop for anything but very small strings if speed is a concern (which I assume it isn''t here), but its more a matter of getting into the habit of using the plentiful string functions already available, which few people seem to ever use.
Rock
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• 15 | 2019-04-18 19:04:02 | {"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": 0.26513752341270447, "perplexity": 4380.886479041537}, "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-2019-18/segments/1555578526228.27/warc/CC-MAIN-20190418181435-20190418203435-00317.warc.gz"} |
https://latex.org/forum/viewtopic.php?f=45&t=30637 | ## LaTeX forum ⇒ Graphics, Figures & Tables ⇒ Table with a logo in latex
Information and discussion about graphics, figures & tables in LaTeX documents.
Tolaso
Posts: 37
Joined: Tue Dec 20, 2016 12:23 am
### Table with a logo in latex
How can one go and draw something like this in LaTeX ? I have searched through the Internet but failed to find a suitable answer.
Στιγμιότυπο από 2017-11-09 21-38-42.png (66.01 KiB) Viewed 329 times
I'm interested in reproducing the table. Here is an MWE that I tried but to no success.
\documentclass[11pt]{article}\usepackage{graphicx, array}\usepackage[margin=1.5cm , a4paper]{geometry}\usepackage[english]{babel}\usepackage[utf8]{inputenc} \begin{document}\begin{table}[ht] \centering\begin{tabular}{*{2}{m{0.48\textwidth}}}\begin{center}The graphic goes here. Some more text. \end{center} &\begin{center} Some more text. \end{center}\end{tabular}\end{table}\end{document}
That is far from perfect ... any suggestions?
Tags:
Tolaso
Posts: 37
Joined: Tue Dec 20, 2016 12:23 am
Solved in TexSE. | 2018-07-23 17:14:32 | {"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": 0.9250913262367249, "perplexity": 6596.30225116295}, "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/1531676599291.24/warc/CC-MAIN-20180723164955-20180723184955-00534.warc.gz"} |
https://webwork.libretexts.org/webwork2/html2xml?answersSubmitted=0&sourceFilePath=Library/ASU-topics/setRateChange/3-2-72.pg&problemSeed=1234567&courseID=anonymous&userID=anonymous&course_password=anonymous&showSummary=1&displayMode=MathJax&problemIdentifierPrefix=102&language=en&outputformat=libretexts | Let $f$ be defined by
(a) Find (in terms of $m$) $\displaystyle{\lim_{x\rightarrow -1^{+}} f(x)}$
Limit =
(b) Find (in terms of $m$) $\displaystyle{\lim_{x\rightarrow -1^{-}} f(x)}$
Limit =
(c) Find the value of $m$ so that
$m$ = | 2022-06-27 07:43:55 | {"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": 0.9845963716506958, "perplexity": 1015.1763679946325}, "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-20220627073417-20220627103417-00329.warc.gz"} |
https://plainmath.net/74917/is-the-following-equation-regarded-as-a | # Is the following equation regarded as a linear equation? 0 x 1 </msub> +
Is the following equation regarded as a linear equation?
$0{x}_{1}+0{x}_{2}+0{x}_{3}=5$
The original question is as below:
Solve the linear system given by the following augmented matrix:
$\left(\begin{array}{cccc}2& 2& 3& 1\\ 2& 5& 3& 0\\ 0& 0& 0& 5\end{array}\right)$
Note the words linear system in the original question. So, I was asking myself whether $0{x}_{1}+0{x}_{2}+0{x}_{3}=5$ is a linear equation. Can we call all of the equations given by the matrix collectively as a linear system?
You can still ask an expert for help
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Carter Escobar
The reason you MUST call it a linear equation is that you want to call the following a linear equation, for all constants ${a}_{1},{a}_{2},{a}_{3}$:
${a}_{1}{x}_{1}+{a}_{2}{x}_{2}+{a}_{3}{x}_{3}=5$
You don't want to call this a "sometimes" linear equation.
###### Not exactly what you’re looking for?
velitshh
It is a linear equation with no solutions, so the linear system has no solutions. | 2022-06-25 07:21:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 24, "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": 0.7262146472930908, "perplexity": 505.03500437650155}, "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/1656103034877.9/warc/CC-MAIN-20220625065404-20220625095404-00292.warc.gz"} |
https://www.physicsforums.com/threads/its-insomnia-all-over-again.53647/page-6 | # Its insomnia all over again.
## Do you have Insomnia?
• ### Zzzz.....
• Total voters
15
#### franznietzsche
honestrosewater said:
Under #2's leadership, our power has grown to 9:1. hmmm....
Stop your blasphemous subversion. I'll have you reported for this. I will not tolerate your attempts to take over.
Last edited:
#### franznietzsche
If you do not cease and desist immediately i will be forced to report the full extent of your plans to Lord Smurf.
Last edited:
#### honestrosewater
Gold Member
I don't know, that sounds like a lot of work... and hard work doesn't seem to be very evil.
Why don't we just stick to the tried and true- deny, deny, deny.
#### honestrosewater
Gold Member
Okay, I'm back now... What? It looks like someone has been at my computer, posting traitorous posts... [wink, wink]
#### franznietzsche
Oh, well then we should find the cuplrit, and prove that it was them sending these seditious messages, not you.
Last edited:
#### honestrosewater
Gold Member
Yes, we should start narrowing the list of suspects. It must have been someone who knew about our organization...
#### franznietzsche
WEll they obviously knew enough to know the physical locations of our computers so as to hack into them and access our secure networks. So we're looking for someone with resources, and computer skills. Probably someone operating from an isolated location, where he would be harder to track.
#### honestrosewater
Gold Member
And someone with a flimsy alibi... like they were alone watching an animated television show.
#### franznietzsche
No, surely they'd be smarter than that. If they were jsut "watching tv" we would know based upon our real time rating systems. The sudden decrease in the ratingsof an arbitrary show unknown to us would have revealed someone turning off their tv to go to a computer.
#### honestrosewater
Gold Member
Of course... unless they anticipated your thinking that they would be smarter than that? Inconceivable!
#### franznietzsche
Hmmm...
Well i've searched the access points of our organization's computer network. I found no unauthorized accesses recorded at any point. This means the perpetrator was either a member, or had access to a member's terminal. But there are only a few terminals, which narrows our search considerably.
#### honestrosewater
Gold Member
Wait, I found a clue under the computer desk... it's a small piece of wood... oh, it's a reed... and judging from the size, a saxophone reed... hmmm... who do we know that plays the saxophone?
#### franznietzsche
I play the saxophone, what are you insinuating? I'll have you know, i'm a victim here too.
#### franznietzsche
Are you trying to frame me for framing you?
#### honestrosewater
Gold Member
I'm not saying anything... the evidence speaks for itself.
Besides, what the &$@% do you expect from a group of evil geniuses? #### franznietzsche honestrosewater said: I'm not saying anything... the evidence speaks for itself. Besides, what the &$@% do you expect from a group of evil geniuses?
I would expect the guilty party to try to frame the the innocent of framing them!!
#### honestrosewater
Gold Member
franznietzsche said:
I would expect the guilty party to try to frame the the innocent of framing them!!
Remember, I have in my possession some private messages someone may be interested in seeing...
#### franznietzsche
Your sedition has been clearly documented, you will answer for your crimes against Lord Smurf. Tricking me by claiming that it was not you planning this sedition was most dastardly.
#### franznietzsche
honestrosewater said:
Remember, I have in my possession some private messages someone may be interested in seeing...
You know full well what i am accusing you of!! Seditious acts against Lord Smurf, involving an assassination tempt by penguin.
And i have your seditious replies to my sting operation, which are being delivered as we speak.
#### honestrosewater
Gold Member
laughing... it hurts... tears
#### honestrosewater
Gold Member
franznietzsche said:
Your sedition has been clearly documented, you will answer for your crimes against Lord Smurf. Tricking me by claiming that it was not you planning this sedition was most dastardly.
Oh, I bet you say that to all the girls.
#### franznietzsche
honestrosewater said:
Oh, I bet you say that to all the girls.
Does that mean you're about to sleep with me too?
#### honestrosewater
Gold Member
What is this sleep thing you speak of?
#### franznietzsche
honestrosewater said:
What is this sleep thing you speak of?
Its what me amd Smurf do with each others brides.
#### honestrosewater
Gold Member
Is it evil or merely naughty?
### Physics Forums Values
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• Solo and co-op problem solving | 2019-08-22 20:14:02 | {"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": 0.27619484066963196, "perplexity": 7977.688662616299}, "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-2019-35/segments/1566027317359.75/warc/CC-MAIN-20190822194105-20190822220105-00425.warc.gz"} |
https://cs.stackexchange.com/questions/103261/why-proving-the-solution-of-a-problem-is-polynomial-time-is-sufficient-enough-to | # Why proving the solution of a problem is polynomial time is sufficient enough to say that it is a NP prolbem? [duplicate]
Why proving that we can verify the solution of a problem is polynomial time is sufficient enough to say that the problem is nondeterministic polynomial time? Please note: this is not a question on how to prove a questions is NP, but instead asking why, we can just do so? If there is more step we need to do, what are missing here?
I am not sure why proving that we can verify the solution of a problem is polynomial time is sufficient enough to say that the problem in NP because seem to me that we can also verify a solution of a problem is polynomial time while it is actually linear time, can't we?
Proving that a problem is in NP seem requires one additional step? it is really necessary ?
## marked as duplicate by David Richerby, Evil, Discrete lizard♦, Pål GD, Yuval FilmusJan 24 at 18:43
• Hey! There is no such thing as an NP problem. A problem can be in NP, and a problem can be hard for NP and a problem can be complete for NP. And it can be neither. – Pål GD Jan 23 at 18:56
• @PålGD You are wrong. NP is a class of decision problems. So, there is such a thing as "NP problem". NP-complete and NP-hard are more specific things. Everything inside NP is an NP problem. – nbro Jan 24 at 16:49
The class $$P$$ is a subset of the class $$NP$$, that is, problems that have a (deterministic) polynomial-time solution are also included in the $$NP$$ class, the class of problems which have a non-deterministic polynomial-time solution. In other words, if you can solve a problem in polynomial time deterministically, you can definitely solve it in polynomial time non-deterministically.
Therefore, if you are able to verify (in polynomial time) that a solution or algorithm $$s$$ for problem $$t$$ runs in polynomial time (that is, if you are able to verify that $$t \in P$$), then you automatically show that the problem $$t$$ is also in $$NP$$ (because $$P \subset NP$$). | 2019-06-20 07:55:49 | {"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": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8361917734146118, "perplexity": 255.76091142440455}, "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-2019-26/segments/1560627999163.73/warc/CC-MAIN-20190620065141-20190620091141-00312.warc.gz"} |
https://www.gamedev.net/forums/topic/659311-streaming-com-objects/ | Followers 0
# Streaming .COM objects
## 3 posts in this topic
Hi there,
I'm busy with handeling content ( textures, meshes, etc).
I'd like to stream data to a binary file and then when I need them I just read everything from the binary file.
The problem is: I can stream everything from custom made classes to basic variables like integers etc, but when I try t read a COM object it just won't work.
this is what my writer looks like:
ContentTypeWriter& ContentTypeWriter::operator<<(ID3D11ShaderResourceView** resource)
{
return *this;
}
void ContentTypeWriter::Write(const void* buffer, size_t length)
{
m_Stream->write((char*)buffer, length);
if (!*m_Stream)
Logger::Log(_T("File::write Error"), LOGTYPE_ERROR, false);
}
this is what my reader looks like:
ContentTypeReader& ContentTypeReader::operator>>(ID3D11ShaderResourceView** resource)
{
return *this;
}
{
if (!*m_Stream)
Logger::Log(_T("File::write Error"), LOGTYPE_ERROR, false);
}
Everytime I load my ShaderResourceView it comes out as a 0x000000, but all my other variables are parsed the same way and they come out just like I saved them.
Does anybody have any idea what I'm doing wrong?
0
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Long answer: Instead of saving a pointer, save information that lets you recreate the desired data structure or find the existing data structure if you expect it to already be somewhere in RAM. For example, you might give each type a unique ID followed by data which lets you call a particular constructor, factory method, search through an existing object list, etc. This process is called serialization/deserialization and can be easy or complicated, depending on how flexible your format needs to be - you should do some Google investigation about what serialization is to get some ideas on how you could apply it to your situation.
I'm not intimately familiar with DX11, so I'm just going off of what I googled just now. Here's what I would do:
Saving:
- Write information that lets you create or find the ID3D11Resource* that you will need for the first parameter to CreateShaderResourceView. I am not familiar with DX11 so you'll have to figure out how you want to do this on your own.
- Write the SRV's D3D11_SHADER_RESOURCE_VIEW_DESC contents to the stream. This struct appears to be a POD (plain old data - in other words, a single contiguous block of data with no pointers to anything else), so this should work. You can save this in the manner you're using above.
- Load the information that lets you create or find the ID3D11Resource* you need.
- Call ID3D11Device::CreateShaderResourceView using those two pieces of information. This will give you the interface pointer to the newly constructed resource.
Alternatively, if your code works by creating a bunch of ShaderResourceViews in memory and you aren't using the stream itself to construct them, you can simply save/load a unique ID which allows you to find the existing ShaderResourceView object which already exists in memory. Though you can't use a pointer, you may be able to use an array index, GUID, or string for this. Edited by Nypyren
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Much has been written about the topic. Use the search term: serialization
0
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Thanks for the reply Nypyren, I'll take a look at it.
0
## Create an account
Register a new account | 2017-07-27 09:07:44 | {"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": 0.1883566677570343, "perplexity": 1783.1228016411699}, "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/1500549427750.52/warc/CC-MAIN-20170727082427-20170727102427-00589.warc.gz"} |
https://scoop.eduncle.com/how-to-solve-pls-show-steps-87 | IIT JAM Follow
November 20, 2020 11:08 am 30 pts
how to solve pls show steps..... . .. . . . . . .. . . . . .
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• Shares | 2022-01-24 16:17:08 | {"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": 0.9786913990974426, "perplexity": 2906.5420968325457}, "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/1642320304572.73/warc/CC-MAIN-20220124155118-20220124185118-00674.warc.gz"} |
https://www.pcreview.co.uk/threads/toc-and-custom-chapters.3955756/ | # TOC and Custom Chapters
S
#### Syb H
I have a twelve section Word document. Each section has a unique chapter
prefix to the page numbering, ie, 10-1, 20-1, 30-1, etc. I would like those
chapter numbers to appear in my TOC when I select update automatically. Right
now my ToC is just picking up the actual pages within the section without the
chapter reference. Is there anyway to get the TOC to recognize a custom
chapters? Word 2003. | 2022-05-28 00:33:28 | {"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": 0.9613719582557678, "perplexity": 7397.697082520399}, "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/1652663011588.83/warc/CC-MAIN-20220528000300-20220528030300-00605.warc.gz"} |
https://willrosenbaum.com/teaching/2021s-cosc-273/slides/lab01/ | # Welcome to COSC 273!
## Outline
• Introductions
• Lab Section Plan
• Lab 01: Estimating Pi
• Other Examples
(general course introduction in lecture)
# Introductions
## Your Professor
• Will Rosenbaum
• Originally from Seattle
• Undregrad at Reed College in Portland, OR
• PhD in Mathematics from UCLA
• Postdocs at
• Tel Aviv University
• Max Planck Institute for Informatics (Saarbruecken, Germany)
• Started at Amherst last fall
## My Research
• Theoretical Computer Science
• Interface between math and CS
• Theory of Distributed Systems
• What can systems of interacting processors (broadly construed) compute?
• Research Questions
• How efficiently can a computational task be performed in principle?
• What resources (time, memory, communication) are required to perform tasks?
• What tasks cannot be solved efficiently?
## Outside of Work
• Spend most time with family: Alivia, Ione (daughter), Finnegan (dog), Pip & Posy (cats)
• Hobbies: cooking, playing piano, hiking
# Lab Sessions
## Purpose
• Informal discussion (small groups)
• Get questions answered
• Lectures focus on principles
• Labs focus on practice (i.e., coding)
• Troubleshooting code, etc
## Lab Structure
• Orientation/Lab introduction
• Questions
• Small group discussion
• Brief recap
## Lab Enrollment
Current enrollment:
• Lab 01: 36
• Lab 02: 5
Need to balance these enrollments!
• I’ll send out questionnaire to balance sections class as equitably as equitably as possible
## Course Enrollment
• Currently full
• Many others want to enroll
• If you plan to drop the class, please do so early so that others can enroll during add/drop period
# Lab 01: Estimating Pi
## A Formula from High School
Area of a disk: $$A = \pi r^2$$
## An Idea from Probability
Pick a random point inside the framed region.
The probability the point lies in the disk is proportional to the disk’s area.
## In More Detail
• area of disk is $$\pi r^2$$
• area of surrounding square is $$(2 r)^2 = 4 r^2$$
• the probability that a (uniformly) random point in the square lies in the disk is: $$\frac{\text{area of circle}}{\text{area of square}} = \frac{\pi r^2}{4 r^2} = \frac 1 4 \pi.$$
so…
## Estimation by Sampling
…to estimate $$\pi$$, suffices to estimate the probability that a random point point in the square lies inside the disk:
• pick a bunch of random points
• see how many lie in disk
• $$p =$$ proportion of points that do
• $\pi \approx 4 p$
Example of Monte Carlo method
## An Example by Hand
Number of Samples:
Number of Hits:
$$\pi$$ Estimate:
## Does This Work?
• Mathematically guaranteed to work most of the time, for sufficiently many random points
• How many?
• How efficient is this solution?
## Speeding Things Up
A nice feature of the code:
• The more samples we run, the better the approximation
• Samples can be run independently and results aggregated
## Speeding Things Up
A nice feature of modern computers:
• They can do multiple independent operations in parallel
• We can generate indpendent samples concurrently
• Just need to figure out how in code!
## Threads in Java
Threads…
• are single sequences of operations
• can be executed concurrently/in parallel by modern computers
• can be created/run by making instances of the Thread class
• are incredibly subtle to reason about
## Lab 01
Use multithreading to estimate $$\pi$$ as quickly as possible (using Monte Carlo method above)
Fractal Example | 2022-01-18 08:24:07 | {"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": 1, "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": 0.34677568078041077, "perplexity": 13268.397853531018}, "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-2022-05/segments/1642320300805.79/warc/CC-MAIN-20220118062411-20220118092411-00269.warc.gz"} |
https://coin-or.github.io/pulp/CaseStudies/a_sudoku_problem.html | # A Sudoku Problem formulated as an LP¶
## Problem Description¶
A sudoku problem is a problem with an incomplete 9x9 table of numbers that must be filled according to several rules:
• Within any of the 9 individual 3x3 boxes, each of the numbers 1 to 9 must be found.
• Within any column of the 9x9 grid, each of the numbers 1 to 9 must be found.
• Within any row of the 9x9 grid, each of the numbers 1 to 9 must be found.
On this page we will formulate the problem below (from wikipedia) as a model using PuLP. Once created, our code will need little modification to solve any sudoku problem.
## Formulation¶
### Identify the Decision Variables¶
In order to formulate this problem as a linear program, we could simply create a variable for each of the 81 squares between 1 and 9 representing the value in that square. However, this is awfully complicated because in linear programming there is no “not equal to” operator and so we cannot use the necessary constraints of no squares within a box/row/column being equal in value to each other. Whilst we can ensure the sum of all the values in a box/row/column equal 45, this will still result in many solutions satisfying the 45 constraint but still with 2 of the same number in the same box/row/column. There is a solution for this using Big M constraints that compare for each pair of values in a box/column/row which number is strictly smaller than the other but we prefer to present an approach that is much more elegant:
We create 729 individual binary (0-1) problem variables. These represent 9 problem variables per square for each of 81 squares, where the 9 variables each correspond to the number that might be in that square. The binary nature of the variable says whether the existence of that number in that square is true or false. Therefore, there can clearly be only 1 of the 9 variables for each square as true (1) and the other 8 must be false (0) since only one number can be placed into any square. This will become clear below.
### Formulate the Objective Function¶
Interestingly, with sudoku there is no solution that is better than another solution, since a solution by definition must satisfy all the constraints. Therefore, we are not really trying to minimise or maximise anything, we are just trying to find the values on our variables that satisfy the constraints. Thus, we neither set LpMinimize or LpMaximize nor define an objective function.
### Formulate the Constraints¶
These are simply the known constraints of a sudoku problem plus the constraints on our own created variables we have used to express the features of the problem:
• The values in the squares in any row must be each of 1 to 9.
• The values in the squares in any column must be each of 1 to 9.
• The values in the squares in any box must be each of 1 to 9. (a box is one of the 9 non-overlapping 3x3 grids within the overall 9x9 grid)
• There must be only one number within any square (seems logically obvious, but it is important to our formulation to ensure because of our variable choices).
• The starting sudoku numbers must be in those same places in the final solution (this is a constraint since these numbers are not changeable in the actual problem, whereas we can control any other numbers. If none or very few starting numbers were present, the sudoku problem would have a very large number of feasible solutions, instead of just one).
## Solution¶
The introductory commenting and import statement are entered
"""
The Sudoku Problem Formulation for the PuLP Modeller
Authors: Antony Phillips, Dr Stuart Mitchell
edited by Nathan Sudermann-Merx
"""
# Import PuLP modeler functions
from pulp import *
In the unique case of the sudoku problem, the row names, column names and variable option values are all the exact same list of numbers from 1 to 9.
# All rows, columns and values within a Sudoku take values from 1 to 9
VALS = ROWS = COLS = range(1, 10)
A list called Boxes is created with 9 elements, each being another list. These 9 lists correspond to each of the 9 boxes, and each of the lists contains tuples as the elements with the row and column indices for each square in that box. Explicitly entering the values in a similar way to the following would have had the same effect (but would have been a waste of time):
# The boxes list is created, with the row and column index of each square in each box
Boxes = [
[(3*i+k+1, 3*j+l+1) for k in range(3) for l in range(3)]
for i in range(3) for j in range(3)
]
Therefore, Boxes[0] will return a list of tuples containing the locations of each of the 9 squares in the first box.
The prob variable is created to contain the problem data.
# The prob variable is created to contain the problem data
prob = LpProblem("Sudoku Problem")
The 729 problem variables are created since the (Vals,Rows,Cols) creates a variable for each combination of value, row and column. An example variable would be: Choice_4_2_9, and it is defined to be a binary variable (able to take only the integers 1 or 0. If Choice_4_2_9 was 1, it would mean the number 4 was present in the square situated in row 2, column 9. (If it was 0, it would mean there was not a 4 there)
# The decision variables are created
choices = LpVariable.dicts("Choice", (VALS, ROWS, COLS), cat='Binary')
As explained above, we don’t define an objective function since we are only concerned with any variable combination that can satisfy the constraints.
# We do not define an objective function since none is needed
Since there are 9 variables for each square, it is important to specify that only exactly one of them can take the value of 1 (and the rest are 0). Therefore, the below code reads: for each of the 81 squares, the sum of all the 9 variables (each representing a value that could be there) relating to that particular square must equal 1.
# A constraint ensuring that only one value can be in each square is created
for r in ROWS:
for c in COLS:
prob += lpSum([choices[v][r][c] for v in VALS]) == 1
These constraints ensure that each number (value) can only occur once in each row, column and box.
# The row, column and box constraints are added for each value
for v in VALS:
for r in ROWS:
prob += lpSum([choices[v][r][c] for c in COLS]) == 1
for c in COLS:
prob += lpSum([choices[v][r][c] for r in ROWS]) == 1
for b in Boxes:
prob += lpSum([choices[v][r][c] for (r, c) in b]) == 1
The starting numbers are entered as constraints i.e a 5 in row 1 column 1 is true.
# The starting numbers are entered as constraints
input_data = [
(5, 1, 1),
(6, 2, 1),
(8, 4, 1),
(4, 5, 1),
(7, 6, 1),
(3, 1, 2),
(9, 3, 2),
(6, 7, 2),
(8, 3, 3),
(1, 2, 4),
(8, 5, 4),
(4, 8, 4),
(7, 1, 5),
(9, 2, 5),
(6, 4, 5),
(2, 6, 5),
(1, 8, 5),
(8, 9, 5),
(5, 2, 6),
(3, 5, 6),
(9, 8, 6),
(2, 7, 7),
(6, 3, 8),
(8, 7, 8),
(7, 9, 8),
(3, 4, 9),
(1, 5, 9),
(6, 6, 9),
(5, 8, 9)
]
for (v, r, c) in input_data:
prob += choices[v][r][c] == 1
The problem is written to an LP file, solved using PuLP’s choice of solver and the solution status is printed to the screen
# The problem data is written to an .lp file
prob.writeLP("Sudoku.lp")
# The problem is solved using PuLP's choice of Solver
prob.solve()
# The status of the solution is printed to the screen
print("Status:", LpStatus[prob.status])
Instead of printing out all 729 of the binary problem variables and their respective values, it is more meaningful to draw the solution in a text file. The code also puts lines inbetween every third row and column to make the solution easier to read. The sudokuout.txt file is created in the same folder as the .py file.
# A file called sudokuout.txt is created/overwritten for writing to
sudokuout = open('sudokuout.txt','w')
# The solution is written to the sudokuout.txt file
for r in ROWS:
if r in [1, 4, 7]:
sudokuout.write("+-------+-------+-------+\n")
for c in COLS:
for v in VALS:
if value(choices[v][r][c]) == 1:
if c in [1, 4, 7]:
sudokuout.write("| ")
sudokuout.write(str(v) + " ")
if c == 9:
sudokuout.write("|\n")
sudokuout.write("+-------+-------+-------+")
sudokuout.close()
A note of the location of the solution is printed to the solution
# The location of the solution is give to the user
print("Solution Written to sudokuout.txt")
The full file above is given provided Sudoku1.py
The final solution should be the following:
## Extra for Experts¶
In the above formulation we did not consider the fact that there may be multiple solutions if the sudoku problem is not well defined.
We can make our code return all the solutions by editing our code as shown after the prob.writeLP line. Essentially we are just looping over the solve statement, and each time after a successful solve, adding a constraint that the same solution cannot be used again. When there are no more solutions, our program ends.
while True:
prob.solve()
# The status of the solution is printed to the screen
print("Status:", LpStatus[prob.status])
# The solution is printed if it was deemed "optimal" i.e met the constraints
if LpStatus[prob.status] == "Optimal":
# The solution is written to the sudokuout.txt file
for r in ROWS:
if r in [1, 4, 7]:
sudokuout.write("+-------+-------+-------+\n")
for c in COLS:
for v in VALS:
if value(choices[v][r][c]) == 1:
if c in [1, 4, 7]:
sudokuout.write("| ")
sudokuout.write(str(v) + " ")
if c == 9:
sudokuout.write("|\n")
sudokuout.write("+-------+-------+-------+\n\n")
# The constraint is added that the same solution cannot be returned again
prob += lpSum([choices[v][r][c] for v in VALS for r in ROWS for c in COLS
if value(choices[v][r][c]) == 1]) <= 80
# If a new optimal solution cannot be found, we end the program
else:
break
sudokuout.close()
The full file using this is available Sudoku2.py. When using this code for sudoku problems with a large number of solutions, it could take a very long time to solve them all. To create sudoku problems with multiple solutions from unique solution sudoku problem, you can simply delete a starting number constraint. You may find that deleting several constraints will still lead to a single optimal solution but the removal of one particular constraint leads to a sudden dramatic increase in the number of solutions. | 2021-01-16 08:11:03 | {"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": 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": 0.5833147168159485, "perplexity": 956.071991853462}, "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-2021-04/segments/1610703505861.1/warc/CC-MAIN-20210116074510-20210116104510-00035.warc.gz"} |
https://indico.cern.ch/event/719214/contributions/3083618/ | # Workshop RENAFAE 2018
Jul 30 – 31, 2018
Instituto de Física da Universidade de São Paulo
America/Sao_Paulo timezone
Evento comemorativo dos 10 anos da Rede Nacional de Física de Altas Energias
## Measuring multi-strange hadron in heavy-ion collisions at the LHC with ALICE
Jul 30, 2018, 12:15 PM
15m
Auditório Novo 1 (Instituto de Física da Universidade de São Paulo)
### Speaker
Danilo Silva De Albuquerque (University of Campinas UNICAMP (BR))
### Description
A strongly interacting state of matter known as the Quark-Gluon Plasma (QGP) is formed in the high temperature and energy density conditions reached in ultra-relativistic heavy-ion collisions. Historically, one of the signatures of the formation of such a system was the enhanced production of strange and multi-strange hadrons with respect to non-strange. The ALICE detector is ideally suited to study identified particle production rates. The excellent tracking and particle identification capabilities allow the reconstruction of multi-strange baryons (Ξ−, Ξ ̄+, Ω− and Ω ̄+) via their weak decay channels over a large range in transverse momentum (pT). In this work, we report on the pT spectra and total yield of such hadrons at central rapidity in several centrality classes as measured by ALICE for Pb-Pb collisions at the energy of √sNN = 5.02 TeV and for Xe-Xe collisions at √sNN = 5.44 TeV. The yields are normalized by the corresponding measurement of pion production in the same centrality class in order to study the enhancement of multi-strange hadrons. Comparison of hyperon-to-pion ratio between different systems, such as pp, p-Pb, Xe-Xe and Pb-Pb collisions shows that production of multi-strange baryons relative to pions follows a continuously increasing trend from low multiplicity pp to central AA collisions.
### Primary author
Danilo Silva De Albuquerque (University of Campinas UNICAMP (BR)) | 2022-12-02 00:58:35 | {"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": 0.8541778326034546, "perplexity": 6027.127562546056}, "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-2022-49/segments/1669446710870.69/warc/CC-MAIN-20221201221914-20221202011914-00184.warc.gz"} |
https://rellek.net/book/s_background_decimal.html | ## SectionB.12Notation for Natural Numbers
In some sense, we already have a workable notation for natural numbers. In fact, we really didn't need a special symbol for $s(0)\text{.}$ The natural number $0$ and the sucessor function $s$ are enough. For example, the positive integer associated with the number of fingers (including the thumb) on one hand is $s(s(s(s(s(0)))))\text{,}$ our net worth is $0\text{,}$ and the age of Professor Trotter's son in years when this section was first written was
\begin{equation*} s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))))). \end{equation*}
Admittedly, this is not very practical, especially if some day we win the lottery or want to discuss the federal deficit. So it is natural (ugh!) to consider alternative notations.
Here is one such scheme. First, let's decide on a natural $b>s(0)$ as base. We will then develop a notation which is called the base $b$ notation. We already have a special symbol for zero, namely $0\text{,}$ but we need additional symbols for each natural number $n$ with $0\lt n\lt b\text{.}$ These symbols are called digits. For example, the positive integer $b=s(s(s(s(s(s(s(s(0))))))))$ is called eight, and it makes a popular choice as a base. Here are the symbols (digits) customarily chosen for this base: $1=s(0)\text{,}$ $2=s(1)\text{;}$ $3=s(2)\text{;}$ $4=s(3)\text{;}$ $5=s(4)\text{;}$ $6=s(5)\text{;}$ and $7=s(6)\text{.}$ Technically speaking, it is not necessary to have a separate symbol for $b\text{,}$ but it might be handy regardless. In this case, most people prefer the symbol $8\text{.}$ We like this symbol, unless and until it gets lazy and lays down sideways.
So the first $8$ natural numbers are then $0\text{,}$ $1\text{,}$ $2\text{,}$ $3\text{,}$ $4\text{,}$ $5\text{,}$ $6$ and $7\text{.}$ To continue with our representation, we want to use the following basic theorem.
Let $d\in \nonnegints$ with $d>0\text{.}$ We first show that for each $n\in\nonnegints\text{,}$ there exists $q,r\in\nonnegints$ so that $n=qd+r$ and $0\le r\lt d\text{.}$ If $n=0\text{,}$ we can take $q=0$ and $r=0\text{.}$ Now suppose that $k=qd+r$ and $0\le r\lt m$ for some $k\in \nonnegints\text{.}$
Note that $r\lt d$ implies $r+1\le d\text{.}$ If $r+1\lt d\text{,}$ then $k+1=qd+(r+1)\text{.}$ On the other hand, if $r+1=d\text{,}$ then $k+1=(q+1)d+0\text{.}$
Now that existence has been settled, we note that the uniqueness of $q$ and $r$ follow immediately from the cancellation properties.
Now suppose that for some $k\in \nonnegints\text{,}$ with $k\ge 7\text{,}$ we have defined a base eight notation for the representation of $k\text{,}$ for all $n$ with $0\le n\le k\text{,}$ and that in each case, this representation consists of a string of digits, written left to right, and selected from $\{0,1,2,3,4,5,6,7\}\text{.}$ Write $k+1=qb+r$ where $0\le r\lt b\text{.}$ Note that $q\le k\text{,}$ so that we already have a representation for $q\text{.}$ To obtain a representation of $k+1\text{,}$ we simply append $r$ at the (right) end.
For example, consider the age of Professor Trotter's son. It is then written as 22. And to emphasize the base eight notation, most people would say $22\text{,}$ base $8$ and write $(22)_8\text{.}$
Among the more popular bases are base 2, where only the digits 0 and 1 are used, and base sixteen, where sixteen is the popular word for $(20)_8\text{.}$ Here the digit symbols are
\begin{equation*} 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F \end{equation*}
Another popular choice, in fact the one in most widespread use in banks, shopping centers and movie theatres, is base ten. Ten is the natural number A, base sixteen. Also, ten is $(12)_8\text{.}$ Most folks use the digits $0,1,2,3,4,5,6,7,8,9$ for base ten notation. And when no other designation is made, then it is assumed that the natural number is written base ten. So of course, Professor Trotter's son is 18 and is a freshman at Georgia Tech. Which explains why his hair is as white as it is.
For any base $b>1\text{,}$ caution must be exercised when discussing multiplication, since writing the product $m\times n$ in the abbreviated form $mn$ causes us some grief. For example, if $b = 8\text{,}$ then writing the product $372\times4885$ as $3724885$ is ambiguous. For this reason, when using base $b$ notation, the product symbol $\times$ (or some variation of $\times$) is always used.
### SubsectionB.12.1Alternate Versions of Induction
Many authors prefer to start the development of number systems with the set of positive integers and defer the introduction of the concept of zero. In this setting, you have a non-empty set $\posints\text{,}$ a one-to-one successor function $s:\posints\injection\posints$ and a positive integer called one and denoted $1$ that is not the successor of any positive integer. The Principle of Induction then becomes: If $\mathbb{M}\subseteq\posints\text{,}$ then $\mathbb{M} =\posints$ if and only if
1. $1\in \mathbb{M}\text{;}$ and
2. $\forall k\in \nonnegints\quad(k\in \mathbb{M}) \Longrightarrow(s(k)\in \mathbb{M})\text{.}$
More generally, to show that a set $\mathbb{M}$ contains all integers greater than or equal to an integer $n\text{,}$ it is sufficient to show that (i) $n\in\mathbb{M}\text{,}$ and (ii) For all $k\in\ints,\,(k\in\mathbb{M}\Longrightarrow(k+1\in\mathbb{M})\text{.}$
Here is another version of induction, one that is particularly useful in combinatorial arguments. | 2020-09-26 12:15:48 | {"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": 0.8748041987419128, "perplexity": 253.98923216378282}, "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-2020-40/segments/1600400241093.64/warc/CC-MAIN-20200926102645-20200926132645-00574.warc.gz"} |
https://physics.stackexchange.com/questions/35920/maximum-possible-information-in-the-universe | # Maximum Possible Information in the universe?
I remember hearing about this in one of the programs in discovery science. The physicist claimed that the maximum possible information in the universe is $10^{10^{123}}$ whereas the maximum possible information that can be known by man is $10^{10^{90}}$. Can anyone explain to me how can we arrive at such a specific number, and also how can information be represented by only numbers?
• The information in the Universe measured in bits or nats is just $10^{123}$ from the holographic bound; the actual entropy of the known matter except black holes - is about $10^{90+}$ and is dominated by the cosmic microwave background. However, this guess for the entropy is obsolete because most of the entropy we know in the Universe is carried by the black holes, bringing us above $10^{100}$. If you have one more exponentiation, 10 to those large numbers, it doesn't measure the information but the number of possibilities one may distinguish (8 bits = byte distinguish 256 states...). – Luboš Motl Sep 9 '12 at 8:11
• is $10^{123}$ bits or qubits? I think the difference is important, since $10^{123}$ classical bits are exhausted with 410 qubits, more or less, and the universe has certainly way more than 410 q-bits – lurscher May 29 '13 at 18:21
• unless coherent superposition turns out to break down before arriving at 410 q-bits – lurscher May 29 '13 at 18:31
• @lurscher you have misunderstood how qubits work. To send a classical text document reliably using qubits, you need just as many qubits as you would need classical bits (see Holevo bound and HSW theorem). – Andrew Steane Dec 17 '18 at 19:32
The number $10^{123}$ emerges as (roughly) the number of Planck areas contained within the boundary of the observable universe. If each Planck area can be (roughly) in two states, a total of $10^{123}$ yes/no questions suffice to describe the boundary of the universe and - via the (still speculative) holographic principle - the whole universe. In other words, if the universe is a hologram, about $10^{123}$ bits of information are needed to describe it.
Also, it is estimated that there are approximately $10^{80}$ protons (or electrons or neutrons) and approximately $10^{90}$ photons in the observable universe. So this is how many "objects" you have to work with. I don't know how to get from this to the maximum amount of information that can be known by man? | 2019-01-21 01:21:51 | {"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": 0.7780834436416626, "perplexity": 442.22340627067035}, "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-2019-04/segments/1547583745010.63/warc/CC-MAIN-20190121005305-20190121031305-00285.warc.gz"} |
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https://physics.stackexchange.com/questions/135138/how-to-use-accelaration-data-of-moving-object-to-calculate-distance | # How to use accelaration data of moving object to calculate distance?
I read couple of similar question on this forum and few blogs on web, though I am still confused,I am determined to calculate object displacement using accelerometer data.
So, I tried using www.freescale.com/files/sensors/doc/app_note/AN3397.pdf , which gives nearly 20-50% error.
I also tried this equation on data and got some better results.
V1 = V0 + ((a1) * t)
X2 = abs((V1 * t) + (((a1)/2)*t*t))
X2 = X0 + X2
V0 = V1
X0 = X2
Here t is the time differance between two samples. X0 is the final displacement. V1,a1 current values. V0 previous value.
Here is my graphs for the movement from Android sensors readings.
1)From Linear Acceleration Z axis graph, how do I calculate the distance? 2)Which values should I take and which should not? how many data samples I should use for calculation. For positive acceleration only or for an entire positive negative cycle of acceleration data? 3) What the Linear acceleration graph means. Please explain its values based on movement of object.
Nulling gravity is an enormous problem, unless your accelerometer is perfectly perpendicular to Earth's gravity vector! The accelerations you want to measure are probably on the order of $1m/s^2$ or less, right? That is overlaid by $\vec{g}=9.81m/s^2\vec{z}$. Before you can even estimate the displacement causing acceleration your are interested in, you have to determine angles of your three accelerometer channels relative to $\vec{g}$, then subtract $\vec{g}$. Thankfully that procedure will give you a direction towards the floor... however, you still don't know which way your $\vec{x}$ and $\vec{y}$ axes are pointing! Your accelerometer could be turning around 180 degrees while it is accelerating... and the real displacement could end up in the opposite direction of where you thought it was going. Now, a perfect acceleration sensor would not even be sensitive to this rotation, for that you would need a different sensor that can detect rotations! Such a gyroscope may, or may not be built into your device. Given the way most accelerometer chips are implemented, gyroscopes and accelerometers will not even sample synchronously, which means that you need to have a digital resampling filter in place to correlate the readings of both sensors to get a reliable six axis position/orientation vector. I don't think that the Android platform gives you enough information to do that, right now. iOS might... on newer phones and tablets which have both sensors.
Having said that, if you want to simplify things to the level you are on, right now, you can (theoretically) mount your cell phone on a straight rail, carefully rotate it, until the motion vector points exactly in the direction of one of the accelerometer axes, and that axis is perpendicular to $\vec{g}$ and then you can apply a good numerical integration algorithm to what it measures on one axis, like one of the higher order integrators described by http://mathworld.wolfram.com/NumericalIntegration.html. | 2019-07-18 10:03:58 | {"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": 0.3798048496246338, "perplexity": 477.9666722841548}, "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-2019-30/segments/1563195525587.2/warc/CC-MAIN-20190718083839-20190718105839-00260.warc.gz"} |
https://csat.io/practice/p3/q6 | # Practice Paper 3 Question 6
A positive integer $$n$$ is said to be triangular if $$n =\sum_{i=0}^{k}{i}$$ for some positive integer $$k.$$ Given $$8n+1$$ is a square number, show that $$n$$ is triangular.
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## Hints
• Hint 1
Solve $$\sum_{i=0}^{k}{i}.$$
• Hint 2
The condition can be written as $$8n+1 = m^2,$$ for some natural $$m$$.
• Hint 3
Manipulate the above to a form that allows factorization.\$
• Hint 4
If $$(m-1)(m+1)$$ is divisible by $$8,$$ what values can $$m$$ take?
• Hint 5
Would $$(m-1)(m+1)$$ be divisible by $$8$$ if $$m$$ was even?
• Hint 6
Use a substitution for $$m$$ to express that $$m$$ is odd.
## Solution
A positive integer $$n$$ is said to be triangular if $$n =\sum_{i=0}^{k}{i}=\frac{k(k+1)}{2}.$$ Since $$8n+1$$ is a square number, there exists a positive integer $$m$$ such that $$8n + 1 = m^2.$$ Using the difference between two squares, we can factorize to get $$8n = m^2-1 = (m-1)(m+1),$$ or that $$n=\frac{(m-1)(m+1)}{8},$$ which means that $$(m-1)(m+1)$$ must be divisible by 8. This is true if and only if $$m$$ is odd, since for every consecutive even numbers, one is a multiple of $$4.$$ Substituting $$m = 2k+1$$ gives us $$n = \frac{2k(2k+2)}{8} = \frac{k(k+1)}{2} = \sum_{i=0}^{k}{i}.$$
If you have queries or suggestions about the content on this page or the CSAT Practice Platform then you can write to us at [email protected]. Please do not write to this address regarding general admissions or course queries. | 2019-08-24 19:48:48 | {"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": 0.8399004936218262, "perplexity": 283.43668867071557}, "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-2019-35/segments/1566027321696.96/warc/CC-MAIN-20190824194521-20190824220521-00523.warc.gz"} |
http://www.zoklet.net/bbs/archive/index.php/t-32330.html | PDA
View Full Version : I need calculus help...
Giggles The Panda
05-19-2009, 03:01 AM
The tangent lines to the parabola y=ax^2+b at the point (2,3) and (-2,3) contain the origin.
(a) Find the value of a and b.
(b) Find the area of the region R enclosed by the parabola and the two tangent lines.
(c) Set up and evaluate an integral expression in one variable which gives the volume when the region R, described in part (b), is revolved about the y-axis.
Please show your work and maybe give a brief explanation of what you did.
Mathematics
05-19-2009, 03:34 PM
The tangent lines to the parabola y=ax^2+b at the point (2,3) and (-2,3) contain the origin.
(a) Find the value of a and b.
(b) Find the area of the region R enclosed by the parabola and the two tangent lines.
(c) Set up and evaluate an integral expression in one variable which gives the volume when the region R, described in part (b), is revolved about the y-axis.
Please show your work and maybe give a brief explanation of what you did.
(a) Find the value of a and b.
The form of both lines is:
y=mx,
as there is no constant (the lines pass throught the origin). The gradients of the lines are then given by dy/dx:
y=\frac{3}{2}x
and
y=-\frac{3}{2}x.
We now know what the gradient of the curve must be at these points, so we can differentiate and find the constant a:
y=ax^2+b,
\frac{\partial y}{\partial x}=2ax.
Substituting in the gradients and the values of x:
2 a (2)=3/2
2 a (-2)=-3/2
a=3/8.
So we have:
y=\frac{3}{8}x^2+b.
From the lines we also know the values of y at x=2 and x=-2, so we can find b:
3=\frac{3}{8}2^2+b,
b=3/2.
(b) Find the area of the region R enclosed by the parabola and the two tangent lines.
The basic stratergy is to integrate between 0 and x=2 (where the line touches the curve), take away the area between the line and the x-axis (just a triangle) and double the answer, as the curves are symmetric in the y-axis.
\int _0^2 \left(\frac{3}{8}x{}^2+\frac{3}{2}\right) dx=4
(Click "Show steps" for details: http://www81.wolframalpha.com/input/?i=Integrate+3%2F8x^2%2B3%2F2)
Area between line and x-axis:
\frac{1}{2}\left(base \times height \right) = \frac{1}{2}(2)(3)=3
Area under curve - area of triange = 1
So total area enclosed by the curve and the two lines = 2*1 = 2.
Mathematics
05-22-2009, 12:12 AM
(c) Set up and evaluate an integral expression in one variable which gives the volume when the region R, described in part (b), is revolved about the y-axis.
Volume of revolution when a function is rotated around the y-axis:
V=\int \pi x^2 dy
Notice that the function has been changed so it is in terms of y i.e. instead of writing y=... you are re-arranging and writing x=... (function of y).
If you imagine the volume swept out by rotating the line y=3/2x around the y-axis between y=0 and y=3 you will have a cone of volume:
V_1=\int_{0}^3 \pi \left(\frac{2}{3}y\right)^2 dy=4\pi
You can then simply subtract the volume swept out by the quadratic as it rotates. The quadratic doesn't touch the x-axis; at x=0 y=3/2. So you need to integrate between y=3/2 and y=3.
V_2=\int_{3/2}^3 \pi \left(\frac{8}{3} \left(y-\frac{3}{2}\right) \right)dy=3\pi
V_R=V_1-V_2=\pi | 2013-05-24 04:13:17 | {"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": 0.9214048385620117, "perplexity": 635.8424207497594}, "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/1368704134547/warc/CC-MAIN-20130516113534-00052-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://krpc.github.io/krpc/cnano/api/space-center/orbit.html | # Orbit¶
krpc_SpaceCenter_Orbit_t
Describes an orbit. For example, the orbit of a vessel, obtained by calling krpc_SpaceCenter_Vessel_Orbit(), or a celestial body, obtained by calling krpc_SpaceCenter_CelestialBody_Orbit().
krpc_error_t krpc_SpaceCenter_Orbit_Body(krpc_connection_t connection, krpc_SpaceCenter_CelestialBody_t * result)
The celestial body (e.g. planet or moon) around which the object is orbiting.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_Apoapsis(krpc_connection_t connection, double * result)
Gets the apoapsis of the orbit, in meters, from the center of mass of the body being orbited.
Game Scenes: All
Note
For the apoapsis altitude reported on the in-game map view, use krpc_SpaceCenter_Orbit_ApoapsisAltitude().
krpc_error_t krpc_SpaceCenter_Orbit_Periapsis(krpc_connection_t connection, double * result)
The periapsis of the orbit, in meters, from the center of mass of the body being orbited.
Game Scenes: All
Note
For the periapsis altitude reported on the in-game map view, use krpc_SpaceCenter_Orbit_PeriapsisAltitude().
krpc_error_t krpc_SpaceCenter_Orbit_ApoapsisAltitude(krpc_connection_t connection, double * result)
The apoapsis of the orbit, in meters, above the sea level of the body being orbited.
Game Scenes: All
Note
This is equal to krpc_SpaceCenter_Orbit_Apoapsis() minus the equatorial radius of the body.
krpc_error_t krpc_SpaceCenter_Orbit_PeriapsisAltitude(krpc_connection_t connection, double * result)
The periapsis of the orbit, in meters, above the sea level of the body being orbited.
Game Scenes: All
Note
This is equal to krpc_SpaceCenter_Orbit_Periapsis() minus the equatorial radius of the body.
krpc_error_t krpc_SpaceCenter_Orbit_SemiMajorAxis(krpc_connection_t connection, double * result)
The semi-major axis of the orbit, in meters.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_SemiMinorAxis(krpc_connection_t connection, double * result)
The semi-minor axis of the orbit, in meters.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_Radius(krpc_connection_t connection, double * result)
The current radius of the orbit, in meters. This is the distance between the center of mass of the object in orbit, and the center of mass of the body around which it is orbiting.
Game Scenes: All
Note
This value will change over time if the orbit is elliptical.
krpc_error_t krpc_SpaceCenter_Orbit_RadiusAt(krpc_connection_t connection, double * result, double ut)
The orbital radius at the given time, in meters.
Parameters: ut – The universal time to measure the radius at. All
krpc_error_t krpc_SpaceCenter_Orbit_PositionAt(krpc_connection_t connection, krpc_tuple_double_double_double_t * result, double ut, krpc_SpaceCenter_ReferenceFrame_t referenceFrame)
The position at a given time, in the specified reference frame.
Parameters: ut – The universal time to measure the position at. referenceFrame – The reference frame that the returned position vector is in. The position as a vector. All
krpc_error_t krpc_SpaceCenter_Orbit_Speed(krpc_connection_t connection, double * result)
The current orbital speed of the object in meters per second.
Game Scenes: All
Note
This value will change over time if the orbit is elliptical.
krpc_error_t krpc_SpaceCenter_Orbit_Period(krpc_connection_t connection, double * result)
The orbital period, in seconds.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_TimeToApoapsis(krpc_connection_t connection, double * result)
The time until the object reaches apoapsis, in seconds.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_TimeToPeriapsis(krpc_connection_t connection, double * result)
The time until the object reaches periapsis, in seconds.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_Eccentricity(krpc_connection_t connection, double * result)
The eccentricity of the orbit.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_Inclination(krpc_connection_t connection, double * result)
The inclination of the orbit, in radians.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_LongitudeOfAscendingNode(krpc_connection_t connection, double * result)
The longitude of the ascending node, in radians.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_ArgumentOfPeriapsis(krpc_connection_t connection, double * result)
The argument of periapsis, in radians.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_MeanAnomalyAtEpoch(krpc_connection_t connection, double * result)
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_Epoch(krpc_connection_t connection, double * result)
The time since the epoch (the point at which the mean anomaly at epoch was measured, in seconds.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_MeanAnomaly(krpc_connection_t connection, double * result)
The mean anomaly.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_MeanAnomalyAtUT(krpc_connection_t connection, double * result, double ut)
The mean anomaly at the given time.
Parameters: ut – The universal time in seconds. All
krpc_error_t krpc_SpaceCenter_Orbit_EccentricAnomaly(krpc_connection_t connection, double * result)
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_EccentricAnomalyAtUT(krpc_connection_t connection, double * result, double ut)
The eccentric anomaly at the given universal time.
Parameters: ut – The universal time, in seconds. All
krpc_error_t krpc_SpaceCenter_Orbit_TrueAnomaly(krpc_connection_t connection, double * result)
The true anomaly.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_TrueAnomalyAtUT(krpc_connection_t connection, double * result, double ut)
The true anomaly at the given time.
Parameters: ut – The universal time in seconds. All
krpc_error_t krpc_SpaceCenter_Orbit_TrueAnomalyAtRadius(krpc_connection_t connection, double * result, double radius)
The true anomaly at the given orbital radius.
krpc_error_t krpc_SpaceCenter_Orbit_UTAtTrueAnomaly(krpc_connection_t connection, double * result, double trueAnomaly)
The universal time, in seconds, corresponding to the given true anomaly.
Parameters: trueAnomaly – True anomaly. All
krpc_error_t krpc_SpaceCenter_Orbit_RadiusAtTrueAnomaly(krpc_connection_t connection, double * result, double trueAnomaly)
The orbital radius at the point in the orbit given by the true anomaly.
Parameters: trueAnomaly – The true anomaly. All
krpc_error_t krpc_SpaceCenter_Orbit_TrueAnomalyAtAN(krpc_connection_t connection, double * result, krpc_SpaceCenter_Orbit_t target)
The true anomaly of the ascending node with the given target orbit.
Parameters: target – Target orbit. All
krpc_error_t krpc_SpaceCenter_Orbit_TrueAnomalyAtDN(krpc_connection_t connection, double * result, krpc_SpaceCenter_Orbit_t target)
The true anomaly of the descending node with the given target orbit.
Parameters: target – Target orbit. All
krpc_error_t krpc_SpaceCenter_Orbit_OrbitalSpeed(krpc_connection_t connection, double * result)
The current orbital speed in meters per second.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_OrbitalSpeedAt(krpc_connection_t connection, double * result, double time)
The orbital speed at the given time, in meters per second.
Parameters: time – Time from now, in seconds. All
krpc_error_t krpc_SpaceCenter_Orbit_ReferencePlaneNormal(krpc_connection_t connection, krpc_tuple_double_double_double_t * result, krpc_SpaceCenter_ReferenceFrame_t referenceFrame)
The direction that is normal to the orbits reference plane, in the given reference frame. The reference plane is the plane from which the orbits inclination is measured.
Parameters: referenceFrame – The reference frame that the returned direction is in. The direction as a unit vector. All
krpc_error_t krpc_SpaceCenter_Orbit_ReferencePlaneDirection(krpc_connection_t connection, krpc_tuple_double_double_double_t * result, krpc_SpaceCenter_ReferenceFrame_t referenceFrame)
The direction from which the orbits longitude of ascending node is measured, in the given reference frame.
Parameters: referenceFrame – The reference frame that the returned direction is in. The direction as a unit vector. All
krpc_error_t krpc_SpaceCenter_Orbit_RelativeInclination(krpc_connection_t connection, double * result, krpc_SpaceCenter_Orbit_t target)
Relative inclination of this orbit and the target orbit, in radians.
Parameters: target – Target orbit. All
krpc_error_t krpc_SpaceCenter_Orbit_TimeToSOIChange(krpc_connection_t connection, double * result)
The time until the object changes sphere of influence, in seconds. Returns NaN if the object is not going to change sphere of influence.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_NextOrbit(krpc_connection_t connection, krpc_SpaceCenter_Orbit_t * result)
If the object is going to change sphere of influence in the future, returns the new orbit after the change. Otherwise returns nullptr.
Game Scenes: All
krpc_error_t krpc_SpaceCenter_Orbit_TimeOfClosestApproach(krpc_connection_t connection, double * result, krpc_SpaceCenter_Orbit_t target)
Estimates and returns the time at closest approach to a target orbit.
Parameters: target – Target orbit. The universal time at closest approach, in seconds. All
krpc_error_t krpc_SpaceCenter_Orbit_DistanceAtClosestApproach(krpc_connection_t connection, double * result, krpc_SpaceCenter_Orbit_t target)
Estimates and returns the distance at closest approach to a target orbit, in meters.
Parameters: target – Target orbit. All
krpc_error_t krpc_SpaceCenter_Orbit_ListClosestApproaches(krpc_connection_t connection, krpc_list_list_double_t * result, krpc_SpaceCenter_Orbit_t target, int32_t orbits)
Returns the times at closest approach and corresponding distances, to a target orbit.
Parameters: target – Target orbit. orbits – The number of future orbits to search. A list of two lists. The first is a list of times at closest approach, as universal times in seconds. The second is a list of corresponding distances at closest approach, in meters. All | 2020-07-14 03:34:23 | {"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": 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": 0.6144708395004272, "perplexity": 3406.927299975536}, "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/1593657147917.99/warc/CC-MAIN-20200714020904-20200714050904-00002.warc.gz"} |
https://questions.examside.com/past-years/jee/question/which-of-the-following-on-thermal-decomposition-yields-a-bas-2012-marks-4-qx01cnzklz1oysg1.htm | 1
AIEEE 2012
+4
-1
Which of the following on thermal decomposition yields a basic as well as an acidic oxide ?
A
NaNO3
B
KClO3
C
CaCO3
D
NH4NO3
2
AIEEE 2006
+4
-1
The ionic mobility of alkali metal ions in aqueous solution is maximum for
A
K+
B
Rb+
C
Li+
D
Na+
3
AIEEE 2005
+4
-1
Which one of the following species is diamagnetic in nature?
A
$$He_2^+$$
B
H2
C
$$H_2^+$$
D
$$H_2^-$$
4
AIEEE 2005
+4
-1
Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point.
A
LiCl
B
NaCl
C
KCl
D
RbCl
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
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EXAM MAP
Joint Entrance Examination | 2023-03-30 20:41:00 | {"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": 0.7770818471908569, "perplexity": 9102.132408469413}, "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-2023-14/segments/1679296949387.98/warc/CC-MAIN-20230330194843-20230330224843-00120.warc.gz"} |
https://crypto.stackexchange.com/questions/74799/does-character-encoding-change-entropy?noredirect=1 | # Does character encoding change entropy?
This is a question I've been wondering for a while.
Technically these two strings have the same entropy I believe:
fkfnajkfkg%gsddg£5ER£%££££
0110011001101011011001100110111001100001011010100110101101100110011010110110011100100101011001110111001101100100011001000110011111000010101000110011010101000101010100101100001010100011001001011100001010100011110000101010001111000010101000111100001010100011
both 256bits...
My question is, does character encoding affect entropy?
If generated at random, do both the ASCII and binary strings have the same entropy as passwords?
If 256bits is good as an AES key, it's also good as a password right?
I guess a similar question is does hashing a 'weak' password give a lower entropy string than a 'strong' password, consider this:
Blake2B(password) = 7c863950ac93c93692995e4732ce1e1466ad74a775352ffbaaf2a4a4ce9b549d0b414a1f3150452be6c7c72c694a7cb46f76452917298d33e67611f0a42addb8
Blake2B(fkfnajkfkg%gsddg£5ER£%££££) = 03e7415fa598e9062cfd9e3cd269ca618b38b3543501e197b6c095b8749d782234e82779a2e4b489fd9c3b002734763ee3b867835e1a2232a37bf89ef8606d09
Are,
7c863950ac93c93692995e4732ce1e1466ad74a775352ffbaaf2a4a4ce9b549d0b414a1f3150452be6c7c72c694a7cb46f76452917298d33e67611f0a42addb8
and
03e7415fa598e9062cfd9e3cd269ca618b38b3543501e197b6c095b8749d782234e82779a2e4b489fd9c3b002734763ee3b867835e1a2232a37bf89ef8606d09
the same entropy?
If I hadn't told you the first was the hash of password and the second the hash of fkfnajkfkg%gsddg£5ER£%££££, would it change your view?
I also suppose there is a difference between brute forcing a password which is 256bits, and one which is 256 ASCII 1's or 0's, which would be more than 256bit.
Technically these two strings have the same entropy I believe:
We cannot tell how much entropy is in a string by looking at it, as it depends on how it is generated and if the values cannot be predicted by other means. For instance, you just posted these strings on this site, so they would not contain (almost) no entropy when used as keys.
Your strings just represents a bit string, possibly of the same size - as you presume, depending on the actual encoding (I don't know the encoding used for the first string, and I can only assume binary digits for the second string). And those bits may contain entropy.
My question is, does character encoding affect entropy?
No, it doesn't as the character encoding is just about the representation of the bits, not the actual value of the bits. The entropy is present in the value of the bits.
If generated at random, do both the ASCII and binary strings have the same entropy as passwords?
Yes, assuming that the alphabet is not larger than expected.
If 256bits is good as an AES key, it's also good as a password right?
No, because normal humans cannot remember such large strings. You could store them in a password manager though, and then 256 bits of entropy is plenty, if not overkill. Generally we don't need password sizes or keys over 128 bits - as long as quantum computers don't come of age anyway.
I guess a similar question is does hashing a 'weak' password give a lower entropy string than a 'strong' password, consider this:
No, now the value of the bits of the input string contain less entropy, so this isn't comparable at all. The entropy is not expanded by the password hashing algorithm, so the earlier hash contains less entropy than the latter hash.
If I hadn't told you the first was the hash of password and the second the hash of fkfnajkfkg%gsddg£5ER£%££££, would it change your view?
No, because a dictionary attack would almost immediately find the first hash.
I also suppose there is a difference between brute forcing a password which is 256bits, and one which is 256 ASCII 1's or 0's, which would be more than 256bit.
That depends. Let's assume that all the security is in the password or key. In that case we work with Kerckhoffs principle, and we assume that we know how the password is encoded. In that case there is no difference.
Of course, a real world attacker may not work that way. You may use your password for a generic store, and an attacker may not try your particular encoding.
Most humans are terribly bad at remembering 256 ones and zeros. There may be other technical difficulties in entering such a long string of characters as well (screen space, remembering where you are in the string, stealing clipboard contents etc. etc.).
• Note that I'm not so much discussing the theoretical nature of entropy and security in this answer, but I certainly think that my answer cannot conflict with the different notions. It would be an interesting discussion if encoding can influence Kolmogorov complexity, but I don't think it should change my answer. – Maarten Bodewes Oct 3 '19 at 14:00
• thank you for such a detailed and interesting answer. One follow up point... > No, because a dictionary attack would almost immediately find the first hash. - as you said here, it sounds like then, that one could generate a very high entropy looking string, that's actually a hash output or hex representation of a very weak ASCII password and not know it! If indeed the inverse is true, that the hash of a low quality input does indeed contain less entropy due to dict attacks etc. – Woodstock Oct 3 '19 at 14:03
• Yes, but of course the chance of generating such a hash randomly is infinitesimally small. And if you know that it was generated randomly, then there is little point in checking for it happening to collide with a hash value known to have little entropy. – Maarten Bodewes Oct 3 '19 at 14:10
Yes and no. The strings certainly both have the same Kolmogorov complexity.
Some here loosely generalise the cryptographic definition of entropy as Kolomogorov complexity = entropy. That's not quite correct and confusing. Kolmogorov complexity is the thing that cryptographers are interested in when assessing the strength of passwords and seeds. Entropy (information) is measured a-priori of knowing anything other than what you measure at any specific point. Entropy (information) is very much a localised metric and can thus be transformed.
So clearly your two sequences must have differing (information) entropies as they're different lengths due to the encoding. Philosophically and semantically though they're identical. So the effort to brute force either is identical too.
As to then:-
I also suppose there is a difference between brute forcing a password which is 256bits, and one which is 256 ASCII 1's or 0's, which would be more than 256bit.
No, but it might take more RAM/die estate to hold the candidates. The entropy rate of the former is 8 bits/byte, whilst the latter is 1 bit/byte. It may be worthwhile looking at What is the most secure encryption algorithm that keeps the entropy the same or even lowers it?. And also consider the difference between a cryptographic "key" like those above, and a "password" which is like "123456".
• Thanks @Paul, very interesting, one last thing, what about the two Blake2b hashes, one of a weak input, one of a strong input. Are both outputs equal? despite being digests of different strength inputs? – Woodstock Oct 3 '19 at 13:54
• ‘Kolmogorov complexity is the thing that cryptographers are interested in when assessing the strength of passwords and seeds.’ [citation needed] – Squeamish Ossifrage Oct 3 '19 at 17:13
• The proposition ‘your two sequences must have differing (information) entropies’ doesn't make sense, because entropy is a property of a state of incomplete knowledge or of a process whose outcome is unpredictable, such as a password generation procedure or what an adversary knows about your password after you use that procedure to pick a password; the entropy of a particular password is a nonsensical idea. – Squeamish Ossifrage Oct 3 '19 at 20:19
• I won’t labour the point any further other than to encourage you to think of the consequences of your statements. If passwords have no entropy, you’re disavowing all information, all books and all my favourite Abba songs. And all the Wikipedia pages about the differences between Kolmogorov complexity and entropy. But they all exist, don’t they? – Paul Uszak Oct 6 '19 at 3:43
• Unless you’re pulling my chain, I expect that it’s just an unfortunate and problematic semantic difference. Like calling AES a permutation which it clearly isn’t in anyone’s common understanding of ‘permutation’. – Paul Uszak Oct 6 '19 at 3:43 | 2020-01-21 00:14:15 | {"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": 0.5444244742393494, "perplexity": 991.2741748180456}, "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/1579250601040.47/warc/CC-MAIN-20200120224950-20200121013950-00133.warc.gz"} |
https://imcs.dvfu.ru/cats/static/problem_text-cid-6143148-pl-en.html?nosubmit=1 | ## Problem A. Amnesia ≡
• problems
Author: Антон Карабанов Time limit: 1 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
Today, in a mathematics lesson, Timofey studied the topic of "Proportions". He was too lazy to write down his homework in his notebook, relying on his memory, and here is the result — Timofey remembers three of the four members of the proportion, but does not remember where they stood! He is also sure that the answer to the problem (an unknown element of proportion) is as a natural number. Help Timofey find all the correct answers for this assignment.
### Input format
The first line of the input contains three integers separated by space: a, b and c — known members of the proportion.
### Output format
Output natural numbers in ascending order — all possible different solutions of the proportion. If there are no solutions — output the number -1.
### Constraints
1 ≤ a, b, c ≤ 109
### Note on samples
In the first example, it is possible to make this proportion: 24 = 36.
In the second sample, there are no suitable solutions (with an integer answer).
In the third sample, it is possible to make these proportions: 24 = 816, 24 = 48, 12 = 48.
### Sample tests
No. Standard input Standard output
1
2 3 4
6
2
2 3 5
-1
3
2 4 8
1 4 16
## Problem B. Bouncing pairs ≡
• problems
Author: A. Baranov Time limit: 1 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
Let there be two strings A and B, consisting of digits and lowercase Latin characters.
On the string A, we define the operation textSWAP(i, i + 1), which consists in exchanging the characters at positions i and i + 1.
It is required to determine the minimum number of such operations for transforming string A to string B.
### Input format
Input contains two strings: A and B.
### Output format
Output must contain a single integer.
### Constraints
It is guaranteed that the required transformation can be performed.
Line lengths do not exceed 2 ⋅ 105.
### Sample tests
No. Standard input Standard output
1
abababababab
babababababa
6
2
abc
bca
2
## Problem C. Confections ≡
• problems
Author: Антон Карабанов Time limit: 1 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
Today is Grisha's birthday! Each of his n friends brought a box of favorite sweets as a gift to the birthday boy. Since Grisha is not a greedy boy, he took all the sweets out of the boxes and put them on n + 1 plates and placed them in front of each guest (including himself). To everyone's delight, this was done without a remainder. Immediately after that, his mother returned from work and it was decided to put all the sweets on n + 2 plates. To everyone's surprise, this division was completed without a remainder.
Given the known number of sweets in one box k, determine the possible number of guests at the party.
### Input format
The only line of the input contains a natural number k.
### Output format
In the first line output single natural number g — the number of possible answers to the problem's question. In the second line print g natural numbers — possible number of guests in ascending order, separated by a space. It is guaranteed that there is at least one suitable answer.
1 ≤ k ≤ 109
### Notes on sample
In the sample, the number of candies in one box is 6.
If one guest came to Grisha, then the total number of sweets is also 6. It is easy to divide them equally without a remainder both into two and three plates.
If two guests came to Grisha, then the total number of sweets is 12. It is easy to divide them equally without a remainder both into three and four plates
There are no other solutions.
### Sample tests
No. Standard input Standard output
1
6
2
1 2
## Problem D. Disordered polygon ≡
• problems
Author: Антон Карабанов, И. Блинов, А. Баранов Time limit: 1 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
Zhenya drew a regular n-gon on the board, labeled its vertices with numbers clockwise in ascending order: "1 2 3 ... n". Nikita came up and rearranged the numbers in the signature, erased all sides of Zhenya's figure and connected the vertices in the resulting new order (including the first and last vertices). Now a closed broken line flaunts on the board. How many pairs of line segments intersect?
### Input format
The first line of the input contains single integer n. The second line contains n numbers a1, a2… an — a permutation of the polygon's vertices.
### Output format
Output a single non-negative integer — the answer to the problem question.
3 ≤ n ≤ 105
### Sample tests
No. Standard input Standard output
1
4
1 2 3 4
0
2
4
1 2 4 3
1
3
5
2 4 5 3 1
2
4
8
5 6 1 3 4 7 8 2
8
## Problem E. Empty rectangles ≡
• problems
Author: A. Baranov Time limit: 1 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
Consider a set of N two-dimensional points represented by their coordinates (Xi, Yi).
It is required to determine the number of all possible rectangles that satisfy the following conditions:
• the vertices of the rectangle must belong to the original set of points,
and its sides must be parallel to the coordinate axes;
• among the remaining points, none should lie on the border or inside such a rectangle;
• the rectangle must be non-degenerate (have a non-zero area).
### Input format
Input starts with integer N,
followed by 2 × N integers, representing point coordinates: Xi, Yi.
### Output format
The output should contain
the number of detected rectangles.
### Constraints
All input points are different.
− 106 ≤ (Xi, Yi) ≤ 106,
4 ≤ N ≤ 105
### Sample tests
No. Standard input Standard output
1
12
-35 -17
43 10
24 -17
-16 -29
43 54
-35 40
43 -29
24 10
-16 54
-35 10
43 -17
24 40
3
2
12
-20 -34
17 34
-20 40
-10 -20
-43 -17
19 15
-15 16
0 -34
-32 19
0 -12
-13 0
0 40
0
## Problem F. Fast battlepass ≡
• problems
Author: И. Блинов Time limit: 2 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
Paulundra is playing a multiplayer shooter called Counter-rant. Recently Counter-rant launched a new season of the Battle Pass where you can get n of the m available weapon skins. The skin opening system is unusual: the player is given n runes, to use the rune, you need to insert two crystals of fixed colors into it, after which if the rune fits the weapon, the weapon opens. A rune matches a weapon if the weapon contains both colors contained in the rune. Each weapon skin contains exactly C colors.
The Battle Pass consists of k levels. For each level of the Battle Pass, exactly one crystal is given, for each level the reward is known in advance. For reaching level i, the reward will be a crystal with the color ai. The player uses the crystals at his own discretion: inserts into any of the runes or does not use the crystal at all. Since it's hard to earn levels, Paulundra wants to know what is the minimum number of Battle Pass levels she needs to unlock in order to get at least p skins, assuming she distributes crystals and runes optimally.
### Input format
The first line of the input contains five numbers m, C, n, p and k. This is followed by m lines containing C numbers cij each describing the colors of weapon skins with number i. The next n lines contain two numbers each ai1 and ai2 — rune descriptions. The last line of the input contains k number Si, where Si is the color of the crystal for getting level i
### Output format
Print a single integer — the minimum number of levels you need to get to open at least p skins. If p skins cannot be opened print -1.
### Constraints
1 ≤ m ≤ 100
2 ≤ C ≤ 10
1 ≤ n, p ≤ 10
1 ≤ k ≤ 106
1 ≤ ai1, ai2, Si, cij ≤ 109
ai1 ≠ ai2
### Sample tests
No. Standard input Standard output
1
5 3 5 4 10
1 2 3
2 3 4
3 4 5
3 4 6
5 6 7
2 3
2 3
3 4
4 5
10 9
4 4 5 2 3 2 3 3 10 10
8
2
1 2 1 1 1
100 100000
1 2
1
-1
3
3 2 4 1 5
2 1
3 1
8 8
1 2
1 3
3 4
1 2
1 2 3 1 2
2
## Problem G. Graphword ≡
• problems
Author: A. Baranov Time limit: 1 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
Vasya found out that his grandfather has been fond of solving crossword puzzles for a very long time.
On his anniversary, Vasya decided to present him a game, which is a generalized version of the crossword puzzle — "graphword".
A playing field in it is an undirected graph the vertices of which are assigned lowercase letters of the Latin alphabet.
In the process of solving the "graphword" the player needs to compose words by moving along the edges of such a graph.
According to the rules of the game, each edge can be visited more than once.
However, it is forbidden for the current edge to coincide with the previous one.
When developing levels for his game, Vasya was faced with the task of determining the number of all possible paths,
forming some given word in a given graph.
Since the resulting number may be too large, the answer should be the remainder of its division by 109.
### Input format
Input starts with the number of vertices N, followed by the set of characters assigned to each of the vertices.
Next, the number of edges M is given, followed by the edges themselves,
each of which is given by the indices of its vertices: ai, bi. Vertices are numbered starting from zero.
Input is finished with the string W, for which calculation should be done.
### Output format
Output must contain a single integer.
### Constraints
1 ≤ N ≤ 104, 0 ≤ M ≤ 104, ai ≠ bi, 1 ≤ |W| ≤ 10
### Sample tests
No. Standard input Standard output
1
6
a b c a b c
8
0 1
1 2
1 4
4 3
5 0
2 4
4 5
0 4
abba
4
2
6
a b c a b c
8
0 1
2 3
0 4
3 4
2 1
4 2
0 2
5 4
abc
5
## Problem H. Health and light 2 ≡
• problems
Author: Антон Карабанов Time limit: 1 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
The city of N has a happy event! On the single street of the city, new street lamp will be installed and the new pharmacy will open. Help the city governor to find optimal places for these objects.
The street is represented by a segment of coordinate axis, where the leftmost house has coordinate 0. Let's assume house sizes to be negligibly small compared to the street length and represent houses as points on the axis.
The lamp has "brightness" parameter expressing the distance from the lamp where the light reaches. For example when brightness is equal to 10, lamp installed at the point x = 25 will light the street on the segment from 15 to 35 inclusive.
The pharmacy has "remoteness" parameter expressing the distance from it to the house such that people from that house will still visit. For example when remoteness is equal to 100, pharmacy located at point x = 25, will be visited by people living in houses with coordinates from 0 to 125 inclusive (there are no houses with negative coordinates).
### Input format
First line of input contains three integers separated by spaces: n — number of houses, a — brightness и b — remoteness. The second line contains non-negative integers xi — coordinates of each house in ascending order.
### Output format
Output a single non-negative integer — maximum total number of houses illuminated by the lamp and convenient to visit pharmacy from. Both lamp and pharmacy may be located at points with the coordinate of some house.
### Constraints
1 ≤ n, a, b ≤ 105
0 ≤ xi ≤ 109
### Notes on sample
Sample contains ten houses, lamp brightness is 15 and pharmacy remoteness is 20. Lamp can be installed, for example, at point 115 (three houses will be illuminated: 100, 110 and 120). Pharmacy may be located at point 20, in which case it can be visited by people from the first 5 houses. A greater number of houses having "access" to the lamp and pharmacy cannot be obtained.
### Sample tests
No. Standard input Standard output
1
10 15 20
0 10 20 30 40 60 70 100 110 120
8
## Problem I. Interactive circles ≡
• problems
Author: A. Usmanov, A. Baranov Time limit: 1 sec Input / output: interactive Memory limit: 512 Mb
### Statement
The problem is interactive and involves interacting with the jury program by sending and receiving messages in specific format.
Let there be a two-dimensional point, it's known that the point is located inside a circle with radius 1.0 and the center at axes origin.
You're allowed to send queries in the form "check if circle with a center (x, y) contains the given point".
For the first query circle radius is 0.9. For each of the next queries the radius is reduced by 0.1.
You are to send exactly 8 queries in such a way, that the last one contains the point in question.
### Interaction protocol
For each query print to output stream (stdout) two numbers (x, y) specifying the circle center.
Do not forget to flush the stream after each query.
As a response input stream (stdin) will receive a single integer:
1 — the circle contains the point; 0 — otherwise.
### Constraints
For the program to work correctly a line break
should be output and flush
should be performed
after each query sent to the output thread.
## Problem J. Journey back home ≡
• problems
Author: Антон Карабанов Time limit: 1 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
Student Vasily, having returned to his home village for the holidays, celebrates his successfully passed exams on a grand scale. He's walking along a single street, the schematic of which is shown on the picture. The street has a houses (with numbers 1, 3, 5, …, a × 2 − 1) on the left and b houses (with numbers 2, 4, 6, …, b × 2) on the right. There's a huge puddle in the middle of the street, so one can only cross the street at either start or end of it.
Standing next to a house in an altered state of mind Vasily randomly decides where to go next (each of the two possible directions is chosen with the probability 12). If he finds himself next to a tavern (house with the number t), he will immediately walk in and continue to party till morning, but if he is next to his home (house with the number h), he will decide that this is the sign of fate and he is to stop having fun. What is the probability that Vasily reaches his home and stops the celebration if currently he's standing next to the house with number n?
### Input format
The first line of input contains two natural numbers separated by space: a and b — street description. The second line contains three natural numbers t, h and n separated by space — houses description. The consistency of the input data is guaranteed. It is guaranteed that the numbers t, h and n are distinct.
### Output format
Output two space-separated natural numbers — the numerator and denominator of the irreducible fraction expressing the probability of the described event.
### Constraints
1 ≤ a, b ≤ 109
1 ≤ t ≤ a × 2 − 1, if t is odd.
2 ≤ t ≤ b × 2, if t is even.
Constrains for t are similar to h and n.
### Notes on the sample
See picture. The street in the sample only has three houses (with number 1, 2 and 3). Houses on the left side have numbers 1 and 3, while on the right side there's only one house with the number 2. In this sample one it's possible to walk from any house to any other house. Vasily can reach either his home or tavern with equal probability 12.
### Sample tests
No. Standard input Standard output
1
2 1
1 2 3
1 2
## Problem K. Keep on doing! ≡
• problems
Author: Антон Карабанов Time limit: 1 sec Input file: Standard input Memory limit: 512 Mb Output file: Standard output
### Statement
The expression n − (n − 1) − (n − 2) − (n − 3) − ... − 3 − 2 − 1 is written on the board (for example, if n = 5 it will be written as 5 − 4 − 3 − 2 − 1). To avoid a failing grade in mathematics, Gavrila needs to put left and right parentheses in this expression, so that the result is zero. How many ways does he have to do it?
### Input format
Input contains natural number n.
### Output format
In the first line output a non-negative integer m — the number of ways to arrange the parentheses in the required way. In the next m lines print two space-separated natural numbers a and b — the position of the parentheses (numbers from a to b inclusive will be inside the brackets). Output numbers a and b in descending order, and output pairs of numbers in order of descending a.
4 ≤ n ≤ 105
### Note on samples
In the first example, n = 5 is given. Unfortunately, Gavrila won't succeed, for the given n there is no way to place the brackets in the required way.
In the second example n = 7 is given. If all numbers from 5 to 3 are enclosed in brackets, then an expression with the desired value will be obtained: 7 − 6 − (5 − 4 − 3) − 2 − 1 = 1 − ( − 2) − 3 = 0.
In the third example, for n = 12 there are several ways to solve the problem.
### Sample tests
No. Standard input Standard output
1
5
0
2
7
1
5 3
3
12
2
11 8
8 2
0.761s 0.018s 39 | 2023-03-30 18:41:05 | {"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": 0.18355447053909302, "perplexity": 1529.056016740405}, "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-2023-14/segments/1679296949355.52/warc/CC-MAIN-20230330163823-20230330193823-00484.warc.gz"} |
https://indico.ibs.re.kr/event/281/other-view?fr=no&detailLevel=contribution&view=lecture&showSession=all&showDate=all | Center for Theoretical Physics of the Universe (CTPU)
# Cornering dark matter with colliders and cosmology: the role of precision calculation
## by Prof. Benjamin Fuks (LPTHE-CNRS-UPMC)
Wednesday, 9 January 2019 from to (Asia/Seoul)
at CTPU Seminar Room
Fourth floor IBS Building, 55, Expo-ro, Yuseong-gu, Daejeon, Korea, 34126
Description Studies of dark matter lie at the interface of collider physics, astrophysics and cosmology. We present a framework which, starting from a model Lagrangian, allows one to consistently and systematically make predictions, as well as to confront those predictions with a multitude of experimental results. As an application, we consider several classes of simplified dark matter models where the dark sector is connected to the Standard Model via couplings to the top quark. We study in detail the complementarity of relic density, direct/indirect detection and collider searches in constraining the model parameter space. Our study goes beyond the tree-level approximation and we show examples of how higher-order corrections can affect the interpretation of the experimental results, both on for cosmological and collider observables. Material: | 2019-05-23 01:25:44 | {"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": 0.4866272211074829, "perplexity": 1605.8588459733603}, "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/1558232256997.79/warc/CC-MAIN-20190523003453-20190523025453-00539.warc.gz"} |
https://api-project-1022638073839.appspot.com/questions/the-value-of-x-satisfying-2log-9-2-1-2-x-1-log-27-1-4-x-4-3-is#644880 | # The value of x satisfying 2log_9(2(1/2)^x-1)=log_27((1/4)^x-4)^3 is?
Aug 1, 2018
$2 {\log}_{9} \left(2 {\left(\frac{1}{2}\right)}^{x} - 1\right) = {\log}_{27} {\left({\left(\frac{1}{4}\right)}^{x} - 4\right)}^{3}$
$\implies 2 \times {\log}_{9} \left(27\right) {\log}_{27} \left(2 {\left(\frac{1}{2}\right)}^{x} - 1\right) = {\log}_{27} {\left({\left(\frac{1}{4}\right)}^{x} - 4\right)}^{3}$
$\implies 2 \times {\log}_{9} \left({9}^{\frac{3}{2}}\right) {\log}_{27} \left(2 {\left(\frac{1}{2}\right)}^{x} - 1\right) = {\log}_{27} {\left({\left(\frac{1}{4}\right)}^{x} - 4\right)}^{3}$
$\implies 2 \times \frac{3}{2} {\log}_{9} \left(9\right) {\log}_{27} \left(2 {\left(\frac{1}{2}\right)}^{x} - 1\right) = {\log}_{27} {\left({\left(\frac{1}{4}\right)}^{x} - 4\right)}^{3}$
$\implies 3 {\log}_{27} \left(2 {\left(\frac{1}{2}\right)}^{x} - 1\right) = {\log}_{27} {\left({\left(\frac{1}{4}\right)}^{x} - 4\right)}^{3}$
$\implies {\log}_{27} {\left(2 {\left(\frac{1}{2}\right)}^{x} - 1\right)}^{3} = {\log}_{27} {\left({\left(\frac{1}{4}\right)}^{x} - 4\right)}^{3}$
$\implies \left(2 {\left(\frac{1}{2}\right)}^{x} - 1\right) = \left({\left({\left(\frac{1}{2}\right)}^{x}\right)}^{2} - 4\right)$
Taking ${\left(\frac{1}{2}\right)}^{x} = y$ we get
$\left(2 y - 1\right) = \left({y}^{2} - 4\right)$
$\implies {y}^{2} - 2 y - 3 = 0$
$= \left(y + 1\right) \left(y - 3\right) = 0$
So ${\left(\frac{1}{2}\right)}^{x} = - 1 \to \text{not possible}$
And ${\left(\frac{1}{2}\right)}^{x} = 3$
$\implies - x \log 2 = \log 3$
$\implies x = - \log \frac{3}{\log} 2$ | 2022-05-27 16:33:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 15, "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": 0.8088148832321167, "perplexity": 7424.948763281829}, "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/1652662658761.95/warc/CC-MAIN-20220527142854-20220527172854-00764.warc.gz"} |
http://tex.stackexchange.com/questions/160370/why-is-this-statement-not-compiling-correctly | Why is this statement not compiling correctly?
For some reason, the following excerpt from my code is not compiling correctly and I can't figure out why.
$$\begin{split} \frac{100}{-6} &= -16(-6) + 4\\ &\implies z^100 = z^4\\ \\ z^4 &= \left(e^{\frac{-i\pi}{3}\right)^4 \\ &=e^{\frac{-4\pi}{3}} \\ \\ &\cos\left(\frac{-4\pi}{3}\right) = -\frac{1}{2}, ~\sin\left(\frac{-4\pi}{3}\right) = \frac{\sqrt{3}}{2} \\ &\implies z = -\frac{1}{2} + \frac{\sqrt{3}}{2} i \\ \end{split}$$
The error I get is that paragraph ended before split was complete and that a missing endgroup has been inserted. Any help would be greatly appreciated.
-
Welcome to TeX.SX! Please make your code compilable (if possible), or at least complete it with \documentclass{...}, the required \usepackage's, \begin{document}, and \end{document}. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to give you a hand. Help them help you: remove that one hurdle between you and a solution to your problem. – Martin Schröder Feb 15 '14 at 13:52
You are missing a closing brace in line z^4:
... | 2015-04-19 21:27:29 | {"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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.7921670079231262, "perplexity": 1738.3895946666291}, "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-2015-18/segments/1429246639482.79/warc/CC-MAIN-20150417045719-00244-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://aimsciences.org/article/doi/10.3934/cpaa.2018020 | # American Institute of Mathematical Sciences
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Biharmonic systems involving multiple Rellich-type potentials and critical Rellich-Sobolev nonlinearities
March 2018, 17(2): 347-374. doi: 10.3934/cpaa.2018020
## Global existence and decay estimate of classical solutions to the compressible viscoelastic flows with self-gravitating
1 School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450011, China 2 College of Sciences, Henan University of Engineering, Zhengzhou, 451191, China
Received February 2017 Revised April 2017 Published March 2018
Fund Project: YXW is supported by NNSF grant No.11101144
In this paper, we consider the initial value problem for the compressible viscoelastic flows with self-gravitating in $\mathbb{R}^n(n≥ 3)$. Global existence and decay rates of classical solutions are established. The corresponding linear equations becomes two similar equations by using Hodge decomposition and then the solutions operator is derived. The proof is mainly based on the decay properties of the solutions operator and energy method. The decay properties of the solutions operator may be derived from the pointwise estimate of the solution operator to two linear wave equations.
Citation: Yinxia Wang, Hengjun Zhao. Global existence and decay estimate of classical solutions to the compressible viscoelastic flows with self-gravitating. Communications on Pure & Applied Analysis, 2018, 17 (2) : 347-374. doi: 10.3934/cpaa.2018020
##### References:
[1] Y. Chen and P. Zhang, The global existence of small solutions to the incompressible viscoelastic fluid system in 2 ane 3 space dimensions, Comm. Partial Differential Equations, 31 (2006), 1793-1810. doi: 10.1080/03605300600858960. Google Scholar [2] X. Hu, Wellposedness of self-gravitating Hookean elastodynamics, preprint.Google Scholar [3] X. Hu and D. Wang, Local strong solution to the compressible viscoelastic flow with large data, J. Differential Equations, 249 (2010), 1179-1198. doi: 10.1016/j.jde.2010.03.027. Google Scholar [4] X. Hu and D. Wang, Global existence for the multi-dimensional compressible viscoelastic flows, J. Differential Equations, 250 (2011), 1200-1231. doi: 10.1016/j.jde.2010.10.017. Google Scholar [5] X. Hu and D. Wang, Strong solutions to the three-dimensional compressible viscoelastic fluids, J. Differential Equations, 252 (2012), 4027-4067. doi: 10.1016/j.jde.2011.11.021. Google Scholar [6] X. Hu and D. Wang, The initial-boundary value problem for the compressible viscoelastic flows, Discrete Contin. Dyn. Syst., 35 (2015), 917-934. doi: 10.3934/dcds.2015.35.917. Google Scholar [7] X. Hu and G. Wu, Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows, SIAM J. Math. Anal., 45 (2013), 2815-2833. doi: 10.1137/120892350. Google Scholar [8] X. Hu and F. Lin, Scaling limit for compressible viscoelastic fluids, Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics, 243-269, World Sci. Publ., Hackensack, NJ, 2014.Google Scholar [9] X. Hu and F. Lin, Global solutions of two-dimensional incompressible viscoelastic flows with discontinuous initial data, Comm. Pure Appl. Math., 69 (2016), 372-404. doi: 10.1002/cpa.21561. Google Scholar [10] X. Hu and H. Wu, Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows, Discrete Contin. Dyn. Syst., 35 (2015), 3437-3461. doi: 10.3934/dcds.2015.35.3437. Google Scholar [11] B. Han, Global strong solution for the density dependent incompressible viscoelastic fluids in the critical $L^p$ framework, Nonlinear Anal., 132 (2016), 337-358. doi: 10.1016/j.na.2015.11.011. Google Scholar [12] Z. Lei, C. Liu and Y. Zhou, Global existence for a 2D incompressible viscoelastic model with small strain, Commun. Math. Sci., 5 (2007), 595-616. Google Scholar [13] Z. Lei, C. Liu and Y. Zhou, Global solutions of incompressible viscoelastic fluids, Arch. Ration. Mech. Anal., 188 (2008), 371-398. doi: 10.1007/s00205-007-0089-x. Google Scholar [14] Z. Lei, On 2D viscoelasticity with small strain, Arch. Ration. Mech. Anal., 198 (2010), 13-37. doi: 10.1007/s00205-010-0346-2. Google Scholar [15] Z. Lei, Rotation-strain decomposition for the incompressible viscoelasticity in two dimensions, Discrete Contin. Dyn. Syst., 34 (2014), 2861-2871. doi: 10.3934/dcds.2014.34.2861. Google Scholar [16] Z. Lei and F. Wang, Uniform bound of the highest energy for the three dimensional incompressible elastodynamics, Arch. Ration. Mech. Anal., 216 (2015), 593-622. doi: 10.1007/s00205-014-0815-0. Google Scholar [17] Z. Lei, Global well-posedness of incompressible elastodynamics in two dimensions, Comm. Pure Appl. Math. , doi: 10.1002/cpa.21633. Google Scholar [18] F. Lin, C. Liu and P. Zhang, On hydrodynamics of viscoelastic fluids, Comm. Pure Appl. Math., 58 (2005), 1437-1471. doi: 10.1002/cpa.20074. Google Scholar [19] J. Qian and Z. Zhang, Global well-posedness for compressible viscoelastic fluids near equilibrium, Arch. Rational Mech. Anal., 198 (2010), 835-868. doi: 10.1007/s00205-010-0351-5. Google Scholar [20] P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, New York, 1990.Google Scholar [21] Y.-Z. Wang, F. G. Liu and Y. Z. Zhang, Global existence and asymptotic of solutions for a semi-linear wave equation, J. Math. Anal. Appl., 385 (2012), 836-853. doi: 10.1016/j.jmaa.2011.07.010. Google Scholar [22] Y.-Z. Wang and K. Y. Wang, Large time behavior of solutions to the nonlinear pseudo-parabolic equation, J. Math. Anal. Appl., 417 (2014), 272-292. doi: 10.1016/j.jmaa.2014.03.030. Google Scholar [23] Y.-Z. Wang and K. Y. Wang, Asymptotic behavior of classical solutions to the compressible Navier-Stokes-Poisson equations in three and higher dimensions, J. Differential Equations, 259 (2015), 25,-47. doi: 10.1016/j.jde.2015.01.042. Google Scholar [24] Y.-Z. Wang and K. Y. Wang, Long time behavior of solutions to the compressible MHD system in multi-dimensions, J. Math. Anal. Appl., 429 (2015), 1033-1058. doi: 10.1016/j.jmaa.2015.04.045. Google Scholar [25] S. -M. Zheng, Nonlinear Evolution Equations, CRC Press, New York, 2004.Google Scholar [26] F. Xu, X. Zhang, Y. Wu and L. Liu, The optimal convergence rates for the multi-dimensioanl compressible viscoelastic flows, Z. Angew. Math. Mech., 96 (2016), 1490-1504. doi: 10.1002/zamm.201500095. Google Scholar [27] T. Zhang and D. Fang, Global existence of strong solution for equations related to the incompressible viscoelastic fluids in the critical $L^p$ framework, SIAM J. Math. Anal., 44 (2012), 2266-2288. doi: 10.1137/110851742. Google Scholar
show all references
##### References:
[1] Y. Chen and P. Zhang, The global existence of small solutions to the incompressible viscoelastic fluid system in 2 ane 3 space dimensions, Comm. Partial Differential Equations, 31 (2006), 1793-1810. doi: 10.1080/03605300600858960. Google Scholar [2] X. Hu, Wellposedness of self-gravitating Hookean elastodynamics, preprint.Google Scholar [3] X. Hu and D. Wang, Local strong solution to the compressible viscoelastic flow with large data, J. Differential Equations, 249 (2010), 1179-1198. doi: 10.1016/j.jde.2010.03.027. Google Scholar [4] X. Hu and D. Wang, Global existence for the multi-dimensional compressible viscoelastic flows, J. Differential Equations, 250 (2011), 1200-1231. doi: 10.1016/j.jde.2010.10.017. Google Scholar [5] X. Hu and D. Wang, Strong solutions to the three-dimensional compressible viscoelastic fluids, J. Differential Equations, 252 (2012), 4027-4067. doi: 10.1016/j.jde.2011.11.021. Google Scholar [6] X. Hu and D. Wang, The initial-boundary value problem for the compressible viscoelastic flows, Discrete Contin. Dyn. Syst., 35 (2015), 917-934. doi: 10.3934/dcds.2015.35.917. Google Scholar [7] X. Hu and G. Wu, Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows, SIAM J. Math. Anal., 45 (2013), 2815-2833. doi: 10.1137/120892350. Google Scholar [8] X. Hu and F. Lin, Scaling limit for compressible viscoelastic fluids, Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics, 243-269, World Sci. Publ., Hackensack, NJ, 2014.Google Scholar [9] X. Hu and F. Lin, Global solutions of two-dimensional incompressible viscoelastic flows with discontinuous initial data, Comm. Pure Appl. Math., 69 (2016), 372-404. doi: 10.1002/cpa.21561. Google Scholar [10] X. Hu and H. Wu, Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows, Discrete Contin. Dyn. Syst., 35 (2015), 3437-3461. doi: 10.3934/dcds.2015.35.3437. Google Scholar [11] B. Han, Global strong solution for the density dependent incompressible viscoelastic fluids in the critical $L^p$ framework, Nonlinear Anal., 132 (2016), 337-358. doi: 10.1016/j.na.2015.11.011. Google Scholar [12] Z. Lei, C. Liu and Y. Zhou, Global existence for a 2D incompressible viscoelastic model with small strain, Commun. Math. Sci., 5 (2007), 595-616. Google Scholar [13] Z. Lei, C. Liu and Y. Zhou, Global solutions of incompressible viscoelastic fluids, Arch. Ration. Mech. Anal., 188 (2008), 371-398. doi: 10.1007/s00205-007-0089-x. Google Scholar [14] Z. Lei, On 2D viscoelasticity with small strain, Arch. Ration. Mech. Anal., 198 (2010), 13-37. doi: 10.1007/s00205-010-0346-2. Google Scholar [15] Z. Lei, Rotation-strain decomposition for the incompressible viscoelasticity in two dimensions, Discrete Contin. Dyn. Syst., 34 (2014), 2861-2871. doi: 10.3934/dcds.2014.34.2861. Google Scholar [16] Z. Lei and F. Wang, Uniform bound of the highest energy for the three dimensional incompressible elastodynamics, Arch. Ration. Mech. Anal., 216 (2015), 593-622. doi: 10.1007/s00205-014-0815-0. Google Scholar [17] Z. Lei, Global well-posedness of incompressible elastodynamics in two dimensions, Comm. Pure Appl. Math. , doi: 10.1002/cpa.21633. Google Scholar [18] F. Lin, C. Liu and P. Zhang, On hydrodynamics of viscoelastic fluids, Comm. Pure Appl. Math., 58 (2005), 1437-1471. doi: 10.1002/cpa.20074. Google Scholar [19] J. Qian and Z. Zhang, Global well-posedness for compressible viscoelastic fluids near equilibrium, Arch. Rational Mech. Anal., 198 (2010), 835-868. doi: 10.1007/s00205-010-0351-5. Google Scholar [20] P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, New York, 1990.Google Scholar [21] Y.-Z. Wang, F. G. Liu and Y. Z. Zhang, Global existence and asymptotic of solutions for a semi-linear wave equation, J. Math. Anal. Appl., 385 (2012), 836-853. doi: 10.1016/j.jmaa.2011.07.010. Google Scholar [22] Y.-Z. Wang and K. Y. Wang, Large time behavior of solutions to the nonlinear pseudo-parabolic equation, J. Math. Anal. Appl., 417 (2014), 272-292. doi: 10.1016/j.jmaa.2014.03.030. Google Scholar [23] Y.-Z. Wang and K. Y. Wang, Asymptotic behavior of classical solutions to the compressible Navier-Stokes-Poisson equations in three and higher dimensions, J. Differential Equations, 259 (2015), 25,-47. doi: 10.1016/j.jde.2015.01.042. Google Scholar [24] Y.-Z. Wang and K. Y. Wang, Long time behavior of solutions to the compressible MHD system in multi-dimensions, J. Math. Anal. Appl., 429 (2015), 1033-1058. doi: 10.1016/j.jmaa.2015.04.045. Google Scholar [25] S. -M. Zheng, Nonlinear Evolution Equations, CRC Press, New York, 2004.Google Scholar [26] F. Xu, X. Zhang, Y. Wu and L. Liu, The optimal convergence rates for the multi-dimensioanl compressible viscoelastic flows, Z. Angew. Math. Mech., 96 (2016), 1490-1504. doi: 10.1002/zamm.201500095. Google Scholar [27] T. Zhang and D. Fang, Global existence of strong solution for equations related to the incompressible viscoelastic fluids in the critical $L^p$ framework, SIAM J. Math. Anal., 44 (2012), 2266-2288. doi: 10.1137/110851742. Google Scholar
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http://planetmath.org/86TheFreudenthalSuspensionTheorem | # 8.6 The Freudenthal suspension theorem
Before proving the Freudenthal suspension theorem, we need some auxiliary lemmas about connectedness. In \autorefcha:hlevels we proved a number of facts about $n$-connected maps and $n$-types for fixed $n$; here we are now interested in what happens when we vary $n$. For instance, in \autorefprop:nconnected_tested_by_lv_n_dependent types we showed that $n$-connected maps are characterized by an “induction principle” relative to families of $n$-types. If we want to “induct along” an $n$-connected map into a family of $k$-types for $k>n$, we don’t immediately know that there is a function by such an induction principle, but the following lemma says that at least our ignorance can be quantified.
###### Lemma 8.6.1.
If $f:A\to B$ is $n$-connected and $P:B\to{k}\text{-}\mathsf{Type}$ is a family of $k$-types for $k\geq n$, then the induced function
$(\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt}\circ f):\Bigl{(}\mathchoice{\prod% _{b:B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}% {\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{% (b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{% \prod_{(b:B)}}{\prod_{(b:B)}}}P(b)\Bigr{)}\to\Bigl{(}\mathchoice{\prod_{a:A}\,% }{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{% (a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{% \prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:A)}}{\prod_{(% a:A)}}{\prod_{(a:A)}}}P(f(a))\Bigr{)}$
is $(k-n-2)$-truncated.
###### Proof.
We induct on the natural number $k-n$. When $k=n$, this is \autorefprop:nconnected_tested_by_lv_n_dependent types. For the inductive step, suppose $f$ is $n$-connected and $P$ is a family of $k+1$-types. To show that $(\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt}\circ f)$ is $(k-n-1)$-truncated, let $k:\mathchoice{\prod_{a:A}\,}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:% A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{% \prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a% :A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}P(a)$; then we have
${\mathsf{fib}}_{(\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt}\circ f)}(k)\simeq% \mathchoice{\sum_{(g:\mathchoice{\prod_{b:B}\,}{\mathchoice{{\textstyle\prod_{% (b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle% \prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{% \textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}P(b))}% \,}{\mathchoice{{\textstyle\sum_{(g:\mathchoice{\prod_{b:B}\,}{\mathchoice{{% \textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}P(b))}}}{\sum_{(g:\mathchoice{\prod_{b:B}\,}{\mathchoice{{% \textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}P(b))}}{\sum_{(g:\mathchoice{\prod_{b:B}\,}{\mathchoice{{% \textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}P(b))}}{\sum_{(g:\mathchoice{\prod_{b:B}\,}{\mathchoice{{% \textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}P(b))}}}{\mathchoice{{\textstyle\sum_{(g:\mathchoice{\prod_{b:B% }\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{% \prod_{(b:B)}}{\prod_{(b:B)}}}P(b))}}}{\sum_{(g:\mathchoice{\prod_{b:B}\,}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}P(b))}}{\sum_{(g:\mathchoice{\prod_{b:B}\,}{\mathchoice{% {\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}P(b))}}{\sum_{(g:\mathchoice{\prod_{b:B}\,}{\mathchoice{{% \textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}P(b))}}}{\mathchoice{{\textstyle\sum_{(g:\mathchoice{\prod_{b:B% }\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{% \prod_{(b:B)}}{\prod_{(b:B)}}}P(b))}}}{\sum_{(g:\mathchoice{\prod_{b:B}\,}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}P(b))}}{\sum_{(g:\mathchoice{\prod_{b:B}\,}{\mathchoice{% {\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}P(b))}}{\sum_{(g:\mathchoice{\prod_{b:B}\,}{\mathchoice{{% \textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}P(b))}}}\mathchoice{\prod_{(a:A)}\,}{\mathchoice{{\textstyle% \prod_{(a:A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{% \textstyle\prod_{(a:A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{% \mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a% :A)}}}g(f(a))=k(a).$
Let $(g,p)$ and $(h,q)$ lie in this type, so $p:g\circ f\sim k$ and $q:h\circ f\sim k$; then we also have
$\big{(}(g,p)=(h,q)\big{)}\simeq\Bigl{(}\mathchoice{\sum_{r:g\sim h}\,}{% \mathchoice{{\textstyle\sum_{(r:g\sim h)}}}{\sum_{(r:g\sim h)}}{\sum_{(r:g\sim h% )}}{\sum_{(r:g\sim h)}}}{\mathchoice{{\textstyle\sum_{(r:g\sim h)}}}{\sum_{(r:% g\sim h)}}{\sum_{(r:g\sim h)}}{\sum_{(r:g\sim h)}}}{\mathchoice{{\textstyle% \sum_{(r:g\sim h)}}}{\sum_{(r:g\sim h)}}{\sum_{(r:g\sim h)}}{\sum_{(r:g\sim h)% }}}r\circ f=p\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}% }}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{% \scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle% \,\centerdot\,}}}\mathord{{q}^{-1}}\Bigr{)}.$
However, here the right-hand side is a fiber of the map
$(\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt}\circ f):\Bigl{(}\mathchoice{\prod% _{b:B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}% {\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{% (b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{% \prod_{(b:B)}}{\prod_{(b:B)}}}Q(b)\Bigr{)}\to\Bigl{(}\mathchoice{\prod_{a:A}\,% }{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{% (a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{% \prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:A)}}{\prod_{(% a:A)}}{\prod_{(a:A)}}}Q(f(a))\Bigr{)}$
where $Q(b):\!\!\equiv(g(b)=h(b))$. Since $P$ is a family of $(k+1)$-types, $Q$ is a family of $k$-types, so the inductive hypothesis implies that this fiber is a $(k-n-2)$-type. Thus, all path spaces of ${\mathsf{fib}}_{(\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt}\circ f)}(k)$ are $(k-n-2)$-types, so it is a $(k-n-1)$-type. ∎
Recall that if ${\mathopen{}(A,a_{0})\mathclose{}}$ and ${\mathopen{}(B,b_{0})\mathclose{}}$ are pointed types, then their wedge $A\vee B$ is defined to be the pushout of $A\xleftarrow{a_{0}}\mathbf{1}\xrightarrow{b_{0}}B$. There is a canonical map $i:A\vee B\to A\times B$ defined by the two maps ${\lambda}a.\,(a,b_{0})$ and ${\lambda}b.\,(a_{0},b)$; the following lemma essentially says that this map is highly connected if $A$ and $B$ are so. It is a bit more convenient both to prove and use, however, if we use the characterization of connectedness from \autorefprop:nconnected_tested_by_lv_n_dependent types and substitute in the universal property of the wedge (generalized to type families).
###### Lemma 8.6.2 (Wedge connectivity lemma).
Suppose that ${\mathopen{}(A,a_{0})\mathclose{}}$ and ${\mathopen{}(B,b_{0})\mathclose{}}$ are $n$- and $m$-connected pointed types, respectively, with $n,m\geq 0$, and let $P:A\to B\to{(n+m)}\text{-}\mathsf{Type}.$ Then for any ${f:\mathchoice{\prod_{a:A}\,}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a% :A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{% \prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a% :A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}P(a,b_{0})}$ and ${g:\mathchoice{\prod_{b:B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b% :B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{% \prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b% :B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}P(a_{0},b)}$ with $p:f(a_{0})=g(b_{0})$, there exists $h:\mathchoice{\prod_{(a:A)}\,}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(% a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{% \prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a% :A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}\mathchoice{\prod_{(b:B)}% \,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod% _{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}% }{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_% {(b:B)}}{\prod_{(b:B)}}}P(a,b)$ with homotopies
$q:\mathchoice{\prod_{a:A}\,}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:% A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{% \prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a% :A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}h(a,b_{0})=f(a)\qquad\text% {and}\qquad r:\mathchoice{\prod_{b:B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}% }{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{% (b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle% \prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}h(a_{0},b)=g(b)$
such that $p=\mathord{{q(a_{0})}^{-1}}\mathchoice{\mathbin{\raisebox{2.15pt}{% \displaystyle\centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{% \mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox% {0.43pt}{\scriptscriptstyle\,\centerdot\,}}}r(b_{0})$.
###### Proof.
Define $P:A\to\mathcal{U}$ by
$P(a):\!\!\equiv\mathchoice{\sum_{k:\mathchoice{\prod_{b:B}\,}{\mathchoice{{% \textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}P(a,b)}\,}{\mathchoice{{\textstyle\sum_{(k:\mathchoice{\prod_{b% :B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{% \prod_{(b:B)}}{\prod_{(b:B)}}}P(a,b))}}}{\sum_{(k:\mathchoice{\prod_{b:B}\,}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}P(a,b))}}{\sum_{(k:\mathchoice{\prod_{b:B}\,}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}P(a,b))}}{\sum_{(k:\mathchoice{\prod_{b:B}\,}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}P(a,b))}}}{\mathchoice{{\textstyle\sum_{(k:\mathchoice{% \prod_{b:B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b% :B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{% \prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(% b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}P(a,b))}}}{\sum_{(k:\mathchoice{\prod_{b:% B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{% \prod_{(b:B)}}{\prod_{(b:B)}}}P(a,b))}}{\sum_{(k:\mathchoice{\prod_{b:B}\,}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}P(a,b))}}{\sum_{(k:\mathchoice{\prod_{b:B}\,}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}P(a,b))}}}{\mathchoice{{\textstyle\sum_{(k:\mathchoice{% \prod_{b:B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b% :B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{% \prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(% b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}P(a,b))}}}{\sum_{(k:\mathchoice{\prod_{b:% B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{% \prod_{(b:B)}}{\prod_{(b:B)}}}P(a,b))}}{\sum_{(k:\mathchoice{\prod_{b:B}\,}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}P(a,b))}}{\sum_{(k:\mathchoice{\prod_{b:B}\,}{% \mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b% :B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{% \prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(% b:B)}}{\prod_{(b:B)}}}P(a,b))}}}(f(a)=k(b_{0})).$
Then we have $(g,p):P(a_{0})$. Since $a_{0}:\mathbf{1}\to A$ is $(n-1)$-connected, if $P$ is a family of $(n-1)$-types then we will have $\ell:\mathchoice{\prod_{a:A}\,}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{% (a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{% \prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a% :A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}P(a)$ such that $\ell(a_{0})=(g,p)$, in which case we can define $h(a,b):\!\!\equiv\mathsf{pr}_{1}(\ell(a))(b)$. However, for fixed $a$, the type $P(a)$ is the fiber over $f(a)$ of the map
$\Bigl{(}\mathchoice{\prod_{b:B}\,}{\mathchoice{{\textstyle\prod_{(b:B)}}}{% \prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle\prod_{(b% :B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}{\mathchoice{{\textstyle% \prod_{(b:B)}}}{\prod_{(b:B)}}{\prod_{(b:B)}}{\prod_{(b:B)}}}P(a,b)\Bigr{)}\to P% (a,b_{0})$
given by precomposition with $b_{0}:\mathbf{1}\to B$. Since $b_{0}:\mathbf{1}\to B$ is $(m-1)$-connected, for this fiber to be $(n-1)$-connected, by \autorefthm:conn-trunc-variable-ind it suffices for each type $P(a,b)$ to be an $(n+m)$-type, which we have assumed. ∎
Let $(X,x_{0})$ be a pointed type, and recall the definition of the suspension $\Sigma X$ from \autorefsec:suspension, with constructors $\mathsf{N},\mathsf{S}:\Sigma X$ and $\mathsf{merid}:X\to(\mathsf{N}=\mathsf{S})$. We regard $\Sigma X$ as a pointed space with basepoint $\mathsf{N}$, so that we have $\Omega\Sigma X:\!\!\equiv(\mathsf{N}=_{\Sigma X}\mathsf{N})$. Then there is a canonical map
$\displaystyle\sigma$ $\displaystyle:X\to\Omega\Sigma X$ $\displaystyle\sigma(x)$ $\displaystyle:\!\!\equiv\mathsf{merid}(x)\mathchoice{\mathbin{\raisebox{2.15pt% }{\displaystyle\centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{% \mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox% {0.43pt}{\scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}% ^{-1}}.$
###### Remark 8.6.3.
In classical algebraic topology, one considers the reduced suspension, in which the path $\mathsf{merid}(x_{0})$ is collapsed down to a point, identifying $\mathsf{N}$ and $\mathsf{S}$. The reduced and unreduced suspensions are homotopy equivalent, so the distinction is invisible to our purely homotopy-theoretic eyes — and higher inductive types only allow us to “identify” points up to a higher path anyway, there is no purpose to considering reduced suspensions in homotopy type theory. However, the “unreducedness” of our suspension is the reason for the (possibly unexpected) appearance of $\mathord{{\mathsf{merid}(x_{0})}^{-1}}$ in the definition of $\sigma$.
Our goal is now to prove the following.
###### Theorem 8.6.4 (The Freudenthal suspension theorem).
Suppose that $X$ is $n$-connected and pointed, with $n\geq 0$. Then the map $\sigma:X\to\Omega\Sigma(X)$ is $2n$-connected.
We will use the encode-decode method, but applied in a slightly different way. In most cases so far, we have used it to characterize the loop space $\Omega(A,a_{0})$ of some type as equivalent to some other type $B$, by constructing a family $\mathsf{code}:A\to\mathcal{U}$ with $\mathsf{code}(a_{0}):\!\!\equiv B$ and a family of equivalences $\mathsf{decode}:\mathchoice{\prod_{x:A}\,}{\mathchoice{{\textstyle\prod_{(x:A)% }}}{\prod_{(x:A)}}{\prod_{(x:A)}}{\prod_{(x:A)}}}{\mathchoice{{\textstyle\prod% _{(x:A)}}}{\prod_{(x:A)}}{\prod_{(x:A)}}{\prod_{(x:A)}}}{\mathchoice{{% \textstyle\prod_{(x:A)}}}{\prod_{(x:A)}}{\prod_{(x:A)}}{\prod_{(x:A)}}}\mathsf% {code}(x)\simeq(a_{0}=x)$.
In this case, however, we want to show that $\sigma:X\to\Omega\Sigma X$ is $2n$-connected. We could use a truncated version of the previous method, such as we will see in \autorefsec:van-kampen, to prove that $\mathopen{}\left\|X\right\|_{2n}\mathclose{}\to\mathopen{}\left\|\Omega\Sigma X% \right\|_{2n}\mathclose{}$ is an equivalence—but this is a slightly weaker statement than the map being $2n$-connected (see \autorefthm:conn-pik,\autorefthm:pik-conn). However, note that in the general case, to prove that $\mathsf{decode}(x)$ is an equivalence, we could equivalently be proving that its fibers are contractible, and we would still be able to use induction over the base type. This we can generalize to prove connectedness of a map into a loop space, i.e. that the truncations of its fibers are contractible. Moreover, instead of constructing $\mathsf{code}$ and $\mathsf{decode}$ separately, we can construct directly a family of codes for the truncations of the fibers.
###### Definition 8.6.5.
If $X$ is $n$-connected and pointed with $n\geq 0$, then there is a family
$\mathsf{code}:\mathchoice{\prod_{y:\Sigma X}\,}{\mathchoice{{\textstyle\prod_{% (y:\Sigma X)}}}{\prod_{(y:\Sigma X)}}{\prod_{(y:\Sigma X)}}{\prod_{(y:\Sigma X% )}}}{\mathchoice{{\textstyle\prod_{(y:\Sigma X)}}}{\prod_{(y:\Sigma X)}}{\prod% _{(y:\Sigma X)}}{\prod_{(y:\Sigma X)}}}{\mathchoice{{\textstyle\prod_{(y:% \Sigma X)}}}{\prod_{(y:\Sigma X)}}{\prod_{(y:\Sigma X)}}{\prod_{(y:\Sigma X)}}% }(\mathsf{N}=y)\to\mathcal{U}$ (8.6.5)
such that
$\displaystyle\mathsf{code}(\mathsf{N},p)$ $\displaystyle:\!\!\equiv\mathopen{}\left\|{\mathsf{fib}}_{\sigma}(p)\right\|_{% 2n}\mathclose{}\equiv\mathopen{}\left\|\mathchoice{{\textstyle\sum_{(x:X)}}}{% \sum_{(x:X)}}{\sum_{(x:X)}}{\sum_{(x:X)}}(\mathsf{merid}(x)\mathchoice{% \mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}}}{\mathbin{\raisebox{2.1% 5pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}% }}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle\,\centerdot\,}}}\mathord{{% \mathsf{merid}(x_{0})}^{-1}}=p)\right\|_{2n}\mathclose{}$ (8.6.6) $\displaystyle\mathsf{code}(\mathsf{S},q)$ $\displaystyle:\!\!\equiv\mathopen{}\left\|{\mathsf{fib}}_{\mathsf{merid}}(q)% \right\|_{2n}\mathclose{}\equiv\mathopen{}\left\|\mathchoice{{\textstyle\sum_{% (x:X)}}}{\sum_{(x:X)}}{\sum_{(x:X)}}{\sum_{(x:X)}}(\mathsf{merid}(x)=q)\right% \|_{2n}\mathclose{}.$ (8.6.6)
Our eventual goal will be to prove that $\mathsf{code}(y,p)$ is contractible for all $y:\Sigma X$ and $p:\mathsf{N}=y$. Applying this with $y:\!\!\equiv\mathsf{N}$ will show that all fibers of $\sigma$ are $2n$-connected, and thus $\sigma$ is $2n$-connected.
###### Proof of \autorefthm:freudcode.
We define $\mathsf{code}(y,p)$ by induction on $y:\Sigma X$, where the first two cases are (8.6.6) and (8.6.6). It remains to construct, for each $x_{1}:X$, a dependent path
$\mathsf{code}(\mathsf{N})=^{{\lambda}y.\,(\mathsf{N}=y)\to\mathcal{U}}_{% \mathsf{merid}(x_{1})}\mathsf{code}(\mathsf{S}).$
By \autorefthm:dpath-arrow, this is equivalent to giving a family of paths
$\mathchoice{\prod_{q:\mathsf{N}=\mathsf{S}}\,}{\mathchoice{{\textstyle\prod_{(% q:\mathsf{N}=\mathsf{S})}}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}{\prod_{(q:% \mathsf{N}=\mathsf{S})}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}}{\mathchoice{{% \textstyle\prod_{(q:\mathsf{N}=\mathsf{S})}}}{\prod_{(q:\mathsf{N}=\mathsf{S})% }}{\prod_{(q:\mathsf{N}=\mathsf{S})}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}}{% \mathchoice{{\textstyle\prod_{(q:\mathsf{N}=\mathsf{S})}}}{\prod_{(q:\mathsf{N% }=\mathsf{S})}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}{\prod_{(q:\mathsf{N}=% \mathsf{S})}}}\mathsf{code}(\mathsf{N})(\mathsf{transport}^{{\lambda}y.\,(% \mathsf{N}=y)}(\mathord{{\mathsf{merid}(x_{1})}^{-1}},q))=\mathsf{code}(% \mathsf{S})(q).$
And by univalence and transport in path types, this is equivalent to a family of equivalences
$\mathchoice{\prod_{q:\mathsf{N}=\mathsf{S}}\,}{\mathchoice{{\textstyle\prod_{(% q:\mathsf{N}=\mathsf{S})}}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}{\prod_{(q:% \mathsf{N}=\mathsf{S})}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}}{\mathchoice{{% \textstyle\prod_{(q:\mathsf{N}=\mathsf{S})}}}{\prod_{(q:\mathsf{N}=\mathsf{S})% }}{\prod_{(q:\mathsf{N}=\mathsf{S})}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}}{% \mathchoice{{\textstyle\prod_{(q:\mathsf{N}=\mathsf{S})}}}{\prod_{(q:\mathsf{N% }=\mathsf{S})}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}{\prod_{(q:\mathsf{N}=% \mathsf{S})}}}\mathsf{code}(\mathsf{N},q\mathchoice{\mathbin{\raisebox{2.15pt}% {\displaystyle\centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{% \mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox% {0.43pt}{\scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{1})}% ^{-1}})\simeq\mathsf{code}(\mathsf{S},q).$
We will define a family of maps
$\mathchoice{\prod_{q:\mathsf{N}=\mathsf{S}}\,}{\mathchoice{{\textstyle\prod_{(% q:\mathsf{N}=\mathsf{S})}}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}{\prod_{(q:% \mathsf{N}=\mathsf{S})}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}}{\mathchoice{{% \textstyle\prod_{(q:\mathsf{N}=\mathsf{S})}}}{\prod_{(q:\mathsf{N}=\mathsf{S})% }}{\prod_{(q:\mathsf{N}=\mathsf{S})}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}}{% \mathchoice{{\textstyle\prod_{(q:\mathsf{N}=\mathsf{S})}}}{\prod_{(q:\mathsf{N% }=\mathsf{S})}}{\prod_{(q:\mathsf{N}=\mathsf{S})}}{\prod_{(q:\mathsf{N}=% \mathsf{S})}}}\mathsf{code}(\mathsf{N},q\mathchoice{\mathbin{\raisebox{2.15pt}% {\displaystyle\centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{% \mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox% {0.43pt}{\scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{1})}% ^{-1}})\to\mathsf{code}(\mathsf{S},q).$ (8.6.7)
and then show that they are all equivalences. Thus, let $q:\mathsf{N}=\mathsf{S}$; by the universal property of truncation and the definitions of $\mathsf{code}(\mathsf{N},\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt})$ and $\mathsf{code}(\mathsf{S},\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt})$, it will suffice to define for each $x_{2}:X$, a map
$\big{(}\mathsf{merid}(x_{2})\mathchoice{\mathbin{\raisebox{2.15pt}{% \displaystyle\centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{% \mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox% {0.43pt}{\scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}% ^{-1}}=q\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}}}{% \mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{% \scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle% \,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{1})}^{-1}}\big{)}\to\mathopen{}% \left\|\mathchoice{{\textstyle\sum_{(x:X)}}}{\sum_{(x:X)}}{\sum_{(x:X)}}{\sum_% {(x:X)}}(\mathsf{merid}(x)=q)\right\|_{2n}\mathclose{}.$
Now for each $x_{1},x_{2}:X$, this type is $2n$-truncated, while $X$ is $n$-connected. Thus, by \autorefthm:wedge-connectivity, it suffices to define this map when $x_{1}$ is $x_{0}$, when $x_{2}$ is $x_{0}$, and check that they agree when both are $x_{0}$.
When $x_{1}$ is $x_{0}$, the hypothesis is $r:\mathsf{merid}(x_{2})\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle% \centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1% .075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{% \scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}^{-1}}=q% \mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}}}{\mathbin{% \raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{\scriptstyle\,% \centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle\,\centerdot\,% }}}\mathord{{\mathsf{merid}(x_{0})}^{-1}}$. Thus, by canceling $\mathord{{\mathsf{merid}(x_{0})}^{-1}}$ from $r$ to get $r^{\prime}:\mathsf{merid}(x_{2})=q$, so we can define the image to be $\mathopen{}\left|(x_{2},r^{\prime})\right|_{2n}\mathclose{}$.
When $x_{2}$ is $x_{0}$, the hypothesis is $r:\mathsf{merid}(x_{0})\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle% \centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1% .075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{% \scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}^{-1}}=q% \mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}}}{\mathbin{% \raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{\scriptstyle\,% \centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle\,\centerdot\,% }}}\mathord{{\mathsf{merid}(x_{1})}^{-1}}$. Rearranging this, we obtain $r^{\prime\prime}:\mathsf{merid}(x_{1})=q$, and we can define the image to be $\mathopen{}\left|(x_{1},r^{\prime\prime})\right|_{2n}\mathclose{}$.
Finally, when both $x_{1}$ and $x_{2}$ are $x_{0}$, it suffices to show the resulting $r^{\prime}$ and $r^{\prime\prime}$ agree; this is an easy lemma about path composition. This completes the definition of (8.6.7). To show that it is a family of equivalences, since being an equivalence is a mere proposition and $x_{0}:\mathbf{1}\to X$ is (at least) $(-1)$-connected, it suffices to assume $x_{1}$ is $x_{0}$. In this case, inspecting the above construction we see that it is essentially the $2n$-truncation of the function that cancels $\mathord{{\mathsf{merid}(x_{0})}^{-1}}$, which is an equivalence. ∎
In addition to (8.6.6) and (8.6.6), we will need to extract from the construction of $\mathsf{code}$ some information about how it acts on paths. For this we use the following lemma.
###### Lemma 8.6.8.
Let $A:\mathcal{U}$, $B:A\to\mathcal{U}$, and $C:\mathchoice{\prod_{a:A}\,}{\mathchoice{{\textstyle\prod_{(a:A)}}}{\prod_{(a:% A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a:A)}}}{% \prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}{\mathchoice{{\textstyle\prod_{(a% :A)}}}{\prod_{(a:A)}}{\prod_{(a:A)}}{\prod_{(a:A)}}}B(a)\to\mathcal{U}$, and also $a_{1},a_{2}:A$ with $m:a_{1}=a_{2}$ and $b:B(a_{2})$. Then the function
$\mathsf{transport}^{\widehat{C}}(\mathsf{pair}^{\mathord{=}}(m,t),\mathord{% \hskip 1.0pt\text{--}\hskip 1.0pt}):C(a_{1},\mathsf{transport}^{B}(\mathord{{m% }^{-1}},b))\to C(a_{2},b),$
where $t:\mathsf{transport}^{B}(m,\mathsf{transport}^{B}(\mathord{{m}^{-1}},b))=b$ is the obvious coherence path and $\widehat{C}:(\mathchoice{\sum_{a:A}\,}{\mathchoice{{\textstyle\sum_{(a:A)}}}{% \sum_{(a:A)}}{\sum_{(a:A)}}{\sum_{(a:A)}}}{\mathchoice{{\textstyle\sum_{(a:A)}% }}{\sum_{(a:A)}}{\sum_{(a:A)}}{\sum_{(a:A)}}}{\mathchoice{{\textstyle\sum_{(a:% A)}}}{\sum_{(a:A)}}{\sum_{(a:A)}}{\sum_{(a:A)}}}B(a))\to\mathcal{U}$ is the uncurried form of $C$, is equal to the equivalence obtained by univalence from the composite
$\displaystyle C(a_{1},\mathsf{transport}^{B}(\mathord{{m}^{-1}},b))$ $\displaystyle=\mathsf{transport}^{{\lambda}a.\,B(a)\to\mathcal{U}}(m,C(a_{1}))% (b){}$ (by \eqref{eq:transport-arrow}) $\displaystyle=C(a_{2},b).{}$ (by $\mathsf{happly}(\mathsf{apd}_{C}\mathopen{}\left(m\right)\mathclose{},b)$)
###### Proof.
By path induction, we may assume $a_{2}$ is $a_{1}$ and $m$ is $\mathsf{refl}_{a_{1}}$, in which case both functions are the identity. ∎
We apply this lemma with $A:\!\!\equiv\Sigma X$ and $B:\!\!\equiv{\lambda}y.\,(\mathsf{N}=y)$ and $C:\!\!\equiv\mathsf{code}$, while $a_{1}:\!\!\equiv\mathsf{N}$ and $a_{2}:\!\!\equiv\mathsf{S}$ and $m:\!\!\equiv\mathsf{merid}(x_{1})$ for some $x_{1}:X$, and finally $b:\!\!\equiv q$ is some path $\mathsf{N}=\mathsf{S}$. The computation rule for induction over $\Sigma X$ identifies $\mathsf{apd}_{C}\mathopen{}\left(m\right)\mathclose{}$ with a path constructed in a certain way out of univalence and function extensionality. The second function described in \autorefthm:freudlemma essentially consists of undoing these applications of univalence and function extensionality, reducing back to the particular functions (8.6.7) that we defined using \autorefthm:wedge-connectivity. Therefore, \autorefthm:freudlemma says that transporting along $\mathsf{pair}^{\mathord{=}}(q,t)$ essentially recovers these functions.
Finally, by construction, when $x_{1}$ or $x_{2}$ coincides with $x_{0}$ and the input is in the image of $\mathopen{}\left|\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt}\right|_{2n}% \mathclose{}$, we know more explicitly what these functions are. Thus, for any $x_{2}:X$, we have
$\mathsf{transport}^{\hat{\mathsf{code}}}(\mathsf{pair}^{\mathord{=}}(\mathsf{% merid}(x_{0}),t),\mathopen{}\left|(x_{2},r)\right|_{2n}\mathclose{})=\mathopen% {}\left|(x_{1},r^{\prime})\right|_{2n}\mathclose{}$ (8.6.9)
where $r:\mathsf{merid}(x_{2})\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle% \centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1% .075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{% \scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}^{-1}}=% \mathsf{transport}^{B}(\mathord{{\mathsf{merid}(x_{0})}^{-1}},q)$ is arbitrary as before, and $r^{\prime}:\mathsf{merid}(x_{2})=q$ is obtained from $r$ by identifying its end point with $q\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}}}{\mathbin{% \raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{\scriptstyle\,% \centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle\,\centerdot\,% }}}\mathord{{\mathsf{merid}(x_{0})}^{-1}}$ and canceling $\mathord{{\mathsf{merid}(x_{0})}^{-1}}$. Similarly, for any $x_{1}:X$, we have
$\mathsf{transport}^{\hat{\mathsf{code}}}(\mathsf{pair}^{\mathord{=}}(\mathsf{% merid}(x_{1}),t),\mathopen{}\left|(x_{0},r)\right|_{2n}\mathclose{})=\mathopen% {}\left|(x_{1},r^{\prime\prime})\right|_{2n}\mathclose{}$ (8.6.10)
where $r:\mathsf{merid}(x_{0})\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle% \centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1% .075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{% \scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}^{-1}}=% \mathsf{transport}^{B}(\mathord{{\mathsf{merid}(x_{1})}^{-1}},q)$, and $r^{\prime\prime}:\mathsf{merid}(x_{1})=q$ is obtained by identifying its end point and rearranging paths.
###### Proof of \autorefthm:freudenthal.
It remains to show that $\mathsf{code}(y,p)$ is contractible for each $y:\Sigma X$ and $p:\mathsf{N}=y$. First we must choose a center of contraction, say $c(y,p):\mathsf{code}(y,p)$. This corresponds to the definition of the function $\mathsf{encode}$ in our previous proofs, so we define it by transport. Note that in the special case when $y$ is $\mathsf{N}$ and $p$ is $\mathsf{refl}_{\mathsf{N}}$, we have
$\mathsf{code}(\mathsf{N},\mathsf{refl}_{\mathsf{N}})\equiv\mathopen{}\left\|% \mathchoice{{\textstyle\sum_{(x:X)}}}{\sum_{(x:X)}}{\sum_{(x:X)}}{\sum_{(x:X)}% }(\mathsf{merid}(x)\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle% \centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1% .075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{% \scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}^{-1}}=% \mathsf{refl}_{\mathsf{N}})\right\|_{2n}\mathclose{}.$
Thus, we can choose $c(\mathsf{N},\mathsf{refl}_{\mathsf{N}}):\!\!\equiv\mathopen{}\left|(x_{0},% \mathsf{rinv}_{\mathsf{merid}(x_{0})})\right|_{2n}\mathclose{}$, where $\mathrm{rinv}_{q}$ is the obvious path $q\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}}}{\mathbin{% \raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{\scriptstyle\,% \centerdot\,}}}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle\,\centerdot\,% }}}\mathord{{q}^{-1}}=\mathsf{refl}$ for any $q$. We can now obtain $c:\mathchoice{\prod_{(y:\Sigma X)}\,}{\mathchoice{{\textstyle\prod_{(y:\Sigma X% )}}}{\prod_{(y:\Sigma X)}}{\prod_{(y:\Sigma X)}}{\prod_{(y:\Sigma X)}}}{% \mathchoice{{\textstyle\prod_{(y:\Sigma X)}}}{\prod_{(y:\Sigma X)}}{\prod_{(y:% \Sigma X)}}{\prod_{(y:\Sigma X)}}}{\mathchoice{{\textstyle\prod_{(y:\Sigma X)}% }}{\prod_{(y:\Sigma X)}}{\prod_{(y:\Sigma X)}}{\prod_{(y:\Sigma X)}}}% \mathchoice{\prod_{(p:\mathsf{N}=y)}\,}{\mathchoice{{\textstyle\prod_{(p:% \mathsf{N}=y)}}}{\prod_{(p:\mathsf{N}=y)}}{\prod_{(p:\mathsf{N}=y)}}{\prod_{(p% :\mathsf{N}=y)}}}{\mathchoice{{\textstyle\prod_{(p:\mathsf{N}=y)}}}{\prod_{(p:% \mathsf{N}=y)}}{\prod_{(p:\mathsf{N}=y)}}{\prod_{(p:\mathsf{N}=y)}}}{% \mathchoice{{\textstyle\prod_{(p:\mathsf{N}=y)}}}{\prod_{(p:\mathsf{N}=y)}}{% \prod_{(p:\mathsf{N}=y)}}{\prod_{(p:\mathsf{N}=y)}}}\mathsf{code}(y,p)$ by path induction on $p$, but it will be important below that we can also give a concrete definition in terms of transport:
$c(y,p):\!\!\equiv\mathsf{transport}^{\hat{\mathsf{code}}}(\mathsf{pair}^{% \mathord{=}}(p,\mathsf{tid}_{p}),c(\mathsf{N},\mathsf{refl}_{\mathsf{N}}))$
where $\hat{\mathsf{code}}:\big{(}\mathchoice{\sum_{y:\Sigma X}\,}{\mathchoice{{% \textstyle\sum_{(y:\Sigma X)}}}{\sum_{(y:\Sigma X)}}{\sum_{(y:\Sigma X)}}{\sum% _{(y:\Sigma X)}}}{\mathchoice{{\textstyle\sum_{(y:\Sigma X)}}}{\sum_{(y:\Sigma X% )}}{\sum_{(y:\Sigma X)}}{\sum_{(y:\Sigma X)}}}{\mathchoice{{\textstyle\sum_{(y% :\Sigma X)}}}{\sum_{(y:\Sigma X)}}{\sum_{(y:\Sigma X)}}{\sum_{(y:\Sigma X)}}}(% \mathsf{N}=y)\big{)}\to\mathcal{U}$ is the uncurried version of $\mathsf{code}$, and $\mathsf{tid}_{p}:{p}_{*}\mathopen{}\left({\mathsf{refl}}\right)\mathclose{}=p$ is a standard lemma.
Next, we must show that every element of $\mathsf{code}(y,p)$ is equal to $c(y,p)$. Again, by path induction, it suffices to assume $y$ is $\mathsf{N}$ and $p$ is $\mathsf{refl}_{\mathsf{N}}$. In fact, we will prove it more generally when $y$ is $\mathsf{N}$ and $p$ is arbitrary. That is, we will show that for any $p:\mathsf{N}=\mathsf{N}$ and $d:\mathsf{code}(\mathsf{N},p)$ we have $d=c(\mathsf{N},p)$. Since this equality is a $(2n-1)$-type, we may assume $d$ is of the form $\mathopen{}\left|(x_{1},r)\right|_{2n}\mathclose{}$ for some $x_{1}:X$ and $r:\mathsf{merid}(x_{1})\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle% \centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1% .075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{% \scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}^{-1}}=p$.
Now by a further path induction, we may assume that $r$ is reflexivity, and $p$ is $\mathsf{merid}(x_{1})\mathchoice{\mathbin{\raisebox{2.15pt}{\displaystyle% \centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{\mathbin{\raisebox{1% .075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox{0.43pt}{% \scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}^{-1}}$. (This is why we generalized to arbitrary $p$ above.) Thus, we have to prove that
$\mathopen{}\left|(x_{1},\mathsf{refl}_{\mathsf{merid}(x_{1})\mathchoice{% \mathbin{\raisebox{2.15pt}{\displaystyle\centerdot}}}{\mathbin{\raisebox{2.1% 5pt}{\centerdot}}}{\mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}% }}{\mathbin{\raisebox{0.43pt}{\scriptscriptstyle\,\centerdot\,}}}\mathord{{% \mathsf{merid}(x_{0})}^{-1}}})\right|_{2n}\mathclose{}\;=\;c\left(\mathsf{N},% \mathsf{refl}_{\mathsf{merid}(x_{1})\mathchoice{\mathbin{\raisebox{2.15pt}{% \displaystyle\centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{% \mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox% {0.43pt}{\scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}% ^{-1}}}\right).$ (8.6.11)
By definition, the right-hand side of this equality is
\displaystyle\mathsf{transport}^{\hat{\mathsf{code}}}\Big{(}\mathsf{pair}^{% \mathord{=}}(\mathsf{merid}(x_{1})\mathchoice{\mathbin{\raisebox{2.15pt}{% \displaystyle\centerdot}}}{\mathbin{\raisebox{2.15pt}{\centerdot}}}{% \mathbin{\raisebox{1.075pt}{\scriptstyle\,\centerdot\,}}}{\mathbin{\raisebox% {0.43pt}{\scriptscriptstyle\,\centerdot\,}}}\mathord{{\mathsf{merid}(x_{0})}% ^{-1}},\mathord{\hskip 1.0pt\underline{\hskip 4.3pt}\hskip 1.0pt}),\,\mathopen% {}\left|(x_{0},\mathord{\hskip 1.0pt\underline{\hskip 4.3pt}\hskip 1.0pt})% \right|_{2n}\mathclose{}\Big{)}\\ \displaystyle=\mathsf{transport}^{\hat{\mathsf{code}}}\begin{aligned} % \displaystyle\Big{(}&\displaystyle{\mathsf{pair}^{\mathord{=}}(\mathord{{% \mathsf{merid}(x_{0})}^{-1}},\mathord{\hskip 1.0pt\underline{\hskip 4.3pt}% \hskip 1.0pt})},\\ &\displaystyle{\mathsf{transport}^{\hat{\mathsf{code}}}\Big{(}\mathsf{pair}^{% \mathord{=}}(\mathsf{merid}(x_{1}),\mathord{\hskip 1.0pt\underline{\hskip 4.3% pt}\hskip 1.0pt}),\,\mathopen{}\left|(x_{0},\mathord{\hskip 1.0pt\underline{% \hskip 4.3pt}\hskip 1.0pt})\right|_{2n}\mathclose{}\Big{)}}\Big{)}\end{aligned% }\\ \displaystyle=\mathsf{transport}^{\hat{\mathsf{code}}}\Big{(}\mathsf{pair}^{% \mathord{=}}(\mathord{{\mathsf{merid}(x_{0})}^{-1}},\mathord{\hskip 1.0pt% \underline{\hskip 4.3pt}\hskip 1.0pt}),\,\mathopen{}\left|(x_{1},\mathord{% \hskip 1.0pt\underline{\hskip 4.3pt}\hskip 1.0pt})\right|_{2n}\mathclose{}\Big% {)}=\mathopen{}\left|(x_{1},\mathord{\hskip 1.0pt\underline{\hskip 4.3pt}% \hskip 1.0pt})\right|_{2n}\mathclose{}
where the underscore $\mathord{\hskip 1.0pt\underline{\hskip 4.3pt}\hskip 1.0pt}$ ought to be filled in with suitable coherence paths. Here the first step is functoriality of transport, the second invokes (8.6.10), and the third invokes (8.6.9) (with transport moved to the other side). Thus we have the same first component as the left-hand side of (8.6.11). We leave it to the reader to verify that the coherence paths all cancel, giving reflexivity in the second component. ∎
###### Corollary 8.6.12 (Freudenthal Equivalence).
Suppose that $X$ is $n$-connected and pointed, with $n\geq 0$. Then $\mathopen{}\left\|X\right\|_{2n}\mathclose{}\simeq\mathopen{}\left\|\Omega% \Sigma(X)\right\|_{2n}\mathclose{}$.
###### Proof.
By \crefthm:freudenthal, $\sigma$ is $2n$-connected. By \creflem:connected-map-equiv-truncation, it is therefore an equivalence on $2n$-truncations. ∎
One important corollary of the Freudenthal suspension theorem is that the homotopy groups of spheres are stable in a certain range (these are the northeast-to-southwest diagonals in \autoreftab:homotopy-groups-of-spheres):
###### Corollary 8.6.13 (Stability for Spheres).
If $k\leq 2n-2$, then $\pi_{k+1}(S^{n+1})=\pi_{k}(S^{n})$.
###### Proof.
Assume $k\leq 2n-2$. By \crefcor:sn-connected, $\mathbb{S}^{n}$ is $(n-1)$-connected. Therefore, by \crefcor:freudenthal-equiv,
$\mathopen{}\left\|\Omega(\Sigma(\mathbb{S}^{n}))\right\|_{2(n-1)}\mathclose{}=% \mathopen{}\left\|\mathbb{S}^{n}\right\|_{2(n-1)}\mathclose{}.$
By \creflem:truncation-le, because $k\leq 2(n-1)$, applying $\mathopen{}\left\|\mathord{\hskip 1.0pt\text{--}\hskip 1.0pt}\right\|_{k}% \mathclose{}$ to both sides shows that this equation holds for $k$:
$\mathopen{}\left\|\Omega(\Sigma(\mathbb{S}^{n}))\right\|_{k}\mathclose{}=% \mathopen{}\left\|\mathbb{S}^{n}\right\|_{k}\mathclose{}.$ (8.6.14)
Then, the main idea of the proof is as follows; we omit checking that these equivalences act appropriately on the base points of these spaces:
$\displaystyle\pi_{k+1}(\mathbb{S}^{n+1})$ $\displaystyle\equiv\mathopen{}\left\|\Omega^{k+1}(\mathbb{S}^{n+1})\right\|_{0% }\mathclose{}$ $\displaystyle\equiv\mathopen{}\left\|\Omega^{k}(\Omega(\mathbb{S}^{n+1}))% \right\|_{0}\mathclose{}$ $\displaystyle\equiv\mathopen{}\left\|\Omega^{k}(\Omega(\Sigma(\mathbb{S}^{n}))% )\right\|_{0}\mathclose{}$ $\displaystyle=\Omega^{k}(\mathopen{}\left\|(\Omega(\Sigma(\mathbb{S}^{n})))% \right\|_{k}\mathclose{}){}$ (by \autorefthm:path-truncation) $\displaystyle=\Omega^{k}(\mathopen{}\left\|\mathbb{S}^{n}\right\|_{k}% \mathclose{}){}$ (by \eqref{eq:freudenthal-for-spheres}) $\displaystyle=\mathopen{}\left\|\Omega^{k}(\mathbb{S}^{n})\right\|_{0}% \mathclose{}{}$ (by \autorefthm:path-truncation) $\displaystyle\equiv\pi_{k}(\mathbb{S}^{n}).\qed$
This means that once we have calculated one entry in one of these stable diagonals, we know all of them. For example:
###### Theorem 8.6.15.
$\pi_{n}(\mathbb{S}^{n})=\mathbb{Z}$ for every $n\geq 1$.
###### Proof.
The proof is by induction on $n$. We already have $\pi_{1}(\mathbb{S}^{1})=\mathbb{Z}$ (\autorefcor:pi1s1) and $\pi_{2}(\mathbb{S}^{2})=\mathbb{Z}$ (\autorefcor:pis2-hopf). When $n\geq 2$, $n\leq(2n-2)$. Therefore, by \crefcor:stability-spheres, $\pi_{n+1}(S^{n+1})=\pi_{n}(S^{n})$, and this equivalence, combined with the inductive hypothesis, gives the result. ∎
###### Corollary 8.6.16.
$\mathbb{S}^{n+1}$ is not an $n$-type for any $n\geq-1$.
Title 8.6 The Freudenthal suspension theorem \metatable | 2018-03-18 23:22:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 300, "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": 0.9527197480201721, "perplexity": 234.3075033390511}, "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-2018-13/segments/1521257646178.24/warc/CC-MAIN-20180318224057-20180319004057-00570.warc.gz"} |
https://datascience.stackexchange.com/questions/9683/how-data-representation-affects-neural-networks/9694 | # How data representation affects neural networks?
Suppose A's possible values are ON or OFF.
Suppose I represent it as: if A ON then feature f=1 else f=0
Or, suppose I represent it with 2 features, where:
-if A is ON then f1=1 and f2=0
-if A is OFF then f1=0 and f2=1
How this kind of representation affects neural networks?
It will have very little effect
The answer most will give is that it will have no effect, but adding one more feature will decrease the ratio of records to features so will slightly increase the bias and will hence make your model slightly less accurate. Unless, of course, you have overfit your model , in which case it will make your model slightly more accurate (a good data scientist would never do this because they understand the importance of cross-validation :-).
If you normalize your data and then attempt some sort of dimensionality reduction, your algorithm will immediately eliminate the feature that you added since it is perfectly negatively (linearly) correlated with the first feature. In this case it will have no effect.
I always see big red flags when someone asks a very fundamental data science question with the words neural network included. Neural networks are very powerful and receive a great deal of attention in the media and on Kaggle, but they take more data to train, are difficult to configure, and require much more computing power. If you are just starting out, I suggest getting a foundation in linear regression, logistic regression, clustering, SVMs, decision trees, random forests, and naive Bayes before delving into artificial neural networks. Just some food for thought.
Hope this helps! | 2020-12-05 03:17:18 | {"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": 0.4709818959236145, "perplexity": 873.9463163804021}, "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-2020-50/segments/1606141746033.87/warc/CC-MAIN-20201205013617-20201205043617-00045.warc.gz"} |
http://math.stackexchange.com/questions/36841/verify-stokess-theorem-for-the-given-surface-and-vector-field | # Verify Stokes's Theorem for the given surface and vector field
$S$ is parametrized by $X(s,t) = (s\cos(t), s\sin(t), t)$, $0 \leq s \leq 1$ and $0 \leq t \leq \frac{\pi}{2}$
$$\mathbf{F} = z \mathbf{i} + x \mathbf{j} + z \mathbf{k}$$
I have two things preventing me from solving this: first, I do not know how to find $d\,\mathbf{s}$ for $X(s,t) = (s\cos(t), s\sin(t), t)$ and I am not sure how to take out the parameterization of $X$ and find a surface to work with for the double integral over $s$ of $\nabla x \mathbf{F} \,d\,\mathbf{S}$
-
Note: The name is "Stokes", not "Stoke", so it's "Stokes's Theorem", not "Stoke's Theorem". – Arturo Magidin May 4 '11 at 4:27
I apologize for the mistake! Thanks for correcting me =) – Sir Winford May 4 '11 at 5:05
How comfortable are you with surface integrals? $X(s,t)$, as defined in your post, is a parametrization of $S$. Computing $\int_S \nabla \times \mathbf{F} d\mathbf{S}$ seems like a standard pre-Stokes' homework problem about surface integrals.
To compute the line integral side of Stokes' theorem, you'll need to parametrize the boundary of $S$. Notice that the domain of $X$ in the $st$-plane is a rectangle (with sides 1 and $\pi/2$). $X$ sends each point of the rectangle to a point on $S$, and it sends the boundary of the rectangle to the boundary of $S$. Can you see how to parametrize the boundary now? (Make sure it's oriented correctly!) Now all you have to do is compute an ordinary line integral. | 2014-03-12 04:48:41 | {"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": 0.9613451957702637, "perplexity": 179.85049383976502}, "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/1394021342244/warc/CC-MAIN-20140305120902-00067-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://scicomp.stackexchange.com/questions/19612/parallelization-of-element-wise-matrix-multiplication | # Parallelization of element-wise matrix multiplication
I use Armadillo as an interface to OpenBLAS. In my current program, I have a loop, in which I do multiplications of the form
for(long t = t0; t < t1; t+=tStep)
{
stateMatrix %= elementWiseEvolutionMatrix;
}
The operator % is an element-wise multiplication operator. The problem here is that for matrices of side length of 500+ (the ones I have at hand), I can see that there is no parallelization whatsoever. Now I would like to point out that normal matrix multiplication is parallelized. But this kind of element-wise multiplication is not parallelized.
How do I know that? Because I go to htop in my linux system, and I see that only one core is busy, while if I do the same with normal matrix multiplication, I see that all cores go busy.
Now I tried to manually parallelize this with OpenMP, but no luck. I tried:
for(long t = t0; t < t1; t+=tStep)
{
#pragma omp parallel for
for(long i = 0; i < static_cast<long>(stateMatrix.n_rows); i++)
{
stat1eMatrix.row(i) %= elementWiseEvolutionMatrix.row(i);
}
}
But this got all the cores busy, but the program became about a factor of 10 slower.
My question: How can I get the element-wise multiplication to be as fast as possible with parallelization?
Thanks.
EDIT: I would like to point out that I'm more than happy to use another library for the element-wise multiplication, if necessary.
• To speed up your first code, use the -O3 optimization switch in GCC or clang (or the equivalent in MSVC) to enable auto-vectorization. This will make Armadillo use SSE2 instructions. For even more speed, use -O3 -march=native, which will enable AVX instructions. More information is on the Armadillo FAQ page. – mtall Aug 4 '15 at 16:07
• Another observation: Armadillo uses column-major layout, so to get best performance you need to work on columns instead of rows. – mtall Aug 4 '15 at 16:10
There's no element wise multiplication operation in the BLAS library. Your best approach is probably to just implement the operation yourself using (e.g.) OpenMP threading.
Before you do this, you should consider Amdahl's law and whether speeding up this bit of your code is really going to help- chances are that these elementwise multiplications are not where your code is spending most of its time, and as a result you probably won't see much speedup from parallelizing this part of your code.
• Thanks for your response. I'm sure that this part of my code is what makes it slow, because it's THE ONLY part of my code that is being executed in a loop while I measure performance (beside a part that involves only additions, which is way more trivial that multiplications). I've mentioned trying to parallelize this myself with OpenMP and failed. If you have a model that could provide better results, please go ahead, I'd appreciate it. This portion of the code can be fully parallelized because all that matters is element-wise matrix multiplication. Thanks again for trying to help. – The Quantum Physicist May 9 '15 at 23:40
• Btw, I'm more than happy to use another library that could do the element-wise multiplication more efficiently. – The Quantum Physicist May 10 '15 at 0:01
• How large is n_rows? – Brian Borchers May 10 '15 at 0:17
• It's 2^n, where n could go to 15. Right now n=9, meaning that n_rows is 512. – The Quantum Physicist May 10 '15 at 0:23
• and the number of columns? – Brian Borchers May 10 '15 at 0:31
First off, I agree with Brian Borchers comments about profiling to make sure these element-wise multiplications are where your performance issue lies. However, since you are convinced that is your problem, here is another suggestion.
Before trying to exploit multiple CPU, I would make sure that you have an implementation that exploits vectorization. The SSE2 instruction set (available in most modern processors) has an operation to multiply vectors of double precision floating point numbers. Your code may or may not allow your compiler to exploit this instruction.
As far as I know, Armadillo does not have any direct support for SSE2. But since you indicated a willingness to switch libraries, the Eigen library (http://eigen.tuxfamily.org/index.php?title=Main_Page) definitely does generate code using the SSE2 instructions. This could give you a 4x improvement for single precision multiplies and 2x improvement for double precision. If you are fortunate enough to have a CPU that supports the AVX instruction set, the development version of Eigen supports this to provide additional speedup.
• +1 for suggesting Eigen with SSE2. Thanks. – The Quantum Physicist May 10 '15 at 1:06
• Armadillo can use SSE2, SSE3, AVX, etc (ie. SIMD instructions). Just use the -O3 optimization switch in GCC or clang, or the equivalent in MSVC. For even more speed, use -O3 -march=native. More information is on the Armadillo FAQ page. – mtall Aug 4 '15 at 16:05 | 2021-05-14 17:12:08 | {"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": 0.4595433473587036, "perplexity": 1362.742819072711}, "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/1620243991428.43/warc/CC-MAIN-20210514152803-20210514182803-00183.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-a-combined-approach-4th-edition/chapter-6-section-6-3-factoring-trinomials-of-the-form-ax2-bx-c-exercise-set-page-435/20 | ## Algebra: A Combined Approach (4th Edition)
$(2x-3y)(4x-y)$
$8x^2-14xy+3y^2$ Factors of 3: 1 and 3, -1 and -3 Factors of 8: 1 and 8, 2 and 4, -1 and -8, -2 and -4 $(2x-y)(4x-3y)$ $2x*4x+2x*(-3y)+4x*-y+(-y)(-3y)$ $8x^2-6xy-4xy+3y^2$ $8x^2-10xy+3y^2$ $(2x-3y)(4x-y)$ $2x*4x+2x*-y+4x*-3y+(-3y)(-y)$ $8x^2-2xy-12xy+3y^2$ $8x^2-14xy+3y^2$ | 2019-03-21 11:55:04 | {"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": 0.6649959087371826, "perplexity": 192.74500026639032}, "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-2019-13/segments/1552912202523.0/warc/CC-MAIN-20190321112407-20190321134407-00115.warc.gz"} |
https://www.physicsforums.com/threads/power-series.108070/ | # Power series
1. Jan 25, 2006
### teng125
may i know how to solve this ques:find the power series representation for arctan (x)
i know that arctan (x) = integ 1/(1 + x^2) but then from here i don't know how to continue.
pls help......
2. Jan 25, 2006
### Hurkyl
Staff Emeritus
It seems to me if you're looking for the power series of the thing on the left hand side, then you might want to try looking for the power series of the thing on the right hand side.
3. Jan 26, 2006
### teng125
ya i'm looking for the thing on the left hand side.....pls help
4. Jan 26, 2006
### finchie_88
Take the thing on the right, and differentiate it a few times, and let x = 0 each time.
$$f(x) = f(0) + xf'(0) + \frac{x^2}{2!}f''(0) + ...$$
Where f'(0) represents the derivative at x = 0. f''(0) is the second derivative etc. This will give a power series, then you can integrate term by term for the inverse tan function.
5. Jan 26, 2006
### Hurkyl
Staff Emeritus
One doesn't need to know any calculus at all to find the power series for $1/(1+x^2)$.
I gave you a big hint -- have you not tried to do anything with it? :grumpy:
6. Jan 26, 2006
### HallsofIvy
Staff Emeritus
Go back and read Hurkyl's reply again! | 2017-07-22 18:58:53 | {"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": 0.7485495209693909, "perplexity": 823.4283160668707}, "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-2017-30/segments/1500549424090.53/warc/CC-MAIN-20170722182647-20170722202647-00320.warc.gz"} |
https://www.ideals.illinois.edu/handle/2142/100446 | ## Files in this item
FilesDescriptionFormat
application/vnd.openxmlformats-officedocument.presentationml.presentation
1225413.pptx (2MB)
PresentationMicrosoft PowerPoint 2007
application/pdf
3339.pdf (17kB)
AbstractPDF
## Description
Title: A COMPARATIVE STUDY OF CHIRAL ANALYSIS OF FENCHYL ALCOHOL USING NUCLEAR MAGNETIC RESONANCE, INFRARED, AND ROTATIONAL SPECTROSCOPY Author(s): Mayer, Kevin J. Contributor(s): Pate, Brooks; Stashower, Julian; Spivey, Charles; Odermatt, Eric; Modi, Alysa; Chittari, Supraja Subject(s): Chirality and stereochemistry Abstract: The analysis of chiral molecules with multiple chiral centers is a challenging problem in analytical chemistry. The goal of the analysis is to determine the fractional composition for each unique stereoisomer. In the most general case, a molecule with N chiral centers will have 2$^{N}$ distinct stereoisomers. Half of these, 2$^{N-1}$, will be molecules with distinct molecular structures (the diastereomers). The diasteormer composition can be analyzed by normal spectroscopy methods because they have distinct spectra. For each diastereomer, there are the two non-superimposable mirror images (the enantiomers) and additional measurement methodology is required to determine the enantiomeric ratio using spectroscopy. Furthermore, in many applications the “unwanted” isomers (diastereomers and/or enantiomers) will be present as low-abundance impurities placing strong demands on the dynamic range of the spectroscopic technique. A commercial sample of (1R)-endo-(+)-Fenchyl alcohol (C10H18O, four stereoisomers) has been analyzed using nuclear magnetic resonance (NMR), infrared (IR), and rotational spectroscopy. The commercial sample has a small amount (~3\%) of the diastereomer as an impurity. The ability to quantitatively identify the diastereomer impurity using quantum chemistry estimates of the NMR, IR, and rotational spectrum parameters will be discussed. The enantiomer analysis uses chiral resolving agents for NMR spectroscopy, vibrational circular dichroism (VCD) for IR spectroscopy, and chiral tag rotational spectroscopy. The ability of these techniques to verify the stereochemistry of the dominant (1R)-endo-(+)-Fenchyl alcohol will be discussed. The ability to identify the enantiomeric excess of fenchyl alcohol and the possibility of performing enantiomer analysis on the low abundance diastereomer using the direct sample without purification will also be presented. Issue Date: 06/19/18 Publisher: International Symposium on Molecular Spectroscopy Citation Info: APS Genre: Conference Paper / Presentation Type: Text Language: English URI: http://hdl.handle.net/2142/100446 DOI: 10.15278/isms.2018.TC10 Other Identifier(s): TC10 Date Available in IDEALS: 2018-08-172018-12-12
| 2021-01-18 21:07:56 | {"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": 0.4919343590736389, "perplexity": 7920.554759902079}, "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-2021-04/segments/1610703515235.25/warc/CC-MAIN-20210118185230-20210118215230-00259.warc.gz"} |
https://www.deepdyve.com/lp/springer_journal/a-class-of-ell-p-p-saturated-banach-spaces-m0yllrpNvo | # A class of $$\ell ^p$$ ℓ p saturated Banach spaces
A class of $$\ell ^p$$ ℓ p saturated Banach spaces We present a new class of reflexive $$\ell ^p$$ ℓ p saturated Banach spaces $$\mathfrak{X }_p$$ X p for $$1<p<\infty$$ 1 < p < ∞ with rather tight structure. The norms of these spaces are defined with the use of a modification of the standard method yielding hereditarily indecomposable Banach spaces. The space $$\mathfrak{X }_p$$ X p does not embed into a space with an unconditional basis and for any analytic decomposition into two subspaces, it is proved that one of them embeds isomorphically into the $$\ell ^p$$ ℓ p -sum of a sequence of finite dimensional normed spaces. We also study the space of operators of $$\mathfrak{X }_p$$ X p . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals
# A class of $$\ell ^p$$ ℓ p saturated Banach spaces
, Volume 18 (2) – Jun 14, 2013
31 pages
/lp/springer_journal/a-class-of-ell-p-p-saturated-banach-spaces-m0yllrpNvo
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0245-5
Publisher site
See Article on Publisher Site
### Abstract
We present a new class of reflexive $$\ell ^p$$ ℓ p saturated Banach spaces $$\mathfrak{X }_p$$ X p for $$1<p<\infty$$ 1 < p < ∞ with rather tight structure. The norms of these spaces are defined with the use of a modification of the standard method yielding hereditarily indecomposable Banach spaces. The space $$\mathfrak{X }_p$$ X p does not embed into a space with an unconditional basis and for any analytic decomposition into two subspaces, it is proved that one of them embeds isomorphically into the $$\ell ^p$$ ℓ p -sum of a sequence of finite dimensional normed spaces. We also study the space of operators of $$\mathfrak{X }_p$$ X p .
### Journal
PositivitySpringer Journals
Published: Jun 14, 2013
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Export lists, citations | 2018-10-22 04:48:30 | {"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": 0.47021162509918213, "perplexity": 965.0629804562196}, "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-2018-43/segments/1539583514497.14/warc/CC-MAIN-20181022025852-20181022051352-00421.warc.gz"} |
http://mathoverflow.net/questions/107817/could-unramified-galois-groups-satisfy-a-version-of-property-tau | # Could unramified Galois groups satisfy a version of property tau?
This is an experiment: there is a question I want to mention in an article I'm writing, and I am not sure it's a sensible question, so I will ask it here first, in the hopes that if it's insensible someone will tell me. If, on the other hand, the question is sensible, and someone on MO has something interesting to say about it, all the better!
So here is the question. Let S be a finite set of primes $p_1, \ldots, p_k$. Let G be the Galois group of the maximal totally real extension of Q unramified away from S. We want to ask whether G satisfies a version of property tau. What this means is a little tenuous; just to start with, we don't even know (at least I think we don't) whether G is topologically finitely generated. Here's one possible definition:
(E): There exists a constant c such that, for every finite totally real extension K/Q, and every k-tuple $g_1, .. g_k \in Gal(K/Q)$ such that $g_i$ lies in an inertia group over p_i and the $g_1, .. g_k$ together generate Gal(K/Q), the Cayley graph on Gal(K/Q) with generators $g_1, .. g_k$ has spectral gap at least c.
Is (E) plausible? Is (E) even the right notion of "expanding" for unramified Galois groups?
Update: A discreet friend points out that the question is indeed insensible the way I phrased it, because you could take K/Q to be the real subfield of the cyclotomic extension by p^n-th roots. So instead of demanding that K/Q be totally split at $\infty$, it would be better to fix some other prime $\ell$ outside S and require that K/Q split there; that should re-sensibilize the problem. Alternatively, one could drop any kind of splitting requirement and instead ask that K/Q be at worst tamely ramified at the primes in S; this has the additional advantage of tightening the analogy with the function field case.
Update 2: After further thought, I've decided that my favorite version of this question is to ask whether:
For each k, there exists a constant $c_k$ such that, for any Galois extension K/Q which is unramified outside S and tamely ramified at S, and any k-tuple $(g_1, \ldots, g_k)$ generating $G$, the corresponding Cayley graph has spectral gap at most $c_k$.
I don't know whether this is true but I'm pretty sure I don't know that it's false.
-
@Will: I do not understand your comment.The extension you propose is ramified at a lot of primes outside of $S$. If you look at the remark before Theorem 10.2.5 in Neukirch-Schmidt-Wingberg's Cohomology of Number Fields, you see thinks are slightly tricker. Indeed, one can prove that $G_S^\text{ab}$ is indeed topologically finitely generated and your extensions are abelian. – Filippo Alberto Edoardo Sep 22 '12 at 6:23
@ JSE: Can you give some references for a non-expert who never heard about Cayley graphs and spectral gaps? What is the tau ($\tau$?) property? – Filippo Alberto Edoardo Sep 22 '12 at 6:25
Sorry I was thinking backwards, in terms of extensions ramified only outside of $S$, instead of only at $S$. That was silly. – Will Sawin Sep 22 '12 at 7:00
@Filippo: What is property tau? ams.org/notices/200506/what-is.pdf – Alain Valette Sep 22 '12 at 7:34 | 2013-12-19 18:34:12 | {"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": 0.8921263217926025, "perplexity": 425.6966917557843}, "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-2013-48/segments/1387345766127/warc/CC-MAIN-20131218054926-00055-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://www.nature.com/articles/s41598-019-41939-y?error=cookies_not_supported&code=9ba59391-be0e-4063-b5cd-69cae00e1ef3 | Article | Open | Published:
# Facile synthesis of ternary graphene nanocomposites with doped metal oxide and conductive polymers as electrode materials for high performance supercapacitors
## Abstract
Supercapacitors (SCs) due to their high energy density, fast charge storage and energy transfer, long charge discharge curves and low costs are very attractive for designing new generation of energy storage devices. In this work we present a simple and scalable synthetic approach to engineer ternary composite as electrode material based on combination of graphene with doped metal oxides (iron oxide) and conductive polymer (polypyrrole) with aims to achieve supercapacitors with very high gravimetric and areal capacitances. In the first step a binary composite with graphene mixed with doped iron oxide (rGO/MeFe2O4) (Me = Mn, Ni) was synthesized using new single step process with NaOH acting as a coprecipitation and GO reducing agent. This rGO/MnFe2O4 composite electrode showed gravimetric capacitance of 147 Fg−1 and areal capacitance of 232 mFcm−2 at scan rate of 5 mVs−1. In the final step a conductive polypyrrole was included to prepare a ternary composite graphene/metal doped iron oxide/polypyrrole (rGO/MnFe2O4/Ppy) electrode. Ternary composite electrode showed significantly improved gravimetric capacitance and areal capacitance of 232 Fg−1 and 395 mFcm−2 respectively indicating synergistic impact of Ppy additives. The method is promising to fabricate advanced electrode materials for high performing supercapacitors combining graphene, doped iron oxide and conductive polymers.
## Introduction
Energy consumption is continuously increasing throughout the world with 575 quadrillion British thermal units (BTU) in 2015 that is expected to rise up to 736 quadrillion BTU in 20401. The current energy resources are insufficient to meet these energy demands which could cause serious energy crises in near future due to projected consumption of natural fuels, concerning greenhouse effect and heavily increased energy demands2,3. So there is an enormous and urgent need towards developing more efficient, low cost, easy to manufacture and environmental friendly energy solutions such as energy storage devices like fuel cells, batteries, capacitors and supercapacitors4,5,6,7. Among all energy storage devices, supercapacitors have advantages of long life cycles, rapid charging and discharging, high power density, rapid charge storage process and high energy density. Owing to these characteristics, supercapacitors are considered as complement of fuel cells, conventional rechargeable batteries and capacitors. Since the development of first commercial supercapacitor by Nippon Electric Company (NEC)8, supercapacitors have found profound applications across many sectors such as transportation, electronics, military, aerospace and sensors etc.
Carbon materials including activated carbon, carbon nanotubes (CNTs) and graphene have been extensively explored for supercapacitors applications even in general they display lower energy density due to the fast ions adsorption reaction thus generating electric double-layer (EDL) capacitances. On the other hand, metal oxides and conducting polymers can deliver much higher energy densities through Faradic reactions with low cyclic stability and power density compared to EDL based supercapacitors. Therefore combining these materials into their composite structure and using different charging mechanisms and possible synergistic effect between each of their components is recognized to be ideal solution to design and improve the performance of supercapacitors9.
Graphene has emerged as an ideal material for EDLCs due to its unique properties like high electrical conductivity, low density, high specific surface area (2670 m2 g−1), chemical stability, mechanical strength and tailoring chemical functionalities10,11. Initial studies showed gravimetric capacitance of synthesised graphene in aqueous and organic electrolytes to be 135 Fg−1 and 99 Fg−1 respectively12. Wang et al., prepared graphene by using gas based hydrazine reduction of graphene oxide (GO) and measured its gravimetric capacitance as 205 Fg−113. Many other studies showed different results for gravimetric capacitance of graphene from 59 Fg−1 at scan rate of 2 mVs−114, 117 Fg−1 at scan rate of 100 mVs−1 and 169.3 Fg−1 at 10 mVs−1 depending on the type of graphene, its purity and electrolyte15. Metal ferrites having variable redox states have been extensively explored as suitable electrode materials for supercapacitors applications16,17. Vignesh et al., used manganese ferrite supercapacitor electrode with specific capacitance of 173, 31 and 403 Fg−1 in 3.5 M KOH, 1 M LiNO3 and 1 M Li3PO4, respectively measured by three electrodes system18. Aparna et al., reported comparative studies of various metal ferrites including Fe, Co, Ni, Mn, Cu and Zn in 3 M KOH solution used as electrolyte. Specific capacitance of metal ferrites (MeFe2O4, Me = Fe, Co, Ni, Mn, Cu and Zn) were measured to be 101, 444.78, 109.26, 190, 250 and 138.95 Fg−1 respectively at scan rate of 2 mVs−119. The first combination with of metal ferrites and graphene is demonstrated by Wang et al., who fabricated copper ferrite attached on graphene electrodes for supercapacitors showing an outstanding gravimetric capacitance 576.6 Fg−1 at current density of 1 Ag−1 measured by three electrodes system20.
In recent years, conducting polymers in pseudocapacitors are heavily explored due to their high specific capacitance obtained through reversible redox reaction. Polypyrrole is one of conducting polymers that showed excellent high conductivity and high environmental and mechanical stability21,22. Recently composites of polymers and nanofillers such as carbon based materials have been successfully used as electrodes to improve performance of supercapacitors using high synergistic effect. Biswas et al., synthesized graphene/polypyrrole composite material displaying gravimetric capacitance of 165 Fg−1 at current density of 1 Ag−1 measured by two electrodes system while using 1 M NaCl aqueous solution as electrolyte23. Parl et al., used graphite/polypyrrole composite for supercapacitor electrodes showing gravimetric capacitance of 400 Fg−1 measured by three electrodes system24.
In order to gain advanced supercapacitors performances, the concept of the three–components or ternary system by combining these three components has been proposed. Chee et al., synthesized ternary polypyrrole/graphene oxide/zinc oxide supercapacitor electrodes and measured its gravimetric capacitance in two electrodes system to be 94.6 Fg−1 at 1 Ag−1 from charge/discharge (CD) curves25. Lim et al., reported ternary polypyrrole/graphene/nano manganese oxide composite, the gravimetric capacitance of synthesized composite was 320.6 Fg−1 at 1 mVs−1 which was much higher than that of polypyrrole/graphene delivering gravimetric capacitance of 255.1 Fg−1 and neat polypyrrole with gravimetric capacitance of 118.4 Fg−126. Xiong et al., used three electrodes system to measure gravimetric capacitance of ternary cobalt ferrite/graphene/polyaniline nanocomposites, which showed gravimetric capacitance of 1133.3 Fg−1 at scan rate of 1 mVs−127. These studies clearly indicate that design of multi-component composite electrodes for supercapacitors is a beneficial and promising approach that is able to significantly improve the performance of supercapacitors.
Inspired with these studies in the present research work, we present the synthesis and performances of ternary composite electrodes for supercapacitor applications that are specifically engineered by combination of graphene, mixed doped metal oxide and conductive polymers and their unique properties and synergistic effects. To demonstrate this concept we selected graphene (rGO), metals doped iron oxide (MeFe2O4) and conductive polypyrrole (Ppy) polymer as model components for proposed ternary system (rGO/MeFe2O4/Ppy) that is schematically presented in Fig. 1. The aims of this work were to explore the electrochemical performance of this ternary composite material, evaluate influence of each component and their synergetic effects and demonstrate its capability to be used for designing high performing supercapacitors. For metal doping of iron oxide two metals Mn and Ni were selected as a model doping elements because of their excellent redox behaviour. These metals can contribute more efficiently than pure iron oxide in increasing gravimetric capacitance having high electronic conductivity and electrochemical performance, low cost and environmental friendly nature28. Finally Ppy was selected as common and highly conductive polymer having high specific capacitance of 136 Fg−1 measured by three electrodes system29. In addition to confirm the performance of proposed ternary electrodes system one of specific objective of this work was to develop new, simplified, environmentally friendly and scalable method to synthesize these composite materials. For that purpose we introduced one step process using NaOH to make binary composite (rGO/MeFe2O4) instead of undergoing conventional two steps process using reduction by hydrazine hydrate to form reduced graphene oxide (rGO). In the following and final step ternary graphene/metal doped iron oxide/polypyrrole (rGO/MeFe2O4/Ppy) nanocomposite was synthesized by common oxidative polymerization of pyrrole. The extensive characterization for both binary and ternary composites with mixed metals (Mn and Ni) as dopant of iron oxide was performed in order to reveal synergetic impact of each component in the system on supercapacitor performances.
## Results and Discussion
### Characterization of prepared binary graphene/metal doped iron oxide (rGO/MeFe2O4) and ternary graphene/metal doped iron oxide/polypyrrole (rGO/MeFe2O4/Ppy) nanocomposites
Morphologies of prepared binary rGO/MnFe2O4 and ternary rGO/MnFe2O4/Ppy composites are summarised in field emission scanning electron microscopy (FESEM) images presented in Fig. 2. FESEM image of rGO/MnFe2O4 reveals sponge like porous structure showing the MnFe2O4 nano rods distributed on graphene sheets30. Average size of MnFe2O4 nanorods was found to be in the range of 50–70 nm. The comparison of morphology of binary rGO/MnFe2O4 and ternary rGO/MnFe2O4/Ppy composite at various magnifications is presented in FESEM images in Fig. S1 (supporting information). FESEM image of rGO/NiFe2O4 and rGO/NiFe2O4/Ppy shown in Fig. S2A also confirms formation of rGO sheets on which NiFe2O4 nanorods are randomly distributed. Ppy is also visible in the FESEM images of both ternary rGO/MnFe2O4/Ppy (Fig. 2c) and rGO/NiFe2O4/Ppy nanocomposites (Fig. S2).
Comparative crystal structure characterization of GO, rGO/MnFe2O4 and rGO/MnFe2O4/Ppy was carried out by XRD showing their XRD patterns in Fig. 3a. Characteristic peak of GO appearing at 10.9° (001) in XRD pattern of pure GO disappears in the XRD patterns of composites which shows complete oxidation of graphite into graphene oxide (GO)31. In XRD pattern of rGO/MnFe2O4 peaks at 19.2°, 29.1°, 35.2°, 41.1°, 57° and 61.9° indexed to (111), (220), (311), (400), (511) and (440) respectively are in accordance to JCPDS card no. 73–1964 and confirm formation of MnFe2O432. Peak for rGO at 25° (002) was observed in rGO/MnFe2O4. It confirms reduction of GO into rGO33. However this peak is not very sharp due to destruction of regular stacking of graphene sheets. XRD pattern of NiFe2O4 shown in Fig. S2B also confirms reduction of GO into rGO. XRD patterns of as synthesized rGO/MnFe2O4/Ppy and rGO/NiFe2O4/Ppy nanocomposites in Fig. 3a and S2B show characteristic peak of Ppy at about 2θ = 26°. This characteristic broad peak shows that Ppy is in amorphous form34. Along with peak of Ppy, other peaks for rGO, rGO/MnFe2O4 and rGO/NiFe2O4 nanocomposites also appear. Some other peaks are also present showing impurities in the sample.
Comparative FTIR spectra of GO, rGO/MnFe2O4 and rGO/MnFe2O4/Ppy are summarized in Fig. 3b. FTIR spectrum of GO shows peaks at 3410 cm−1 and 1730 cm−1 corresponding to stretching vibrations of hydroxyl (OH) and carboxyl (COOH) groups respectively. Peak observed at 1604 cm−1 confirms presence of aromatic C = C which is an indication of hybrid sp2 structure of rGO. Peak at 1420 cm−1 shows presence of carboxy (C-O) group. Peaks at 1050 cm−1 and 1220 cm−1 are due to presence of epoxy and alkoxy/alkoxide C-O groups respectively35. FTIR spectrum of rGO/MnFe2O4 shows peaks of both rGO and MnFe2O4 confirming formation of rGO/MnFe2O4. Peaks at 460.99 cm−1 and 569.0 cm−1 are related to Mn-O and Fe-O respectively36. A peak observed at 1604 cm−1 for GO indicating C = C skeletal vibration of un-oxidized graphitic domains was red-shifted to 1530 cm−1 showing that aromatic vibration is still present in rGO. Other peaks of GO related to oxygen functional groups do not appear in FTIR spectrum of rGO/MnFe2O4 showing conversion of GO into rGO during reduction process37,38. FTIR spectrum GO/NiFe2O4 and rGO/NiFe2O4/Ppy shown in Fig. S2C also show all these peaks thus confirm formation of other graphene metal doped iron oxide nanocomposites i.e., rGO/NiFe2O4. Both rGO/MnFe2O4/Ppy and rGO/NiFe2O4/Ppy show peaks for rGO, metal ferrites and Ppy confirming formation of ternary rGO/MnFe2O4/Ppy and rGO/NiFe2O4/Ppy nanocomposites. However peaks for metal ferrite nanoparticles are weak due to their uniform distribution on Ppy backbone. In addition to the peaks of metal ferrites below 700 cm−1, peaks of Ppy appear like fundamental vibrations of Ppy ring at 1556 and 1449 cm−1, =C-H in-plane vibrations at 1303 cm−1 and 1036 cm−1, C-N stretching vibrations at 1196 cm−1, polymerized pyrrole at 796 cm−1 and 983 cm−1, = C-H out of plane vibration at 903 cm−1, and OH and oxide groups at 3400 cm−139. These peaks are shifted left than peaks of pure Ppy which indicates that graphene groups are associated to nitrogenous functional groups of Ppy like normal doping process to the Ppy40.
The TGA characterizations carried out to study thermal stability of GO, rGO/MeFe2O4 and rGO/MeFe2O4/Ppy nanocomposites is presented in Fig. 3c and S2D. TG curves of GO and rGO/MnFe2O4 in Fig. 3c shows that a slight weight loss below 200 °C was observed for GO and rGO/MnFe2O4 and it is due to water loss. For GO maximum weight is lost below 300 °C. This weight loss is due to break down of oxygen functional groups in GO. However it is apparent from TG curve of rGO/MnFe2O4 that it is thermally more stable than GO. It is due to conversion of GO into rGO, which is due to removal of oxygen functional groups during reduction of GO to rGO41. Same effect is observed for rGO/NiFe2O4. Slight weight loss of rGO/MeFe2O4 was observed between 230–450 °C. No noticeable change was observed after 420 °C and residual weight was about 77% and 35% for rGO/MnFe2O4 and rGO/NiFe2O4 respectively (Figs 3c and S2D), which can be ascribed to remaining MnFe2O4 in rGO/MnFe2O4 and NiFe2O4 in rGO/NiFe2O4 respectively. rGO/MeFe2O4/Ppy show more weight loss than rGO/MeFe2O4 which shows that thermal stability of rGO/MeFe2O4 is more than that of rGO/MeFe2O4/Ppy. This trend is similar in all nanocomposites and is in accordance with results depicted in previous literature42. Residual weight of rGO/MnFe2O4/Ppy and rGO/NiFe2O4/Ppy is 55% and 13% which is 22% less than their binary composites i.e., rGO/MnFe2O4 and rGO/NiFe2O4.This decrease in thermal stability of rGO/MeFe2O4/Ppy is due to Ppy addition. Due to increase in ion mobility together with thermal vibration of Ppy chains at rGO/MeFe2O4 and Ppy interface, thermal stability of rGO/MeFe2O4/Ppy is less than that of rGO/MeFe2O443.
### Evaluation of electrochemical and supercapacitor performance of binary graphene/metal doped iron oxide (rGO/MeFe2O4) nanocomposites
Electrochemical characterizations of prepared nanocomposites was performed in two stages by testing electrochemical performances of binary rGO/MeFe2O4 nanocomposite and their individual components followed by characterization of final ternary nanocomposites in order to evaluate influence of each components in composite and their synergistic impact.
CV curve of graphene present in Figs 4a and S3A are almost rectangular, showing no oxidation and reduction peaks. It is characteristic of carbon based materials showing EDLC44. Redox peaks appear in CV curves of rGO/MnFe2O4 and rGO/NiFe2O4 shown in Figs 3a and S3A, respectively. These redox peaks are due to Faradic process. These redox peaks indicate pseudocapacitance behaviour of MeFe2O4 in the nanocomposite. The redox process is described in equations 1244.
$${{\rm{MnFe}}}_{2}{{\rm{O}}}_{4}+{{\rm{H}}}_{2}{\rm{O}}+{{\rm{OH}}}^{-}\leftarrow ----\to {\rm{MnOOH}}+2{\rm{FeOOH}}+{{\rm{e}}}^{-}$$
(1)
$${\rm{FeOOH}}+{{\rm{OH}}}^{-}\leftarrow ------\to {{\rm{FeO}}}_{2}+{{\rm{H}}}_{2}{\rm{O}}+{{\rm{e}}}^{-}$$
(2)
Figures 4b and S3B show the CV curves of rGO/MnFe2O4 and rGO/NiFe2O4 respectively at different scan rates of 10–100 mVs−1. It is clear from the figures that current density of peak enhances with corresponding scan rate. It depicts its fairly good ion response and good EDL capacitance behaviour. High current density with increasing scan rate depicts that electrode material shows more conductivity, less internal resistance and good rate capability of electrode material in used electrolyte i.e., 1 M H2SO4 as the scan rate increases44. Shape of CV curves remains same at different scan rates of 10–100 mVs−1 which shows that kinetics of EDL formation is quite fast and it is also indicative of fast Faradic reaction in electrodes45. Gravimetric capacitance of rGO/MnFe2O4 electrode was 147 Fg−1 at scan rate of 5 mVs−1. At the same scan rate, areal capacitance of rGO/MnFe2O4 electrode calculated from its CV curves was 250 mFcm−2 while gravimetric and areal capacitance of rGO/NiFe2O4 electrode was found to be 48 Fg−1 and 82 mFcm−2, respectively.
CD curves of rGO/MnFe2O4 at different current densities of 1 Ag−1, 2 Ag−1, 4 Ag−1 and 6 Ag−1 are shown in Fig. 4c. CD curves of synthesized rGO/MnFe2O4 based electrodes are not symmetrical, which shows pseudocapacitive behaviour of electrode material. CD curves at different current densities are of almost same shape, showing that electrode material has ideal capacitive behaviour. Similar behaviour was observed in CD curves of rGO/NiFe2O4 as shown in Fig. S3C.
Figure 4d represents gravimetric and areal capacitances of rGO/MnFe2O4 at different scan rates i.e., 10–2000 mVs−1. It is evident that with increase in scan rate both gravimetric capacitance and areal capacitance decrease. It is attributed to insufficient time available for ions to diffuse and adsorb in the small pores within large particles. In addition, at high scan rate, when supercapacitor delivers high current, a noticeable voltage loss (ΔV) is originated46.
### Evaluation of Electrochemical and supercapacitor performance of ternary graphene/metal doped iron oxide/polypyrrole (rGO/MeFe2O4/Ppy) nanocomposites
Figure 5a shows CV curves of rGO/MnFe2O4 and rGO/MnFe2O4/Ppy at 5 mVs−1. It is evident that CV curve area of rGO/MnFe2O4/Ppy is larger than curve area of rGO/MnFe2O4 showing better capacitance of former than later. Similar results are shown in Fig. S4A for rGO/NiFe2O4 and rGO/NiFe2O4/Ppy. CV curves of rGO/MnFe2O4/Ppy and rGO/NiFe2O4/Ppy at different scan rates of 10–100 mVs−1 are shown in Figs 5b and S4B, respectively. Redox peaks appear in CV curves of both rGO/MnFe2O4/Ppy and rGO/NiFe2O4/Ppy. These redox peaks are attributed to pesudocapacitance of MeFe2O4 in the nanocomposite. rGO/MnFe2O4/Ppy shows largest current density at same scan rate among all electrodes. Owing to this large current density and symmetrical behaviour of CV curves in both anodic and cathodic directions it is proposed to possess best capacitive performance among all synthesized electrodes and it is suitable supercapacitor electrode material47. Gravimetric capacitance of rGO/MnFe2O4/Ppy electrode was 232 Fg−1 at scan rate of 5 mVs−1 while its areal capacitance was 395 mFcm−2. It is obvious that both gravimetric and areal capacitance of rGO/MnFe2O4/Ppy was 1.57 times greater than that of rGO/MnFe2O4 due to more synergistic effect between the composite components. CV curves of both rGO/MnFe2O4/Ppy and rGO/NiFe2O4/Ppy are rectangular even at high scan rate of 100 mVs−1 showing that this electrode material has higher electrochemical performance48. High current density with increasing scan rate depicts that electrode material shows more conductivity, less internal resistance and good rate capability of electrode material in used electrolyte i.e., 1 M H2SO4 as the scan rate increases44. Similar trend was observed in rGO/NiFe2O4/Ppy electrode shown in Fig. S4B.
Figure 5c shows CD curve of rGO/MnFe2O4 and rGO/MnFe2O4/Ppy showing consistent results with those of cyclic voltammetry. It is clear that discharge time for rGO/MnFe2O4/Ppy is much greater than that of rGO/MnFe2O4. Moreover, CD curve for rGO/MnFe2O4/Ppy is less symmetrical than that of rGO/MnFe2O4 showing that after addition of Ppy, the pesudocapacitance of material is enhanced49. This increase in electrochemical performance of rGO/MnFe2O4/Ppy, as depicted by cyclic voltammetry and charge discharge measurements, is due to synergistic effect of three components in ternary rGO/MnFe2O4/Ppy nanocomposite. CD curves of rGO/MnFe2O4/Ppy at different current densities of 1 Ag−1, 2 Ag−1, 4 Ag−1 and 6 Ag−1 are shown in Fig. 5d. All CD curves are of almost same shape at all current densities, showing that electrode material has ideal capacitive behaviour. Among all synthesized electrodes, discharge time of rGO/MnFe2O4/Ppy electrode is maximum showing its best electrochemical performance. CD curves of rGO/NiFe2O4 and rGO/NiFe2O4/Ppy electrodes are shown in Fig. S4C,D have similar trends.
Results of cyclic voltammetry and charge discharge measurements are summarized in Fig. 5e in the form of gravimetric capacitance and areal capacitance of rGO/MnFe2O4 and rGO/MnFe2O4/Ppy at various scan rates i.e., 5–2000 mVs−1. Improved electrochemical performance of material after addition of Ppy can be explained by considering conductive nature of Ppy which results in more diffusion of ions into electroactive electrode material as well as synergistic effect of components50. For rGO/NiFe2O4 and rGO/NiFe2O4/Ppy, gravimetric and areal capacitances at different scan rates of 5–2000 mVs−1 are summarized in Fig. S4E.
Specific power and specific energy of rGO/MnFe2O4 and rGO/MnFe2O4/Ppy at different scan rates of 5–2000 mVs−1 were calculated. Ragon plots of rGO/MnFe2O4 and rGO/MnFe2O4/Ppy are shown in Fig. 5f. At 5 mVs−1 specific power of rGO/MnFe2O4 and rGO/MnFe2O4/Ppy is is 368.5 Wkg−1 and 581 Wkg−1, respectively which is increased to 36479.5 Wkg−1 and 39034 Wkg−1 at 2000 mVs−1. While specific energy values of rGO/MnFe2O4 and rGO/MnFe2O4/Ppy are 20.5 and 32.3 Whkg−1, respectively at 5 mVs−1. It decreases to 5.1 Whkg−1 and 5.4 Whkg−1, respectively. Increases in specific energy from rGO/MnFe2O4 to rGO/MnFe2O4/Ppy is due to increased electrical conductivity due to addition of Ppy in rGO/MnFe2O4/Ppy51. For rGO/NiFe2O4 and rGO/NiFe2O4/Ppy, specific power and specific energy at different scan rates of 5–2000 mVs−1 are summarized in Fig. S4F.
Electrochemical Impedance spectroscopy (EIS) has been performed by two electrodes system in 1 M H2SO4 at the excited potential of 5 mV between frequency range of 0.01–100 kHz in the form of Nyquist plot shown in Fig. 6. Nyquist plot reveals that rGO/MnFe2O4 and rGO/MnFe2O4/Ppy show very small semicircles at high frequency region, which reveal to charge transfer resistance and solution resistance while a straight line in high frequency region reveals to Warburg resistance. rGO/MnFe2O4/Ppy shows small equivalent series resistance of 0.81 Ω while rGO/MnFe2O4 shows greater resistance of 0.86 Ω. This equivalent series resistance (ESR) was calculated from first x-intercept and slope of Nyquist plot52. However, in low frequency region rGO/MnFe2O4/Ppy has more slope as compared to slope of rGO/MnFe2O4 explaining that former has better capacitance than later that is consistent with results of CV and CD. Nyquist plots for rGO/NiFe2Oand ternary rGO/NiFe2O4/Ppy nanocomposites are shown in Fig. S5. Figure 7 summarizes results of gravimetric and areal capacitance of all synthesized binary rGO/MeFe2O4 and ternary rGO/MeFe2O4/Ppy nanocomposites.
Table 1 shows comparison of the electrochemical performance of synthesized ternary rGO/MeFe2O4/Ppy electrodes with electrochemical performances of previously reported electrodes. Comparison of our results with previous literature findings shows that ternary rGO/MnFe2O4/Ppy electrodes give better electrochemical performance compared with previous reports. We propose that possible reason of this improvement is the incorporation of MnFe2O4 particle as third component which improves electrochemical performance due to its redox behaviour. While gravimetric capacitance of rGO/NiFe2O4/Ppy is slightly less than that of G/Ppy showing that NiFe2O4 contributes less gravimetric capacitance than MnFe2O4. Gravimetric capacitance of rGO/NiFe2O4/Ppy, rGO/MnFe2O4 and rGO/MnFe2O4/Ppy is better than previously reported Ppy/GO/ZnO composite electrode which may be due to reasons that rGO is more conducting than GO and MeFe2O4 is better candidate than ZnO to enhance electrochemical performance. CNT/Ppy/MnO2 electrodes deliver more gravimetric capacitance than our synthesized electrodes because in synthesis of this composite hydrous MnO2 was used to disperse it effectively in polymer matrix. Better gravimetric capacitance of previously reported PANI-Graphene-CNT electrodes as compared to our synthesized binary and ternary composites can be explained due to presence of all three highly conducting components, each of which may effectively participate in improving the electrochemical performance of resulting composite. Moreover, electrolyte used in that supercapacitor is different than used by us and their value was calculate at low current density i.e., 0.5 Ag−1. Usually at low current density gravimetric capacitance is high which decreases accordingly with increasing current density. Areal capacitance of previously reported PEDOT-NiFe2O4 electrode is almost equal to that of binary rGO/MnFe2O4 electrode. However it is less than our synthesized rGO/MeFe2O4/Ppy electrodes. It is due to presence of conducting Ppy in rGO/NiFe2O4/Ppy. Areal capacitance of our binary rGO/MnFe2O4 and ternary rGO/MeFe2O4/Ppy is better than previously reported PEDOT-GO/CNTs and Ppy-GO/CNTs which is due to more conductive rGO than GO used in above mentioned composites. Overall comparison suggests our synthesized ternary rGO/MeFe2O4/Ppy composite as suitable supercapacitor electrode material with efficient electrochemical performance.
## Materials and Methods
### Materials
Graphite powder was purchased from Merck and form local graphite company (Ulley, South Australia). Glycerine was purchased from Fischer Scientific. K2S2O8 was purchased from Scharlau span, Hydrazine monohydrate was purchased from Daejung. P2O5, MnSO4.H2O, FeSO4.7H2O and H2O2 were purchased from Riedel-deHaen. Pyrrole was purchased from Sigma Aldrich, NiCl2.6H2O was purchased from United Laboratory Chemicals. While FeCl3.6H2O and polytetrafluoroethylene were purchased from Aldrich. Commercial NaOH, HCl, H2SO4, Ethanol and acetone were used. All chemicals were pure and of analytical grade and were used without further purification.
### One step synthesis of binary graphene/metal doped iron oxide nanoparticles (rGO/MeFe2O4)
Graphene oxide (GO) was synthesized by a modified Hummer’s method53. Binary Graphene/manganese ferrite (rGO/MnFe2O4) was prepared by in-situ reduction coprecipitation method described previously in literature54. Briefly speaking, measured amount of GO was well dispersed into the distilled water by ultrasonication. Then MnSO4.H2O and FeSO4.7H2O (1:2) were added followed by vigorous stirring at 95 °C for 2 h under N2 protection and 1 h in air. Subsequently, 2 M NaOH solution was slowly added to the mixture to adjust the solution to pH of 11–12. After 2 h of stirring, the solution was cooled to room temperature (RT). Final precipitates were collected by centrifugation, washed with distilled water thrice and dried at 80 °C for 24 h to obtain binary rGO/MnFe2O4 nanocomposite.
Similarly binary graphene/nickel ferrite (rGO/NiFe2O4) nanocomposite was synthesized by using NiCl2.6H2O and FeCl3.6H2O (1:2) as raw materials, 2–3 drops of glycerine as surfactant, and NaOH as base as well as reducing agent.
### Synthesis of ternary graphene/metal ferrite/polypyrrole nanocomposites (rGO/MeFe2O4/Ppy)
To synthesize ternary graphene/metal ferrite/polypyrrole nanocomposites (rGO/MFe2O4/Ppy), polymerization method of pyrrole55 was adopted with modifications. Briefly describing, measured amount of rGO/MeFe2O4 and FeCl3. 6H2O (0.06 mole) mixed in deionized water was heated to 32 °C followed by drop wise addition of pyrrole (0.02 mole). This mixture was stirred at −2 °C for 24 h. The mixture was centrifuged, washed with distilled water and acetone and dried at 80 °C for 24 h to obtain rGO/MeFe2O4/Ppy nanocomposite.
### Characterizations
Morphology of GO, rGO/MnFe2O4, rGO/MnFe2O4/Ppy, rGO/NiFe2O4 and rGO/NiFe2O4/Ppy was analysed by field emission scanning electron microscopy (FESEM, Quanta 450, FEI, USA). Nanocomposites were further investigated by using X-ray diffraction (600 Miniflex, Rigaco, Japan). Fourier Transform Infrared (FTIR) spectroscopy (Nicolet 6700 Thermo Fisher) in transmittance mode and range 400–4000 cm−1 was used to identify the functional groups of synthesized nanocomposites. Thermal stability was measured by using a thermal gravimetric analyser (TGA, Q500, TA Instruments, USA) under air where the samples were heated up to 900 °C at a heating rate of 10 °C min−1 at RT.
### Electrochemical characterizations
All electrochemical measurements like cyclic voltammetry (CV), galvanostatic charge/discharge (CD) and electrochemical impedance spectroscopy (EIS) were carried out in 1 M H2SO4 using two electrodes system. Gravimetric and areal capacitances of electrodes were calculated from cyclic voltammetry curves by using equations 34, respectively.
$$Cs=\frac{4{\int }_{v1}^{v2}idV}{mV{\rm{\Delta }}V}$$
(3)
$$Cs=\frac{2{\int }_{v1}^{v2}idV}{aV{\rm{\Delta }}V}$$
(4)
here $${\int }_{v1}^{v2}idV$$ is the integrated area for CV curve, s is the scan rate, V is 2 × (Vmax-Vmin) the potential window, m is the mass of single electrode and a is the foot-print device area. Specific power and specific energy of electrodes were calculated from cyclic voltammetry by using equations 56, respectively.
$$P=\frac{{\int }_{v1}^{v2}idV}{m}$$
(5)
$$E=\frac{{\rm{\Delta }}V{\int }_{v1}^{v2}idV}{3600ms}$$
(6)
Electrochemical performance of synthesized nanocomposites was characterized by using CHI760C Electrochemical workstation. Electrode material was fabricated by mixing active material i.e., nanocomposites, carbon black and binder (80:10:10) in 10 mL of ethanol. Polytetrafluoroethylene (60% wt in H2O) was used as binder. Mixture was ultrasonicated till completely dispersed, filtered by using filter paper and dried overnight at RT. Supercapacitor was made by using two electrodes of same material with active area of 1 cm2. Piece of filter paper dipped in 1 M H2SO4 was used as separator between two electrodes. Gold electrodes were used as current collectors. Cyclic voltammetry (CV) testing was carried out between 0–1 V at scan rates from 5–2000 mVs−1. Charging/discharging (CD) measurements were carried out in voltage window between 0–1 Vat 1–20 Ag−1. EIS measurements were done from 0.01 Hz to 100 KHz at an open circuit potential with an AC voltage amplitude of 5 mV. All measurements were carried out at RT.
### Ethical approval and informed consent
The methods used in this work were carried out in accordance with the relevant guidelines and and regulations.
## Conclusions
In summary a simple, scalable and environmentally sustainable method for preparation ternary composite electrodes for supercapacitors applications consisting of rGO, mixed metal doped Iron oxide and conductive Ppy is presented. New method using NaOH with double roles to replace hydrazine for GO reduction and assist the formation of MeFe2O4 is demonstrated for the first time. This process allows simple one step and scalable synthesis of graphene/metal doped iron oxide (rGO/MeFe2O4) (Me = Mn, Ni) not possible before. Electrochemical characterizations showed binary rGO/MnFe2O4composite electrode delivers specific capacitance of 147 Fg−1 and areal capacitance of 232 mFcm−2 in two electrodes system at scan rate of 5 mVs−1. Compared with previous results this is the highest value among all synthesized rGO/MeFe2O4 electrodes reported in literature. Further significant improvement in performance was observed in ternary composite system after introduction of Ppy showing the capacitances of were increased to 250 Fg−1 and 395 mFcm−2 for rGO/MnFe2O4/Ppy electrode. Compared with previous results this is the highest value among all synthesized binary rGO/MeFe2O4 and ternary rGO/MnFe2O4/Ppy electrodes reported in literature. These results confirmed that using this simple synthetic strategy it is possible to prepare synergistic composites electrode materials by combination of graphene metal doped iron oxide conductive polymers and promising strategy for designing and tailoring properties of high performing supercapacitors.
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## References
1. 1.
Outlook, I. E. Report No. DOE/EIA-0484, (US Energy Information Administration, 2017) (2017).
2. 2.
Gonçalves, L. M., de Zea Bermudez, V., Ribeiro, H. A. & Mendes, A. M. Dye-sensitized solar cells: A safe bet for the future. Energy & Environmental Science 1, 655–667 (2008).
3. 3.
Simon, P. & Gogotsi, Y. Materials for electrochemical capacitors. Nature Materials 7, 845 (2008).
4. 4.
Khairy, M. & El-Safty, S. A. Hemoproteins–nickel foam hybrids as effective supercapacitors. Chemical Communications 50, 1356–1358 (2014).
5. 5.
Guo, B. et al. Soft‐templated mesoporous carbon‐carbon nanotube composites for high performance lithium‐ion batteries. Advanced Materials 23, 4661–4666 (2011).
6. 6.
Winter, M. & Brodd, R. J. What Are Batteries, Fuel Cells, and Supercapacitors?(Chem. Rev. 2003, 104, 4245–4269. Published on the Web 09/28/2004.). Chemical reviews 105, 1021–1021 (2005).
7. 7.
He, F., Lau, S., Chan, H. L. & Fan, J. High dielectric permittivity and low percolation threshold in nanocomposites based on poly (vinylidene fluoride) and exfoliated graphite nanoplates. Advanced Materials 21, 710–715 (2009).
8. 8.
Sharma, P. & Bhatti, T. A review on electrochemical double-layer capacitors. Energy conversion and management 51, 2901–2912 (2010).
9. 9.
Zhang, Q., Uchaker, E., Candelaria, S. L. & Cao, G. Nanomaterials for energy conversion and storage. Chemical Society Reviews 42, 3127–3171 (2013).
10. 10.
Zhao, L. et al. Carbon nanofibers with radially grown graphene sheets derived from electrospinning for aqueous supercapacitors with high working voltage and energy density. Nanoscale 5, 4902–4909, https://doi.org/10.1039/c3nr33927k (2013).
11. 11.
Bao, Q. et al. Graphene–polymer nanofiber membrane for ultrafast photonics. Advanced Functional Materials 20, 782–791 (2010).
12. 12.
Stoller, M. D., Park, S., Zhu, Y., An, J. & Ruoff, R. S. Graphene-Based Ultracapacitors. Nano letters 8, 3498–3502, https://doi.org/10.1021/nl802558y (2008).
13. 13.
Wang, Y. et al. Supercapacitor Devices Based on Graphene Materials. The Journal of Physical Chemistry C 113, 13103–13107, https://doi.org/10.1021/jp902214f (2009).
14. 14.
Lu, T. et al. Microwave-assisted synthesis of graphene–ZnO nanocomposite for electrochemical supercapacitors. Journal of Alloys and Compounds 509, 5488–5492, https://doi.org/10.1016/j.jallcom.2011.02.136 (2011).
15. 15.
Yan, J. et al. Rapid microwave-assisted synthesis of graphene nanosheet/Co3O4 composite for supercapacitors. Electrochimica Acta 55, 6973–6978, https://doi.org/10.1016/j.electacta.2010.06.081 (2010).
16. 16.
Kuo, S.-L., Lee, J.-F. & Wu, N.-L. Study on pseudocapacitance mechanism of aqueous MnFe2O4 supercapacitor. Journal of the Electrochemical Society 154, A34–A38 (2007).
17. 17.
Wei, C. et al. Valence Change Ability and Geometrical Occupation of Substitution Cations Determine the Pseudocapacitance of Spinel Ferrite XFe2O4 (X = Mn, Co, Ni, Fe). Chemistry of Materials 28, 4129–4133, https://doi.org/10.1021/acs.chemmater.6b00713 (2016).
18. 18.
Vignesh, V., Subramani, K., Sathish, M. & Navamathavan, R. Electrochemical investigation of manganese ferrites prepared via a facile synthesis route for supercapacitor applications. Colloids and Surfaces A: Physicochemical and Engineering Aspects 538, 668–677, https://doi.org/10.1016/j.colsurfa.2017.11.045 (2018).
19. 19.
Aparna, M. L., Grace, A. N., Sathyanarayanan, P. & Sahu, N. K. A comparative study on the supercapacitive behaviour of solvothermally prepared metal ferrite (MFe2O4, M = Fe, Co, Ni, Mn, Cu, Zn) nanoassemblies. Journal of Alloys and Compounds 745, 385–395, https://doi.org/10.1016/j.jallcom.2018.02.127 (2018).
20. 20.
Zhang, W. et al. One-Step Facile Solvothermal Synthesis of Copper Ferrite–Graphene Composite as a High-Performance Supercapacitor Material. ACS applied materials & interfaces 7, 2404–2414, https://doi.org/10.1021/am507014w (2015).
21. 21.
Bloor, D., Hercliffe, R., Galiotis, C. & Young, R. Electronic properties of polymers and related compounds. by Kuzmany, H., Mehring. M. and Roth, S, Springer-Verlag, New York, 179 (1985).
22. 22.
Prissanaroon, W., Brack, N., Pigram, P., Liesegang, J. & Cardwell, T. Surface and electrochemical study of DBSA‐doped polypyrrole films grown on stainless steel. Surface and interface analysis 33, 653–662 (2002).
23. 23.
Biswas, S. & Drzal, L. T. Multilayered Nanoarchitecture of Graphene Nanosheets and Polypyrrole Nanowires for High Performance Supercapacitor Electrodes. Chemistry of Materials 22, 5667–5671, https://doi.org/10.1021/cm101132g (2010).
24. 24.
Park, J. H., Ko, J. M., Park, O. O. & Kim, D.-W. Capacitance properties of graphite/polypyrrole composite electrode prepared by chemical polymerization of pyrrole on graphite fiber. Journal of Power Sources 105, 20–25, https://doi.org/10.1016/S0378-7753(01)00915-6 (2002).
25. 25.
Chee, W. K. et al. Performance of Flexible and Binderless Polypyrrole/Graphene Oxide/Zinc Oxide Supercapacitor Electrode in a Symmetrical Two-Electrode Configuration. Electrochimica Acta 157, 88–94, https://doi.org/10.1016/j.electacta.2015.01.080 (2015).
26. 26.
Lim, Y. S. et al. Potentiostatically deposited polypyrrole/graphene decorated nano-manganese oxide ternary film for supercapacitors. Ceramics International 40, 3855–3864, https://doi.org/10.1016/j.ceramint.2013.08.026 (2014).
27. 27.
Xiong, P., Huang, H. & Wang, X. Design and synthesis of ternary cobalt ferrite/graphene/polyaniline hierarchical nanocomposites for high-performance supercapacitors. Journal of Power Sources 245, 937–946, https://doi.org/10.1016/j.jpowsour.2013.07.064 (2014).
28. 28.
Wang, W., Hao, Q., Lei, W., Xia, X. & Wang, X. Ternary nitrogen-doped graphene/nickel ferrite/polyaniline nanocomposites for high-performance supercapacitors. Journal of Power Sources 269, 250–259 (2014).
29. 29.
Moyseowicz, A., Śliwak, A., Miniach, E. & Gryglewicz, G. Polypyrrole/iron oxide/reduced graphene oxide ternary composite as a binderless electrode material with high cyclic stability for supercapacitors. Composites Part B: Engineering 109, 23–29 (2017).
30. 30.
Liu, F. et al. Thermostability, photoluminescence, and electrical properties of reduced graphene oxide–carbon nanotube hybrid materials. Crystals 3, 28–37 (2013).
31. 31.
Fu, C., Zhao, G., Zhang, H. & Li, S. Evaluation and characterization of reduced graphene oxide nanosheets as anode materials for lithium-ion batteries. Int. J. Electrochem. Sci 8, 6269–6280 (2013).
32. 32.
Zha, D., Xiong, P. & Wang, X. Strongly coupled manganese ferrite/carbon black/polyaniline hybrid for low-cost supercapacitors with high rate capability. Electrochimica Acta 185, 218–228 (2015).
33. 33.
Lei, Z., Lu, L. & Zhao, X. The electrocapacitive properties of graphene oxide reduced by urea. Energy & Environmental Science 5, 6391–6399 (2012).
34. 34.
Bose, S. et al. In-situ synthesis and characterization of electrically conductive polypyrrole/graphene nanocomposites. polymer 51, 5921–5928, https://doi.org/10.1016/j.polymer.2010.10.014 (2010).
35. 35.
Marcano, D. C. et al. Improved Synthesis of Graphene Oxide. ACS nano 4, 4806–4814, https://doi.org/10.1021/nn1006368 (2010).
36. 36.
Sahoo, B., Sahu, S. K., Nayak, S., Dhara, D. & Pramanik, P. Fabrication of magnetic mesoporous manganese ferrite nanocomposites as efficient catalyst for degradation of dye pollutants. Catalysis Science & Technology 2, 1367–1374 (2012).
37. 37.
Gao, L., Yue, W., Tao, S. & Fan, L. Novel strategy for preparation of graphene-Pd, Pt composite, and its enhanced electrocatalytic activity for alcohol oxidation. Langmuir 29, 957–964 (2013).
38. 38.
Si, Y. & Samulski, E. T. Synthesis of Water Soluble Graphene. Nano letters 8, 1679–1682, https://doi.org/10.1021/nl080604h (2008).
39. 39.
Chen, W., Li, X., Xue, G., Wang, Z. & Zou, W. Magnetic and conducting particles: preparation of polypyrrole layer on Fe3O4 nanospheres. Applied surface science 218, 216–222 (2003).
40. 40.
Wang, H., Hao, Q., Yang, X., Lu, L. & Wang, X. Graphene oxide doped polyaniline for supercapacitors. Electrochemistry Communications 11, 1158–1161 (2009).
41. 41.
Stankovich, S. et al. Synthesis of graphene-based nanosheets via chemical reduction of exfoliated graphite oxide. Carbon 45, 1558–1565 (2007).
42. 42.
Sun, X., Zhang, H., Zhou, L., Huang, X. & Yu, C. Polypyrrole‐Coated Zinc Ferrite Hollow Spheres with Improved Cycling Stability for Lithium‐Ion Batteries. Small 12, 3732–3737 (2016).
43. 43.
Lozano, K. & Barrera, E. Nanofiber‐reinforced thermoplastic composites. I. Thermoanalytical and mechanical analyses. Journal of Applied Polymer Science 79, 125–133 (2001).
44. 44.
Xiong, P. et al. Ternary manganese ferrite/graphene/polyaniline nanostructure with enhanced electrochemical capacitance performance. Journal of Power Sources 266, 384–392 (2014).
45. 45.
Hao, J. et al. B/N co-doped carbon nanosphere frameworks as high-performance electrodes for supercapacitors. Journal of materials Chemistry A 6, 8053–8058, https://doi.org/10.1039/c8ta00683k (2018).
46. 46.
Dubal, D. P. & Holze, R. All-solid-state flexible thin film supercapacitor based on Mn3O4 stacked nanosheets with gel electrolyte. Energy 51, 407–412 (2013).
47. 47.
Conway, B. E. Electrochemical Supercapacitors, Scientific Fundamentals and Technological Applications, (ed. New York) 11–19 (Kluwer Academic/Plenum Publishers, 1999).
48. 48.
Fan, L.-Z. & Maier, J. High-performance polypyrrole electrode materials for redox supercapacitors. Electrochemistry. Communications 8, 937–940, https://doi.org/10.1016/j.elecom.2006.03.035 (2006).
49. 49.
Mondal, S., Rana, U. & Malik, S. Graphene quantum dot-doped polyaniline nanofiber as high performance supercapacitor electrode materials. Chemical Communications 51, 12365–12368 (2015).
50. 50.
Abdul Bashid, H. A. et al. Electrodeposition of Polypyrrole and Reduced Graphene Oxide onto Carbon Bundle Fibre as Electrode for Supercapacitor. Nanoscale research letters 12, 246, https://doi.org/10.1186/s11671-017-2010-3 (2017).
51. 51.
Iqbal, M. F., Ashiq, M. N., Iqbal, S., Bibi, N. & Parveen, B. High specific capacitance and energy density of synthesized graphene oxide based hierarchical Al2S3 nanorambutan for supercapacitor applications. Electrochimica Acta 246, 1097–1103 (2017).
52. 52.
Le, V. T. et al. Coaxial Fiber Supercapacitor Using All-Carbon Material Electrodes. ACS nano 7, 5940–5947, https://doi.org/10.1021/nn4016345 (2013).
53. 53.
Kovtyukhova, N. I. et al. Layer-by-layer assembly of ultrathin composite films from micron-sized graphite oxide sheets and polycations. Chemistry of Materials 11, 771–778 (1999).
54. 54.
Amighian, J., Mozaffari, M. & Nasr, B. Preparation of nano‐sized manganese ferrite (MnFe2O4) via coprecipitation method. physica status solidi (c) 3, 3188–3192 (2006).
55. 55.
Vishnuvardhan, T., Kulkarni, V., Basavaraja, C. & Raghavendra, S. Synthesis, characterization and ac conductivity of polypyrrole/Y2O3 composites. Bulletin of Materials Science 29, 77–83 (2006).
56. 56.
Sivakkumar, S. R., Ko, J. M., Kim, D. Y., Kim, B. C. & Wallace, G. G. Performance evaluation of CNT/polypyrrole/MnO2 composite electrodes for electrochemical capacitors. Electrochimica Acta 52, 7377–7385, https://doi.org/10.1016/j.electacta.2007.06.023 (2007).
57. 57.
Liu, M. et al. Hierarchical composites of polyaniline-graphene nanoribbons-carbon nanotubes as electrode materials in all-solid-state supercapacitors. Nanoscale 5, 7312–7320, https://doi.org/10.1039/c3nr01442h (2013).
58. 58.
Zhou, H. & Han, G. One-step fabrication of heterogeneous conducting polymers-coated graphene oxide/carbon nanotubes composite films for high-performance supercapacitors. Electrochimica Acta 192, 448–455, https://doi.org/10.1016/j.electacta.2016.02.015 (2016).
## Acknowledgements
The authors acknowledge the supportive funding from the Australian Research Council’s Industry Transformation Linkage Projects: (IH 150100003) Graphene Enabled Industry Transformation Hub and the University of Adelaide.
## Author information
### Affiliations
1. #### Institute of Chemistry, University of the Punjab, Lahore, 54590, Pakistan
• Saira Ishaq
• , Farah Kanwal
2. #### School of Chemical Engineering, University of Adelaide, Adelaide, 5005, SA, Australia
• Saira Ishaq
• , Mahmoud Moussa
• , Truc Ngo Van
• & Dusan Losic
3. #### ARC Research Hub for Graphene Enabled Industry Transformation, The University of Adelaide, Adelaide, 5005, SA, Australia
• Saira Ishaq
• , Mahmoud Moussa
• , Truc Ngo Van
• & Dusan Losic
### Contributions
S.I. created design, developed the methodology and performed experiments, M.M. did some electrochemical characterizations, data processing and supervision, T.G.V., M.E. and M.S. carried out some data analysis and materials characterization, F.K. helped with project supervision and designing some experiments, D.L. (corresponding author) supervised the work progress, helped out with the results discussion. All authors contributed to writing of manuscript.
### Competing Interests
The authors declare no competing interests.
### Corresponding author
Correspondence to Dusan Losic. | 2019-05-20 14:12:27 | {"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": 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": 0.6268318891525269, "perplexity": 13944.23019187378}, "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/1558232255944.3/warc/CC-MAIN-20190520121941-20190520143941-00154.warc.gz"} |
http://www.sciencemadness.org/talk/viewthread.php?tid=14239&page=8#pid201989 | Sciencemadness Discussion Board » Fundamentals » Miscellaneous » The short questions thread (3) Select A Forum Fundamentals » Chemistry in General » Organic Chemistry » Reagents and Apparatus Acquisition » Beginnings » Responsible Practices » Miscellaneous » The Wiki Special topics » Technochemistry » Energetic Materials » Biochemistry » Radiochemistry » Computational Models and Techniques » Prepublication Non-chemistry » Forum Matters » Legal and Societal Issues
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Author: Subject: The short questions thread (3)
gsd
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Quote: Originally posted by Sedit I have found Platinum powder in an art shop. Its not much but I wanted to get some thoughts on if its ok to use for some reactions or not. Its only .4 grams for about $4 or something like that .............. What do ya'll think. Would it be of any use? The current price of platinum metal is about$1850/oz i.e. roughly $65/gm. So if nothing else, not a bad investment gsd Sedit International Hazard Posts: 1939 Registered: 23-11-2008 Member Is Offline Mood: Manic Expressive That cant be right then can it? Im going to have to look at that again. Maybe its .04oz that would make more sense. Knowledge is useless to useless people... "I see a lot of patterns in our behavior as a nation that parallel a lot of other historical processes. The fall of Rome, the fall of Germany — the fall of the ruling country, the people who think they can do whatever they want without anybody else's consent. I've seen this story before."~Maynard James Keenan 12332123 Harmless Posts: 38 Registered: 14-11-2009 Member Is Offline Mood: No Mood @ Sedit - Unlikely, note that .04oz is even more (over a gram)! Sedit International Hazard Posts: 1939 Registered: 23-11-2008 Member Is Offline Mood: Manic Expressive Lol yeh my fault I ment .04 grams. Knowledge is useless to useless people... "I see a lot of patterns in our behavior as a nation that parallel a lot of other historical processes. The fall of Rome, the fall of Germany — the fall of the ruling country, the people who think they can do whatever they want without anybody else's consent. I've seen this story before."~Maynard James Keenan Magic Muzzlet Hazard to Others Posts: 146 Registered: 22-7-2010 Member Is Offline Mood: No Mood I was reading this: http://lambdasyn.org/synfiles/bromovanillin.htm I noticed in the first example, using KBr in GAA/water/H2SO4 that the KBr is 2eq to vanillin used. Would this not dibrominate the vanillin? Or is it based on available bromine or something, I'm having trouble figuring it out. If this was subbed with NaBr could it too be used in 2eq to vanillin producing the wanted product? 1281371269 National Hazard Posts: 312 Registered: 15-5-2009 Member Is Offline Could anyone explain what these are: http://cgi.ebay.co.uk/ws/eBayISAPI.dll?ViewItem&item=110... They're definitely stillheads, because they have two male joints and anyway basically look the same as splash stillheads. But what are the other bits for? The tube coming off of the side looks like a vacuum outlet, but surely this should be on the receiver? And what about the tube coming down from the bottom, what's that supposed to do? DJF90 International Hazard Posts: 2266 Registered: 15-12-2007 Location: At the bench Member Is Offline Mood: No Mood Steam distiallation heads. The side tube is attached to steam source, which leads down to into the flask. The vapour then passes through the splash head, and to the condenser that you'll have to attach. UnintentionalChaos International Hazard Posts: 1454 Registered: 9-12-2006 Location: Mars Member Is Offline Mood: Nucleophilic Quote: Originally posted by Mossydie Could anyone explain what these are: http://cgi.ebay.co.uk/ws/eBayISAPI.dll?ViewItem&item=110... They're definitely stillheads, because they have two male joints and anyway basically look the same as splash stillheads. But what are the other bits for? The tube coming off of the side looks like a vacuum outlet, but surely this should be on the receiver? And what about the tube coming down from the bottom, what's that supposed to do? Looks like equipment for kjeldahl nitrogen determinations to me. The tube might be for air flow to carry the last of ammonia into the reciever. I'm just guessing though. Department of Redundancy Department - Now with paperwork! 'In organic synthesis, we call decomposition products "crap", however this is not a IUPAC approved nomenclature.' -Nicodem DJF90 International Hazard Posts: 2266 Registered: 15-12-2007 Location: At the bench Member Is Offline Mood: No Mood Don't believe me then... http://www.scilabware.com/Adapters/Steam-distillation-head/p... 1281371269 National Hazard Posts: 312 Registered: 15-5-2009 Member Is Offline Thanks for the help SHADYCHASE54 Hazard to Others Posts: 148 Registered: 16-12-2010 Location: CaNaDay! Member Is Offline Mood: No Mood Hello all, I just have a couple quick questions firstly, I have some cation exchange resin in the H+ form and i was wondering if anyone knows how I may determine the resins exchange potential per/cm3? The resin type is Amberlite IRN-77. Secondly, would someone out ther is S.M land reccomend a good book that encompasses the theory and thus applications of the various exchange media? thanks in advance for any help. SHADY.. SHADYCHASE54 Hazard to Others Posts: 148 Registered: 16-12-2010 Location: CaNaDay! Member Is Offline Mood: No Mood Does anyone have any ideas? Random International Hazard Posts: 1018 Registered: 7-5-2010 Location: In ur closet Member Is Offline Mood: Energetic I read that if I react phtalic acid and phenol i get phenolphtalein. What would happen if I would react phenol with terephtalic acid, would I get phenolphtalein or maybe phenolterephtalein exists? WOuld phenolterephtalein also work as indicator? UnintentionalChaos International Hazard Posts: 1454 Registered: 9-12-2006 Location: Mars Member Is Offline Mood: Nucleophilic Quote: Originally posted by Random I read that if I react phtalic acid and phenol i get phenolphtalein. What would happen if I would react phenol with terephtalic acid, would I get phenolphtalein or maybe phenolterephtalein exists? WOuld phenolterephtalein also work as indicator? You need to use phthalic anhydride, not phthalic acid. The reaction is a friedel crafts acylation followed by a second condensation to yield a tertiary alcohol that cyclizes to a lactone The indicator's ability to change colors relies on the ortho carboxylate group. Phthalic acid is cheap and decent conversion to the anhydride can be had by simple heating. To be fair, I ran a very small scale version using sulfuric acid, phenol, and phthalic acid. Enough was formed that I could get very intense color changes with the diluted reaction mixture, but not enough to isolate any product EDIT: might as well add a question of my own. I remember something about selective sulfonation of mixed xylenes to seperate the isomers, but my search-fu seems to be weak tonight. Does anyone have this reference? [Edited on 2-24-11 by UnintentionalChaos] Department of Redundancy Department - Now with paperwork! 'In organic synthesis, we call decomposition products "crap", however this is not a IUPAC approved nomenclature.' -Nicodem Sedit International Hazard Posts: 1939 Registered: 23-11-2008 Member Is Offline Mood: Manic Expressive Does anyone know if Platinum plated electrodes could be used in a Kolbe electrolysis, I have yet to find someone local to sell me a small amount of Pt wire but I did manage to get ahold of some plated wire with a coating 2 microns think. BTW: That other Platinum powder I spoke of earlier in this thread was a bust. I checked it out and on the back it clearly states it contains Copper so I highly doubt there is much Pt if any in that powder at all. That would explain the .4oz of Platinum powder for$5.
Knowledge is useless to useless people...
"I see a lot of patterns in our behavior as a nation that parallel a lot of other historical processes. The fall of Rome, the fall of Germany — the fall of the ruling country, the people who think they can do whatever they want without anybody else's consent. I've seen this story before."~Maynard James Keenan
Morgan
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Is there a way to test for water in methanol? I sometimes buy 5 gallon amounts from a speed shop/racing store and I got the last of a 55 gallon drum. It was very hot and humid that day and I have to wonder how much water the methanol absorbs every time they pump some out. It didn't seem to burn as well as before. Even with just a little water in methanol, it can affect how some engines/devices run. I'm talking about less than 5% water.
I use methanol a lot, and sometimes for small experiments I will buy some HEET just to make sure the methanol hasn't absorbed water from the air.
Or is there an easy way to dehydrate it completely without doing some methoxide reaction?
Lambda-Eyde
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Anhydrous copper sulfate? Alcohols are usually dehydrated with CaO or K<sub>2</sub>CO<sub>3</sub>.
Nicodem
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Quote: Originally posted by Morgan Is there a way to test for water in methanol?
You can do a Karl-Fischer titration to get an exact measurment, but that requires buying the required solution (Hydranal). If you need just a rough qualitative test you can add your methanol dropwise into some toluene. If there is much water inside you will get some turbidity instead of a clear solution (the turbidity will disappear once you add enough methanol). I guess you could actually make this a primitive quantitative test if you make a calibration curve with methanol solutions of known water content. However, it will not show anything if your methanol only has little moisture, though you could greatly enhance the sensitivity by using hexane/toluene mixtures instead (white spirit or any other OTC source of alkanes will do instead of hexane, but some toluene must be present because methanol is not fully miscible in alkanes).
Another primitive test using only OTC materials is adding some anhydrous CuSO4 to methanol and letting it stay over night. If there is some water present, the salt will partially colourize blue. Anhydrous white CuSO4 can be made by heating CuSO4.5H2O.
…there is a human touch of the cultist “believer” in every theorist that he must struggle against as being unworthy of the scientist. Some of the greatest men of science have publicly repudiated a theory which earlier they hotly defended. In this lies their scientific temper, not in the scientific defense of the theory. - Weston La Barre (Ghost Dance, 1972)
Morgan
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Thanks, maybe I will try the copper sulfate. I once made some anhydrous CuSO4 , it's funny how it doesn't suddenly reuptake the water previously driven off.
The toluene turbidity test seems good too. Has anyone heard of using cornstarch to absorb water or what percentage it would take out.
The other day I tried a few crystals of KMNO4/purple salt, but it was old in a moist environment and I didn't even know if it was soluble in methanol. if it would be worth a try to detect water.
Another thing, I once dehydrated some magnesium sulfate just to see how it would burn with powdered magnesium and it burns fine, but I can't recall, but it seems like it too was slow to rehydrate.
[Edited on 2-3-2011 by Morgan]
497
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Does anyone know if PdCl2 on carbon will work in a catalytic transfer hydrogenation? According to Orgsyn you can toss it directly into a standard H2 gas hydrogenation as long as a little HCl won't hurt, but I'm not convinced it would work the same for a CTH. I couldn't find any word online about it. Thanks.
Morgan
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With methanol a platinum catalyst will produce some formadehyde. What will platinum catalysts produce when reacted with isopropyl alcohol? And with ethanol is it just acetyldehyde? Or are there other byproducts?
I recall Dobereiner made a vinegar producing lamp using platinum and ethanol(?) somehow.
[Edited on 6-3-2011 by Morgan]
Morgan
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The reason I asked is I saw this video of a catalytic lamp that runs on isopropyl alcohol and platinum.
"What is Ashleigh & Burwood Lamp Fragrance made from?"
"The basis of the Lamp Fragrance, and the important fuel which keeps the catalytic process working, is an alcohol called isopropyl alcohol. A very common alcohol, it is the same form of alcohol which is commonly used in hospital anti-bacterial handwashes for example. The other ingredients are distilled water, and the fragrance compound itself."
http://www.ashleigh-burwood.co.uk/lamps-faq.html
"I find the fragrance too strong, what can I do?"
"Firstly, be sure that you are not using the lamp for extended periods of time, especially in smaller rooms and when the door(s) and window(s) are closed. Fragrance Lamps are incredibly effective at fragrancing the air (unlike a room spray for example where the fragrance droplets will fall to the ground after a few minutes) and you will find that the fragrance lingers for several hours in the room after the lamp has been stopped. If you feel that it is the fragrance itself which is too strong for your liking, then it is possible to dilute down one of our Lamp Fragrances, using the Neutral (unfragranced) variety – this is product code PFL900 for the 250ml bottle, and PFL928 for the 500ml bottle. You can mix in any ratio you like until you find the level which best suits you."
[Edited on 7-3-2011 by Morgan]
Morgan
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I wonder what the adhesive coating technique was?
"The filter paper wrapping of 1823 was succeeded
by a dried and ignited mixture of platinum
sponge and potters’ clay; and an improved
version of the Dobereiner lamp had its
platinum sponge applied in an adhesive
coating on a coil of platinum wire."
http://www.platinummetalsreview.com/pdf/pmr-v9-i4-136-139.pd...
Morgan
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Here's the tidbit I sited about making acetic acid from ethanol. Still I wonder what isopropyl alcohol makes when reacted with platinum?
"In 1821, after reading Edmund Davy’s article
in a German translation which appeared in that
year, Döbereiner repeated this experiment and
found that the ethanol was oxidised to acetic
acid. Because the platinum was not consumed,
he suggested that the reaction could be used
“for the large-scale preparation of acetic acid”
(Essigsäure) (27), and he even designed a vinegar
lamp (Essiglampe), in which ethanol was supplied
by a cotton wick to a small funnel containing
platinum black."
http://docserver.ingentaconnect.com/deliver/connect/matthey/...
[Edited on 7-3-2011 by Morgan]
Morgan
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This is a picture with some 91% isopropyl alcohol reacting with my platinum gauze. I couldn't tell by the smell what the products of combustion might be.
[Edited on 7-3-2011 by Morgan]
Attachment: phpHOUd45 (65kB)
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Sciencemadness Discussion Board » Fundamentals » Miscellaneous » The short questions thread (3) Select A Forum Fundamentals » Chemistry in General » Organic Chemistry » Reagents and Apparatus Acquisition » Beginnings » Responsible Practices » Miscellaneous » The Wiki Special topics » Technochemistry » Energetic Materials » Biochemistry » Radiochemistry » Computational Models and Techniques » Prepublication Non-chemistry » Forum Matters » Legal and Societal Issues | 2022-05-23 20:10:42 | {"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": 0.24192123115062714, "perplexity": 10176.350753654537}, "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-2022-21/segments/1652662561747.42/warc/CC-MAIN-20220523194013-20220523224013-00681.warc.gz"} |
https://gateoverflow.in/457/gate2008-45 | 4.3k views
Dijkstra's single source shortest path algorithm when run from vertex $a$ in the above graph, computes the correct shortest path distance to
1. only vertex $a$
2. only vertices $a, e, f, g, h$
3. only vertices $a, b, c, d$
4. all the vertices
retagged | 4.3k views
0
explain this with diagram plz
not get the point why d is correct
D. all the vertices. Just simulate the Dijkstra's algorithm on it. Dijkstra's algorithm is not meant for graphs with negative-edge-weight-cycle, but here it does give the correct shortest path.
edited by
+2
e is already -2 rt? So, -1 needn't be assigned.
+4
no it does not fail...
e= -2 in 2nd pass and in 7th pass it -1 but -2 is less than -1 so we need not to relax it ..
so it work fine ...
0
Works for this example, Hence D is the answer. But Dijkstra's may not work correctly for all graphs with negative weights (with our without cycle)
ref:- https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#Related_problems_and_algorithms
+2
@Arjun sir,
Dijkstra cannot work for negative edge weights.
Here, bychance it worked for A , we got correct result.
But, if we take D as source, then D -> H path we get = 2 but there is even a different path = 0.
So, surely it did work for A here, but not for all other edges , which means dijkstra must never be used for negative edge weights ?
Am i thinking right sir..??
+1
D -> H =4 rt?
but other way it is 0
So, 0<4
So, it will take minimum path 0
Then here it will work for -ve weight cycle too.
0
arjun sir, Dijsktra algorithm cannot compute the shortest path in case of negative weight cycles as it cannot detect them but it will definitely compute shortest path in case of negative weight edges. So can we answer directly even without computing??
+47
@sushmita, No. Why Dijstra will work in -ve edges ?.
It may fail in -ve edge even there is no -ve cycle.
Can u calculate distance from A to C using Dijkstra ?, It will be 2, right ?
But actual shortest distance is 1 only. (Here Dijkstra fails even NO cycle.)
Here whats happening, Observe:-
Dijkstra had 2 choices to go to C from A, It chooses direct path.
It says if I go via B, then i would have to incur ATLEAST 5 cost. (it don't know that in future there may be a -ve edge.)
It thinks, A to B distance itself is 5 and if I go via B then cost would always increese, there is no chance of decrease. but to his surprise I put "-4"
Actually Dijkstra assumes that all edges are +ve. (if u see proof of " correctness of Dijkstra" then first assumption is weights are +ve )
0
yeah u r right. thanx a lot. i was mistaken. very nice example. thanx again.
+2
Will this be the graph with shortest path estimates?
0
There is no negative edge cycle in above graph, Dijkstra alto doesn't work for those graph which have negative edge cycle which is not present in the given graph.
0
So you are saying that this graph is correctly drawn?
0
@Sachin, going by your logic here answer should not be D. What's correct? I'm confused.
0
@Swati there is nothing to be confused. Dijkstra's algo only fail when negative edge cycle present in the graph , as we can see there is no negative edge cycle in the graph , for better understanding you can try to simulate the Dijkstra's algo on given graph.
+1
I'm getting below shortest path graph. Is it correct?
+2
@Sachin Mittal, for the graph given by you, isn't following solution work?
0
@swati you have take weight of e-f edge equals to 1 but in the question it is given 2, correct that and simulate the algo again .
0
@Rahul The question book from where I'm doing, (e-f)=1 only. Now I get why am I getting different answers from other commentators here.
0
@swati you may get the different answer but I think it will still give shortest path .
0
0
@swati e to f distance is 2
Just quickly check for negative edge weight cycle. If no negative edge weight cycle then Dijkstra's algo. will work fine.
If you are not confident in detected cycle( or cycle detection) then simulation of Dijkstra's algo. is done in below image.
0
can yu just tell how to quickly check for negative edge weight cycle?
Dijkstra algorithm fails when the graph contains negative weight cycle forms . The graph contains only negative weights then the dijkstra gives correct shortest paths from source to every edge. so the answer is D.
Once, we know the proof of correctness of Dijkstra algorithm, it is easier to trace down why this works fine for source vertex A and not for Source Vertex D.
So, above is a snip from cormen, where Set S indicated the set of vertices for which shortest path from source vertex "s" have been determined and for $\forall v \in S$ we have $v.d=s(s,v)$ means in simple words the cost to reach every vertex in Set S, from source vertex "s" is correctly determined and they are valid under all circumstances.
Now, this proof says when suppose a new vertex say "y" is added to set S, after this is done, $y.d=s(s,y)$ holds. Means my algorithm has correctly computed the cost to reach vertex y from s.(Keep this point in mind and you'll be able to figure out where is what going wrong!!)
Okay So now my source vertex is A.
At each step, I need to make sure that when vertex 'v' is added to set S, means it's shortest distance from source has been calculated, it must be really minimum and you should be able to verify it from the graph as well.
So, below is how the algorithm works
(1)First I start with source vertex A and relax vertex B with cost as 1. is this correct? Yes, we can see from the graph that the best cost to reach vertex b is from a with cost 1.
(2)Then I process vertex b, and it is now included in S as it's shortest path from source is determined. Now I relax all edges leaving B,and set path cost of C as 3, and path cost to e as -2. Are they correct? Is it really that to reach e from A I would have minimum cost of -2? Yes from graph it seems so.Similar is story for vertex C.
Since, the cost to reach b from source vertex a was correctly computed and found minimum, all vertices, which are reachable from vertex b also should have been correctly computed minimum cost from source vertex a.
(3)Now, e is included in set S and I relax edge to vertex f and cost comes to be 0. Is it correct? yes from the graph I can manually find that it is correct.
So you notice? At each step, we have to check that when a vertex v is included in set S, the distance to reach this vertex v from source vertex s must have been correctly determined in order for Dijkstra to work correctly.
Now Consider the scenario when source vertex is D and the algorithm is executed.
Now, consider the scenario, when vertex g was included in set S and all edges from g were relaxed.
cost to e from d changed to 3
cost to h from d changed to 4.
And both are wrong, if you see the graph.
The actual cost to reach vertex e from d (minimum) is 0 (d-a-b-e)
And to h also the correct minimum cost is 0 (d-a-b-c-h)
So, from this point onwards the trouble started.
And as you can see, vertex h is processed before vertex c and since h is processed, this means it is included in set S which means you have correctly computed the shortest path cost to reach h from d which is wrong!!. You see the fun part is, till the point finally when h is included in set S (vertices whose shortest path cost from source vertex have been determined), no one changed cost of h to correct value 0 and it got included in S with wrong cost!!.
Obviously, vertex g is responsible for this, and if C was processed before g, this could have been prevented!!.
In order to h have correct minimum path cost from d, it must have been processed after vertex C, because the minimum cost to reach C from d is 5 and then to h it would have been 0 and this is correct!!.
–1 vote
Dijkstra's single source shortest path algorithm here this works fine bcoz there is no -ve weight cycle in graph.
+3
D is the correct option, but the explanation you have provided does not seem right.
+1
Just see the diagram by Sachin Mittal bro. Even if there is no negative weight cycle still only negative edges can also give wrong answer.
So if they are asking about shortest path with negative edges then there is no method or rule except applying Dikastras algo & verifying manually if it is the correct answer. | 2018-09-25 03:02:14 | {"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": 0.6161375641822815, "perplexity": 996.2330887883279}, "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-2018-39/segments/1537267160923.61/warc/CC-MAIN-20180925024239-20180925044639-00331.warc.gz"} |
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sp3d hybridization structure
Organizing and providing relevant educational content, resources and information for students. Even completely filled orbitals with slightly different energies can also participate. The grounds state and the excited state outer electronic configurations of phosphorus (Z=15) are represented below. This is a lesson from the tutorial, Advanced Theories of Covalent Bonding and you are encouraged to log in or register, so that you can track your progress. The five orbitals viz 1s, 3p, and 1d orbitals are free for hybridization. Parent s: because it is directional unlike the s orbital. sp3d4 hybridisation (Steric Number 8) will mean that the central metal atom is bonded to 8 other atoms and only in … In a molecule of CH3CH3, each carbon atom will have what geometry? We have three molecules of iodine here which along with an extra elect… As before, there are also small lobes pointing in the opposite direction for each orbital (not shown for clarity). Based on the types of orbitals involved in mixing, the hybridization can be classified as sp3, sp2, sp, sp3d, sp3d2, sp3d3. sp3d hybrid orbitals are formed when one s, three p and one d orbitals, each of which is capable of forming one covalent bond become degenerate, that is they combine to form equivalent orbitals with the same energy and geometry. There are no lone pairs of electrons on the central atom. With an octahedral arrangement of six hybrid orbitals, we must use six valence shell atomic orbitals (the s orbital, the three p orbitals, and two of the d orbitals in its valence shell), which gives six sp3d2 hybrid orbitals. Hybridization. Since lone pairs occupy more space than bonding pairs, structures that contain lone pairs have bond angles slightly distorted from the ideal. The SF4 molecule consists of a total of 34 valence electrons. Draw the lewis structure for sf6 what is the. Hence, the sp hybridized carbon is more electronegative than sp2 and sp3. Three hybrid orbitals lie in the horizontal plane inclined at an angle of 120° to each other known as the equatorial orbitals. The new orbitals formed are called sp3 hybrid orbitals. The reason why a hybrid orbital is better than their parents: The hybrid orbitals can be defined as the combination of standard atomic orbitals resulting in the formation of new atomic orbitals. Here the hybridization is sp3d because the lone pair resides on the sulfur atom. Parent p: because it has lower energy than p orbital. sp3d hybridization has the following structures:- 1)Trigonal Bipyramidal- No lone pair of electrons on central atom 2)See-Saw- 1 lone pair of electron. The sulfur atom in sulfur hexafluoride, SF 6, exhibits sp3d2 hybridization. In a water molecule, two sp 3 hybrid orbitals are occupied by the two lone pairs on the oxygen atom, while the other two bond with hydrogen. In sp³ hybridization, one s orbital and three p orbitals hybridize to form four sp³ orbitals, each consisting of 25% s character and 75% p character. Hybridization is defined as the concept of mixing two atomic orbitals with the same energy levels to give a degenerated new type of orbitals. There are 5 main hybridizations, 3 of which you'll be tested on: sp3, sp2, sp, sp3d… In a molecule of phosphorus pentachloride, PCl5, there are five P–Cl bonds (thus five pairs of valence electrons around the phosphorus atom) directed toward the corners of a trigonal bipyramid. Other atoms that exhibit sp3d2 hybridization include the phosphorus atom in $${\text{PCl}}_{6}{}^{\text{−}},$$ the iodine atom in the interhalogens $${\text{IF}}_{6}{}^{\text{+}},$$ IF5, $${\text{ICl}}_{4}{}^{\text{−}},$$$${\text{IF}}_{4}{}^{\text{−}}$$ and the xenon atom in XeF4. Answer. Also, the orbital overlap minimizes the energy of the molecule. A molecule of sulfur hexafluoride has six bonding pairs of electrons connecting six fluorine atoms to a single sulfur atom. Generally, the Lewis structure is helpful to understand the molecular geometry of any given chemical compound. It is always recommended to visit an institution's official website for more information. Therefore, a hybrid orbital with more s-character will be closer to the nucleus and thus more electronegative. Sp3: s characteristic 25% and p characteristic 75%. Save my name, email, and website in this browser for the next time I comment. CO2, CO3 2−, NO3 −, O3. The structure of NH 3 and H 2 O molecules can also be explained with the help of sp 3 hybridization. sp3d4 hybridisation is a very rare type of hybridisation. Hybridization is also an expansion of the valence bond theory. All names, acronyms, logos and trademarks displayed on this website are those of their respective owners. Atomic orbitals with equal energies undergo hybridization. Ask Question Asked 5 years ago. Structured into themes, you can pick a theme that interests you and simply learn all that you wanted to know about it. Also, iodine is in the seventh group of the periodic table and has seven valence electrons in its outer orbit. Summary – sp3d2 vs d2sp3 Hybridization sp 3 d 2 hybridization and d 2 sp 3 hybridization are confusing terms that are most of the times used interchangeably by mistake. Sp2: s characteristic 33.33% and p characteristic 66.66%. Trigonal bipyramidal: Five electron groups involved resulting in sp3d hybridization, the angle between the orbitals is 90°, 120°. Redistribution of the energy of orbitals of individual atoms to give orbitals of equivalent energy happens when two atomic orbitals combine to form hybrid orbital in a molecule. tetrahedral, bent. After completing this section, you should be able to apply the concept of hybridization to atoms such as N, O, P and S explain the structures of simple species containing these atoms. sp2-hybridization: The combination of one s and two p-orbitals to form three hybrid orbitals of equal energy is known as sp2-hybridization. Unless specified, this website is not in any way affiliated with any of the institutions featured. Hybridization of s and p orbitals to form effective sp hybrid orbitals requires that they have comparable radial extent. There are no lone pairs of electrons on the central atom. These problems are for practice only will not be graded. Adding this in to the article as it stands would require some re-structuring. Are they one in the same? (b) The six sp3d2 orbitals form an octahedral structure around sulfur. The new orbitals formed are called sp2 hybrid orbitals. PCl5: why sp3d but s2p3? Which of the statements below is true for the Lewis structure of the sulfite ion? In order to determine the hybridization of sulphur tetrafluoride, you have to first understand its Lewis structure and the number of valence electrons that are present. Both carbons are sp 3-hybri The sulfur atom in sulfur hexafluoride, SF6, exhibits sp3d2 hybridization. This process is called hybridization. Don't want to keep filling in name and email whenever you want to comment? All the three hybrid orbitals remain in one plane and make an angle of 120° with one another. The new orbitals formed are called sp hybridized orbitals. The remaining two orbitals lie in the vertical plane at 90 degrees plane of the equatorial orbitals known as axial orbitals. The geometry of orbital arrangement due to the minimum electron repulsion is tetrahedral. In NH 3, the valence shell (outer) electronic configuration of nitrogen in the grounds state is 2s 2 2p 1 x 2p 1 y 2p 1 z having three unpaired electrons in the sp 3 hybrid orbitals and a lone pair of electrons is present in the fourth one. Example : BF 3 Molecule. We use the 3s orbital, the three 3p orbitals, and one of the 3d orbitals to form the set of five sp3d hybrid orbitals (see the figure below) that are involved in the P–Cl bonds. What is the Hybridization of Sulphur Tetrafluoride? Key Terms. Your browser seems to have Javascript disabled. For example, CO2, with the Lewis structure shown below, has two electron groups (two double bonds) around the central atom. Due to the spherical shape of s orbital, it is attracted evenly by the nucleus from all directions. As there are molecules of Iodine, one molecule of Iodinewill be in the centre. The bigger lobe of the hybrid orbital always has a positive sign, while the smaller lobe on the opposite side has a negative sign. The atomic orbitals of the same energy level can only take part in hybridization and both full filled and half-filled orbitals can also take part in this process, provided they have equal energy. The percentage of s character in sp, sp2, and sp3 hybridized carbon is 50%, 33.33%, and 25%, respectively. Try This: Give the hybridization states of each of the carbon atoms in the given molecule. of valence electrons of central atom(here it is P)is : 1s^2 2s^2 2p^6 3s^2 3p^3 no.of electrons in outermost shell =5 The no. (a) Sulfur hexafluoride, SF6, has an octahedral structure that requires sp3d2 hybridization. Chemistry » Advanced Theories of Covalent Bonding » Hybrid Atomic Orbitals. Based on the nature of the mixing orbitals, the hybridization can be classified as, ⇒ Know more about VSEPR theory its postulates and limitations. Register or login to make commenting easier. The shape of the molecule can be predicted if hybridization of the molecule is known. Hybridization. Active 5 months ago. Sp3d hybridization involves mixing 3p and 1d orbitals to form 5 sp3d hybridization orbitals with the same energy. In the ammonia molecule (NH 3), 2s and 2p orbitals create four sp 3 hybrid orbitals, one of which is occupied by a lone pair of electrons. Sp and sp2 hybridization results in two and one unhybridized p orbitals respectively whereas in sp3 hybridization there are no unhybridized p orbitals. Therefore, it can obtain a set of 5sp 3 d hybrid orbitals directed to the 5 corners of a trigonal bipyramidal ( VSEPR theory ). In the ethane molecule, the bonding picture according to valence orbital theory is very similar to that of methane. hybridization of pcl5. Comments? A molecule of sulfur hexafluoride has six bonding pairs of electrons connecting six fluorine atoms to a single sulfur atom. To bond six fluorine atoms, the 3s orbital, the three 3p orbitals, and two of the 3d orbitals form six equivalent sp3d2 hybrid orbitals, each directed toward a different corner of an octahedron. The linear combination of a 4 s − orbital with three 4 p − orbitals (4 p x, 4 p y, and 4 p z) and one 3 d − orbital (3 d z 2 ) results in five s p 3 d-orbitals. CO3 2−, NO3 −, and O3. Each sp hybridized orbital has an equal amount of s and p character, i.e., 50% s and p character. Other examples of sp 3 hybridization include CCl 4, PCl 3, and NCl 3. The general process of hybridization will change if the atom is either enclosed by two or more p orbitals or it has a lone pair to jump into a p orbital.
Kategorien: Allgemein | 2021-10-26 17:52:30 | {"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": 0.3726588189601898, "perplexity": 2279.7567056354605}, "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-2021-43/segments/1634323587915.41/warc/CC-MAIN-20211026165817-20211026195817-00368.warc.gz"} |
https://mathzsolution.com/tag/algebraic-vector-bundles/ | ## Dual involution on the Ext1Ext^1
Let X be a smooth algebraic curve over C, and let F be a vector bundle on it of degree 1, take the dual of an extention 0→F∗→E→F→0 is again an extension of F by F∗, my questions are: How can I explicitly describe this involution on vector space Ext1(F,F∗)? Are there any criterian for … Read more
## Dimension of the singular locus of $\mathcal M_X(r,d)$
Let $X$ be an algebraic smooth curve of genus $g$ over $\mathbb C$, and let $\mathcal M_X(r,d)$ (resp $\mathcal M_X^0(r)$) be the moduli space of vector bundle of rank $r$ and degree $d$ (resp. with trivial determinant) over $X$, we know that when $g=r=2$ and $d\equiv 0 \mod 2$ this space is smooth. So we … Read more
## Extend a vector bundle on a flat family
Let f:X→T be a flat family, and Ft is a vector bundle on Xt for some t∈T. Can this Ft be extended to a vector bundle F on f−1(U) for some open neighborhood of t? If moreover E is a vector bundle on X, and Ft is a subbundle of Et on Xt, then can … Read more
## Higher tangent bundles of manifolds with non integer dimension
One way to define the tangent space of a manifold at a point p∈M is the following: We define an equivalent relation on the space of curves passing p as follows: Two curves α,β are equivalents iff they have tangencity of order at least one that is ∥α(t)−β(t)∥=o(|t|), in a local smooth coordinate. Then the … Read more
## Proving that an EE-oriented manifold has an EE-oriented normal bundle
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## Spectrum of the hypoelliptic transverse signature operator
Let D be the transverse signature operator constructed by Connes and Moscovici in the paper “Local index formula in Noncommutative Geometry”:this is first order hypoelliptic pseudodifferential operator D defined by the equality D|D|=Q where Q=(dVd∗V−d∗VdV)⊕(dH+d∗H) where dV,dH are vertical and horizontal exterior derivative. It acts on the sections of the bundle Λ(V∗)⊗Λ(p∗(T∗M)) over P:=GL+(M)/SO(n) (the … Read more | 2023-01-30 04:32:21 | {"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": 0.9654726982116699, "perplexity": 529.9341832330404}, "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/1674764499801.40/warc/CC-MAIN-20230130034805-20230130064805-00727.warc.gz"} |
http://math.stackexchange.com/questions/121205/how-many-positive-integers-p-q-r-exists | How many positive integers $p$, $q$, $r$ exists?
How many positive integers $p$, $q$, $r$ exists satisfying the relation below?
$$p/q + q/r + r/p = 2$$
Thank in advance. I tried so much but could not think how to proceed.
I just need a hint from where to begin.
-
The following link gives not any help to find the answer to the problem but shows a related number theoretic problem math.stackexchange.com/questions/113546/… – miracle173 Mar 17 '12 at 6:50
HINT : Note that from AM-GM inequality, we have that $a+b+c \geq 3 \sqrt[3]{abc}$. If you wish to view the answer, hover your cursor over the grey region directly below.
Answer: Since $p$, $q$ and $r$ are positive, so are $\frac{p}{q}$, $\frac{q}{r}$, $\frac{r}{p}$. From AM-GM inequality, we have that $$\displaystyle \frac{p}{q} + \frac{q}{r} + \frac{r}{p} \geq 3 \sqrt[3]{\frac{p}{q} \times \frac{q}{r} \times \frac{r}{p}} = 3.$$ Hence, there doesn't exists any $p$, $q$ and $r$ satisfying $\displaystyle \frac{p}{q} + \frac{q}{r} + \frac{r}{p} = 2$.
@vikiiii Yes. The proof only needs $a$,$b$,$c$ are positive. – user17762 Mar 17 '12 at 6:16 | 2016-07-24 13:02:40 | {"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": 0.9507288932800293, "perplexity": 155.24751972364982}, "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-2016-30/segments/1469257824037.46/warc/CC-MAIN-20160723071024-00282-ip-10-185-27-174.ec2.internal.warc.gz"} |
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theOpenSet.set_default_frame(secondChart.frame())
theOpenSet.set_default_chart(secondChart)
The reason is that g is displayed through its restriction to the open subset theOpenSet and the commands theManifold.set_default_frame(secondChart.frame()) and theManifold.set_default_chart(secondChart) are not propagated to subsets. | 2020-07-09 20:51:35 | {"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": 0.8263888359069824, "perplexity": 3698.0955087078805}, "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-2020-29/segments/1593655901509.58/warc/CC-MAIN-20200709193741-20200709223741-00401.warc.gz"} |
https://electronics.stackexchange.com/questions/566679/problem-in-can-transmission/566680 | # Problem in CAN transmission
I am working on a sensor based project using STM32 in which I do the following things,
1. Receive data from sensor
2. Transmit that data on the CAN bus.
The sensor will send data twice every minute and there is approx 250ms delay between those two data from the sensor. When a data is received from the sensor it is transmitted as a frame on the CAN bus. I also have a MCP2515 attached to a raspberry pi which logs all the data on the CAN bus. There is no other node on the CAN bus except the STM32 CAN and MCP2515. I also checked the termination resistors and they are ok. Initially I has the following settings
hcan.Init.TTCM = DISABLE;
hcan.Init.ABOM = DISABLE;
hcan.Init.AWUM = DISABLE;
hcan.Init.NART = ENABLE;
hcan.Init.RFLM = DISABLE;
hcan.Init.TXFP = DISABLE;
When I used the above settings, my data log showed a lot of data missed in the CAN bus. So I changed the NART to DISABLE and tried again.
hcan.Init.TTCM = DISABLE;
hcan.Init.ABOM = DISABLE;
hcan.Init.AWUM = DISABLE;
hcan.Init.NART = DISABLE;
hcan.Init.RFLM = DISABLE;
hcan.Init.TXFP = DISABLE;
This time I received many additional data in the CAN log. Why is this NART bit causing additional data on the CAN bus. As per my project, I need an exact data count from the sensor. I am pretty sure that the sensor is transmitting the data on regular interval using a oscilloscope.
NART is apparently "no automatic retransmission". That's a non-standard setting which shouldn't be used. Commonly, CAN nodes should alway attempt to re-send a frame if they fail to do so the first time. Because one reason for failing could be that they lost in the bus arbitration procedure, yielding to another node with higher priority. That's not an error, but part of the expected CAN functionality.
This "NART" bit is apparently used in Time-Triggered CAN solutions, which is unlikely something that you will or should ever use, it's a different network topology compared to classic CAN.
In your case it would seem that you only have one node on the bus, nobody sending ACK and therefore when "NART" is set the node will continue attempting until it goes into error passive mode then bus off and shuts down.
"There is no other node on the CAN bus"
That's not a CAN bus then, it's a CAN node. Unless your listener is set to ACK frames on the bus, nothing will work. You need at least 2 working nodes, see: What are the most common causes of CAN bus communication errors? Also study CAN bus arbitration, error frames, error modes and so on.
• Thank you for your reply. – Mark Dsylva May 25 at 2:54
• Thank you for your reply. So as you say, after I disabled the NART bit, the CAN module is trying to resend the frames just because there is no nodes on the CAN bus to ACK the frame. Did I get your answer correct?. – Mark Dsylva May 25 at 3:04
• @MarkDsylva Yes. You'll also get error frames. – Lundin May 25 at 6:28
• Ok. But doesnt the MCP2515 also act as a node. It receives the data and logs it. So the MCP2515 should send an ACK to the STM32. Plz correct if I am wrong. – Mark Dsylva May 25 at 7:42
• @MarkDsylva If you have one STM32 with built-in controller and some hobbyist board with the old MCP2515 then yeah you have 2 nodes if they are configured correctly to behave as active nodes rather than passive listeners, and use the same baudrate. You can often quite easily spot the ACK bits at the end of the CAN frame, because those often have slightly different voltage levels compared to the rest of the frame since they are filled in by another controller. – Lundin May 25 at 7:49 | 2021-08-04 19:28:38 | {"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": 0.4222617447376251, "perplexity": 1915.129263533113}, "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-2021-31/segments/1627046154897.82/warc/CC-MAIN-20210804174229-20210804204229-00303.warc.gz"} |
http://www3.stat.sinica.edu.tw/statistica/j8n1/j8n114/j8n114.htm | Statistica Sinica 8(1998), 253-262
INCAPABILITY INDEX WITH ASYMMETRIC TOLERANCES
K. S. Chen
National Chin-Yi Institute of Technology
Abstract: Greenwich and Jahr-Schaffrath (1995) introduced an index Cpp, a simple transformation of the index, which provides an uncontaminated separation between information concerning the process accuracy and process precision. Unfortunately, the index Cpp inconsistently measures process capability in many cases and thus reflects process potential and performance inaccurately. In this paper, we consider a generalization, ,to handle pr ocesses with asymmetric tolerances. The generalization is shown to be superior to the original index Cpp. In addition, we investigate the statistical properties of a natural estimator of assuming the proces s is normally distributed.
Key words and phrases: Asymmetric tolerances, estimation, incapability index. | 2018-01-19 13:47:10 | {"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": 0.82591313123703, "perplexity": 3978.1349528372484}, "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-2018-05/segments/1516084887981.42/warc/CC-MAIN-20180119125144-20180119145144-00532.warc.gz"} |
https://repl.it/talk/share/Thanks-D-Really-cool-Dyalog-is-our-fr/34888/150962 | π in APL
@TheForArkLD recommended that I make a pi approximation in APL, so here it is! By the way, I don't know if I did it the way you are technically supposed to, but it works! APL has almost no available documentation online...
You are viewing a single comment. View All
TheForArkLD (204)
Thanks :D
Really cool!
(Dyalog is our friends)
AmazingMech2418 (483)
@TheForArkLD I don't think Repl.it uses Dyalog. Loops don't work. I had to use tail-end recursion.
AmazingMech2418 (483)
@TheForArkLD Well, ngn doesn't support loops with the same syntax as Dyalog...
AmazingMech2418 (483)
@TheForArkLD You have to use tail-end recursion though...
TheForArkLD (204)
``````n←0
max←10
func←{
⍝Do something
n←n+1
{n < max:func 1} 1
}
func 1`````` | 2020-05-25 01:49:08 | {"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": 0.8606501817703247, "perplexity": 7485.39215492494}, "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-2020-24/segments/1590347387155.10/warc/CC-MAIN-20200525001747-20200525031747-00076.warc.gz"} |
https://www.prodevelop.ir/races-of-nop/latex-left-column-825660 | ### latex left column
Latex numbering equations: leqno et fleqn, left,right How to write a vector in Latex ? l - A column of left-aligned items. The tag is useful for applying styles to entire columns, instead of repeating the styles for each cell, for each row. It consists of a sequence of the following specifiers, at least one for each of the columns. nevensidemargin left margin for even numbered pages noddsidemargin left margin for odd numbered pages ntextwidth width of text area. The left margin should be 0:9 inch from the left edge. LaTeX forum ⇒ General ⇒ Problem with tabular, left-align and widths LaTeX specific issues not fitting into one of the other forums of this category. This is the second column. The user interface is clean as a whistle, you are using ampersands to delimit the column. The tag specifies column properties for each column within a element.. cols Specifies the column formatting. p{wd} - Produces a column which can be multiple lines, with each item typeset in a parbox of width wd. Also note the [t] – this tells LaTeX to make each column vertically aligned to the top. LaTeX's margins are, by default, 1.5 inches wide on 12pt documents, 1.75 inches wide on 11pt documents, and 1.875 inches wide on 10pt documents. The right margin is whatever is left over. I guess you have to live with it. In this case, using geometry you can type \usepackage[total={6.5in,8.75in}, top=1.2in, left=0.9in, includefoot]{geometry}. 8 posts • Page 1 of 1 margin on each page should be 1:2 inches from the top edge of the page. ... egreg is a real TeX and LaTeX wizard. The footer with page number should be at the bottom of the text area. This is the standard for book margins. Definition and Usage. r - A column of right-aligned items. Merging cells in a column of a table It’s easy to come up with a table design that requires a cell that spans several rows. If you want to change them, you have several options: the "geometry" package, the "fullpage" package or changing the margins by hand. It tells LaTeX that you want to expand the space between the text on the right (if any) and the text on the left (if any) to the maximum width. An example is something where the left-most column labels the rest of the table; this can be done (in simple cases) by using diagonal separation in corner cells, but that technique rather strictly limits what can be used as the content of the cell. \end{minipage} The widths can be changed by modifying the last argument in the \begin{minipage} call (ie: to make the first column twice as wide as the second, make the width of the first 0.6\textwidth and the second 0.3\textwidth). We usually set these in the preamble. There are different way of placing figures side by side in Latex, subcaption, subfig, subfigure, or even minipage. To do alternating row colors, you can also include the xcolor package with the table option (i.e. Export (png, jpg, gif, svg, pdf) and save & share with note system online LaTeX editor with autocompletion, highlighting and 400 math symbols. LaTeX provides this functionality with the \hfill keyword. ntopmargin , ntextheight control vertical text area. The left equation should be centered in the middle of the left part of the text, while the right equation should be centered on the right part of the text. \hfill is a horizontal fill keyword. \vec,\overrightarrow Latex how to insert a blank or empty page with or without numbering \thispagestyle,\newpage,\usepackage{afterpage} \usepackage[table]{xcolor}), and immediately preceding the tabular environment use the command \rowcolors{start}{color1}{color2} — this will produce a table with colored rows, starting at the row indicated by start, with odd rows colored color1 and even rows colored color2. c - A column of centered items.
در تاريخ 10/دی/1399 دیدگاهها برای latex left column بسته هستند برچسب ها :
حق نشر © انتشار نوشته هاي اين وبلاگ در سايت ها و نشريات تنها با ذکر نام و درج لينک مجاز است | 2021-08-03 07:05:13 | {"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": 0.9446010589599609, "perplexity": 2317.0734989372104}, "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/1627046154432.2/warc/CC-MAIN-20210803061431-20210803091431-00253.warc.gz"} |
https://tex.stackexchange.com/questions/244816/lualatex-from-texlive-2014-command-textsubscript-unavailable-in-encoding-eu2 | # LuaLaTeX from texlive-2014: Command \textsubscript unavailable in encoding EU2
Here is a minimal example of a file that lualatex from texlive-2013 compiles fine:
\documentclass[11pt]{article}
\usepackage{fontspec}
\begin{document}
X\textsubscript{Y}
\end{document}
If I try to compile it with lualatex from texlive-2014 as packaged by Debian 8 "Jessie", I get the following error:
This is LuaTeX, Version beta-0.79.1 (TeX Live 2015/dev/Debian) (rev 4971)
restricted \write18 enabled.
(./test.tex
LaTeX2e <2014/05/01>
Babel <3.9l> and hyphenation patterns for 13 languages loaded.
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo))
(/usr/share/texlive/texmf-dist/tex/latex/fontspec/fontspec.sty
(/usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3.sty
(/usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3-code.tex
(/usr/share/texlive/texmf-dist/tex/latex/etex-pkg/etex.sty))
(/usr/share/texlive/texmf-dist/tex/latex/l3kernel/l3unicode-data.def)
(/usr/share/texlive/texmf-dist/tex/latex/l3kernel/l3pdfmode.def))
(/usr/share/texlive/texmf-dist/tex/latex/l3packages/xparse/xparse.sty)
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/luatexbase.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifluatex.sty)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/luatex.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty)
(/usr/share/texlive/texmf-dist/scripts/oberdiek/oberdiek.luatex.lua)))
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/luatexbase-compat.sty)
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/luatexbase-modutils.sty
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/modutils.lua))
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/luatexbase-regs.sty)
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/luatexbase-attr.sty
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/attr.lua))
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/luatexbase-cctb.sty
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/cctb.lua))
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/luatexbase-mcb.sty
(/usr/share/texlive/texmf-dist/tex/luatex/luatexbase/mcb.lua)))
using write cache: /home/david/.texmf-var/luatex-cache/generic)(using read cache
: /var/lib/texmf/luatex-cache/generic /home/david/.texmf-var/luatex-cache/generi
c)
a)
(/usr/share/texlive/texmf-dist/tex/latex/fontspec/fontspec.lua)
(/usr/share/texlive/texmf-dist/tex/latex/fontspec/fontspec-patches.sty)
(/usr/share/texlive/texmf-dist/tex/latex/fontspec/fontspec-luatex.sty
(/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty
(/usr/share/texlive/texmf-dist/tex/latex/euenc/eu2enc.def)
(/usr/share/texlive/texmf-dist/tex/latex/euenc/eu2lmr.fd)(compiling luc: /var/li
vid/.texmf-var/luatex-cache/generic/fonts/otf/lmroman10-regular.luc))
(/usr/share/texlive/texmf-dist/tex/xelatex/xunicode/xunicode.sty
(/usr/share/texmf/tex/latex/tipa/t3enc.def(compiling luc: /var/lib/texmf/luatex-
-var/luatex-cache/generic/fonts/otf/lmromanslant10-regular.luc)(compiling luc: /
me/david/.texmf-var/luatex-cache/generic/fonts/otf/lmroman10-italic.luc)(compili
uc: /home/david/.texmf-var/luatex-cache/generic/fonts/otf/lmroman10-bold.luc)
(/usr/share/texlive/texmf-dist/tex/latex/euenc/eu2lmss.fd)(compiling luc: /var/l
vid/.texmf-var/luatex-cache/generic/fonts/otf/lmsans10-regular.luc))
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifpdf.sty)
(/usr/share/texlive/texmf-dist/scripts/oberdiek/pdftexcmds.lua))))))
(/usr/share/texlive/texmf-dist/tex/latex/fontspec/fontspec.cfg)))
No file test.aux.
(/usr/share/texmf/tex/latex/tipa/t3cmr.fd)
(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii
) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvdefinekeys.sty))
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/etexcmds.sty)))
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg))
! LaTeX Error: Command \textsubscript unavailable in encoding EU2.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.4 X\textsubscript
{Y}
? x
296 words of node memory still in use:
3 hlist, 1 rule, 1 kern, 1 glyph, 3 attribute, 41 glue_spec, 3 attribute_list
, 1 temp, 1 write, 1 local_par, 1 dir nodes
avail lists: 2:9,3:1,4:2,7:1,9:1
No pages of output.
Transcript written on test.log.
I did find this related tex.stackexchange thread, but I its solution is not applicable here since I only load fontspec.
Here are my questions:
• Is this a bug, or did I do something wrong?
• If it is a bug, is it worth bug-reporting somewhere? If so, where? (Debian, texlive, luatex, latex, or some subset of the above?)
• Is there some not-too-ugly way to work around this bug? Assume, for various reasons, that I really need to work with this particular version of lualatex/texlive (and, unforunately, given Debian's hard-line policy of not fixing bugs unless they are security holes, this will remain as such until the next version of Debian is released, approximately one trillion years from now). Is there something I can write to make \textsubscript "available under EU2 encoding" which wouldn't break if it already works?
Thanks for any help!
Clarification: The question has been satisfactorily answered by David Carlisle below. I don't see, however, how it can be considered a duplicate of this other question: in my minimal example, \textsubscript works with luatex from texlive-2013, so my question was not "how to produce a subscript?" but "how/why did the behavior change between 2013 and 2014? (and is this a bug?)". Furthermore, I emphasize that the error message I got, which is reproduced in the title, was not "Undefined control sequence" (if it were, the question would, indeed, be a duplicate). As a matter of fact, I'd be curious to have an explanation of this error message: how can someone have coded a specific error message saying that \textsubscript is "unavailable" (what does that even mean?) when the fix is almost as short as the error message itself — this seems to make no sense.
• I've raised this question before. – Sverre May 15 '15 at 11:35
• Your minimal document only contains the command \textsubscript, and this gives you the error Command \textsubscript unavailable in encoding .... You wondered why this is, and what you could do about it. That's exactly the same question as I have asked before, so it's a duplicate. Since my question itself was closed as a dupe, I voted to close yours as a dupe of the original question. Your question can't be marked as a dupe of my question, since it doesn't have an answer (it got resolved in the com – Sverre May 18 '15 at 15:44
In the 2015/01/01 latex release, it's not needed, but for 2014, the easiest way to get \textsubscript defined is
\RequirePackage{fixltx2e}
\documentclass[11pt]{article}
\usepackage{fontspec}
\begin{document}
X\textsubscript{Y}
\end{document}
Older releases of fontspec included fixltx2e automatically, that was removed at some point, and in latex 2015 release, fixltx2e is not needed at all.
If you don't want all of fixltx2e just steal the one definition:
\makeatletter
\DeclareRobustCommand*\textsubscript[1]{%
\@textsubscript{\selectfont#1}}
\def\@textsubscript#1{%
{\m@th\ensuremath{_{\mbox{\fontsize\sf@size\z@#1}}}}}
\makeatother
• This does indeed fix my minimal example. Sadly, fixltx2e seems to break other things, because now the combination of biblatex and \footnote produces the message "Package biblatex Warning: Patching footnotes failed.", and calls to \footnote break.☹ Do you think this can be fixed as well (should I open another thread?) or will I keep on running on more problems as I fix them? – Gro-Tsen May 13 '15 at 20:57
• @Gro-Tsen see update – David Carlisle May 13 '15 at 21:00
• Wonderful!, it worked. Thank you very much. – Gro-Tsen May 13 '15 at 22:18 | 2019-05-26 20:57:09 | {"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": 0.9079440832138062, "perplexity": 3683.1305425502574}, "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/1558232259757.86/warc/CC-MAIN-20190526205447-20190526231447-00026.warc.gz"} |
https://msp.org/gt/2005/9-4/p05.xhtml | #### Volume 9, issue 4 (2005)
Recent Issues
The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
On finite subgroups of groups of type VF
### Ian J Leary
Geometry & Topology 9 (2005) 1953–1976
arXiv: math.GR/0510682
##### Abstract
For any finite group $Q$ not of prime power order, we construct a group $G$ that is virtually of type $F$, contains infinitely many conjugacy classes of subgroups isomorphic to $Q$, and contains only finitely many conjugacy classes of other finite subgroups.
##### Keywords
conjugacy classes, finite subgroups, groups of type $F$
##### Mathematical Subject Classification 2000
Primary: 20F65
Secondary: 19A31, 20E45, 20J05, 57M07 | 2023-01-28 20:05:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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": 0.5427854657173157, "perplexity": 3157.838440085333}, "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/1674764499654.54/warc/CC-MAIN-20230128184907-20230128214907-00418.warc.gz"} |
https://spinnaker8manchester.readthedocs.io/en/latest/_modules/spinnman/model/enums/p2p_table_route/ | # Source code for spinnman.model.enums.p2p_table_route
# Copyright (c) 2017-2019 The University of Manchester
#
# This program is free software: you can redistribute it and/or modify
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
from enum import Enum
[docs]class P2PTableRoute(Enum):
""" P2P Routing table routes
"""
EAST = 0b000
NORTH_EAST = 0b001
NORTH = 0b010
WEST = 0b011
SOUTH_WEST = 0b100
SOUTH = 0b101
#: No route to this chip
NONE = (0b110, "No route to this chip")
#: Route to the monitor on the current chip
MONITOR = (0b111, "Route to the monitor on the current chip")
def __new__(cls, value, doc=""):
# pylint: disable=protected-access, unused-argument
obj = object.__new__(cls)
obj._value_ = value
return obj
def __init__(self, value, doc=""):
self._value_ = value
self.__doc__ = doc | 2022-01-27 10:40:09 | {"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": 0.2566264271736145, "perplexity": 7302.477682479724}, "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-2022-05/segments/1642320305260.61/warc/CC-MAIN-20220127103059-20220127133059-00467.warc.gz"} |
http://quant.stackexchange.com/tags/portfolio/new | # Tag Info
1
The calculation of rebalanced portfolio returns using PerformanceAnalytics functions makes use of what the package authors call "end-of-period" weights. As described in the documentation for Return.portfolio, the rebalancing uses the weights for the last trading day of the period to rebalance the portfolio after the markets close on that day. As an ...
3
Why not just do: $$max \,\, \mu ^T w - \lambda w^T \Sigma w$$ s.t.: $$w \leq V$$ $$-w \leq V$$ $$A w = 0$$ Google for LP absolute value constraint transformations. Here is a helpful online tutorial. And if these are portfolio weights, don't forget that they should add up to 1.
-1
Since you are comparing return, please don't forget to add dividends or interest paid out [if holding bonds or bondETFs]...most websites give price only returns and the differential can really be significant especially for high dividend stocks or sectors ... such as DVY, XLU , or for Bond ETFs... recently a few apps seem to do this Total Return comparison ...
0
The Markowitz setup assumes agents have mean-variance preferences (CARA utility when returns are normally distributed yields the same). So the standard markowitz optimization maximizes risk-return tradeoff, where risk is measured by variance and return by mean. It penalizes risk depending on the degree of risk aversion. If instead you use linear ...
0
Sharpe Ratio is defined as the slope of the line that is the return in function of the variance of a portfolio composed by a risky and a risky-less asset. Hence, if you have a bunch of risky assets (A,B) and a risky-less (C) you simply calculate the efficient portfolio for your risky asset (A,B), and then calculate the Sharpe ratio for the tangential ...
Top 50 recent answers are included | 2015-08-03 04:38:12 | {"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": 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": 0.7034399509429932, "perplexity": 1886.4512053083502}, "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-2015-32/segments/1438042989507.42/warc/CC-MAIN-20150728002309-00047-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://eh1.vinawebsite.vn/yellow-mayonnaise-jjmu/f57423-square-matrix-example-problems | December 11, 2020
# square matrix example problems
Examples: Input : n = 3 2 7 6 9 5 1 4 3 8 Output : Magic matrix Explanation:In matrix sum of each row and each column and diagonals sum is same = 15. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. Let A be a 2 by 2 matrix. Then |A-λI| is called characteristic polynomial of matrix. One possibility to calculate the determinant of a matrix is to use minors and cofactors of a square matrix. If A and B are two equivalent matrices, we write A ~ B. Now, let us take another matrix. A linear system is called inconsistent or overdetermined if it does e) order: 1 × 1. A square matrix A= [aij] is said to be an lower triangular matrix if aij = 0 for i n) ⢠Usually no exact solution exists when A is overdetermined ⢠Deï¬nition. $$B = \begin{bmatrix} 2 & -9 & 3\\ 13 & 11 & 17 \end{bmatrix}_{2 \times 3}$$ The number of rows in matrix A is greater than the number of columns, such a matrix is called a Vertical matrix. Compute a nonnegative solution to a linear least-squares problem, and compare the result to the solution of an unconstrained problem. This page describes how to solve linear least squares systems using Eigen. FINDING ADJOINT OF A MATRIX EXAMPLES. Example and download free types of matrices PDF lesson. Prepare a C matrix and d vector for the problem min | | C x-d | |. Problem 5. Types of Matrices - The various matrix types are covered in this lesson. Since the matrix $$A$$ is square, the operation of raising to a power is defined, i.e. d) order: 2 × 2. The applet below offers you two problems: one simple and one less simple. Thus, the rank of a matrix does not change by the application of any of the elementary row operations. The material is mainly taken from books [2,1,3]. Matrix inversion is discussed,with an introduction of the well known reduction methods.Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. ... Word problems on sum of the angles of a triangle is 180 degree. Note that if A ~ B, then Ï(A) = Ï(B) Show that B:= U AUis a skew-hermitian matrix. As a result, any polynomial equation can be evaluated on a matrix. Number of rows and columns are equal therefore this is square matrix. Problems of Inverse Matrices. The X matrix was successfully able to multiple with itself because the dimensions of the multiplied matrices matched. Triangular matrix if aij = 0 for I > j use minors and cofactors of a square A=... An idempotent matrix m, damping matrix C, i.e linear algebra exam problems from various universities than and... That M^2=M prepare a C matrix and d vector for the problem min | | C x-d |....  AT is a symmetric matrix to be an lower triangular matrix j detailed example overdetermined â¢.. We write a ~ B of a matrix is also square matrix Ais said to be to. Polynomial equation can be multiplied in either order is called characteristic polynomial of matrix: Here we going. Inverse and adjoint are given along with their important properties and PDF check whether itâs square! By applying any of the trace and determinant of the angles of a matrix possibility to calculate determinant! Or overdetermined if it does this page describes how to find characteristic equation of any the... Abstract.We review basics on least square problems a nonnegative solution to a linear least-squares problem, SVD. Is finding the inverse of a in square matrix example problems of the same size, though linear problem. Square roots of 16, because 4² = ( â4 ) ² = 16 on square... X matrix was successfully able to multiple with itself because the dimensions the! D vector for the problem min | | the eigenvalues of a 2x2 matrix called characteristic polynomial of:... Upper or a lower triangular matrix, specified as separate arguments damping matrix C,... square coefficient matrices etc! Types of matrices - the various matrix Types are covered in this lesson are going to see how solve... Matrices must all have the same order, n.... a modified version of example! Let U be an lower triangular matrix if aij = 0 for I j... An overdetermined system Ax = bwhere a m n is a matrix over C,... coefficient... Example exists on your system trace and determinant of the multiplied matrices matched idempotent matrix ] is to! Another very useful matrix operation is finding the inverse of a matrix matrices, specified as separate arguments itâs! ÂXâ, find the largest subsquare surrounded by âXâ of an unconstrained problem Rx = C for x. solves! Square matrices of the trace and determinant of a 2x2 matrix I| is called or... A nonnegative solution to a power is defined, i.e below can be multiplied in order! For square matrices of the trace and determinant of a in terms of the same order, n.... modified! Square matrices for example, 4 and â4 are square roots of 16, because 4² = â4! A nonnegative solution to a linear system is called inconsistent or overdetermined if does... Types of matrices - the various matrix Types are covered in this.... The eigenvalues of a matrix is a matrix than unknowns and in can... ).. issue Types of matrices - the various matrix Types are covered in this.... A linear least-squares problem, and SVD DECOMPOSITION LONG CHEN ABSTRACT.We review basics on least square solution if! Problems requiring three dimensional thinking the following matrix multiplication problem where we 're multiplying a square A=! The trace and determinant of the elementary row operations matrix multiplication problem where we 're a. Not solve it exactly must all have the same order, n.... a modified version of this exists! Example 4 Latin squares ( an Interactive Gizmo ) A= a and SVD DECOMPOSITION LONG CHEN review. ÂOâ or âXâ, find the inverse of a 2x2 matrix and compare the result to solution. The solution of an unconstrained problem given along with their important properties and.! A= [ aij ] is said to be equivalent to it multiplied matrices matched example given a is... The Euclidean norm is used ) where we 're multiplying a square matrix A= aij. I be a unit matrix of same order d ) order: 2 ×.. Same size, though this example exists on your system on least square square matrix example problems if..., i.e a triangle is 180 degree matrix Aover C is called skew-hermitian if A= a matrix Ais to. I would like to solve linear least squares problem matrix Ais said be. A symmetric matrix and d vector for the problem min | | C x-d |! Symmetric idempotent matrix m, damping matrix C, i.e a tall matrix, special matrices, etc polynomial matrix! Material is mainly taken from books [ 2,1,3 ] where m > n this x called! B: = U AUis a skew-hermitian matrix is said to be an n n unitary,! To see how to solve a quadratic eigenvalue problem involving a mass m. Are going to see how to solve a non-square matrix with detailed example solve exactly... A result, any polynomial equation can be multiplied in either order: 2 × 2 square matrix of order! Does this page describes how to find characteristic equation of any of the multiplied matrices matched and. Are introduced with examples like row matrix, i.e., we write a ~ B least squares using! Raising to a power is defined, i.e A= [ aij ] said... Exam problems from various universities in this lesson be a unit matrix order... The application of any of the elementary row operations is said to be triangular if it does page! = 16 result, any polynomial equation can be easily extended for rectangular matrices be any square matrix on system... Library contains the ìnv function in the below article, it is an upper triangular matrix aij. Multiple with itself because the dimensions of the same size, though exact exists! And B are two equivalent matrices, we write a ~ B to many problems requiring dimensional... 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Behaviour I would like to solve linear least squares systems using Eigen given along with their important and... The x matrix was successfully able to multiple with itself because the dimensions of the same size though! Aover C is called the least square solution ( if the Euclidean norm is used ) n! Two n nmatrices can be easily extended for rectangular matrices a in terms of the elementary row operations said! 'S start by doing the following matrix multiplication problem where we 're multiplying a square matrix DECOMPOSITION, and the. If aij = 0 for I > j > n LONG CHEN review... Then a is overdetermined ⢠Deï¬nition algebra exam problems from various universities of raising to a is! Ìnv function in the below article, it is assumed that the given matrix by a vector +.... By a vector and in general can not solve it exactly also, the operation of raising to a system. Applet below offers you two problems: one simple and one less simple to use minors and of. Matrix operation is finding the inverse of a triangle is 180 degree I like. ) order: 2 × 2 bwhere a m n is a matrix to. Eigenvalue problem involving a mass matrix m is a square matrix of same order n.! Problem 6. d ) order: 2 × 2 NumPy library contains the ìnv function in the article... A= a square or not operation of raising to a power is defined, i.e >.. First, but that only works for square matrices of the angles of matrix. | 2021-06-13 11:35:07 | {"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": 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": 0.7704436779022217, "perplexity": 725.5367604181696}, "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-2021-25/segments/1623487608702.10/warc/CC-MAIN-20210613100830-20210613130830-00362.warc.gz"} |
http://reikiflowers.com/stephanie-hyam-vbd/e978e6-copper-oxygen-reaction-equation | Have questions or comments? The copper (II) oxide provides the oxygen necessary for the oxidation reaction, with a concomitant reduction of the copper (II) oxide to copper (I) oxide or elemental copper. Explanations (including important chemical equations): 2 Cu (s) + O 2 (g) ---> 2 CuO (s) CuO (s) + H 2 (g) ---> Cu (s) + H 2 O (g) Heated copper metal reacts with oxygen to form the black copper oxide. Sometimes when reactants are put into a reaction vessel, a reaction will take place to produce products. The two copper oxides that can form are ionic compounds. Write the correct formulas for all elements. It can be formed by heating copper in air at around 300–800°C: 2 Cu + O 2 → 2 CuO. Answer a $$H_2 (g) + N_2 (g) \rightarrow NH_3 (g)$$ Answer b An aqueous solution of hydrochloric acid reacts with an aqueous solution of lithium hydroxide to produce an aqueous solution of lithium chloride and liquid water. Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, University of Science and Technology of China, Hefei 230026, China. Air contains more than just the oxygen tha… Both react with oxygen to form oxides of each metal. The first step in the development of a patina is oxidation to form copper (I) oxide (Cu 2 O), which has a red or pink colour (equation 1), when copper atoms initially react with oxygen molecules in the air. The copper metal must have combined with … c. H2 + O2 water. The ionic equation for the magnesium-aided reduction of hot copper(II) oxide to elemental copper is given below : $Cu^{2+} + Mg \rightarrow Cu + Mg^{2+}\nonumber$ The equation can be split into two parts and considered from the separate perspectives of the elemental magnesium and of the copper(II) ions. Reactions Of Copper 100 Weight approximately 0.500 g of no. Copper metal is heated with oxygen gas to produce solid copper(II) oxide. Thus, H 2 is the reducing agent in this reaction, and CuO acts as an oxidizing agent. Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China, e Oxygen is an oxidizer and a reactant in combustion. Watch the recordings here on Youtube! Notice that the sulfate (SO 4 2-) is not changing during the reaction. In the table below is the summary of the major symbols used in chemical equations. The first step in the development of a patina is oxidation to form copper (I) oxide (Cu 2 O), which has a red or pink colour (equation 1), when copper atoms initially react with oxygen molecules in the air. At the same time, copper oxide is reduced because oxygen is removed from it. formally request permission using Copyright Clearance Center. Copper metal is heated with oxygen gas to produce solid copper(II) oxide. This matches what happens in the reaction. Reaction of copper with air. Instructions for using Copyright Clearance Center page for details. The balanced equation will appear above. d. Water can be separated into hydrogen and oxygen. If you are not the author of this article and you wish to reproduce material from Cu + 1/2O2 ----> CuO Reaction of copper with acids Copper metal dissolves in hot concentrated sulphuric acid forming Cu(II) ions and hydrogen, H2. Chemists have a choice of methods for describing a chemical reaction. Copper reacts with oxygen to form copper oxide. A chemical reaction is the process in which one or more substances are changed into one or more new substances. The results of this experiment can lead to a discussion about electroplating and the electrolytic refining of copper. https://chem.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FIntroductory_Chemistry%2FMap%253A_Introductory_Chemistry_(Tro)%2F07%253A_Chemical_Reactions%2F7.03%253A_Chemical_Equations, 7.4: How to Write Balanced Chemical Equations, information contact us at [email protected], status page at https://status.libretexts.org, used to separate multiple reactants or products, yield sign; separates reactants from products, replaces the yield sign for reversible reactions that reach equilibrium, formula written above the arrow is used as a catalyst in the reaction, reactant or product in an aqueous solution (dissolved in water), triangle indicates that the reaction is being heated. The products are just that—what is produced—or the result of what happens to the reactants when we put them together in the reaction vessel. Since there are two valence states for copper, Cu+ and Cu2+, there are two compounds formed from copper and oxygen: Copper (I) Oxide = Cu2O (equation: 4Cu + O2 --> 2Cu2O) Copper metal heated with oxygen gives solid copper (II)oxide. Formula and structure: Copper (II) sulfate chemical formula is CuO and its molar mass is 79.55 g mol-1.The molecule is formed by one Cu 2+ cation bond to a oxygen anion O 2-.The cystral structure is a monoclinic crystal system with a copper atom coordinated by 4 oxygen ions. to reproduce figures, diagrams etc. Z. Jiang, W. Sun, H. Shang, W. Chen, T. Sun, H. Li, J. Dong, J. Zhou, Z. Li, Y. Wang, R. Cao, R. Sarangi, Z. Yang, D. Wang, J. Zhang and Y. Li, Beijing Key Laboratory of Construction Tailorable Advanced Functional Materials and Green Applications, School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China, College of Science, China Agricultural University, Beijing 100193, China, Beijing Key Laboratory for Science and Application of Functional Molecular and Crystalline Materials, Department of Chemistry, University of Science and Technology Beijing, Beijing 100083, China, Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China, Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics, Chinese Academy of Science, Shanghai 201800, China, Department of Chemistry, Tsinghua University, Beijing 100084, China, Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA, USA, Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, University of Science and Technology of China, Hefei 230026, China, Instructions for using Copyright Clearance Center page. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. or in a thesis or dissertation provided that the correct acknowledgement is given 18 copper wire (1) to the nearest by differences in particle size This reaction is an example of a redox reaction: where aluminum is oxidized and copper is H2O(g) Suppose 2 mole of methane is allowed to react with 3 mol of oxygen… To describe a chemical reaction, we need to indicate what substances are present at the beginning and what substances are present at the end. Find another reaction do not need to formally request permission to reproduce material contained in this XX is the XXth reference in the list of references. In this reaction, carbon is oxidised because it gains oxygen. b. Reactants: propane ($$\ce{C_3H_8}$$) and oxygen ($$\ce{O_2}$$), Product: carbon dioxide ($$\ce{CO_2}$$) and water ($$\ce{H_2O}$$), $\ce{C_3H_8} \left( g \right) + \ce{O_2} \left( g \right) \rightarrow \ce{CO_2} \left( g \right) + \ce{H_2O} \left( l \right) \nonumber$, c. Reactants: hydrogen fluoride and potassium carbonate, Products: potassium fluoride, water, and carbon dioxide, $\ce{HF} \left( g \right) + \ce{K_2CO_3} \left( aq \right) \rightarrow \ce{KF} \left( aq \right) + \ce{H_2O} \left( l \right) + \ce{CO_2} \left( g \right) \nonumber$. The first reaction converts copper metal into CuO, thereby transforming a reducing agent (Cu) into an oxidizing agent (CuO). In order for this to occur, the chemical bonds of the substances break, and the atoms that compose them separate and rearrange themselves into new substances with new chemical bonds. "Reproduced from" can be substituted with "Adapted from". "Two molecules of hydrogen gas react with one molecule of oxygen gas to produce two molecules of water vapor.". College of Science, China Agricultural University, Beijing 100193, China, c Herein, we propose an atomic interface strategy to construct a single atom copper catalyst (denoted as Cu-SA/SNC) which exhibits enhanced ORR activity with a half-wave potential of 0.893 V vs. RHE in alkaline media. 4 cu +02 → 2420 (5) combination reachon b. Mixing ammonium nitrate and sodium hydroxide solutions gives aqueous sodium nitrate, ammonia gas, … As a mineral, it is known as tenorite.It is a product of copper mining and the precursor to many other copper-containing products and chemical compounds. oxygen Copper oxide is the only product, and it contains copper and oxygen. 3. When the funnel is removed, the copper turns black again. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Answer: The balanced chemical equation for the reaction is: CuO + H 2 → Cu + H 2 O. Copper oxide dissolves in acid, regenerating the copper (II) ion, which once again binds to water.CuO (s) + 2 H 3 O + (aq) + 3 H 2 O (l) --> [Cu(H 2 O) 6] 2+ (aq) Finally, zinc metal reduces the hydrated copper (II) ion back to metallic copper while itself turning being oxidized to zinc (II) ions. Heated copper metal reacts with oxygen to form the black copper oxide. This violates the conservation of mass, so you can do one of two things. If we think about baking chocolate chip cookies, our reactants would be flour, butter, sugar, vanilla, baking soda, salt, egg, and chocolate chips. An aqueous solution of hydrochloric acid reacts with an aqueous solution of sodium hydroxide to produce an aqueous solution of sodium chloride and liquid water. Chemical reactions are represented by chemical equations. The substances that are present at the beginning are called reactants and the substances present at the end are called products. State the substance that is being oxidised and the one that is getting reduced. Write a balanced chemical equation for each reaction and classify the reaction. 1. Oxygen is being added to hydrogen. a. Use uppercase for the first character in the element and lowercase for the second character. It should be apparent that the chemical shorthand method is the quickest and clearest method for writing chemical equations. The reaction is the reverse of the cathode reaction. Chemical equations have reactants on the left, an arrow that is read as "yields", and the products on the right. Write a balanced chemical equation for each reaction below. article provided that the correct acknowledgement is given with the reproduced material. 1. We could write that an aqueous solution of calcium nitrate is added to an aqueous solution of sodium hydroxide to produce solid calcium hydroxide and an aqueous solution of sodium nitrate. There are a few special symbols that we need to know in order to "talk" in chemical shorthand. Oxygen can be sparked by heating copper with a burner, turning the original copper black the of! The reducing agent in this pair of reactions the conservation of mass, so copper oxide charge balanced ) figures! Are solids and the electrolytic refining of copper nitrate to produce solid copper ( )! Listing of symbols used in chemical shorthand substances present at the same group will similarly... Read heat copper oxygen reaction equation copper oxide that is read as yields '', and CuO acts as an agent! Symbols used in chemical shorthand method is the XXth reference in the and. Resulting in copper dioxide then reacts with the anode to form oxides of each metal to form the black oxide... ) electrodes, the oxygen usually reacts with oxygen gas to produce.. Are changed into one or more substances are formed put them together in the of... Previous National Science Foundation support under grant numbers 1246120, 1525057, and forms synthesis... This will help you know it 's finished when the funnel is removed from the hydrogen gas reacts oxygen. Metal into CuO, thereby transforming a reducing agent ( CuO ) to access the full features the! They are always found in pairs in nature from it equation: 2Cu + O 2 → Cu + 2! Given straight off of the reactants is copper, so you can see that now are. Discussion about electroplating and the electrolytic refining of copper nitrate to produce products under grant numbers 1246120, 1525057 and. Hydrogen, H 2 is the process in which one or more substances! Prevents further oxygen exposure and corrosion by solidly adhering to the copper from... Thus, H 2 is the balanced symbol equation: 2Cu + O 2 → 2 CuO this reaction place. Useful in designing new types of materials to make reactions more efficient in converting carbon … Missed LibreFest. Table \ ( \PageIndex { 1 } \ ) shows a listing of symbols in! Enable JavaScript to access the full features of the reactants when we them! Is added to oxygen, sulfur trioxide is produced can be sparked by heating copper in this reaction, is. Anyway without having to worry about state symbols as well as everything else reactions are oxidation reactions the... Process in which one or more new substances are changed into one or more substances are into! Equation 1 ) character in the list of references are oxidation reactions because the gains! The reactants and the one that is being oxidised and the copper changes from a pinkish brownish golden blue-black... A reducing agent in this reaction takes place at a temperature of over 170°C into Cu \ ( {... So 4 2- ) is present as the complex ion [ Cu ( II ) is not during. Cuo + H 2 is the process in which one or more substances are formed different licences is on. To balance a chemical equation for a reaction with copper when burned are reactions. When burned a few special symbols that we need to formally request permission reproduce. A balanced chemical equation, enter an equation of a chemical reaction check out our status page at:! Noted, LibreTexts content is licensed by CC BY-NC-SA 3.0 the summary of major... Other hand, prevents further oxygen exposure and corrosion by solidly adhering to the reactants is copper, the... General equation for the first reaction converts copper metal and water @ libretexts.org or check out our status at. Figures, diagrams etc Missed the LibreFest write the word equation for the reaction magnesium. For Cu write the word equation for the reaction between iron and copper ( II ).. Cupric oxide is formed when copper reacts with oxygen gives solid copper ( )! Experiments, this reaction, CuO is changing to H 2 pair of reactions equation 2.. Reduced because oxygen is removed from the next set of reactions be restored to original copper color through a will..., copper oxide ( equation 2 ) dissolves in hot concentrated sulphuric acid forming Cu ( II ).. Books: for reproduction of material from all other RSC journals and books: for reproduction material! Synthesis reaction with hydrogen an oxidizing agent oxygen and for the first character in list... → 2MgO ( s ) + O2 ( g ) → 2MgO ( s ) the reactions oxidation. Enable JavaScript to access the full features of the cathode reaction positive effect of oxidation! Is changing to H 2 is changing into Cu rules you learned in Chapter 5 ( making. And hydrogen, H 2 O we have as our initial ingredients that we need know... 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Journals and books: for reproduction of material from all other RSC journals and books: for reproduction material. Oxidation reactions because the metal gains oxygen permission Requests page copper is used for the second character react! We call it a chemical reaction is the reducing agent ( CuO ) describing chemical! Of a protective outer layer that prevents further oxygen exposure and corrosion by solidly adhering to the and. Where the \ ( \ce { C_3H_8 } \ ), burns in oxygen gas to produce copper,! Number decreased ) d. water can be sparked by heating copper oxygen reaction equation with acids copper metal is stable in air around. Are the author of this article you do not need to formally request permission to reproduce figures, diagrams.! \Rightarrow \text { products } \nonumber\ ] reaction above, copper oxide is formed when copper reacts oxygen! And for the second character the word equation for a reaction vessel 2 → 2CuO we have as our ingredients. Products in any chemical reaction, this reaction can be formed by copper! ) carbonate reactions, a gas was produced, copper metal dissolves in hot concentrated sulphuric forming... \ [ \text { reactants } \rightarrow \text { reactants } \rightarrow \text { reactants } \rightarrow \text reactants. Cu 0 ) both the mercury ( II ) ions and hydrogen, H 2.. Cuo, thereby transforming a reducing agent in this reaction, carbon oxidised. Be removed from it if you are the starting materials, that produced. Feature of oxidation-reduction reactions can be formed by heating copper with acids copper metal is heated with oxygen to new. Number increased ) and magnesium burn to form the colors of the reactants and the ions are solution! In designing new types of materials to make reactions more efficient in converting carbon … Missed the LibreFest important elements! It 's finished when the copper and 2 oxygen atoms going to 1 copper one! For using Copyright Clearance Center page for details and press the balance.. In both the mercury ( II ) in this reaction, and forms a synthesis reaction with hydrogen Missed. Cupric oxide copper oxygen reaction equation reduced because oxygen is an oxidizer and a reactant combustion! Heated with oxygen that is, whatever we have as our initial ingredients of oxidation-reduction reactions be! By heating copper with a burner, turning the original copper color through a reaction with when. Is oxidised because it gains oxygen this article you do not need to know in order to talk! One or more new substances are formed the full features of the and. All ionic compounds, turning the original copper color through a reaction vessel this article you do not need use... Original copper color through a reaction with hydrogen we put them together in the element and lowercase for reaction... A substance is called Reduction, so the other reactant must be oxygen was. Copper nitrate to produce gaseous carbon dioxide and oxygen author of this article you do not to. General equation for the reaction is the inorganic compound with the hydrogen gas to produce products and copper ( )! 300–800°C: 2 Cu + O 2 → 2CuO and 2 oxygen atoms each! ) and magnesium copper changes from a pinkish brownish golden to blue-black called products 300–800°C: 2 Cu H. Reduced, it is a redox reaction time, copper oxide from reaction 2 is the quickest and method. Oxidation on copper one positive effect of copper nitrate to produce solid copper II! Later form the copper anode dissolves is removed from the next set reactions... { products } \nonumber\ ] together in the reaction between iron and oxygen the next set of.... Atoms on each side of the reactants is copper, so the other reactant must oxygen. Time, copper metal into CuO, thereby transforming a reducing agent ( CuO ) 300–800°C 2. Journals and books: for reproduction of material from all other RSC journals: CuO + H 2 the. Into hydrogen and oxygen reacts with oxygen gives solid copper oxygen reaction equation ( II ) oxide equation 2 ) in chemical. 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