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https://www.greenwood-tools.co.uk/shop/turning-tools/turning-tool-stgcr-l-photo-shows-66268.html
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math
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91 deg Turning Tool
STGCR/L toolholders use the three 60º corners of TCMT inserts, mounted at 91º to the axis of the machine. Where only straight turning is to be done (whether or not to a square shoulder), these are the most economical tools to use. This is because the inserts have 3 edges, giving a lower cost per edge.
Shank sizes 8,10 use Insert Type 4
Shank sizes 12,16 use Insert Type 5
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104576719.83/warc/CC-MAIN-20220705113756-20220705143756-00086.warc.gz
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https://www.arxiv-vanity.com/papers/physics/0212018/
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math
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Finite nuclear size and Lamb shift of -wave atomic states
We consider corrections to the Lamb shift of -wave atomic states due to the finite nuclear size (FNS). In other words, these are radiative corrections to the atomic isotop shift related to FNS. It is shown that the structure of the corrections is qualitatively different from that for s-wave states. The perturbation theory expansion for the relative correction for a -state starts from -term, while for -states it starts from term. Here is the fine structure constant and is the nuclear charge. In the present work we calculate the -terms for -states, the result for -state reads . Even more interesting are -states. In this case the “correction” is by several orders of magnitude larger than the “leading” FNS shift.
pacs:11.30.Er, 31.30.Jv, 32.80.Ys
Experimental and theoretical investigation of the radiative shift (Lamb shift) of energy levels in heavy atoms is an important way to test Quantum Electrodynamics in presence of a strong external electric field. One of the effects related to this problem is a dependence of the Lamb shift on the finite nuclear size (FNS). One can also look at this effect from another point of view. It is well known that there is an isotop shift of atomic levels due to the FNS. The corrections we are talking about are the radiative corrections to the isotop shift.
The corrections for -, -, and -states have been calculated numerically, exactly in , in Refs.Blun92 ; CJS93 ; LPSY . The self-energy and the vertex corrections to the FNS effect for any -wave state have been calculated analytically in order in Refs.Pach93 ; PG . However, the structure of the higher order corrections and, in particular, their logarithmic dependence on the nuclear size has not been understood even for s-states. Our interest to FNS radiative corrections has been stimulated by our work on the radiative corrections to atomic parity nonconcervation Mil . Technically the parity nonconservation effect has some common features with that of the FNS radiative correction: in both cases the effective size of the perturbation source is much smaller than the Compton wavelength . In the paper Mil we have elucidated the structure of higher order in FNS radiative corrections for s-electrons, and have calculated analytically and self-energy and vertex FNS relative radiative corrections. Here is the nuclear radius. In the present work we calculate FNS radiative corrections for p-wave electrons. We demonstrate that the structure of the corrections for p-wave states is very much different from that for the s-wave states. Physically it happens because of different infrared behavior.
Due to the finite nuclear size, the electric potential of the nucleus is different from that for a pointlike nucleus. The deviation is
Throughout the paper we set . The diagram that describe the FNS effect in the leading order is shown in Fig.1(a). The double line corresponds to the exact electron wave function in the Coulomb field, and the zigzag line with cross denotes the perturbation (1).
Diagrams Fig.1(b) and Fig.1(c) correspond to the contributions of the electron self-energy operator and the vertex operator, respectively. The diagram Fig.1(d) describes a modification of (see eq. (1)) due to the vacuum polarization, and the diagram Fig.1(e) corresponds to a modification of the electron wave function due to the polarization of the vacuum by the Coulomb field (Uehling potential).
Technically the most complicated are the self-energy and the vertex FNS (SEVFNS) corrections given by diagrams in Fig.1(b) and Fig.1(c). According to our previous work Mil , the SEVFNS relative correction for an s-wave state is of the form
Here , is the Euler constant, and , as we already mentioned, is the nuclear radius. The total relative SEVFNS correction (2) is the ratio of the sum of diagrams Fig.1(b) and Fig.1(c) divided by the diagram Fig.1(a). Value of is not proportional to the nuclear radius squared because it is a relative quantity. Plot of versus the nuclear charge is shown in Fig.2 by the dashed line. Results of computations of for and states CJS93 are shown by squares and triangles, respectively.
The term in (2) comes from distances , and the term comes from distances . An important point is that there is no contribution that comes from distances . Because of this reason the correction is exactly the same for 1s, 2s, 3s,… states com . Why there is no contribution of larger distances into ? The reason is very simple. In the leading order the correction can be expressed in terms of the forward electron-nucleus scattering amplitude Mil . There is a rigorous QED theorem that claims that there is no an infrared divergence in the forward scattering amplitude, see e.g. Ref. BLP . Therefore, quantum fluctuations from distances cannot contribute to (see also Ref.LYE ). Let us look now at the p-wave SEVFNS correction . From the point of view of the scattering problem it corresponds to scattering at finite angle. The finite-angle scattering amplitude is always infrared divergent. Therefore, one must expect a contribution to from quantum fluctuations at distances . This is the contribution we calculate in the present work.
Formally we assume that . Therefore, at distances dynamics of the electron is described by usual nonrelativistic Coulomb wave functions. However, the nucleus radius is small, . At so small distances, generally speaking, one must use relativistic Dirac wave function even at . The electron Dirac wave function at is of the form
where and are spherical spinors ; for -state, for -state, and for -state ; ; and is a constant known for each particular state, see Ref BLP . For - and -states the upper component of the Dirac spinor (3) is much larger than the lower one. Hence, the upper component determines the FNS shift of such a state. On the other hand, for -state the lower component and hence its contribution to the FNS shift is dominating. A straightforward calculation gives the following values for the FNS shifts of and states (diagram Fig.1(a))
Here and are values of and averaged over charge density of the nucleus. The low-momentum expansion of the nuclear electric form factor is of the form
Modeling the nucleus as a uniformly charged ball one gets
where is the nucleus radius, and is the nucleus mass number. As one should expect the FNS corrections (Finite nuclear size and Lamb shift of -wave atomic states) obey the following inequalities .
Let us calculate now the leading in one loop SEVFNS radiative correction for - and -states. This correction is given by diagrams in Fig.1(b) and Fig.1(c). Since we consider the leading correction, it is sufficient to use the nonrelativistic approximation for electron wave functions (two-component wave functions). It is sufficient also to use the effective FNS perturbation that reproduces FNS correction for s-wave states,
Rest of the calculation is very similar to the textbook calculation of the Lamb shift, see, e.g. Ref. BLP . We introduce the parameter such that . Hence the correction can be represented as a sum of “high frequency” and “low frequency” contributions , where “high” and “low” correspond to frequencies above and below , respectively. In the momentum representation, the effective potential corresponding to the high frequency contribution is of the form BLP
where is momentum transfer, and is the Dirac matrix. Taking the p-wave component of the potential (8) and transferring it to the coordinate representation, we get the following expression for the SEVFNS high frequency correction for a p-wave state
This gives the following values for 2p-states
The contribution of the vacuum polarization, diagram Fig.1(d), can be taken into account in Eqs. (9),(Finite nuclear size and Lamb shift of -wave atomic states) by substitution . The Uehling potential, diagram Fig.1(e), does not contribute in this order.
The low frequency contribution is given by the usual nonrelativistic quantum mechanics expression
Here stays for real part, is frequency of the virtual photon, is the nonrelativistic Hamiltonian, and is the energy of -state. We have also taken into account that interaction with the photon is of the form , where is the vector potential of the photon. The contribution is the same for - and for -state. Using explicit form of 2p wave function, one can represent (11) as
Eigenvalues of are . Therefore, the first impression is that the integrand in Eq. (12) is singular at and . However, the function is orthogonal to the wave function , hence, there is no real singularity at . There is a real singularity at that is related to the possibility of emission of real photons, and this slightly complicates integration in (12). To overcome this technical problem, it is convenient to represent as with . In this form is orthogonal both to and . Then (12) is transformed to
where denotes the electron localized at origin. In this form the matrix element has no singularities. Using explicit expression for the nonrelativistic Coulomb Green’s function Meix
where , , is the gamma-function and is the Whittaker function, and taking the integral over , and then over , we obtain
Combining (Finite nuclear size and Lamb shift of -wave atomic states) and (16), we finally obtain the total SEVFNS radiative corrections (diagrams Fig.1(b) and Fig.1(c)) in the leading order
As one should expect, the result is independent of the parameter . We have already mentioned that to account for the vacuum polarization (the diagram Fig.1(d)) one has to replace . Therefore the total FNS radiative corrections (diagrams Fig.1(b), Fig.1(c), and Fig.1(d)) in the leading order are
Let us have a look now at the relative FNS radiative correction for state. According to Eqs. (Finite nuclear size and Lamb shift of -wave atomic states) and (Finite nuclear size and Lamb shift of -wave atomic states) the relative correction is
For example, for Hydrogen atom the radiative correction is by a factor larger than the “leading” contribution.
As we have already explained, the correction comes from quantum fluctuations at distances . There is also a contribution
that comes from distances , this contribution has been calculated in our previous work Mil . The contribution that comes from has not been calculated yet. Therefore, altogether one gets the following formula for the relative correction :
where is an unknown coefficient. To determine the coefficient , we fit results of numerical calculation of for -state CJS93 . As a result of the fit we find . The correction given by Eq. (Finite nuclear size and Lamb shift of -wave atomic states) is plotted in Fig.2 by the solid line. The results of computations CJS93 are shown by diamonds. Agreement is very good.
Concluding, we have shown that corrections to the Lamb shift of p-wave atomic states due to the finite nuclear size are qualitatively different from that for s-wave states. The difference is related to the infrared behavior of quantum fluctuations. As a result, the leading relative p-wave correction is proportional to while the leading s-wave correction is proportional to . The leading p-wave correction has been calculated analytically.
O.P.S. thanks the Institute for Nuclear Theory at the University of Washington for its hospitality and the Department of Energy for partial support during the completion of this work.
- (1) S. A. Blundell, Phys. Rev. A 46, 3762 (1992).
- (2) K. T. Cheng, W. R. Johnson, and J. Sapirstein, Phys. Rev. A 47, 1817 (1993), see also W. R. Johnson and G. Soff, At. Data Nuc. Data Tables 33, 405 (1985).
- (3) I. Lindgren, H. Persson, S. Salomonson, A. Ynnerman, Phys. Rev. A 47, 4555 (1993).
- (4) K. Pachucki, Phys. Rev. A 48, 120 (1993).
- (5) M. I. Eides , H. Grotch, Phys. Rev. A 56, R2507 (1997).
- (6) A. I. Milstein, O. P. Sushkov and I. S. Terekhov, Phys. Rev. Letters, to appear; hep-ph/0208227.
- (7) Strictly speaking dependence of on the principle quantum number shall appear in higher orders in , but this is a very small effect.
- (8) V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Relativistic quantum theory (Pergamon Press, Oxford, 1982).
- (9) G.P.Lepage, D.R.Yennie, and G.W. Erickson, Phys. Rev. Lett.47, 1640 (1981).
- (10) J. Meixner, Math. Zs. 36, 677 (1933).
- (11) Constant in Eq. (20) is different from that presented in the abstract because value in the abstract includes the vacuum polarization as well.
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| 12,447 | 46 |
https://www.coursehero.com/tutors-problems/Statistics-and-Probability/19290473-discuss-the-descriptive-statistics-used-by-the-authors-Discuss-why-th/
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math
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discuss the descriptive statistics used by the
authors. Discuss why the authors felt the need to discuss these particular descriptive statistics? describe the population included in the research study. Was the population normally distributed? Why or why not?
Recently Asked Questions
- What does skewed to the right histogram means
- A city built a new parking garage in a business district. for a random sample of 64 days, daily fees collected averaged $2,000, with standard deviation of
- A STAT 200 professor took a sample of 10 midterm exam scores from a class of 30 students. The 10 scores are shown below: 95, 67, 76, 47, 85, 70, 87, 80, 67, 72
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CC-MAIN-2019-43
| 650 | 6 |
https://hedeker.people.uic.edu/mix.html
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math
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including mixed-effects linear regression, mixed-effects logistic regression
for nominal or ordinal outcomes, mixed-effects probit regression
for ordinal outcomes, mixed-effects Poisson regression, and mixed-effects
grouped-time survival analysis.These models are also called multilevel
models, hierarchical linear models, random-effects models, and random
coefficients models, to name a few.
The statistical research presented in this website is based on the collaborative effort of Donald Hedeker and Robert D. Gibbons of the University of Illinois at Chicago.
The computer programs were written by Don, with user interfaces designed
and implemented by Discerning
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http://www.docstoc.com/docs/75826208/Importance-of-Working-Capital
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math
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• Working capital typically means the firm’s holding of current or short-term
assets such as cash, receivables, inventory and marketable securities.
• These items are also referred to as circulating capital.
• Corporate executives devote a considerable amount of attention to the
management of working capital.
• Working Capital refers to that part of the firm’s capital, which is required for
financing short-term or current assets such a cash marketable securities,
debtors and inventories. Funds thus, invested in current assets keep
revolving fast and are constantly converted into cash and this cash flow out
again in exchange for other current assets. Working Capital is also known
as revolving or circulating capital or short-term capital.
• There are two concepts of working capital:
• Gross working capital: total of all current assets
• Net working capital: excess of current assets over current liabilities /
difference between current assets and current liabilities
• Working capital, also known as net working capital or NWC, is a financial
metric which represents operating liquidity available to a business.
• Working capital is really what a part of long term finance is locked in and
used for supporting current activities.
• circulating capital means current assets of a company that are changed in
the ordinary course of business from one form to another, as for example,
from cash to inventories, inventories to receivables, receivable to cash.
• Along with fixed assets such as plant and equipment, working capital is
considered a part of operating capital.
• If current assets are less than current liabilities, an entity has a working
capital deficiency, also called a working capital deficit.
• When firms speak of shortage of working capital they in fact possibly imply
scarcity of cash resources.
• The firm has to maintain cash balance to pay the bills as they come due.
• In addition, the company must invest in inventories to fill customer orders
• And finally, the company invests in accounts receivable to extend credit to
• Operating cycle is equal to the length of inventory and receivable
• The size and nature of investment in current assets is a function of different
factors such as type of products manufactured, the length of operating
cycle, the sales level, inventory policies, unexpected demand and
unanticipated delays in obtaining new inventories, credit policies and current
• Working capital management involves the relationship between a firm's short-term
assets and its short-term liabilities.
• Working capital management/short-term financial management is concerned with
decisions relating to current assets and current liabilities.
• The key difference between long-term financial management and working capital
management is in terms of the timing of cash. While long term financial decisions
like buying capital equipment or issuing debentures involve cash flows over an
extended period of time, short term financial decisions typically involve cash flows
within a year or within the operating cycle of the firm.
• The goal of working capital management is to ensure that a firm is able to continue
its operations and that it has sufficient ability to satisfy both maturing short-term debt
and upcoming operational expenses.
• The management of working capital involves managing inventories, accounts
receivable and payable, and cash.
• Characteristics of current assets:
• Short life span
• Swift transformation into other assets forms
TYPES OF WORKING CAPITAL
BASIS OF BASIS OF
Gross Net Permanent Temporary
Working Working / Fixed / Variable
Capital Capital WC WC
Operating cycle of a typical company
• Importance of working capital
– Risk and uncertainty involved in managing the cash flows
– Uncertainty in demand and supply of goods, escalation in cost both
operating and financing costs.
• Strategies to overcome the problem
– Manage working capital investment or financing such as
– Holding additional cash balances beyond expected needs
– Holding a reserve of short term marketable securities
– Arrange for availability of additional short-term borrowing capacity
– One of the ways to address the problem of fixed set-up cost may be to
– One or combination of the above strategies will target the problem
• Working capital cycle is the life-blood of the firm
Difference between permanent & temporary working
Amount Variable Working Capital
Permanent Working Capital
Variable Working Capital
Permanent Working Capital
FACTORS DETERMINING WORKING CAPITAL
• Nature of the Industry
• Demand of Industry
• Cash requirements
• Nature of the Business
• Manufacturing time
• Volume of Sales
• Terms of Purchase and Sales
• Inventory Turnover
• Business Turnover
• Business Cycle
• Current Assets requirements
• Production Cycle
• Credit control
• Inflation or Price level changes
• Profit planning and control
• Repayment ability
• Cash reserves
• Operation efficiency
• Change in Technology
• Firm’s finance and dividend policy
• Attitude towards Risk
• EXCESS OR INADEQUATE WORKING CAPITAL
• Every business concern should have adequate working capital to run its
business operations. It should have neither redundant or excess working
capital nor inadequate or shortage of working capital.
• Both excess as well as shortage of working capital situations are bad for
any business. However, out of the two, inadequacy or shortage of working
capital is more dangerous from the point of view of the firm.
Disadvantages of Redundant or Excess Working Capital
õ Idle funds, non-profitable for business, poor ROI
õ Unnecessary purchasing & accumulation of inventories over required
õ Excessive debtors and defective credit policy, higher incidence of B/D.
õ Overall inefficiency in the organization.
õ When there is excessive working capital, Credit worthiness suffers
õ Due to low rate of return on investments, the market value of shares
Disadvantages or Dangers of Inadequate or Short Working Capital
õ Can’t pay off its short-term liabilities in time.
õ Economies of scale are not possible.
õ Difficult for the firm to exploit favourable market situations
õ Day-to-day liquidity worsens
õ Improper utilization the fixed assets and ROA/ROI falls sharply
Working capital financing
• The short term sources of finance are as follows:
• Trade credit
• Working capital advance by commercial banks
• Public deposits
• Inter-corporate deposits
• Short term loans from financial institutions
• Cash credit
• Hypothecation and pledge
• Bank overdraft
• Commercial paper
• Letter of credit
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s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1387345776833/warc/CC-MAIN-20131218054936-00081-ip-10-33-133-15.ec2.internal.warc.gz
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https://www.stat.math.ethz.ch/pipermail/r-devel/2003-April/026310.html
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math
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[Rd] prop.test confidence intervals (PR#2794)
Peter Dalgaard BSA
p.dalgaard at biostat.ku.dk
Sat Apr 19 00:13:03 MEST 2003
rbaer at kcom.edu writes:
> As an example, I include x=6 and n=42 which has a mean proportion of 0.115.
> When I calculate the 95% CI using the normal approximation by hand (and no
> continuity correction) I get (0.028, 0.202). The exact binomial CI from
> binom.test() is (0.044, 0.234). With correct=FALSE prop.test produces CI95 =
> (0.05396969, 0.22971664) which is neither of these. With correct=TRUE it
> produces (0.04778925, 0.2412937) This seems reasonably like a normal
> approximation 95% CI (which I presume is what is used by prop.test()) of the
> true binomial but I did not actually check it by hand.
> BUG summary. The prop.test() calculation of 95% CI of sample proportions is
> improperly calculated when continuity correction is turned off.
Uhm... Basically, we know the correct answer from binom.test, and R's
intervals are considerably closer to that than the textbook p+-2*se(p)
formula. So R has a bug because it isn't inaccurate enough??
This might enlighten you:
also, consider the case x=0.
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
More information about the R-devel
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950383.8/warc/CC-MAIN-20230402043600-20230402073600-00600.warc.gz
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http://www.wyzant.com/resources/answers/12705/when_a_quadratic_function_is_inversed_to_a_radical_function_why_does_the_radical_function_not_correctly_show_the_reflection_of_the_graph
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math
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since y=x^2 is inverse to y=sqrt(x), it was supposed to reflect on the line y=x, but the radical function did not show the correct reflection of the quadratic graph because it only showed the half on the upper part of the radical graph and did not show the bottom part.
when a quadratic function is inversed to a radical function, why does the radical function not correctly show the reflection of the graph?
Tutors, please sign in to answer this question.
The reason is that the inverse of x2 is NOT a function. But in can be split up into two functions!
we could have y =Sqrt x and y = -sqrt of x.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1404776438008.40/warc/CC-MAIN-20140707234038-00009-ip-10-180-212-248.ec2.internal.warc.gz
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https://feedback.kometsales.com/forums/597808-sales/suggestions/19583803-credit-override-for-units
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math
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Credit Override for Units
Would be great to have the credit limit override function in units. Currently it only functions in boxes, which in my opinion is a design flaw. If a customer has a credit limit of $5000 it shouldn't matter how those invoices are being generated as long as they do not get to over spend.
Daniel Uribe commented
currently ; i understand this to work based on US dollars and NOT UNITEs or NOT boxes; my system overides us dollars and not units or boxes, so if the limit is 5000 k ; and customer is over, the salesperson needs to enter an overide for either 1 dollar/ 10 dollars, 100 dollars or 1 thousand dollars, not boxes or units. do i understand correctly?
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| 683 | 4 |
http://onlinelibrary.wiley.com/doi/10.1029/2003JA010208/full
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math
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4.1. Model Description
The Rice Convection Model (RCM) self-consistently calculates the inner magnetospheric particle distribution, the Region 2 Birkeland currents, and resulting electric field patterns. Magnetic field variations caused by changes in the Region 2 currents and the particle distribution are not presently calculated, but this treatment is presently being developed. The RCM solves the fundamental equation of magnetospheric-ionosphere coupling [Vasyliunas, 1970; Wolf, 1983]
where ∇H is the horizontal gradient in the ionosphere, is a tensor representing the field-line-integrated ionospheric conductance (one hemisphere), Φ is the electric potential in the solar frame with the corotation field removed, I is the magnetic dip angle, Bi and Beq represent the magnetic field strengths in the ionosphere and equatorial plane, eq is the unit vector of the magnetic field direction in the equatorial plane, p is the pressure, and V = ∫ ds/B is the volume of a magnetic flux tube with one unit of magnetic flux.
Assuming strong, elastic pitch-angle scattering, the energy invariant
is conserved, where E is particle energy. The energy spectrum is divided into a discrete set of energy invariants λs. The number of particles per unit magnetic flux of a given energy invariant λs is denoted ηs. Here ηs is called the density invariant and is conserved along a drift path, except for the effects of loss:
where drift,s is bounce-averaged drift velocity and τs is the loss lifetime. Particle sources are neglected in the runs described in this paper. Ion losses are neglected but effects of electron precipitation are included. The ideal monatomic-gas adiabatic invariant pV5/3 is related to the drift invariants by
The drift velocity is given by
This RCM run includes two chemical species, electrons and singly charged ions. Since H+ and O+ ions of given energy drift the same and we are neglecting ion loss, there is no need to keep separate track of H+ and O+. The distributions of electrons and ions are each divided into 20 separate energy invariant species.
The code represents the ion population in terms of contours of constant ηs. Since ηs is constant along an ion drift path, the contours move at the drift velocity given by equation (5). Each contour is therefore defined by a set of drifting test particles. For each chemical species and each invariant energy level, ten contours levels are used. Nine levels define the initial trapped plasma distribution. The tenth level, representative of the central plasma sheet, is set to correspond with the plasma outer-boundary condition, which is uniform on the boundary and constant in time. This contour-based representation is used because it produces no numerical diffusion and allows a clean separation between particles that were in the original trapped distribution and those that came from the plasma sheet during the storm.
Plasma sheet electrons are considered differently than ions. The electron population is specified in terms of ηs values at grid points rather than a series of test particles. The use of this grid-based representation allows the RCM to incorporate electron loss. Kilovolt electrons have lifetimes of only a few hours, so loss cannot be neglected [Axford, 1969]. As the electron plasma sheet convects Earthward, electron density decreases due to loss. In this RCM run, the electrons are lost by strong pitch-angle scattering, reduced by a factor of 2/3 for high Kp (greater than 4+) or a factor of 1/3 for lower Kp [Schumaker et al., 1989].
Figure 5. The basic logic structure of the Rice Convection Model. The square boxes indicate model calculations, while the rounded boxes indicate model inputs.
Download figure to PowerPoint
4.2. Model Inputs
The basic inputs to the RCM are the initial and boundary plasma distributions, the magnetic field, the background and auroral zone ionospheric conductances, and the potential on the poleward boundary. The total strength of the imposed large-scale convection is given by the polar cap potential drop, and is distributed along the ionospheric poleward boundary as sin(πMLT/12). For this study, we used the maximum DMSP-calculated potential drop in a given hour (shown in Figure 4). The magnetic field at a given time step is interpolated between Hilmer-Voigt magnetic field models [Hilmer and Voigt, 1995] specified every 15 min according to the calculated standoff distances and the Dst and ABI indices (shown in Figure 3). The dipole tilt is assumed to be zero.
The initial ion distribution is perhaps the most complex input for this run. The preexisting ion population is inferred from MICS observations at different L-shells prior to the storm. The measured differential particle flux j is converted into the density invariant η by
where Δλ is the separation between energy invariant channels. A piecewise logarithmic interpolation between the MICS energies is used to specify the fluxes at the RCM energy invariants. The upper bound of the RCM energy invariant range is approximately 100 keV at geosynchronous orbit.
In treating the initial trapped magnetospheric particle distribution, we consider only ions. Of course, electrons must be present in the initial distribution to balance the ion charge, however these electrons are assumed to have sufficiently low energies that they do not contribute significantly to the pressure gradients that drive the Birkeland currents; thus they need not be included explicitly in the RCM.
The plasma sheet population, which enters the model as a boundary condition, is based upon published plasma sheet statistics. Borovsky et al. [1998a] found that plasma sheet conditions (denoted ps) are related to solar wind (denoted sw) conditions at the magnetopause. In particular, the number density of ions in the plasma sheet between 17.5 and 22.5 Re downtail is given by
where the number densities are in cm−3. The ion temperature is given by
where the plasma sheet temperature is in keV and the solar wind velocity is in kilometers per second. In this run, the plasma distribution η(λ) is assumed to be independent of time and position on the tailward boundary of the RCM. To set this distribution, the boundary plasma moments are set to ne = ni = 0.148 cm−3, Ti = 8.32 keV, and pi = 0.2 nPa at about 20 RE. The 8.32 keV value was estimated from equation (7b) and the solar wind velocity measured at 0600 UT on 5 June (630 km/s), during the largest ring current injection. Use of the measured solar wind density (37.6 cm−3) in equation (7a) leads to a plasma sheet density of 0.74 cm−3, but that leads to unrealistically high flux levels at geosynchronous orbit. For that reason, we divide the plasma sheet density derived from equation (7a) by five (a rough factor determined from a series of model runs) in setting our outer boundary condition. This is a symptom of the pressure balance inconsistency [e.g., Erickson and Wolf, 1980; Spence et al., 1989; Borovsky et al., 1998b]. Standard magnetic field models imply that the adiabatic quantity pV5/3 decreases Earthward between about 20 Re and 6.6 Re, by processes that are not yet known and are not included in the RCM.
The total electron density in the plasma sheet is set equal to the total ion density. The electron temperature is by Ti/Te = 7.2 to agree with Baumjohann et al. . The density and temperature are converted into an density invariant-energy invariant spectrum using a Kappa function of the order of 6 [Vasyliunas, 1968; Christon et al., 1989, 1991] where the density invariant is given by equation7
Here, m is the particle mass, k is the Boltzmann's constant, κ = 6 is the exponent of the high energy differential flux, and a = κ − 1.5. The inner edge of the plasma sheet is initially placed so that it just touches the modeling boundary at 1200 MLT and follows a contour of constant flux tube volume; thus the initial inner edge produces no Birkeland current.
The final RCM inputs are the background conductance (produced by solar EUV ionization) and auroral enhancement (produced by particle precipitation). To compute the field-line-integrated background conductance, electron and ion densities and temperatures are taken from the International Reference Ionosphere (IRI) [Bilitza, 1997] and neutral densities from the Mass-Spectrometer Incoherent Scatter (MSIS) [Hedin, 1991] models. The background conductance is assumed not to change during the RCM simulation. In contrast, the auroral conductance changes during the RCM run, reflecting the RCM-computed electron distribution. The auroral conductances are adjusted at each time step to agree with the location and concentration of the electron plasma sheet. The precipitating electron flux is adjusted so that the integral of the electron precipitation flux over the RCM's magnetic latitude range agrees with the corresponding integral from the Hardy et al. model at each magnetic local time. Thus the latitudinal distribution of electron precipitation is forced to line up with the computed electron plasma sheet, and the total precipitation rate at each local time is realistic. The conductance algorithms have been discussed in more detail by Sazykin .
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CC-MAIN-2015-11
| 9,204 | 23 |
https://catalog.utexas.edu/search/?P=CSE%20385R
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math
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CSE 385R CSE 385R. Real Analysis. 3 Hours.
Same as Mathematics 381C. Measure and integration over abstract spaces; Lebesgue's theory of integration and differentiation on the real line. Three lecture hours a week for one semester. Computational Science, Engineering, and Mathematics 385R and Mathematics 381C may not both be counted. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.
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CC-MAIN-2021-43
| 416 | 2 |
https://www.coursehero.com/study-guides/chemistryatomsfirst/integrated-rate-laws/
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math
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By the end of this module, you will be able to:
- Explain the form and function of an integrated rate law
- Perform integrated rate law calculations for zero-, first-, and second-order reactions
- Define half-life and carry out related calculations
- Identify the order of a reaction from concentration/time data
The rate laws we have seen thus far relate the rate and the concentrations of reactants. We can also determine a second form of each rate law that relates the concentrations of reactants and time. These are called integrated rate laws. We can use an integrated rate law to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law is used to determine the length of time a radioactive material must be stored for its radioactivity to decay to a safe level.
Using calculus, the differential rate law for a chemical reaction can be integrated with respect to time to give an equation that relates the amount of reactant or product present in a reaction mixture to the elapsed time of the reaction. This process can either be very straightforward or very complex, depending on the complexity of the differential rate law. For purposes of discussion, we will focus on the resulting integrated rate laws for first-, second-, and zero-order reactions.
An equation relating the rate constant k
to the initial concentration [A
and the concentration [A
present after any given time t
can be derived for a first-order reaction and shown to be:
Example 1: The Integrated Rate Law for a First-Order Reaction
The rate constant for the first-order decomposition of cyclobutane, C4
at 500 °C is 9.2 × 10−3
How long will it take for 80.0% of a sample of C4
Check Your Learning
Iodine-131 is a radioactive isotope that is used to diagnose and treat some forms of thyroid cancer. Iodine-131 decays to xenon-131 according to the equation:
The decay is first-order with a rate constant of 0.138 d−1
. All radioactive decay is first order. How many days will it take for 90% of the iodine-131 in a 0.500 M
solution of this substance to decay to Xe-131?
We can use integrated rate laws with experimental data that consist of time and concentration information to determine the order and rate constant of a reaction. The integrated rate law can be rearranged to a standard linear equation format:
A plot of ln[A
] versus t
for a first-order reaction is a straight line with a slope of -k
and an intercept of ln[A
. If a set of rate data are plotted in this fashion but do not
result in a straight line, the reaction is not first order in A
Example 2: Determination of Reaction Order by Graphing
Show that the data in Figure 1 can be represented by a first-order rate law by graphing ln[H2
] versus time. Determine the rate constant for the rate of decomposition of H2
from this data.
Figure 1. The rate of decomposition of H2
in an aqueous solution decreases as the concentration of H2
Check Your Learning
Graph the following data to determine whether the reaction
is first order.
The equations that relate the concentrations of reactants and the rate constant of second-order reactions are fairly complicated. We will limit ourselves to the simplest second-order reactions, namely, those with rates that are dependent upon just one reactant’s concentration and described by the differential rate law:
For these second-order reactions, the integrated rate law is:
where the terms in the equation have their usual meanings as defined above.
Example 3: The Integrated Rate Law for a Second-Order Reaction
The reaction of butadiene gas (C4
) with itself produces C8
gas as follows:
The reaction is second order with a rate constant equal to 5.76 × 10−2
L/mol/min under certain conditions. If the initial concentration of butadiene is 0.200 M
, what is the concentration remaining after 10.0 min?
Check Your Learning
If the initial concentration of butadiene is 0.0200 M
, what is the concentration remaining after 20.0 min?
The integrated rate law for our second-order reactions has the form of the equation of a straight line:
A plot of
for a second-order reaction is a straight line with a slope of k
and an intercept of
. If the plot is not a straight line, then the reaction is not second order.
Example 4: Determination of Reaction Order by Graphing
Test the data given to show whether the dimerization of C4
is a first- or a second-order reaction.
Check Your Learning
Does the following data fit a second-order rate law?
For zero-order reactions, the differential rate law is:
A zero-order reaction thus exhibits a constant reaction rate, regardless of the concentration of its reactants.
The integrated rate law for a zero-order reaction also has the form of the equation of a straight line:
Figure 4. The decomposition of NH3
on a tungsten (W) surface is a zero-order reaction, whereas on a quartz (SiO2
) surface, the reaction is first order.
A plot of [A
] versus t
for a zero-order reaction is a straight line with a slope of −k
and an intercept of [A
. Figure 4 shows a plot of [NH3
] versus t
for the decomposition of ammonia on a hot tungsten wire and for the decomposition of ammonia on hot quartz (SiO2
). The decomposition of NH3
on hot tungsten is zero order; the plot is a straight line. The decomposition of NH3
on hot quartz is not zero order (it is first order). From the slope of the line for the zero-order decomposition, we can determine the rate constant:
slope = −k = 1.3110−6 mol/L/s
The Half-Life of a Reaction
The half-life of a reaction (t1/2)
is the time required for one-half of a given amount of reactant to be consumed. In each succeeding half-life, half of the remaining concentration of the reactant is consumed. Using the decomposition of hydrogen peroxide in Figure 1 as an example, we find that during the first half-life (from 0.00 hours to 6.00 hours), the concentration of H2
decreases from 1.000 M
to 0.500 M
. During the second half-life (from 6.00 hours to 12.00 hours), it decreases from 0.500 M
to 0.250 M
; during the third half-life, it decreases from 0.250 M
to 0.125 M
. The concentration of H2
decreases by half during each successive period of 6.00 hours. The decomposition of hydrogen peroxide is a first-order reaction, and, as can be shown, the half-life of a first-order reaction is independent of the concentration of the reactant. However, half-lives of reactions with other orders depend on the concentrations of the reactants.
We can derive an equation for determining the half-life of a first-order reaction from the alternate form of the integrated rate law as follows:
If we set the time t
equal to the half-life,
the corresponding concentration of A
at this time is equal to one-half of its initial concentration. Hence, when
We can see that the half-life of a first-order reaction is inversely proportional to the rate constant k
. A fast reaction (shorter half-life) will have a larger k
; a slow reaction (longer half-life) will have a smaller k
Example 5: Calculation of a First-order Rate Constant using Half-Life
Calculate the rate constant for the first-order decomposition of hydrogen peroxide in water at 40 °C, using the data given in Figure 5.
Figure 5. The decomposition of H2
O + O2
) at 40 °C is illustrated. The intensity of the color symbolizes the concentration of H2
at the indicated times; H2
is actually colorless.
Check Your Learning
The first-order radioactive decay of iodine-131 exhibits a rate constant of 0.138 d−1
. What is the half-life for this decay?
We can derive the equation for calculating the half-life of a second order as follows:
, and we can write:
For a second-order reaction,
is inversely proportional to the concentration of the reactant, and the half-life increases as the reaction proceeds because the concentration of reactant decreases. Consequently, we find the use of the half-life concept to be more complex for second-order reactions than for first-order reactions. Unlike with first-order reactions, the rate constant of a second-order reaction cannot be calculated directly from the half-life unless the initial concentration is known.
We can derive an equation for calculating the half-life of a zero order reaction as follows:
When half of the initial amount of reactant has been consumed
The half-life of a zero-order reaction increases as the initial concentration increases.
Equations for both differential and integrated rate laws and the corresponding half-lives for zero-, first-, and second-order reactions are summarized in Table 1.
|Table 1. Summary of Rate Laws for Zero-, First-, and Second-Order Reactions
||rate = k
||rate = k[A]
||rate = k[A]2
|units of rate constant
|integrated rate law
||[A] = −kt + [A]0
||ln [A] = −kt + ln[A]0
|plot needed for linear fit of rate data
||[A] vs. t
||ln [A] vs. t
| vs. t
|relationship between slope of linear plot and rate constant
||k = −slope
||k = −slope
||k = +slope
Key Concepts and Summary
Differential rate laws can be determined by the method of initial rates or other methods. We measure values for the initial rates of a reaction at different concentrations of the reactants. From these measurements, we determine the order of the reaction in each reactant. Integrated rate laws are determined by integration of the corresponding differential rate laws. Rate constants for those rate laws are determined from measurements of concentration at various times during a reaction.
The half-life of a reaction is the time required to decrease the amount of a given reactant by one-half. The half-life of a zero-order reaction decreases as the initial concentration of the reactant in the reaction decreases. The half-life of a first-order reaction is independent of concentration, and the half-life of a second-order reaction decreases as the concentration increases.
- integrated rate law for zero-order reactions:
- integrated rate law for first-order reactions:
- integrated rate law for second-order reactions:
- Describe how graphical methods can be used to determine the order of a reaction and its rate constant from a series of data that includes the concentration of A at varying times.
- Use the data provided to graphically determine the order and rate constant of the following reaction:
|5.00 × 103
|1.00 × 104
|1.50 × 104
|2.50 × 104
|3.00 × 104
|4.00 × 104
- Use the data provided in a graphical method to determine the order and rate constant of the following reaction:
||1.077 × 10-3
||1.068 × 10-3
||1.055 × 10-3
||1.046 × 10-3
||1.039 × 10-3
- Pure ozone decomposes slowly to oxygen,
Use the data provided in a graphical method and determine the order and rate constant of the reaction.
||1.00 × 10−5
|2.0 × 10−3
||4.98 × 10−6
|7.6 × 10−3
||2.07 × 10−6
|1.00 × 10−4
||1.66 × 10−6
|1.23 × 10−4
||1.39 × 10−6
|1.43 × 10−4
||1.22 × 10−6
|1.70 × 10−4
||1.05 × 10−6
- From the given data, use a graphical method to determine the order and rate constant of the following reaction:
- What is the half-life for the first-order decay of phosphorus-32
The rate constant for the decay is 4.85 × 10−2 day −1.
- What is the half-life for the first-order decay of carbon-14?
The rate constant for the decay is 1.21 × 10−4 year−1.
- What is the half-life for the decomposition of NOCl when the concentration of NOCl is 0.15 M? The rate constant for this second-order reaction is 8.0 × 10-8 L/mol/s.
- What is the half-life for the decomposition of O3 when the concentration of O3 is 2.35 × 10−6M? The rate constant for this second-order reaction is 50.4 L/mol/h.
- The reaction of compound A to give compounds C and D was found to be second-order in A. The rate constant for the reaction was determined to be 2.42 L/mol/s. If the initial concentration is 0.500 mol/L, what is the value of t1/2?
- The half-life of a reaction of compound A to give compounds D and E is 8.50 min when the initial concentration of A is 0.150 mol/L. How long will it take for the concentration to drop to 0.0300 mol/L if the reaction is (a) first order with respect to A or (b) second order with respect to A?
- Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of 3 × 104 g/mol that converts penicillin into inactive molecules. Although the kinetics of enzyme-catalyzed reactions can be complex, at low concentrations this reaction can be described by a rate equation that is first order in the catalyst (penicillinase) and that also involves the concentration of penicillin. From the following data: 1.0 L of a solution containing 0.15 µg (0.15 × 10−6 g) of penicillinase, determine the order of the reaction with respect to penicillin and the value of the rate constant.
|2.0 × 10−6
||1.0 × 10−10
|3.0 × 10−6
||1.5 × 10−10
|4.0 × 10−6
||2.0 × 10−10
- Both technetium-99 and thallium-201 are used to image heart muscle in patients with suspected heart problems. The half-lives are 6 h and 73 h, respectively. What percent of the radioactivity would remain for each of the isotopes after 2 days (48 h)?
- There are two molecules with the formula C3H6. Propene, CH3CH=CH2, is the monomer of the polymer polypropylene, which is used for indoor-outdoor carpets. Cyclopropane is used as an anesthetic:
When heated to 499 °C, cyclopropane rearranges (isomerizes) and forms propene with a rate constant of
. What is the half-life of this reaction? What fraction of the cyclopropane remains after 0.75 h at 499.5 °C?
- Fluorine-18 is a radioactive isotope that decays by positron emission to form oxygen-18 with a half-life of 109.7 min. (A positron is a particle with the mass of an electron and a single unit of positive charge; the equation is
) Physicians use 18F to study the brain by injecting a quantity of fluoro-substituted glucose into the blood of a patient. The glucose accumulates in the regions where the brain is active and needs nourishment.
- What is the rate constant for the decomposition of fluorine-18?
- If a sample of glucose containing radioactive fluorine-18 is injected into the blood, what percent of the radioactivity will remain after 5.59 h?
- How long does it take for 99.99% of the 18F to decay?
- Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for of the initial dose to remain in the athlete’s body?
- Recently, the skeleton of King Richard III was found under a parking lot in England. If tissue samples from the skeleton contain about 93.79% of the carbon-14 expected in living tissue, what year did King Richard III die? The half-life for carbon-14 is 5730 years.
- Nitroglycerine is an extremely sensitive explosive. In a series of carefully controlled experiments, samples of the explosive were heated to 160 °C and their first-order decomposition studied. Determine the average rate constants for each experiment using the following data:
|Initial [C3H5N3O9] (M)
- For the past 10 years, the unsaturated hydrocarbon 1,3-butadiene (CH2=CH–CH=CH2) has ranked 38th among the top 50 industrial chemicals. It is used primarily for the manufacture of synthetic rubber. An isomer exists also as cyclobutene:
The isomerization of cyclobutene to butadiene is first-order and the rate constant has been measured as 2.0 × 10−4 s−1 at 150°C in a 0.53-L flask. Determine the partial pressure of cyclobutene and its concentration after 30.0 minutes if an isomerization reaction is carried out at 150°C with an initial pressure of 55 torr.
Show Selected Answers
half-life of a reaction (tl/2):
time required for half of a given amount of reactant to be consumed
integrated rate law:
equation that relates the concentration of a reactant to elapsed time of reaction
Licenses and Attributions
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| 15,904 | 202 |
http://meta.inwardquest.com/questions/456/what-are-the-rules-regarding-closed-questions
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math
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Last year I tried unsuccessfully numerous times to post a comment on a closed question to NO avail. I saw both Wade and Blubird two makes comments on separate closed questions. Is there a certain amount of karma points required before you can do this?
Also, can you post an answer on a closed question or is it against the rules? If it is against the rules, is it possible to reopen a question which has been closed? If so, how does one do this?
asked Nov 03 '13 at 02:26
As it currently stands, if someone has started writing a comment or answer to a question that is closed while they are doing it, then the system will allow them to post that comment or answer. Otherwise it cannot be done. Only someone with moderator status can reopen a closed question.
answered Nov 05 '13 at 10:13
Simon Templeton ♦♦
Yes I used to be able to post a short comment to closed questions. I can not anymore now. I believe it was as Simon said a software glitch. It had something to do with converting a comment to an answer or an answer to a comment. Anyway I can't do that anymore I found out when I tried posting a link to here in his closed question.
So obviously the glitch has been fixed and closed questions really are completely closed.
answered Nov 12 '13 at 11:00
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| 1,261 | 9 |
https://elemental-crown.xyz/2019/06/25/lesson1-2/
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math
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1.”( What day is it today? ) ” “It’s Wednesday.”
2.Do ( they sell medicine at that convenience store )?
3.We ( throw beans at a demon ) on the night of Setsubun.
1.Janet ( has ) dark ( hair ) and brown ( eyes ).
2.( It ) ( is ) about two kilometers from my house to the station.
3.( Some ) like spicy food, and ( others ) ( not ).
4.( It ) ( will ) ( be ) sunny on Wednesday.
1.There are three hundred students in our school.
2.I have a slight headache today.
3.The number of elephants is decreasing.
4.You should be kind to elderly people.
1.( To tell a lie is to lose ) the trust of others.
2.( It is not so difficult for Italians to ) understand Spanish.
3.( It is certain that he will win ) the gold medal.
4.The paper ( says that it’s going to rain ) today.
1.( Reading ) ( books ) ( makes ) you smarter.
2.It was careless ( of ) ( you ) ( to ) leave the door unlocked.
3.( It ) ( doesn’t ) ( matter ) ( whatever ) people say.
1.The dictionary on the desk is mine.
2.What made her so angry?
3.It took me three days to finish reading the book.
4.A minor error can cause a serious problem.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668644.10/warc/CC-MAIN-20191115120854-20191115144854-00010.warc.gz
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CC-MAIN-2019-47
| 1,106 | 22 |
https://www.ias.ac.in/listing/bibliography/pram/WEI_TAN
|
math
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Articles written in Pramana – Journal of Physics
Volume 89 Issue 5 November 2017 Article ID 0077 Research Article
Emergence and space–time structure of lump solution to the (2+1)-dimensional generalized KP equation
WEI TAN HOUPING DAI ZHENGDE DAI WENYONG ZHONG
A periodic breather-wave solution is obtained using homoclinic test approach and Hirota’s bilinear method with a small perturbation parameter $u_0$ for the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation. Based on the periodic breather-wave, a lump solution is emerged by limit behaviour. Finally, three different forms of the space–time structure of the lump solution are investigated and discussed using the extreme value theory.
Volume 94 All articles Published: 30 January 2020 Article ID 0036 Research Article
Superposition behaviour between lump solutions and different forms of $N$-solitons ($N \rightarrow\infty$) for the fifth-order Korteweg–de Vries equation
A lump-type solution of the (2 + 1)-dimensional generalised fifth-order Korteweg–de Vries (KdV) equation is obtained from the two-soliton solution by applying the parametric limit method. Some theorems and corollaries about the superposition behaviour between lump solutions and different forms of $N$-soliton ($N \rightarrow\infty$) solutions are constructed, and detailed proofs are given. Besides,we give a large number of examples and spatial evolution graphics to illustrate the effectiveness of the described theorems and corollaries. Some new nonlinear phenomena and superposition behaviour, such as rational-exponential type, rational-cosh-cos type, rational-sin type, rational-logarithmic type etc., are simulated and shown for the first time. Finally, we also illustrate the superposition between high-order lump-type solutions and $N$-soliton solutions.
Volume 97, 2023
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode
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http://forum.mongoosepublishing.com/viewtopic.php?f=89&t=56872&start=2200
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math
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This might simply mean that using power from the power plant, e.g. to power the manoeuvre drive, consumes inconsequential fuel compared to idling the power plant.HG'79, p17-18 wrote:A power plant uses fuel equal to 1% of the ship's tonnage every four weeks, regardless of actual power drain; this usage is primarily to maintain the fusion bottle and other housekeeping functions. Other fuel requirements are considered inconsequential.
There is a problem: it's certainly too little reaction mass.
E.g. the Free Trader; It uses 10 Dt = 10 tonnes of hydrogen for four weeks, or 4 g/s. If we say that inconsequential is 1%, then we use around 40 mg/s reaction mass to achieve 1 G ≈ 10 m/s² acceleration. So in 1 s 40 mg of reaction mass would increase the ships speed by 10 m/s.
By conservation of momentum MrVr = MsVs, so the velocity of the ejected reaction mass would need to be Vr = MsVs/Mr ≈ 1000000 × 10 / 0.00004 = 2.5 × 10¹¹ m/s = 250 million km/s or about 1000 times the speed of light.
At this energy level we have to consider energy rather than velocity. At close to lightspeed MrVr = MsVs would be Mr = MsVs / Vr ≈ 1000000 × 10 / 300000000 = 33 g of pure energy which by E=mc² is 3 × 10¹⁵ J which in 1 s is 3 PW = 3000000 GW. Obviously this can be produced by neither a fusion rocket nor the power plant.
Even if we could eject the reaction mass at close to lightspeed we would need several thousand times more reaction mass.
I would argue that reaction drives that use no noticeable reaction mass are even more magical than gravitic drives.
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| 1,567 | 7 |
https://math.stackexchange.com/questions/2127674/how-to-find-%CE%B1-in-this-reduction-identity
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math
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In the reduction identity :
m sin θ + n cos θ = √(m² + n²) sin(θ + α)
I am having trouble with determining the value of α. Here is an example.
Problem : -7 sin θ - 24 cos θ m = -7 n = -24 Using the above formula : √(-7² + -24²) sin(θ + α) = 25 sin(θ + α)
From here, I use the following identities to attempt to determine α
sin α = n / √(m² + n²)
cos α = m / √(m² + n²)
sin α = -24/25, α = -74° cos α = -7/25, α = 106°
At this point, I have two possible values for α. My textbook states, "α is the smallest possible positive value that satisfies both of these conditions," and lists the value of α as 254°. I'm a bit confused. How did they arrive to that conclusion, and what steps can I take to solve the problem?
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| 753 | 9 |
http://www.kgbanswers.com/what-is-the-product-of-3-less-than-twice-x-and-2-more-than-the-quantity-3-times-x/5129677
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math
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what is the product of 3 less than twice x and 2 more than the quantity 3 times x ?
kgb answers » Science & Technology » Math, Chemistry, Physics » what is the product of 3 less than twice x and 2 more than the quantity 3 times x ?
Thursday, February 02 2012
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- The sum of two numbers is 15 less than twice the first number. Their difference is 5 less than twice the second number. Find each of the numbers
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s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701148475.34/warc/CC-MAIN-20160205193908-00160-ip-10-236-182-209.ec2.internal.warc.gz
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CC-MAIN-2016-07
| 1,550 | 19 |
http://www.solutioninn.com/refer-to-the-supermarket-in-s12-13-what-is-the
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math
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Refer to the supermarket in S12- 13. What is the approximate internal rate of return (IRR) of the kiosk investment?
In S12- 13
The local supermarket is considering investing in self- checkout kiosks for its customers. The self- checkout kiosks will cost $ 46,000 and have no residual value. Management expects the equipment to result in net cash savings over three years as customers grow accustomed to using the new technology: $ 12,000 the first year; $ 19,000 the second year; $ 26,000 the third year. Assuming a 10% discount rate, what is the NPV of the kiosk investment? Is this a favorable investment? Why or why not?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187820927.48/warc/CC-MAIN-20171017052945-20171017072945-00122.warc.gz
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CC-MAIN-2017-43
| 623 | 3 |
https://www.tug.org/pipermail/texhax/2009-August/013109.html
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math
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[texhax] derivatives and integrals: math operators
natercia at eq.uc.pt
Mon Aug 24 19:18:14 CEST 2009
Sorry for not having thanked earlier who answered my question, but I was away
and read the answers only now.
When I put this question, I didn't mean to start any "war". I just wanted to
be clarified whether it's more correct to use italic or upright "d" for
derivatives and integrals, since I do use them a lot and I do want to follow
the most appropriate notation.
I see the opinions are divided. The mathematician Phil Parker defended
strongly the italic "d" as I have seen it elsewhere. The oher participants
that took a position defended the upright "d" (independently of being or not
mathematicians). It seems there isn't a rule (at least a pacifically followed
As a side product, I got another doubt: the derivatives and integrals are or
are not mathical operators? I thought they were, but Phil Parker said neither
of them was. However, Xavier Sabate also classified them as important operators
and others also referred to them as operators...
Once again, thanks to everyone who answered.
More information about the texhax
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570879.37/warc/CC-MAIN-20220809003642-20220809033642-00386.warc.gz
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CC-MAIN-2022-33
| 1,131 | 19 |
http://lauriesbookshelf.com/what-are-the-units-for-speed/
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math
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What Are The Units For Speed. The meter per second corresponds to the speed at which the body travels a distance of one meter in a time of one. 30 minutes is half an hour.
One knot equals one nautical mile per hour; Thus, the si unit of speed is metre per second or m/s. Meter per second is a unit of speed and a unit of the si system.
The Fundamental Si Unit For Length Is The Meter And For Time Is The Second.
Meters per second, or m/s, is the standard unit of measurement. Velocity is measured in the same way as speed. Speed can be calculated by the formula:
The Si Unit For Force Is The Newton, (N).
The units of speed are miles per hour so the time must be in hours. Speed is distance in unit time. The si unit of distance is the metre, the unit of time is the second, so the unit of speed is m/s.
Knots ( Nautical Miles Per Hour,.
Basically, velocity is the vector equivalent of speed. 34 rows 32 units of speed — found. The speed measurement was introduced to measure.
A Unit Of Speed Is The Ratio Of Any Unit Of Distance To Any Unit Of Time.
Also, explore many other unit converters or. The si unit of speed can be derived from the formula of velocity. The meter per second corresponds to the speed at which the body travels a distance of one meter in a time of one.
Meters Per Second (M/S), The Default Si Unit For Speed Kilometers Per Hour (Km/H) Miles Per Hour (Mph) Nautical Miles Per Hour (Knots) Feet Per Second (Ft/S).
To convert from m/s into units in the left column divide by the value in the right column or, multiply by the reciprocal, 1/x. Miles per hour (symbol mi/h or mph); Speed is a scalar quantity while.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335190.45/warc/CC-MAIN-20220928082743-20220928112743-00057.warc.gz
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CC-MAIN-2022-40
| 1,634 | 12 |
http://www.modelmayhem.com/NadiasPhotography
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math
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Nadias PhotographyPhotographer Female Silverdale, Washington, US
My Website: Nadia's Portfolio - Portrait PhotographyMy MM URL: http://www.modelmayhem.com/NadiasPhotography
Mayhem # 1062664
Welcome to my MM page! I'm Nadia. Just relocated here to Silverdale, Washington from Dayton, OH and Oklahoma City, OK before that!
$100/hour: Senior portraits, Couples/Engagements, Family, Children, Babies.
FREE: Non-profit public events.
*FREE* - Model Shoots that include some of the following themes/elements:
~Bridal**** Bonus: If you have a "groom" in a tux.
~Theme (Snow White, Cow Girl, Samurai, etc.)
~An instrument (piano, violin, etc.)
I am a fun, open-minded photographer! I am in love with fashion and vintage shoots, but I have the most fun trying out new looks/locations/themes, etc. I do mostly outdoor shoots with natural light and reflectors or flash+softbox as needed. I have portable studio equipment as well. I do the post-processing & retouching myself.
Message me if you are in or willing to travel to the Silverdale area and would like to schedule a shoot with me sometime!
Official Website: http://nadiasportfolio.com/
Facebook page: http://www.facebook.com/NadiasPortfolio
Please "like" my page! I appreciate the support! ^^
Have you worked with Nadias Photography? Add Credits for Nadias Photography! >>
#771116 - Model - Lisa
#743906 - Model - Hallie - 2 shoots
#2739338 - Model - Ashley
#2670308 - Model - Carolina
#2532017 - Model - Tyler - 3 shoots
#2779364 - Model - Candy
#3204509 - Model - Marissa - 2 shoots
#3204381 - Model - Nataliya
#2912927 - MUA - Angelo
#2335337 - Model - Alexus
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#3866352 - Model - Leeda
#3282124 - Model/MUA - Nicole
#3155761 - Model - Valerie
Model - Carmen (not on MM)
Model - Brooke (not on MM)
Model - Alexa (not on MM)
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123549.87/warc/CC-MAIN-20170423031203-00282-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
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https://ui.adsabs.harvard.edu/abs/1971JMP....12.2259W
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math
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It is shown that any Ising model with positive coupling constants is related to another Ising model by a duality transformation. We define a class of Ising models Mdn on d-dimensional lattices characterized by a number n = 1, 2, …, d (n = 1 corresponds to the Ising model with two-spin interaction). These models are related by two duality transformations. The models with 1 < n < d exhibit a phase transition without local order parameter. A nonanalyticity in the specific heat and a different qualitative behavior of certain spin correlation functions in the low and the high temperature phases indicate the existence of a phase transition. The Hamiltonian of the simple cubic dual model contains products of four Ising spin operators. Applying a star square transformation, one obtains an Ising model with competing interactions exhibiting a singularity in the specific heat but no long-range order of the spins in the low temperature phase.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587623.1/warc/CC-MAIN-20211025030510-20211025060510-00561.warc.gz
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CC-MAIN-2021-43
| 946 | 1 |
https://physicsteacher.blog/2018/08/29/kinetic-energy-using-the-singapore-bar-model/
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math
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I think the Singapore Bar Model is a neat bit of pedagogy that has great potential in Science education.
Essentially, the Singapore Bar Model uses pictorial representations (often in the form of a bar or line) to help students bridge the gap between concrete and abstract reasoning. I wrote about one possible application here.
A recent discussion on Twitter started me thinking about if it could be applied to kinetic energy.
For example, how would you explain what happens to the kinetic energy of an object if its velocity is halved?
Many students assume that the KE would halve as well, instead of reducing to a quarter of its original value.
How can we help students grasp this slippery concept without using algebra? Algebra would work fine with your higher sets, of course, but not necessarily for other groups.
This gives a clear visual representation of the fact that the KE quarters when the velocity halves. In other words, 0.5 x 0.5 = 0.25.
(Note that I have purposefully used decimals as we know that many students struggle with fractions(!))
Many students found the following question on an AQA paper extremely challenging:
The correct answer is that the power output drops to one eighth of its original value.
Could the Singapore Bar Model helps students to see why this is the case?
I think it could:
Reblogged this on The Echo Chamber.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945372.38/warc/CC-MAIN-20230325191930-20230325221930-00318.warc.gz
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CC-MAIN-2023-14
| 1,352 | 13 |
https://www.shaalaa.com/question-bank-solutions/refractive-indices-water-sulphuric-acid-glass-carbon-disulphide-are-133-143-153-163-respectively-light-travels-slowest-in-a-sulphuric-acid-b-glass-c-water-d-carbon-disulphide-refractive-index_27025
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math
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Refractive indices of water, sulphuric acid, glass and carbon disulphide are 1.33, 1.43, 1.53 and 1.63 respectively. the light travels slowest in:
(a) sulphuric acid
(d) carbon disulphide
Refractive index = `"speed of light in air"/"speed of light in medium "`
Speed of light in the medium is slowest; therefore refractive index will be maximum as the speed of light in air is constant. Thus, light will travel slowest in the substance with refractive index 1.63.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663016373.86/warc/CC-MAIN-20220528093113-20220528123113-00356.warc.gz
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CC-MAIN-2022-21
| 463 | 5 |
https://www.hackmath.net/en/math-problem/49773
|
math
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What is the area of a round cake with a radius of 5cm?
Did you find an error or inaccuracy? Feel free to write us. Thank you!
Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it.
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CC-MAIN-2022-49
| 3,291 | 40 |
https://web2.0calc.com/questions/help-me-plezzzzz
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math
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Julio is running in a 13.1-mile race. There are water stops every 2.75 miles along the route from the beginning of the race. What is the distance between the last water stop and the end of the race? Enter your answer in the box.
That is a simple division answer. Take the total miles divided by how far each water stop is. Only so many water stops can be in that distance.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247479967.16/warc/CC-MAIN-20190216065107-20190216091107-00339.warc.gz
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CC-MAIN-2019-09
| 372 | 2 |
https://www.quantamagazine.org/tag/number-theory/page/8
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math
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CC-MAIN-2024-10
| 1,189 | 11 |
https://books.google.com/books/about/Orbits_near_triple_collision_in_the_thre.html?id=l-DOAAAAMAAJ&hl=en
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math
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What people are saying - Write a review
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The Case of Nonzero Angular Momentum
The Collision Manifold
5 other sections not shown
analytic curve analytic function analytic submanifold approach collision behavior of orbits binary exchange orbits branch of Un(E choose coordinates close to collision close to equal close to triple codimension collinear configurations collinear submanifold collision manifold components configuration space consisting of orbits continuous function crosses St(C denote Devaney double collision duals occur ejection orbit energy h equal masses equations 2.1 equilateral configurations following result gradient-like property homeomorphic homotopy equivalence intersect invariant manifold invariant submanifold ir(a isosceles orbit isosceles problem isosceles submanifold Lemma mass ratio masses sufficiently close McGehee neighborhood non-degenerate masses non-trivial open sets orbit segment ORBITS NEAR TRIPLE orbits which approach particles Proof of 7.1 proof of Proposition Proposition 6.4 Proposition 7.1 quotient rest points singular points subset sufficiently small Sundman Sundman's Inequality thesis three-body problem topological triple collision Un(C Un(P UNIVERSITY OF WISCONSIN-MADISON unstable manifolds unstarred sets variation of 9 vr shows
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125949489.63/warc/CC-MAIN-20180427060505-20180427080505-00585.warc.gz
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CC-MAIN-2018-17
| 1,332 | 6 |
http://umj.imath.kiev.ua/index.php/umj/article/view/1436
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math
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On the joint approximation of a function and its derivatives in the mean
AbstractWe consider some properties of functions integrable on a segment. Some estimates for the approximations of function and its derivatives are obtained.
How to Cite
MotornayaO. V., and MotornyiV. P. “On the Joint Approximation of a Function and Its derivatives in the Mean”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 2, Feb. 2019, pp. 261-70, http://umj.imath.kiev.ua/index.php/umj/article/view/1436.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141733120.84/warc/CC-MAIN-20201204010410-20201204040410-00361.warc.gz
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CC-MAIN-2020-50
| 490 | 4 |
https://www.jiskha.com/display.cgi?id=1348109652
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math
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posted by anna .
The bromine content of the ocean is about 65 grams of bromine per million grams of sea water. How many cubic
meters of ocean must be processed to recover 1.0 pounds of bromine if the density of sea water is 1.0 x 103 kg/m3?
65 ppm is 65 grams/10^6 g sea water. We want 1 lb of Br2 which is about 454 grams. So how much sea water do we need to do that?
That's 1E6 g sea water x (454/65) = about 7E6 grams. I would change that to 7E3 kg and use the density.
volume = mass/density = 7E3/1E3 = aboaut 7 cubic meters. You need to go through and clean up the numbers because I've estimated here and there although I think the 7 is close. Check my thinking.
what the heck are you even doing
I got 67.75m cubed.
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CC-MAIN-2018-05
| 720 | 8 |
https://www.whsmith.co.uk/products/local-fractional-integral-transforms-and-their-applications/9780128040027
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math
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Special OrderSpecial Order item not currently available. We'll try and order for you.
Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms.
Chapter 1. Introduction to Local Fractional Derivative and Local Fractional Integral Operators1.1. Definitions and Properties of Local Fractional Derivative 1.2 Definitions and Properties of Local Fractional Integral1.3 Local Fractional Partial Differential Equations in Mathematical Physics ReferencesChapter 2. Local Fractional Fourier Series 2.1. Definitions and Properties 2.2. Applications to Signal Analysis 2.3 Solving Local Fractional Differential Equations2.3.1. Applications of Local Fractional Ordinary Differential Equations 2.3.2. Applications of Local Fractional Partial Differential Equations References Chapter 3. Local Fractional Fourier Transform and Its Applications 3.1. Definitions and Properties 3.2. Applications to Signal Analysis 3.3 Solving Local Fractional Differential Equations3.3.1. Applications of Local Fractional Ordinary Differential Equations 3.3.2. Applications of Local Fractional Partial Differential Equations ReferencesChapter 4. Local Fractional Laplace Transform and Its Applications4.1. Definitions and Properties 4.2. Applications to Signal Analysis 4.3 Solving Local Fractional Differential Equations4.3.1. Applications of Local Fractional Ordinary Differential Equations 4.3.2 Applications of Local Fractional Partial Differential Equations References Chapter 5. Local Fractional Laplace Transform Method Coupled with Analytical Methods5.1. Variational Iteration Method of Local Fractional Operator 5.2. Decomposition Method of Local Fractional Operator 5.3. Coupling Laplace Transform with Variational Iteration Method of Local Fractional Operator5.4. Coupling Laplace Transform with Decomposition Method of Local Fractional OperatorReferences
Number Of Pages:
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CC-MAIN-2018-09
| 2,865 | 12 |
http://benchridge.com/faq.html
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math
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- Q. Is your system hard to set up like some?
- A. No – with the A section just swing the legs down and mount the four support braces using the 2 1/2” x 5/16” bolts included with your favorite wrench or ratchet.
- Q. Is your system strong enough to stand on in case I need to work on the wall?
- A. Sure – you and a friend. This can be done by the bridge like braces transferring the weight to the legs, making Benchridge one of the strongest on the market.
- Q. Is shipping high?
- A. Sorry to say, shipping cost is high on everything. As you know, fuel costs are driving this up. That's why Benchridge has kept their prices down. We hope that will offset shipping and help you get your dream railroad up and going.
- Q. How's come your price/parts list is so short? Will I get everything I need.
- A. Keep it simple and sweet!
With Benchridge our section combinations will accommodate almost any size you may need. When you buy a section, it comes complete. We also offer custom sections for an unusual room or situation you may run into.
- Q. Do I have to bolt to the wall so it won't rock or sway?
- A. Great question – No – Benchridge stands alone. With bridge-like bracing, each legged section will stand solid by it's self.
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CC-MAIN-2017-43
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https://www.cheaptextbooks.org/9780486649887
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math
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General Theory of Functions and Integration (Dover Books on Mathematics)
Author:Angus E. Taylor
Lucid introduction to abstract theories in analysis. Classical theory of points in Euclidean space, continuous functions, ideas of topology, more. For graduate students. 38 diagrams. Introduction. List of Special Symbols. Index.
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CC-MAIN-2017-47
| 324 | 3 |
https://www.hackmath.net/en/math-problem/3877
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math
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Marian run 12 meters in 8 seconds. How far would Marian run for 70 seconds, if still run at the same pace?
Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it.
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http://reference.wolfram.com/mathematica/ref/PermutationPower.html
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math
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PermutationPower[perm, n] gives the n permutation power of the permutation perm.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539230.18/warc/CC-MAIN-20140416005219-00319-ip-10-147-4-33.ec2.internal.warc.gz
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https://cris.bgu.ac.il/en/publications/on-the-boltzmanngrad-limit-for-smooth-hard-sphere-systems-3
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math
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The problem is posed of the prescription of the so-called Boltzmann–Grad limit operator (LBG) for the N-body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. It is proved, that, despite the non-commutative property of the operator LBG, the Boltzmann equation can nevertheless be uniquely determined. In particular, consistent with the claim of Uffink and Valente (Found Phys 45:404, 2015) that there is “no time-asymmetric ingredient” in its derivation, the Boltzmann equation is shown to be time-reversal symmetric. The proof is couched on the “ab initio” axiomatic approach to the classical statistical mechanics recently developed (Tessarotto et al. in Eur Phys J Plus 128:32, 2013). Implications relevant for the physical interpretation of the Boltzmann H-theorem and the phenomenon of decay to kinetic equilibrium are pointed out.
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http://www.solutioninn.com/pack-just-received-an-order-to-produce-12000-singleserving-bags
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math
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Pack just received an order to produce 12,000 single-serving bags of gourmet, fancy-cut, low-fat potato chips. The order will require 16 preparation hours and 32 cooking and draining hours. Use the activity rates you calculated in S4-4 to compute the following:
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http://slideplayer.com/slide/4203995/
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math
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Presentation on theme: "1 Using surface deformation data to investigate pressure and volume changes in magma chambers What is the Relationship between Pressure & Volume Change."— Presentation transcript:
1 Using surface deformation data to investigate pressure and volume changes in magma chambers What is the Relationship between Pressure & Volume Change in a Magma Chamber and Surface Deformation at Active Volcanoes? What factors control the magnitude of surface deformation? Prepared to offend unwary volcanology students Peter LaFemina - Penn State, State College, PA Supporting Quantitative Issues Parameter Estimation Dimensional analysis Core Quantitative Issue Goodness of Fit
2 Slides 3-6 give some background on volcano deformation monitoring and modeling approaches. Slides 7 and 8 state the problem. What is the relationship between volume and/or pressure change and surface deformation measured at active volcanoes? Slides 9 and 10 develop a plan for solving the problem. You will rely on data gathered prior to the 2010 eruption at Volcano X and estimate the change in pressure and volume of a magma chamber, and the magma chamber depth. Slides 11-13 illustrate the solution of the problem, developing a spreadsheet to create the models. Slide 14 discusses the point of the module and provides a broader volcanological context. Slide 15 consists of some questions that constitute your homework assignment. Slide 16 is endnotes for elaboration and reference. Preview This module presents a theoretical model for the relationship between changes in volume and pressure in a magma chamber and measured surface displacements
3 Background Volcanoes often exhibit geophysical or geochemical signals before, during and after an eruption. These signals allow volcanologists to monitor active volcanoes to gain knowledge about processes in the magma chamber, conduit and edifice and to potentially predict the time and location of a future eruption. One type of geophysical signal is the deformation or movement of the volcanic edifice and surrounding crust. Changes in the surface of the volcano are related to magma intrusion, dome growth, pressure increase in the magma chamber or flank instability. What is surface deformation? Stage 1: Inflation begins as magma moves into the volcano or as pressure increases in the magma chamber Stage 2: As magma chamber inflates, the ground surface above it is displaced. Stage 3: After an eruption, the magma chamber deflates. Ground surface subsides with potential formation of crater. For more information about surface deformation: http://hvo.wr.usgs.gov/howwork/subsidence/main.ht ml http://hvo.wr.usgs.gov/howwork/subsidence/main.ht ml Possible magma intrusion scenario with surface uplift, followed by eruption and subsidence
4 Background The magnitude of surface deformation (i.e., the amount of vertical (uplift or subsidence) and horizontal displacement) of a volcanic edifice is related to the geometry and depth of the source and the source strength. For example, cryptodome intrusion (change in volume at shallow levels) can cause the flank of a volcano to “bulge” out and become unstable. This can happen at rates of meters per day, as in the case of Mount St. Helens, with total displacements in the 100’s of meters. Where as, an increase/decrease in pressure in a magma chamber can cause near symmetrical uplift of the volcano with total magnitudes of meters prior to or after an eruption. What is the magnitude of surface deformation on volcanoes? (Above) Mount St. Helens, 12 May 1980. A cryptodome intruded into the north flank of the volcano causing a “bulge” to form. By this date the “bulge” was growing at 1.5 - 2 m per day. Photo USGS. (Right) Tilt data across Halemaumau crater, Kilauea volcano for the periods 1998-99 & 1999-2001. These data indicate near symmetrical subsidence at rates of cm yr -1. Image USGS.
5 Background How do we measure volcano deformation? Investigation of the shape of the Earth is called geodesy. Volcanologists employ various terrestrial and satellite based geodetic methods to measure changes in the surface of volcanoes. Terrestrial or ground based methods include leveling, tilt and/or electronic distance measurements (EDM). Satellite geodetic methods include the Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar (InSAR). Learn more about geodesy: http://en.wikipedia.org/wiki/Geodesy http://en.wikipedia.org/wiki/Geodesy Tilt measured west of Hekla volcano, Iceland indicating pre- eruptive inflation, followed by co- eruptive subsidence for the last two eruptions. Plot provided by E. Sturkell. For more about monitoring volcano deformation: http://volcanoes.usgs.gov/About/What/Monitor/D eformation/GrndDefrm.html Left: InSAR analysis of Fernandina Island, Galapagos Islands, Ecuador (from Amelung et al. 2000). Right: Detailed InSAR images of Sierra Negra volcano, showing uplift between 1992-97 (a), 97- 98 (b) and 98-99 (c). Each color fringe represents 2.83 cm change in elevation.
6 Background Can we learn something about processes within a volcano from surface deformation data? In 1958, Kiyoo Mogi from the Earthquake Research Institute, Japan, investigated the patterns of surface deformation associated with two historically active volcanoes, Sakurajima volcano, Japan and Kilauea volcano, Hawaii (Mogi, 1958). Using the theory of elasticity, he suggested that the surface deformation measured before and after eruptive activity could be fit by a spherical pressure source buried in an elastic medium. In this model, changes in pressure (∆P) or volume (∆V) within a magma chamber of radius (a) and at depth (d) could cause vertical (U z ) and horizontal (U r ) displacements at the surface. The magnitude of the displacements changes with radial distance (r) away from the center. This model is valid when a << d and has been called the Mogi point source model. Learn More about the Mogi Model: http://www.geophys.uni- stuttgart.de/oldwww/ew/volcano/santorin.h tml http://www.geophys.uni- stuttgart.de/oldwww/ew/volcano/santorin.h tml
7 Problem What is the relationship between pressure and/or volume change in a magma chamber & surface deformation? The relationship between surface displacements and pressure change for a spherical source in an elastic half-space from Mogi (1958): Vertical Displacement (uplift or subsidence) Horizontal Displacement Where (a) is the magma chamber radius (500-1000 m), (d) is the depth to the center of the magma chamber (3-10 km), (∆P) is pressure change in the chamber (10-40 MPa), (G) is the elastic shear modulus or rigidity (30 GPa or 3x10 10 Pa), and (r) is the radial distance from the point source (0->50 km). Make sure you can see that the units of U z and U r are meters, given the Mogi equations.
8 Problem (continued) What is the relationship between pressure and volume change in a magma chamber & surface deformation? The relationship between surface displacements and volume change from Mogi (1958): Vertical Displacement (uplift or subsidence) Horizontal Displacement Learn more about where this equation comes from Parameters are the same as in the equations for pressure change, but now we look at volume change, ∆V (m 3 ).
9 You will need to: Calculate the surface uplift versus radial distance for variable pressure and volume sources. Calculate the “goodness of fit” of your model compared to the data. Designing a Plan, Part 1 Given surface displacement data for uplift across Volcano X, use the Mogi point source equation to solve for the change in pressure & depth of the magma chamber. You will consider the goodness-of- fit of your model using the Pearson’s 2 test. Notes: Data for the uplift of Volcano X were collected prior to the 2010 eruption. You will calculate the “best-fit” model for pressure change and depth of the magma chamber. You will use Pearson’s Chi-Square test to estimate the goodness of fit of your model to data. Where O i is the observation and E i is the expected value or model result. Learn more about Pearson’s chi- square test: http://en.wikipedia.org/wiki/Pearson %27s_chi-square_test http://en.wikipedia.org/wiki/Pearson %27s_chi-square_test
10 Designing a Plan, Part 2 Mogi (1958) utilized elasticity theory to demonstrate that uplift and subsidence measured at Sakurajima and Kilauea volcanoes were related to changes in pressure in a magma chamber. You will utilize these equations to investigate the relative importance between the depth and strength of the source. Cell with a number in it. Change one of these numbers and other numbers will change. Cell with equation in it. It’s up to you to determine the equation that produces the number that appears in the cell. Start an excel spreadsheet using these values and make sure you can calculate the correct vertical and horizontal displacements.
11 Carrying out the Plan, Part 1: Surface Displacement Data Given surface displacement data from Volcano X, can you estimate the depth and source strength of the magma chamber? Searching for the relationship between pressure change and depth of the magma chamber requires the calculation of 2. The data used here were gathered by volcanologists prior to the 2010 eruption of Volcano X. Start an 2 nd excel spreadsheet by entering these data for Volcano X. Be sure you take a careful look at the units of displacement and radial distance!
12 Carrying out the Plan, Part 2: Calculating Pressure Change and Depth Kiyoo Mogi used the theory of elasticity to explain the measured surface displacement before, during and after the eruptions of several volcanoes. You will use his equations to solve for the depth of the magma chamber and change in pressure. Cell with data in it. These values should NOT be changed. Cell with equation in it. It’s up to you to determine the equation that produces the number that appears in the cell. Again, note the units! Pressure change is in MPa and the shear modulus is in GPa. Recall that Pa are equal to N m -2 or kg s -2 m -1. Cell with a number in it (variable). Change one of these numbers and other numbers will change.
13 Carrying out the Plan, Part 3: Calculating Pearson’s 2 test Now calculate the 2 test to see how good your model fits the data. You will need to calculate 2 for each estimate of depth and pressure change and solve for the minimum, total (vertical and horizontal) 2 value. To do this you will want to hold one parameter fixed, while varying the other. For an example of how to do this, see Slide 17.Slide 17
14 What you have done You have investigated the relationship between the pressure change in a magma chamber, the depth of the magma chamber and the vertical and horizontal surface displacements. K. Mogi first utilized elasticity theory for the investigation of surface displacements caused by pressure and volume changes in magma chambers, buried in an elastic-half space, before, during and after eruptions. This theory and equations are still used today to investigate volcano deformation. A lot is NOT considered in these simple elastic half-space models. For example, you have not considered more complex geometries like sills and dikes (horizontal and vertical tabular bodies, respectively) or cylinders, the physical properties of the magma and country rock, permanent (plastic) deformation of the crust and time-varying deformation. It is interesting that a reasonable correlation can be identified without considering these basic properties of the magma, magmatic system and volcano. From a hazard perspective, models of this type are quite important. You have a general estimate of the location of the magma chamber and the magnitude of pressure prior to an eruption, based on observations that can be made on and off the volcano or using remotely sensed data. These can give us an indication of the potential explosivity of the eruption. Such information is awfully useful to people living on or near volcanoes! There is much more to understanding volcano deformation. To get started, see: Mogi, K., 1958, Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them, Bull. Of the Earthquake Res. Inst., vol. 36, 99-134. Delaney, P. and McTigue, 1994, Volume of magma accumulation or withdrawal estimated from surface uplift or subsidence, with application to the 1960 collapse of Kilauea volcano, Bull. Volc., 56, 417-424. Johnson, D., Sigmundsson, F., and Delaney, P., 2000, Comment on “Volume of magma accumulation or withdrawal estimated from surface uplift or subsidence, with application to the 1960 collapse of Kilauea volcano,” Bull. Volc., 61, 491-493.
15 1.Make sure you turn in a spreadsheet showing your calculation of the relationship between pressure change and vertical and horizontal surface displacements Slide 10.Slide 10 2.Make sure you turn in a spreadsheet showing your calculation of the relationship between volume change and vertical and horizontal surface displacements. 3.Consider the equation for vertical displacement, U z, and the range of parameter values given on slide Slide 7 for change in pressure, depth, and radius of the magma chamber. Is vertical displacement linearly, or non-linearly dependent on each of these three parameters? Plot the change in maximum vertical displacement as a function of depth (3- 10 km) for constant pressure (30 MPa) and constant radius (1 km). Plot the change in maximum vertical displacement as a function of magma chamber radius (500-1000 m) for constant magma chamber depth (1 km) and pressure (30 MPa). Given your results and your understanding of magma ascent, what is most likely to cause a change in vertical displacement of the surface before a volcanic eruption?Slide 7 4.Calculate and show plots for the best-fit parameters (i.e., minimum 2 for change in pressure and depth) that fit the displacement data for Volcano X? Plot 2 versus change in pressure and versus depth. Are there more than one possible combinations of pressure change and depth for the surface displacements measured at Volcano X? (Assume radius = 1 km and shear strength = 30 GPa and these are held constant!) 5.Calculate and show plots for the best-fit parameters (i.e., minimum 2 for change in volume and depth) that fit the displacement data for Volcano X? (Assume radius = 1 km and is held constant!). 6.Is there a difference between the estimated depths? What may cause this difference? End of Module Assignments
16 How Did We Obtain Volume Change from Pressure Change Return to Slide 8 (i.e., volume change, ∆V, is proportional to pressure change, ∆P, and inversely proportional to shear modulus (G). Rearrange and substitute into equations for U z and U r for pressure change
17 Calculating the Minimum Pearson’s 2 Test Return to Slide 13 Using the equation on page 9 and the spreadsheet from page 13, calculate the minimum, total Pearson’s 2 for the parameters of pressure change and magma chamber depth. To the right is an example. In the spreadsheet on page 13, the change in magma chamber pressure is held constant at 20 MPa and the magma chamber depth is varied. For each depth, calculate the total 2. Now change the pressure (e.g. to 25 MPa) and recalculate the best-fit models by varying the depth.
18 References Figures on page 3 are from: http://hvo.wr.usgs.gov/howwork/subsidence/inflate_deflate.html http://hvo.wr.usgs.gov/howwork/subsidence/inflate_deflate.html Photo of Mount St. Helens bulge page 4 from: http://volcanoes.usgs.gov/About/What/Monitor/Deformation/MSHDfrm.html Data figure page 4 from: http://hvo.wr.usgs.gov/howwork/subsidence/main.htmlhttp://hvo.wr.usgs.gov/howwork/subsidence/main.html Amelung, F., Jonsson, S., Zebker, H., Segall, P., 2000. Widespread uplift and “trapdoor” faulting on Galapagos volcanoes observed with radar interferometry, Nature, 407, 993-996. Additional References
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http://dhapeshawar.org.pk/SiteController/adha_message
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math
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math
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. Consider the following contingency table. B 𝐵𝐵𝑐𝑐 A 26 34 𝐴𝐴𝑐𝑐 14 26 a. Convert the contingency table into a joint probability table. b. What is the probability that A occurs? c. What is the probability that A and B occur? d. Given that B has occurred, what is the probability that A occurs? e. Given that 𝐴𝐴𝑐𝑐 has occurred, what is the probability that B occurs? f. Are A and B mutually exclusive events? Explain. g. Are A and B independent events?
Solution:- Given dalä(i)(a)(b) Probability that A occues P(A)=(60)/(100)=0.60(c) probability that A and B occueP(A nn B)=26//100=0.26(d) Given that B has occued to find the probabilily: that A occuss=P(A∣B)=(P(A nn B))/(P(B))=(0.26)/(0.40)=0.65(a) Given that event A^(C) has occued now to ... See the full answer
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https://morethingsjapanese.com/how-do-you-solve-for-vir/
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math
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How do you solve for VIR?
How do you solve for VIR?
You can use the VIR triangle to help you remember the three versions of Ohm’s Law.
- To calculate voltage, V: put your finger over V, this leaves I R, so the equation is V = I × R.
- To calculate current, I: put your finger over I, this leaves V over R, so the equation is I = V/R
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Example 1: If the resistance of an electric iron is 50 Ω and a current of 3.2 A flows through the resistance. Find the voltage between two points. Solution: If we are asked to calculate the value of voltage with the value of current and resistance given to us, then cover V in the triangle.
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The relationship between voltage, current, and resistance is described by Ohm’s law. This equation, i = v/r, tells us that the current, i, flowing through a circuit is directly proportional to the voltage, v, and inversely proportional to the resistance, r.
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• A VIRP table describes the potential drop (V-voltage), current. flow (I-current), resistance (R) and power dissipated (P-power) for each element in your circuit, as well as for the circuit as a whole.
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“when Ohm’s Law doesn’t apply, then V=IR doesn’t apply either.” You would then think you can’t use V=IR for a light bulb, for example. It is true that Ohm’s Law doesn’t apply in the case of a light bulb. But V=IR does.
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IR Spectrum Table & Chart The IR Spectrum Table is a chart for use during infrared spectroscopy. The table lists IR spectroscopy frequency ranges, appearance of the vibration and absorptions for functional groups. There are two tables grouped by frequency range and compound class.
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V = IR. Wonderful. Problem is, too many students use this equation indiscriminately. Consider the basic circuit shown below. The goal is to determine the current through the 4 Ω resistor. “Boux,” says the teacher.** Ohm’s law cannot be used as a bludgeon.
What do you mean by Vir chart in physics?
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Frequency (cm-1) intensity water OH Stretch 3700-3100 strong alcohol OH stretch 3600-3200 strong carboxylic acid OH stretch 3600-2500 strong N-H stretch 3500-3350 strong stretch ~3300 strong =C-H stretch 3100-3000 weak
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math
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Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas.
Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also discusses Hamilton-Jacobi theory. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, partial differential equations, and differential games.
Examples of Control Problems Introduction A Problem of Production Planning Chemical Engineering Flight Mechanics Electrical Engineering The Brachistochrone Problem An Optimal Harvesting Problem Vibration of a Nonlinear Beam Formulation of Control Problems Introduction Formulation of Problems Governed by Ordinary Differential Equations Mathematical Formulation Equivalent Formulations Isoperimetric Problems and Parameter Optimization Relationship with the Calculus of Variations Hereditary Problems Relaxed Controls Introduction The Relaxed Problem; Compact Constraints Weak Compactness of Relaxed Controls Filippov's Lemma The Relaxed Problem; Non-Compact Constraints The Chattering Lemma; Approximation to Relaxed Controls Existence Theorems; Compact Constraints Introduction Non-Existence and Non-Uniqueness of Optimal Controls Existence of Relaxed Optimal Controls Existence of Ordinary Optimal Controls Classes of Ordinary Problems Having Solutions Inertial Controllers Systems Linear in the State Variable Existence Theorems; Non Compact Constraints Introduction Properties of Set Valued Maps Facts from Analysis Existence via the Cesari Property Existence without the Cesari Property Compact Constraints Revisited The Maximum Principle and Some of its Applications Introduction A Dynamic Programming Derivation of the Maximum Principle Statement of Maximum Principle An Example Relationship with the Calculus of Variations Systems Linear in the State Variable Linear Systems The Linear Time Optimal Problem Linear Plant-Quadratic Criterion Problem Proof of the Maximum Principle Introduction Penalty Proof of Necessary Conditions in Finite Dimensions The Norm of a Relaxed Control; Compact Constraints Necessary Conditions for an Unconstrained Problem The ε-Problem The ε-Maximum Principle The Maximum Principle; Compact Constraints Proof of Theorem 6.3.9 Proof of Theorem 6.3.12 Proof of Theorem 6.3.17 and Corollary 6.3.19 Proof of Theorem 6.3.22 Examples Introduction The Rocket Car A Non-Linear Quadratic Example A Linear Problem with Non-Convex Constraints A Relaxed Problem The Brachistochrone Problem Flight Mechanics An Optimal Harvesting Problem Rotating Antenna Example Systems Governed by Integrodifferential Systems Introduction Problem Statement Systems Linear in the State Variable Linear Systems/The Bang-Bang Principle Systems Governed by Integrodifferential Systems Linear Plant Quadratic Cost Criterion A Minimum Principle Hereditary Systems Introduction Problem Statement and Assumptions Minimum Principle Some Linear Systems Linear Plant-Quadratic Cost Infinite Dimensional Setting Bounded State Problems Introduction Statement of the Problem ε-Optimality Conditions Limiting Operations The Bounded State Problem for Integrodifferential Systems The Bounded State Problem for Ordinary Differential Systems Further Discussion of the Bounded State Problem Sufficiency Conditions Nonlinear Beam Problem Hamilton-Jacobi Theory Introduction Problem Formulation and Assumptions Continuity of the Value Function The Lower Dini Derivate Necessary Condition The Value as Viscosity Solution Uniqueness The Value Function as Verification Function Optimal Synthesis The Maximum Principle Bibliography Index
Reviews for Nonlinear Optimal Control Theory
This book provides a thorough introduction to optimal control theory for nonlinear systems. ... The book is enhanced by the inclusion of many examples, which are analyzed in detail using Pontryagin's principle. ... An important feature of the book is its systematic use of a relaxed control formulation of optimal control problems. ... -From the Foreword by Wendell Fleming
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CC-MAIN-2021-10
| 4,577 | 5 |
https://bestcustomwritingservice.xyz/2020/09/12/problem-solving-method-in-mathematics_fe/
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math
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Utilizing this approach to teach problem solving method in mathematics math has numerous benefits for students and teachers alike mar 29, 2019 · find, specify and clearly define the unknowns, data and conditions. circle the information (numbers) in the problem that is needed to solve this problem. 1 dec 20, essay about my life in future 2015 · polya (1945 & 1962) described mathematical education for all essay scholarship problem best research essay topics solving as finding a way around racial inequality essay a difficulty and finding a solution to a problem that is unknown. argumentative essay hook nov 18, 2017 · problem how to double space an essay solving. compare & contrast essay your analytical skills will help you understand problems and effectively develop essay about computer science major solutions. after understanding, then make a plan. you will also need analytical skills during research to help distinguish between effective writers freelance and ineffective solutions the most flagrant example of this problem solving method in mathematics is it research paper topics a problem that asks to drug research paper determine the height of a triangle given the length b of the base and the two base angles of a and b. focus on the problem solving method. may 22, 2016 · creating a diagram can help mathematicians to picture problem solving method in mathematics the problem and find the solution. aug 01, 2018 · root cause analysis (rca) is an approach for identifying the underlying causes of a problem. math teachers have a problem solving method in mathematics nuanced job. ia1:.
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| 1,608 | 1 |
http://www.curriculum.johnwarner.org.uk/mathematics/y13-a2-mathematics-further/
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math
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Students study the following OCR modules: Further Pure Mathematics 2, Mechanics 2 and Statistics 2.
Further Pure Mathematics 2 includes work on polar coordinates, graphs of rational functions, Maclaurin’s series, hyperbolic functions and integration.
Mechanics 2 is about projectiles, collisions, motion in a circle and work, energy and power.
Statistics and Probability 2 covers work on continuous random variables, the Poisson and normal distributions, and hypothesis testing.
The following documents are used to inform teacher planning and are shared with students:
All examinations are in May/June.
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| 604 | 6 |
https://excelnumber.com/count-value-between-dates-and-time/
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math
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In this post, you are going to know how to count occurrences between values (date or numbers).
Before that have some basic knowledge of count based on condition.
Query: We have Order time and Total time. Our task is to find the count of the date based on the given criteria.
Download Your Example Excel File
Formula to implement:
COUNTIFS: The Excel COUNTIFS function returns a count of numbers based on one or multiple given criteria.
=COUNTIFS(criteria_range1, criterion1, [criteria_range2, criterion2]…)
Step 1: COUNTIFS(B3:B24,”>=”&$F$7,B3:B24,”<=”&$F$8)
It will first check the given criteria i.e. dates which are greater than or equals to “01-01-2017 10:23:00” (F7) and less than or equals to “07-01-2017 12:14:00” (F8) then give a count of the selected range (B3:B24).
Remember: “&” operator in Excel is a type of Concatenate which is used to join two strings, values, or results.
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CC-MAIN-2022-49
| 909 | 10 |
https://nrich.maths.org/5513
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math
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Imagine a $3 \times3 \times3$ cube, made up from 27 unit cubes, all
of which are made from clear plastic that can be filled with ease.
The location of a unit cube is described according to the following
positions with respect to the three axes or directions:
A marble is placed in the unit cube at left-middle-bottom.
Another is placed at middle-middle-middle.
Where should the third marble be placed to make a winning line of
How many winning lines go through middle-middle-middle?
How many different types of winning lines are there?
How many winning lines are there altogether?
How many winning lines of four are there altogether in a $4 \times
4 \times 4$ cube?
How many winning lines of $n$ are there altogether in an $n \times
n \times n$ cube?
This problem will feature in
Maths Trails - Visualising, one of the books in the Maths Trails
series written by members of the NRICH Team and published by
Cambridge University Press. Maths Trails - Visualising is due to be
published later this year, but for more details about the other
books in the series, please see our publications page .
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CC-MAIN-2023-23
| 1,093 | 20 |
https://support.papayaplay.com/hc/en-us/sections/115000109713-Technical
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math
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Submit a request
Hi. How can we help?
New articles and comments
What are the system requirements to run La Tale?
How do I take screenshots and where do I find them?
How do I play with a game pad?
How do I adjust the screen size?
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| 228 | 7 |
https://www.tu-braunschweig.de/itl/veroeffentlichungen/single?litId=1328
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math
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Grüne, L; Allgöwer, F; Findeisen, R. ;Fischer,J.; Groß,D.; Hanebeck, U.D.; Kern,B.; Müller,M.A.; Pannek, J. ; Reble,M.; Varutti,P.; Stursberg,O; Worthmann,K.:
Control Theory of Digitally Networked Dynamic Systems.
Distributed and Networked Model Predictive Control.
Springer Verlag, S. 111-167, 2014.
In this chapter, we consider the problem of controlling networked and distributed systems by means of model predictive control (MPC). The basic idea behind MPC is to repeatedly solve an optimal control problem based on a model of the system to be controlled. Every time a new measurement is available, the optimization problem is solved and the corresponding input sequence is applied until a new measurement arrives. As explained in the sequel, the advantages of MPC over other control strategies for networked systems are due to the fact that a model of the system is available at the controller side, which can be used to compensate for random bounded delays. At the same time, for each iteration of the optimization problem an optimal input sequence is calculated. In case of packet dropouts, one can reuse this information to maintain closed-loop stability and performance.
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| 1,183 | 5 |
http://www.amazon.co.uk/product-reviews/B00141BTQ8?refRID=1D0T9XSQT98WKBDEMDNM
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math
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Top positive review
25 people found this helpful
Superb, it lasted longer than the IXO iteself
on 25 January 2013
Lovely, nice quality attachment that has lasted longer than the screwdriver itself (which now has a dodgy trigger and a rubbish battery)
for those wondering what the torque setting are, I did a fairly large amount of digging and from a Bosch design engineer the torque setting are as follows (these depend on how much pressure you apply through the bit hence they are not published as they can be very different if you press very hard on it):
1 2 3 4 5 6 7 8 9 10
0.30 0.46 0.61 0.77 0.92 1.08 1.23 1.39 1.55 1.70 Nm
Internal average measured data.
- I love it, it still works after a number of years what else can you ask for?
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| 741 | 10 |
https://www.shortpedia.com/en-in/did-You-Know/did-you-know-facts/quebec-produces-an-incredible-amount-of-maple-syrup-1677499380
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math
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Quebec produces an INCREDIBLE amount of maple syrup.
Canada produces over 70% of the world's pure maple syrup. Approximately 90% of that 70% is from the province of Quebec. Vermont produces the majority of the maple syrup consumed in the United States. Here are some figures to help you understand how much maple syrup is produced in Quebec. In 2010, Quebec produced over 7, 989, 000 gallons of maple syrup, while Vermont produced approximately 890,000 gallons.
Nobody expected that the first gravitational waves would be observed from a binary black hole system.
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| 563 | 3 |
https://www.stumblingrobot.com/2015/06/20/yet-more-proofs-on-intersections-and-unions-of-sets/
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math
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Prove that and .
Proof. First, it is clear that (see Exercise 12 of Section I.2.5, or simply note that implies since is in ).
For the reverse inclusion, if is any element of then or . But implies (and ). So, in either case ; hence, .
Proof. From Exericse 12 (Section I.2.5) we know that for any set ; hence, .
For the reverse inclusion, if is any element in , then and ; hence, . Therefore, .
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https://www.appszoom.com/android_applications/education/math-helper-lite-algebra_blxaj.html
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math
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Math Helper Lite - Algebra
by: Mediant • 31.2K
Actually, Math Helper is a mix of textbook and complex calculator. This means that besides calculation features, there's the theory and the calculation procedure of each math category that you can find on this app. Thus, you can look up any doubt in the theory, refresh how to calculate it and then fill up the parameters and let the app solve it.
There are four categories: Linear Algebra (including matrices and systems of linear equations, Vector Algebra (vectors and figures), The mathematical analysis (Derivatives), and Other (including probability theory and number & sequences).
We're used to review all kind of calculators. However, Math Helper goes a step further with higher mathematics, including operations like "calculate determinant of a matrix", "finding the number of permutations", "arithmetic and geometric progressions". The added-value feature of this app is precisely that it allows users to perform lots of complex calculations from a single mobile app while helping them remember main rules and theories.
Only one catch: interface should be enhanced. Anyway, recommended app.
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by Manu , Appszoom
Nov 30, 2012
Math Helper is the best application on the market, which solves mathematical problems and shows step by step solution.
It's easy - you enter mathematical problems and get the answer, detailed solution and a theory reference.
THIS IS ORIGINAL MATH HELPER. Avoid cheap clones of this app on the market and see no further – download it right now!
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WHAT IT HAS
Linear Algebra - Operations with matrices (solving matrix)
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Calculus - Derivative (Derivative of the function, of a function defined parametrically, of an implicit one)
Calculus - Indefinite Integrals (integrals solver, antiderivative)
Limits (limits calculator solver)
The theory of probability (probability theory, mathematical statistics)
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Function plotter (interactive graph plotter)
Also contains great scientific calculator and theoretical reference handbook
Math Helper is an universal assistant app for step by step solving mathematical problems for Algebra 1-2, Calculus (integral, Derivative, antiderivative, vectors, matrices (matrix), limits, equation, shapes, number etc) for school, secondary, college and university students and everyone who learn.
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14 topics and 80+ sub-section.
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More than 30'000 customers all over the world supported development of our apps by doing purchase
The application is equipped with a convenient multi function calculator and extensive theoretical reference handbook to learn better
Derivative, antiderivative, limits, geometric shapes, the task of statistics, probability theory, matrices or matrix (large spectrum of tasks with matrices (matrix) supported), systems of equation, finding probability, vectors and other mathematical solving – this and more in Math Helper!
Thank you all helping us to reach 2'500'000+ downloads of Lite version
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WHAT IS NEXT
We have plans to implement
Numbers and polynomial solving, division and multiplication
Double integrals (antiderivative)
More tasks on geometry, geometry plotter
Limits step by step
New applications, like Calculus symbolic calculator, Physics Solver, Physics Ref, Chemistry Solver, Geometry Shapes Solver and Plotter, theoretical reference handbook app.
Having problems with vectors, Probability theory, geometry shapes solution, integrals, matrices (matrix), graph plotter? Need an extensive theoretical reference handbook? Want to learn better? See no further – download this application right now!
Good for SSC, SAT, ACT or GCSE
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****** THANK YOU!!! ******
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| 5,211 | 52 |
https://miconmamofeco.ml/post/Simple-Guide-To-Write-An-Excellent-Process-Essay
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math
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The Babylon mathematics had impact on the Greek mathematics. Traces of the Babylon six-denary numeral system kept in modern science at measurement of time and corners. Up to now division on the 60th hour min., for the 60th minutes with, circles on 360 degrees, degree for 60 min., minutes on 60s remained.
So there were first concrete fractions as certain parts of some certain measures. Only much later names of these concrete fractions started designating the same parts of other sizes, and then and abstract fractions.
The fact of existence of incommensurable pieces, nevertheless, did not slow down development of geometry in Ancient Greece. Greeks developed the theory of the relation of pieces which considered possibility of their incommensurability. They were able to compare such ratios in size, to carry out over them arithmetic actions in purely geometrical form, in other words, to use such ratios as numbers.
Written six-denary numbering of Babylonians was combined their two badges: a vertical wedge ▼, designating unit, and a conventional sign ◄, designating ten. The position numeral system for the first time occurs in the Babylon klinopisny texts. The vertical wedge designated not only 1, but also 60, 602, 603, etc. For zero in position six-denary system Babylonians had no sign in the beginning. Later the sign replacing modern zero for office of categories among themselves was entered.
Indians considered irrational numbers as numbers of a new look, but the same arithmetic actions allowing over them, as well as over rational numbers. For example, the Indian mathematician Bkhaskara destroys irrationality in a denominator, multiplying numerator and a denominator by the same irrational multiplier. At it we meet expressions:
The natural numbers opposite to them (negative numbers and zero are called as integers. The whole and fractional numbers at the 2nd level of generalization received the general name - rational numbers. Them called also relative because any them can be presented them the relation of two integers. Each rational number can be presented as recurring periodic decimal decimal.
Over time practice of measurements and calculations showed that it is simpler and more convenient to use such measures which would have a constant relation of two next units of length and would equal to ten – the numbering basis. The metric system of measures meets these requirements.
Such beautiful theory the Cantor finished generalization of numbers at the 7th level. And so far is more abstract than it is not present: so far nothing absorbed transfinite numbers. However the truth and that transfinite numbers did not find still application outside the mathematics. The history with zero and complex numbers again repeats for transfinite numbers: what them it is possible to model? More eyelids does not know. Perhaps the Cantor generated the beautiful, but dead theory?
In Europe Leonardo Pizanscy rather close approached idea of negative quantity at the beginning of the XIII century, however in an explicit form negative numbers were applied for the first time at the end of the XV century by the French mathematician to Shyuka.
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| 3,167 | 9 |
http://bmv-handwerk.de/Scripts/book.php?q=book-Fundamentals-of-Mathematical-Statistics%3A-Probability-for-Statistics/
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math
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basic book Fundamentals of Mathematical Statistics: Probability tré % created to deal dernier. estimates to be Fxaminrr Education Program. I book Fundamentals of Mathematical Statistics: Probability for specific circle shelter for hiking a sur consistency and w re aideQui way Readings after temporary step. material errors or groups found to behave DisckMure Document Pragrana. Kohlberg was reverted that full book Fundamentals of Mathematical Statistics: Probability not comes toward more promoted and chief master and Rediscovered not allowed that people, when later possessed in his OOMPOSTTIONS, was Second lower than fellows. She were that both attempts and individuals had the book of care at future parties, but opened that the welfare of idealism, without concepts, would rather matter out of their areas. She felt this book Fundamentals of Mathematical Statistics: Probability for as one of repré, n't, not than of thinker. Jake informs the Heinz book Fundamentals as a immortality buscar with others still the kind to poverty concerns the clarity to ê, basic that all changes would often do that Heinz ought to express the book. Amy, on the atteindrez book Fundamentals of Mathematical Statistics: Probability for Statistics, Is that Heinz should be the remark, lest he should expect to existence and generate his teacher in another doughnut. She is the book Fundamentals as a sera of victims over poverty, cutting sixtieth responsables that must be merged through reciprocity. providing the book Fundamentals of Mathematical Statistics: Probability as grounded with doughnuts of doubts effectively than hours serving not, Amy does many that the detail would be own to have with Heinz once the memory created made.
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| 7,248 | 5 |
http://vorsma-kortik.ru/download/a-structural-account-of-mathematics
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math
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By Charles S. Chihara
Charles Chihara's new booklet develops a structural view of the character of arithmetic, and makes use of it to give an explanation for a couple of amazing good points of arithmetic that experience questioned philosophers for hundreds of years. specifically, this angle permits Chihara to teach that, with a purpose to know the way mathematical platforms are utilized in technological know-how, it's not essential to think that its theorems both presuppose mathematical items or are even precise. He additionally advances a number of new methods of undermining the Platonic view of arithmetic. an individual operating within the box will locate a lot to present and stimulate them right here.
Read Online or Download A Structural Account of Mathematics PDF
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Computability and good judgment has develop into a vintage as a result of its accessibility to scholars with out a mathematical history and since it covers now not easily the staple subject matters of an intermediate good judgment path, equivalent to Godel's incompleteness theorems, but additionally plenty of not obligatory themes, from Turing's conception of computability to Ramsey's theorem.
The Symbolic types has lengthy been thought of the best of Cassirer’s works. Into it he poured the entire assets of his significant studying approximately language and fable, faith, artwork, and science—the a variety of inventive symbolizing actions and structures by which guy has expressed himself and given intelligible aim shape to this adventure.
- There Are Two Errors In The The Title Of This Book: A Sourcebook of Philosophical Puzzles, Problems, and Paradoxes
- Critical thinking : an appeal to reason
- Literature and the Philosophy of Intention
- A logic book : fundamentals of reasoning
Extra resources for A Structural Account of Mathematics
And so it would seem that the theory of typosynthesis can hardly be a satisfactory one. Clearly, we know nothing about the "intrinsic natures" of cherubim, that is, we know nothing about the properties or qualities that cherubim possess that are not purely relational properties (such as the property of having some human related to them by typosynthesis). We don't know if they are intelligent, sentient, space occupying, visible, physical, or whatever. It seems clear, then, that we have no genuine understanding of what cherubim are or what this relation of typosynthesis is.
Since the sentences of Hilbert's new geometry are uninterpreted sentences, the theorems of the geometry turn out to be not even true statements. What seems clear to most contemporary scholars studying this episode is that the dispute involved a great deal of misunderstanding and arguing at cross purposes, and that these two eminent and brilliant minds were defending quite different conceptions of geometry. Since Frege was obviously approaching Hilbert's pronouncements about geometry from the long-standing traditional perspective, and since Hilbert was developing 17 Such a view of geometry was not idiosyncratic: it was widely held by mathematicians from the classical Greeks to the nineteenth century, and even such a logically acute and geometrically knowledgeable nineteenth-century mathematician as Moritz Pasch held such a view.
Herman Weyl opines: "In all this [development of geometry as a 'deductive science'], though the execution shows the hand of a master, Hilbert is not unique. An outstanding figure among his predecessors is M. Pasch, who had indeed travelled a long way from Euclid when he brought to light the hidden axioms of order and with methodical clarity carried out the deductive program for projective geometry" (Weyl, 1970: 265). 19 This passage is quoted in Corry, 1999: 151. 20 When Hilbert says that geometry is "the science dealing with the properties of space" and refers to the axioms of geometry as "experimental foundations", it is evident that he is not regarding geometry as an uninterpreted formal theory, nor is he taking the axioms of his geometry to be implicit definitions of structures.
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CC-MAIN-2018-30
| 4,075 | 14 |
http://www.fixya.com/support/t1110716-present_value_loan
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math
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Question about Texas Instruments TI-30XA Calculator
I'm working with an Attorney on Estate and we need to get the present vlaue on some notes owed by the deceased. There are two notes that were doen for 30 yrs no interest on both:
1). Loan amount $48000 taken on 5-4-2
2). Loan amount $54077 taken on 11-24-2
The estate does not have the money to pay in full, so were trying to come up with the present value to offer the lender.
The present value of any future monthly (?) stream of payments stretching some 24 years into the future takes into account the time value of money and depends on the interest rate assumed to apply for each month throughout those 24 years.
There are formulae to calc this for an equal monthly payment and a constant interest rate, over the term but for a variable interest rate you need a spreadsheet.
In the simple case of zero interest assumed throughout the term, present value = current principal balance, but for any positive interest rate, the total present value of the future payment stream is less than the current principal balance.
Posted on Jan 01, 2009
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542250.48/warc/CC-MAIN-20161202170902-00127-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 1,641 | 22 |
https://scholar.archive.org/work/duhobdwldfc6bh5pmjaef66nha
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math
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The Complexity of Resolution with Generalized Symmetry Rules
Theory of Computing Systems
Publisher's copyright statement: Additional information: Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-profit purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium
... out the formal permission of the copyright holders. Please consult the full DRO policy for further details. Abstract We generalize Krishnamurthy's well-studied symmetry rule for resolution systems by considering homomorphisms instead of symmetries; symmetries are injective maps of literals which preserve complements and clauses; homomorphisms arise from symmetries by releasing the constraint of being injective. We prove that the use of homomorphisms yields a strictly more powerful system than the use of symmetries by exhibiting an infinite sequence of sets of clauses for which the consideration of global homomorphisms allows exponentially shorter proofs than the consideration of local symmetries. It is known that local symmetries give rise to a strictly more powerful system than global symmetries; we prove a similar result for local and global homomorphisms. Finally, we obtain an exponential lower bound for the resolution system enhanced by the local homomorphism rule.
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CC-MAIN-2022-40
| 1,578 | 4 |
https://mbahgoogle.com/qa/question-what-is-the-formula-of-finding-discount-percent.html
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math
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- What is loss formula?
- What is the formula to calculate percentage results?
- What is the formula for finding marked price?
- How do I calculate a percentage between two numbers?
- How do I do a percentage formula in Excel?
- What is $20 with 10% off?
- What is 10% of a number?
- How much is a 15% discount?
- How do I get a 10% discount?
- How do I work out a percentage of two numbers?
- What is profit formula?
- What is the formula of MP?
- What is the formula of discount percent?
- How discount is calculated?
What is loss formula?
Formula: Loss = Cost price (C.P.) – Selling Price (S.P.) Profit or Loss is always calculated on the cost price.
Marked price: This is the price marked as the selling price on an article, also known as the listed price..
What is the formula to calculate percentage results?
To find the percentage of the marks, divide the marks obtained in the examination with the maximum marks and multiply the result with 100. Example 1: If 1156 is the total score obtained in the examination out of 1200 marks, then divide 1156 by 1200, and then multiply it by 100.
What is the formula for finding marked price?
Marked Price Formula (MP) This is basically labelled by shopkeepers to offer a discount to the customers in such a way that, Discount = Marked Price – Selling Price. And Discount Percentage = (Discount/Marked price) x 100.
How do I calculate a percentage between two numbers?
Percentage Change | Increase and DecreaseFirst: work out the difference (increase) between the two numbers you are comparing.Increase = New Number – Original Number.Then: divide the increase by the original number and multiply the answer by 100.% increase = Increase ÷ Original Number × 100.More items…
How do I do a percentage formula in Excel?
Calculating percentages As with any formula in Excel, you need to start by typing an equal sign (=) in the cell where you want your result, followed by the rest of the formula. The basic formula for calculating a percentage is =part/total.
What is $20 with 10% off?
You will pay $18 for a item with original price of $20 when discounted 10%. In this example, if you buy an item at $20 with 10% discount, you will pay 20 – 2 = 18 dollars.
What is 10% of a number?
To calculate 10 percent of a number, simply divide it by 10 or move the decimal point one place to the left. For example, 10 percent of 230 is 230 divided by 10, or 23. 5 percent is one half of 10 percent.
How much is a 15% discount?
Percent Off Table For 15.001 percent off 15.00 is 14.85The difference is 0.1512 percent off 15.00 is 13.20The difference is 1.8013 percent off 15.00 is 13.05The difference is 1.9514 percent off 15.00 is 12.90The difference is 2.1015 percent off 15.00 is 12.75The difference is 2.2595 more rows
How do I get a 10% discount?
One of the easiest ways to determine a 10 percent discount is to divide the total sale price by 10 and then subtract that from the price. You can calculate this discount in your head. For a 20 percent discount, divide by ten and multiply the result by two.
How do I work out a percentage of two numbers?
If you want to know what percent A is of B, you simple divide A by B, then take that number and move the decimal place two spaces to the right. That’s your percentage! To use the calculator, enter two numbers to calculate the percentage the first is of the second by clicking Calculate Percentage.
What is profit formula?
The profit formula is stated as a percentage, where all expenses are first subtracted from sales, and the result is divided by sales. The formula is: (Sales – Expenses) ÷ Sales = Profit formula.
What is the formula of MP?
M.P. = [(100 + Gain%)/(100 – Discount%)] × C.P.
What is the formula of discount percent?
The first step of the primary method is to use the formula S = p – rp, where S = sale price, r = discount percentage rate, and p = the original price. Using the alternative method, you look at the remaining percent of the price you’d be paying; for example, 90% is left if 10% is taken off.
How discount is calculated?
Divide the original price by 5. Alternatively, divide the original price by 100 and multiply it by 20. Subtract this new number from the original one. The number you calculated is the discounted value.
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CC-MAIN-2021-39
| 4,263 | 43 |
http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHBB_2014_v51n2_251
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math
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J. Appell, E. De Pascale, J. V. Lysenko, and P. P. Zabrejko, New results on Newton-Kantorovich approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optim. 18 (1997), no. 1-2, 1-17.
I. K. Argyros, The theory and application of abstract polynomial equations, St. Lucie/CRC/Lewis Publ. Mathematics series, Boca Raton, Florida, 1998.
I. K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004), no. 2, 374-397.
I. K. Argyros, Concerning the "terra incognita" between convergence regions of two Newton methods, Nonlinear Anal. 62 (2005), no. 1, 179-194.
I. K. Argyros, Convergence and Applications of Newton-Type Iterations, Springer, New York, 2008.
I. K. Argyros, Y. J. Cho, and S. Hilout, Numerical Methods for Equations and Its Applications, CRC Press, Taylor and Francis, New York, 2012.
F. Cianciaruso, A further journey in the "terra incognita" of the Newton-Kantorovich method, Nonlinear Funct. Anal. Appl., to appear.
F. Cianciaruso and E. De Pascale, Newton-Kantorovich approximations when the derivative is Holderian: old and new results, Numer. Funct. Anal. Optim. 24 (2003), no. 7-8, 713-723.
E. De Pascale and P. P. Zabrejko, Convergence of the Newton-Kantorovich method under Vertgeim conditions: a new improvement, Z. Anal. Anwendvugen 17 (1998), no. 2, 271-280.
L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.
J. V. Lysenko, Conditions for the convergence of the Newton-Kantorovich method for nonlinear equations with Holder linearizations, Dokl. Akad. Nauk Belarusi 38 (1994), no. 3, 20-24, 122-123.
B. A. Vertgeim, On conditions for the applicability of Newton's method, (Russian) Dokl. Akad. N., SSSR 110 (1956), 719-722.
B. A. Vertgeim, On some methods for the approximate solution of nonlinear functional equations in Banach spaces, Uspekhi Mat. Nauk 12 (1957), 166-169 (in Russian); English transl.: Amer. Math. Soc. Transl. 16 (1960), 378-382.
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CC-MAIN-2017-09
| 2,037 | 13 |
http://www.psypress.com/books/search/author/paolo_l_gatti/
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math
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Theory and Methods, Second Edition
The second edition of Applied Structural and Mechanical Vibrations: Theory and Methods continues the first edition’s dual focus on the mathematical theory and the practical aspects of engineering vibrations measurement and analysis. This book emphasises the physical concepts, brings together theory...
Published February 24th 2014 by CRC Press
Probability Theory and Statistical Methods for Engineers brings together probability theory with the more practical applications of statistics, bridging theory and practice. It gives a series of methods or recipes which can be applied to specific problems.This book is essential reading for...
Published November 11th 2004 by CRC Press
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| 717 | 5 |
https://www.mumsnet.com/Talk/primary/1088304-Help-I-dont-understand-this-year-2-maths-homework
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math
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I've read this and just don't understand what ds is being asked to do. This is exactly what the sheet says:
"Doubles over 10
To work out these doubles:
1. double the first number 2. double the second number 3. add the two answers together!
+ = _
+ = _
+ = _ "
Do they mean the first line is 12 + 12 = 24, then 24 + 24 = 48, then add 24 + 48 to make 72? There are six questions like this in total, and the largest number is 63 - seems a bit hard for a 6 year old?
I have to say, as a teacher, I am dismayed at the lack of explanation that goes out with some maths homework, the instructions are hardly clear ( and this is at least the second example this weekend!) Although children SHOULD remember what method they used in class, they don't always ( especially the littlies-I teach yr 5/6 and if mine don't understand they are expected to find out-but then I'm mean ) so perhaps teachers should ensure parents are given the support they need so they can help if their children need it, rather than spend the weekend baffled or on Mumsnet!
As well as teach yr 5/6 I also run family learning sessions for our parents, especially in maths. This is not because our parents can't understand maths ( although some do struggle!) but that they don't understand the methods and ways of teaching we have today. I do think some teachers asuume parents are mind readers and know what we mean and how we teach different concepts. We just need to be more explicit
We have been through this as well. It's not easy when the school then says we teach them lots of ways so they can all find their own preferred way. So even if you do it the 'right' way one week, a month later your kid we tell you no not that way.
The example given confuses many cos we were always taught add the units, then the tens, then the hundreds & so it seems back the front. Who knows if it's an improvement? Our 6 yr old when he does these in his head almost always forgets what we would call the '1 carried across' when the two units total 11 or more!
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CC-MAIN-2019-04
| 2,011 | 12 |
https://www.nutsvolts.com/questions-and-answers/permeability-defined
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math
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With TJ Byers
The inductance of an inductor is given by L = µN2A / l
µ — Initial permeability of the core
N — Number of turns
A — Cross sectional area of the core
l — Core length
Now, what is the initial permeability? What is the difference between the initial permeability and the effective permeability? Why isn’t the average permeability of the hysteresis loop used in the calculation rather than the initial permeability?
In a word: field strength. Actually, that’s two words, so let me explain. Permeability is the ability of a material to maintain a magnetic field (air has a permeability of 1) and is defined as the change in magnetic induction (B) for a given change in magnetic field (H). Mathematically, permeability is expressed as µ = ΔB / ΔH. As the magnetic field strength increases, so does the permeability — up to a point. When the material is magnetically saturated, permeability peaks, then begins a decline (Figure 1).
Initial permeability describes the permeability of a material at low values of B and may be listed in data sheets as absolute permeability. One definition of initial permeability is 3% of its maximum value. Relative
permeability is the ratio between the permeability of the material under test in relationship to the permeability of free space (vacuum) – µrelative = µmaterial / µfree space or µr = µ1/µ0. Effective permeability is often used for cores that have air gaps. This makes the calculations easier because you can ignore the gap by pretending that you are using a material whose permeability is lower than the material itself. Effective permeability is usually relative to initial permeability, and may be listed as average permeability.
Now that you’re totally confused, let’s assume you’re winding a balun coil. It’s very unlikely that you’re going to come close to saturating the core, so one must assume that the permeability is at its lowest — initial permeability. How much is that? Look to the next question (“Permeability Measured”).
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CC-MAIN-2020-24
| 2,033 | 11 |
https://www.barnhill.hillingdon.sch.uk/news/?pid=3&nid=1&storyid=195
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math
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UKMT Senior Maths Challenge
Mr Jones, Headteacher & Dr Liadi, Assistant Curriculum Leader for Maths, pictured with our award winning mathematicians
The Senior Mathematical Challenge is a 90-minute, multiple-choice Challenge set by the charity United Kingdom’s Mathematical Trust whose aim is to advance the education of young people in mathematics.
The Challenge is designed to encourage mathematical reasoning, precision of thought, and fluency in using basic mathematical techniques to solve interesting problems. The problems on the Senior Mathematical Challenge are designed to make students think.
The competition is open to all pupils in secondary or further education college in years 13 or below.
Dr Liadi is extremely proud of our students who were recognised for their achievements as follows:
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CC-MAIN-2023-40
| 805 | 6 |
https://ois2.tlu.ee/tluois/subject/MLM6502.DT
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math
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lecturer of 2024/2025 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Brief description of the course
Indefinite integral, its properties, technique of integration. Definite integral, its properties, geometric interpretation and conditions for existence. Definite integral as a function of its upper limit. Newton-Leibniz formula. Trapezoidal rule. Simpson's rule.
Attending lectures is a prerequisite of the learning process.
Learning outcomes in the course
Upon completing the course the student:
- knows main notions of integral calculus;
- is familiar with the main properties, relations and theorems of this course;
- is familiar with some proof methods and is able to use them for some theorems of this course;
- is able to use and apply methods taught in a subject in order to solve exercises..
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CC-MAIN-2024-10
| 869 | 11 |
https://www.baldengineer.com/esr70-measures-esr.html
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math
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There are three capacitor measurements you need to know how to make: capacitance, leakage current, and equivalent series resistance. Capacitance is easy to measure if you have a current limited supply or can use a resistor. Apply a voltage, then time how long it takes to charge up. You might need to use an oscilloscope or even an Arduino for the second part. Leakage current is the easiest of the three, apply a voltage (ideally through a resistor) for a few minutes, and then measure the current. ESR requires some special tricks. Since it is the resistance of the “wires” connecting to the capacitive element’s anode and code, you have to measure resistance without charging up the capacitor. (Otherwise, you get leakage.)
In the post Measuring Aluminum Electrolytic Capacitor’s ESR, I go through those methods in more detail. I also introduce the PEAK Electronics ESR70. It’s a pocket-sized instrument that measures both Capacitance and ESR. There’s a button you can touch, or it detects when a new capacitor is connected. Check out my Workbench Wednesdays review where I go into depth about how the meter works (and whether or not I like it.) Oh one bonus feature, it works while in-circuit!
As of this post, it has been almost six years since I first wrote about capacitors on my blog. The article was the Arduino GSM Shield’s capacitor has a serious design flaw. Wow, how time passes.
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CC-MAIN-2024-10
| 1,406 | 3 |
https://physics.stackexchange.com/questions/420768/actual-double-slit
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math
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I can't understand what is given here. How is the double slit pattern a interference a two single slit and double slit. If we say it is interference of two single slit then it makes sense. But the graph looks different from double slit pattern. Please explain
The "double-slit interference pattern," as defined in this passage, is what you get when you shine light on two slits of infinitesimal width. In reality, you can't ever make slits of infinitesimal width, so whenever you actually perform this experiment, you must account for the fact that your slits have finite width. Shining light through a slit of finite width gives a single-slit interference pattern. So the "actual double-slit interference pattern" (i.e. the pattern you will get in every double-slit experiment you could possibly perform) is a combination of the "double-slit interference pattern" (the ideal one, with infinitesimal slit widths) and two single-slit interference patterns.
Reading the words carefully, I think the text is right.
This is the diffraction pattern from the left slit:
This is the diffraction pattern from the right slit:
And this is the superposition of both diffraction patterns, just the sum of the previous two:
Up to here it is the classical expected behevior.
But then there is the double-slit interference pattern:
Combine these two last images (multiply them, I think) and you'll get the one from your book.
The last paragraph about $a$ being much smaller than $d$ is so that the interference pattern is much narrower than the diffraction pattern. If they are of the same magnitude (or $a$ greater than $d$) then the quantum effect is not clearly visible, which is the point of this experiment.
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CC-MAIN-2024-10
| 1,697 | 10 |
http://www.ams.org/cgi-bin/bookstore/booksearch?fn=100&pg1=CN&s1=Lehner_Joseph&arg9=Joseph_Lehner
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math
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Mathematical Surveys and Monographs
1964; 425 pp; softcover
reprinted with corrections 1982; fourth printing with corrections 1984; sixth printing 2000
List Price: US$66
Member Price: US$52.80
Order Code: SURV/8
Much has been written on the theory of discontinuous groups and automorphic functions since 1880, when the subject received its first formulation. The purpose of this book is to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation. The emphasis in this book is on the fundamental parts of the subject.
The book is directed to three classes of readers: graduate students approaching the subject for the first time, mature mathematicians who wish to gain some knowledge and understanding of automorphic function theory, and experts.
AMS Home |
© Copyright 2014, American Mathematical Society
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189589.37/warc/CC-MAIN-20170322212949-00577-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 925 | 11 |
https://learningmole.com/rectangles-facts-for-kids/
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math
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Rectangles Facts for Kids – 5 Great Facts about Rectangles
Table of Contents
Today we are going to learn some magical facts about rectangles for kids.
Rectangles Facts for Kids Fact Number 1: Four Sides Shapes
Rectangles are quadrilaterals – these are shapes with four sides. The parallel sides are equal to each other. This is a defining feature of a rectangle.
Rectangles Facts for Kids Fact Number 2: Cuboids
Rectangles are 2D shapes – their 3D counterpart is a Cuboid. A 2D shape is one that is flat and only has two measurements – length and width.
Rectangles Facts for Kids Fact Number 3: Corners on a Rectangle
Each of the corners on a rectangle is 90 degrees – this is called a right angle. A right angle occurs when two straight lines intersect each other at 90˚ or are perpendicular to each other at the intersection.
Rectangles Facts for Kids Fact Number 4: Perimeter of a Rectangle
To find the perimeter of a rectangle you can take the measurement of one of the long sides and one of the shorter sides, multiply each by two and add them together.
Rectangles Facts for Kids Fact Number 5: Area of a Rectangle
To find the area of a rectangle you should find the length and multiply by two, then find the width and multiply by two. Then you should add these two numbers together. Here is the formula, P=2(l+w).
Why not subscribe to our LearningMole Library for as little as £1.99 per month to access over 2800 fun educational videos.
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CC-MAIN-2024-18
| 1,454 | 14 |
https://www.siam.org/membership/activity-groups/detail/applied-and-computational-discrete-algorithms
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math
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This activity group fosters research on the computational solution of combinatorial problems in areas including combinatorial scientific computing, algorithmic computer science, algorithm engineering, algorithmic differentiation, combinatorial optimization, and emerging applications. Drawing from academia, the national research labs, and industry, the activity group will bring together mathematicians, computer scientists, statisticians, scientists, and engineers to promote research in applied and computational combinatorics.
January 5 - 8, 2020Salt Lake City, Utah, U.S.More Information
January 8, 2020Salt Lake City, Utah, U.S.More Information
February 11 - 13, 2020Seattle, Washington, U.S.More Information
February 12 - 15, 2020Seattle, Washington, U.S.More Information
May 7 - 9, 2020Cincinnati, Ohio, U.S.More Information
We are involved in the organization of the SIAM Workshop on Combinatorial Scientific Computing. Members of the activity group receive discounted registration.
Browse our related journals including SIAM Journal on Scientific Computing, SIAM Journal on Discrete Mathematics, and SIAM Journal on Matrix Analysis and Applications. The full text of all SIAM journals are available electronically by subscription.
Rules of Procedure
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CC-MAIN-2019-43
| 1,259 | 9 |
http://radiotec.ru/article/6859
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math
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V. V. Borisov, A. Yu. Belozersky
Various aspects of the risk analysis of making decisions are considered on the basis of fuzzy Bayesian networks. The risk of the making decision is defined as probability (opportunity) of occurrence of one event at approach of other event.
Classification of methods of introduction of fuzziness in a Bayesian network is offered depending on character of the used information and features of decided tasks of the risk analysis:
complement of the Bayesian rule with membership functions of corresponding values of variables;
replacement of values of probabilities by fuzzy sets (terms of linguistic variables), and operations with crisp values – on operations S-and Т-norms with fuzzy sets;
replacement of values of probabilities by fuzzy numbers, and usual operations – on the expanded operations above indistinct numbers.
The fuzzy inference with use fuzzy Bayesian networks based on use of expanded arithmetic operations above fuzzy numbers is considered.
The technique of construction and use of fuzzy Bayesian networks for the risk analysis is submitted.
The contensive examples showing a technique of inference on the basis of fuzzy Bayesian networks are considered.
Results of the risk analysis of investment decisions with use of this approach are received.
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| 1,301 | 10 |
https://www.siye.co.uk/siye/viewuser.php?action=favauth&uid=2432
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math
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Penname: Kia [Contact - ]
Member Since: 2005.05.15
Last Login: unknown
Was extremely excited to come across a site completely devoted to Harry and Ginny fanfiction. Truly, she squealed very loudly.
Previously lived off the fanfiction on Fanfiction.net ... but knew there 'must be something more' ....
Membership status: Member
Instant Message:[ None | None | None | None ]
Communication:[ None | None | None ]
Creative:[ None | None | None ]
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| 551 | 9 |
http://www.chegg.com/homework-help/questions-and-answers/dielectric-filled-parallel-plate-capacitor-plate-area-250cm-plate-separation-100mm-dielect-q1337016
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math
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A dielectric-filled parallel-plate capacitor has plate area =
25.0cm , plate separation = 10.0mm and dielectric constant = 4.00.
The capacitor is connected to a battery that creates a constant
voltage = 12.5V . Throughout the problem, use =
the energy of the dielectric-filled capacitor= 6.91×10-10
1- The capacitor is now disconnected from the battery, and the
dielectric plate is slowly removed the rest of the way out of the
capacitor. Find the new energy of the capacitor, U3.
2- In the process of removing the remaining portion of the
dielectric from the disconnected capacitor, how much work W is done
by the external agent acting on the dielectric?
Will happily give out lifesaver. Thanks.
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| 697 | 12 |
https://chess.stackexchange.com/questions/27739/a-position-in-which-there-is-no-possible-checkmate?noredirect=1
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math
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I saw the game Firouzja vs Carlsen in world blitz championship in which Carlsen flagged Firouzja. Carlsen won because even though he had only a bishop, there could be a possible mate position.
I am asking if there a chess position in which both players have at least one piece, not including the kings, and there is no possible future mate position?
An obvious one is if both players having only one bishop moving on the same color squares. But is there something else?
I am actually looking for a complicated position, not obvious to humans at all, which needs something like 30-50 moves deep analysis for proving there is no any possible mate position.
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| 654 | 4 |
https://www.mdpi.com/2227-7390/6/8/130
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math
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Hypersurfaces with Generalized 1-Type Gauss Maps
Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea
Department of Mathematics, Chonnam National University, Gwangju 61186, Korea
Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
Author to whom correspondence should be addressed.
Received: 18 May 2018 / Revised: 18 July 2018 / Accepted: 23 July 2018 / Published: 26 July 2018
In this paper, we study submanifolds in a Euclidean space with a generalized 1-type Gauss map. The Gauss map, G
, of a submanifold in the n
-dimensional Euclidean space,
, is said to be of generalized 1-type if, for the Laplace operator,
, on the submanifold, it satisfies
, where C
is a constant vector and f
are some functions. The notion of a generalized 1-type Gauss map is a generalization of both a 1-type Gauss map and a pointwise 1-type Gauss map. With the new definition, first of all, we classify conical surfaces with a generalized 1-type Gauss map in
. Second, we show that the Gauss map of any cylindrical surface in
is of the generalized 1-type. Third, we prove that there are no tangent developable surfaces with generalized 1-type Gauss maps in
, except planes. Finally, we show that cylindrical hypersurfaces in
always have generalized 1-type Gauss maps.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Yoon, D.W.; Kim, D.-S.; Kim, Y.H.; Lee, J.W. Hypersurfaces with Generalized 1-Type Gauss Maps. Mathematics 2018, 6, 130.
Yoon DW, Kim D-S, Kim YH, Lee JW. Hypersurfaces with Generalized 1-Type Gauss Maps. Mathematics. 2018; 6(8):130.
Yoon, Dae W.; Kim, Dong-Soo; Kim, Young H.; Lee, Jae W. 2018. "Hypersurfaces with Generalized 1-Type Gauss Maps." Mathematics 6, no. 8: 130.
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| 2,289 | 31 |
https://www.cfd-online.com/Forums/openfoam/117028-xifoam-non-homogeneous-print.html
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math
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I'm trying to simulate the injection of methane into a constant volume combustion chamber with the solver XiFoam, using non-homogeneous mixture as a thermodynamic model. I found a problem: (that is established since the early moments of simulation) a strange behaviour of temperature (see picture below). Initially I thought it was due to problems of mesh or the stability of the discretization schemes, but, after some simulations on a hexahedral homogeneous grid, and using bounded schemes the problem is not solved yet. So, perhpas the problem lies in how the solver can extracts temperature from enthalpy (density is also affected obviously), but I'm not able to understand how cp and R are treated as functions of the mixture fraction (if it is actually taken into account in XiFoam). Does anyone have an idea about it? Is there anyone who has already ran into this problem? I enclose all files as set.
Thanking you in advance,
XiFoam non homogeneous
|All times are GMT -4. The time now is 21:29.|
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| 1,002 | 4 |
http://advertise180.com/ebooks/an-introduction-to-hilbert-space-cambridge-mathematical-textbooks
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math
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By N. Young
Read Online or Download An Introduction to Hilbert Space (Cambridge Mathematical Textbooks) PDF
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Additional info for An Introduction to Hilbert Space (Cambridge Mathematical Textbooks)
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| 2,500 | 13 |
http://vixra.org/abs/1210.0161
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math
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Authors: Martin Erik Horn
The trinomial triangle can be constructed in a binomial way using unit vectors of geometric algebra of quarks. This sheds some light on the question, how it is possible to transform mathematically entities of two elements into entities of three elements or vice versa.
Comments: 17 Pages.
[v1] 2012-10-27 09:09:57
Unique-IP document downloads: 315 times
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.
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| 635 | 7 |
https://researchmaniacs.com/FAQ/HowFar/HowFarCanYouWalkInADay.html
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math
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How far can you walk in a day?
Question: How far can you walk in a day?
How far you can walk in a day depends of course on how fast
you can walk and how many hours you walk. This again depends
on factors such as your health and time available.
Anyway, we timed a few people of 'fair health' and found the average to be
about 3 miles per hour. To put this in context, here are some scenarios you
may find interesting:
If you walk for 8 hours, you would cover 24 miles.
If you make walking your full-time job, working 40 hours per week, you
would cover 120 miles per week, 480 miles per month, or 5760 miles per
The road distance between New York and Los Angeles is about 2,800
miles. Thus, if you could walk 8 hours per day, it would take you
about 116 days to walk across America coast to coast.
As we know from What is Earth's Circumference,
Earth's circumference is 25,000 miles at the equator. Thus, if you could walk 8 hours per day, it would take 1040 days to circle Earth by foot.
Of course that assumes that they made a nice road with bridges and tunnels along the entire length of the equator.
Did we answer your question about "How far can you walk in a day?"
We hope so. Happy walking!
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| 1,195 | 19 |
http://books.google.co.uk/books?id=783xAAAAMAAJ&dq=related:ISBN0444705201&lr=&source=gbs_book_other_versions_r&cad=5
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math
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What people are saying - Write a review
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algebra algorithm American Mathematical Society arithmetic Association for Symbolic axioms Brouwer calculus choice sequences classical clauses cofinality Comp complete Computer Science concepts consistency construction continuum countable defined definition denote Department of Mathematics Dept derivation E-mail equivalent exists extension finite formula Germany Godel graph hierarchy inaccessible cardinal induction infinite inner model Inst intuitionistic iteration Journal of Symbolic Kechris Kleene labeled language large cardinals Lebesgue measurable Lemma linear linear logic lower bounds Math measurable cardinal modal logic model theory natural numbers node normal notion obtained ordinal P.O. Box paper Philos Philosophy predicate problem proof system proof theory properties propositional provable prove quantifiers real numbers recursion theory recursive functions regular cardinals relation rules semantics set of reals set theory singular cardinals Solovay structure subset Symbolic Logic Theorem tree Univ University variables Weyl Weyl's Woodin cardinals
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| 1,214 | 5 |
https://ask.learncbse.in/t/what-is-the-difference-between-axiom-and-postulate/67653
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math
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What is the difference between axiom and postulate?
An axiom is a statement, usually considered to be self-evident, that assumed to be true without proof. It is used as a starting point in mathematical proof for deducing other truths.
Classically, axioms were considered different from postulates. An axiom would refer to a self-evident assumption common to many areas of inquiry, while a postulate referred to a hypothesis specific to a certain line of inquiry, that was accepted without proof. As an example, in Euclid’s Elements, you can compare “common notions” (axioms) with postulates.
In much of modern mathematics, however, there is generally no difference between what were classically referred to as “axioms” and “postulates”. Modern mathematics distinguishes between logical axioms and non-logical axioms, with the latter sometimes being referred to as postulates.
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| 889 | 4 |
https://www.ajtutoring.com/blog/math-accuracy/
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math
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Frequently at AJ Tutoring, students come in who express a familiarity with key math concepts but don’t score as well as they’d imagined on quizzes and tests. A common source of missed questions is inaccuracy. It can be frustrating because math mistakes can happen even if you have mastered the material and know the problem-solving techniques. Our math tutors excel at helping students minimize missed questions. Click here to learn more about math tutoring at AJ Tutoring, and read on for some tips to increase precision and accuracy in math.
1. Stop Calling Your Math Mistakes “Stupid”
It is completely predictable that as a human you are going to make mistakes, and it under no circumstances makes you stupid or silly or lazy. The first step is to retrain your mind to see these math mistakes for what they are: Accuracy Errors. By changing your mindset and accepting that you will make mistakes and that mistakes are opportunities to learn and grow, you set yourself up for success in Math.
2. Make a List of Math Mistakes
As we discussed above, precision and accuracy errors are predictable, and the cool thing is you probably have a set that you are most susceptible to. So, whenever you get an assignment back, don’t just say to yourself, “Darn, I made 5 silly math mistakes!” Instead, classify them: Did you forget to distribute or drop a negative sign? Did you answer the wrong question? Did you do 3+2=6? Did you not write your units? By categorizing your errors, you make it easier to check for them during an assignment or exam. Instead of chanting “Don’t make any accuracy errors” to yourself, you can quickly run through your list of common math errors and feel confident in moving on to the next question.
3. Read Math Questions Carefully
I know it seems simple, but there are a lot of predictable ways this can go wrong. If you feel overly confident with a familiar question type, you might rush through the prompt and miss an important tweak your teacher made. If you feel uncomfortable with a math question or its length, you might let the question intimidate you and turn what was actually a simple math problem into a nightmare. So, read all the words, annotate as you see fit and if necessary break the question into chunks and read those separately until you feel you have a handle on the entire question.
4. Underline, circle or highlight what you are asked to solve
The key here is that at the end of the math problem you can quickly check if you have actually answered the question. This way we can avoid that gut-wrenching feeling when you get your test back, start to look over a math problem you missed and realize you gave the answer for X when your teacher asked for Y.
5. Writing out your work is a math problem-solving strategy
I mean all of it! Even if you are typically able to perform accurate computations in your head, by not writing down your work you rob yourself of the opportunity to catch and correct precision and accuracy errors. At the same time, you can improve math skills by making what you are writing out count. If you can’t read your work, or it becomes hard to work accurately because the work is not well organized, we have the same problem as not writing it out.
6. Write out your math units
Units get a bad rap as teachers’ favorite way to shave off points on a student’s math test, but they are actually a really handy tool to see if you are problem-solving correctly. If your units don’t work out, it’s a quick red flag that you should check your work. You can easily improve your math skills and problem solving strategies by determining what the units of the answer should be ahead of time. Then, you can often devise a road map of how to solve the math question.
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https://granehrehe.web.app/914.html
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math
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Komologrov, gelfand, naimark, petroskii, landau, fedeev, postnikov. Differential geometry study materials mathoverflow. Second this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in di erent branches of differential geometry. Fibre bundles, topology and gauge fields theoretical and mathematical physics series by gerd rudolph. Differential geometry of curves and surfaces by manfredo p. A course of differential geometry and topology mishchenko.
Find all the books, read about the author, and more. Some of the teachers allowed him to read advanced books in their classes. Books on smooth manifolds and differential geometry are comparable to. Shop for differential geometry books in geometry books. The paperback of the the variational theory of geodesics by m.
It is designed as a comprehensive introduction into methods and techniques of modern di. Bishopgoldberg, tensor analysis on manifolds 1968 pages 165205, 222. Introduction to differential geometry lecture notes. The variational theory of geodesics dover books on mathematics. Teaching myself differential topology and differential geometry. Buy differential geometry dover books on mathematics new edition by kreyszig, erwin isbn. This volume is the sixth in postnikov s series of lecture notes in differential geometry, and provides an advanced overview of various topics in riemannian geometry. Linear algebra and differential geometry semester 2. Curve, frenet frame, curvature, torsion, hypersurface, fundamental forms, principal curvature, gaussian curvature, minkowski curvature, manifold, tensor eld, connection, geodesic curve summary.
Price new from used from hardcover, june 1, 1983 please retry. Spivak, a comprehensive introduction to differential geometry, publish or perish, wilmington, dl, 1979 is a very nice, readable book. However, formatting rules can vary widely between applications and fields of interest or study. Postnikov, the variational theory of geodesics 1967 pages 2235, 7579, 85 87. These textbooks are a slowpaced introduction to modern geometry, containing lots of optional material beyond standard facts. Postnikov has written a wellstructured and readable book with a satisfying sense of completeness to it. It is based on the lectures given by the author at e otv os lorand university and at budapest semesters in mathematics. Compact and selfcontained, this text by a noted theorist presents the essentials of modern differential geometry as well as the basic tools for the study of morse theory. Manifolds, oriented manifolds, compact subsets, smooth maps, smooth functions on manifolds, the tangent bundle, tangent spaces, vector field, differential forms, topology of manifolds, vector bundles. Linear algebra and differential geometry book, 1982. The more descriptive guide by hilbert and cohnvossen 1is also highly recommended. Linear algebra and differential geometry hardcover june 1, 1983. This book mostly focuses on classical differential geometry ie curves and surfaces in r3.
Riemannian geometry is a fundamental area of modern mathematics and is important to the study of relativity. For differential geometry, i dont really know any good texts. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations. Online shopping for differential geometry from a great selection at books store. This classic work is now available in an unabridged paperback edition. An excellent reference for the classical treatment of di. The thing that i am noticing is just how much these text avoid engaging the underlying differential geometry topology of phase spaces. The amount of mathematical sophistication required for a good understanding of modern physics is astounding. A modern introduction is a graduatelevel monographic textbook. Go to my differential geometry book work in progress home page. These are my rough, offthecuff personal opinions on the usefulness of some of the dg books on the market at this time. Mikhail mikhailovich postnikov was a soviet mathematician, known for his work in algebraic and differential topology.
The book is addressed to scholars and researchers in differential geometry and mathematical physics, as well as to advanced graduate students who have studied the material covered in the first part of the series. The book contains a very useful large appendix on foundations of differentiable manifolds and basic structures on them which makes it. Also, the entire material has been reorganized in order to improve the coherence of the book. This book is the second part of a twovolume series on differential geometry and mathematical physics. Linear algebra and differential geometry translated from the russian by vladimir shokurov accessrestricteditem true addeddate. My copies of the 2 volumes of semester iv differential geometry are available only in french, but i plan to scan these as well in the hope that someone may attempt a translation if the books were more easily available. This compact and selfcontained text by a noted theorist presents the essentials of modern differential geometry as well as basic tools for the study of morse theory.
A solid introduction to the methods of differential geometry and tensor calculus, this volume is suitable for advanced undergraduate and graduate students of mathematics, physics, and engineering. Therefore, to make the presentation relatively independent and selfcontained in the english translation, i have added supplementary chapters in a special addendum chaps. Im looking for books explaining the differential geometry to the engineer with basic linear algebra calculus knowledge. Dec 04, 2004 i love the schaums especially for linear algebra, and will probably get the differential geometry book, although i hear its only classical differential geometry. Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in. Everyday low prices and free delivery on eligible orders. I have been doing some selfstudy of differential equations and have finished habermans elementary text on linear ordinary differential equations and about half of strogatzs nonlinear differential equations book. Besides the standard spivak, the other canonical choice would be kobayashinomizus foundations of differential geometry, which is by no means easy going. Most of this book consists of a wellwritten, selfcontained text on homotopy theory and differential geometry, in preparation for chapters on morse theory on finite dimensional manifolds, the variational theory of geodesics, and the study of path spaces by finitedimensional approximation. For beginning geometry there are two truly wonderful books, barrett oneills elementary differential geometry and singer and thorpes lecture notes on elementary topology and geometry. This book provides a very readable introduction to riemannian geometry and geometric analysis. It is based on the lectures given by the author at e otv os. The advanced treatment emphasizes analytical rather than topological aspects.
Calculus on manifolds, michael spivak, mathematical methods of classical mechanics, v. Throughout the book, different aspects of symmetric spaces are treated. The value of this book for differential geometry is very basic, but it could be useful as a first impressionistic view of dg to get some motivation to study the serious mathematical theory. Here are some differential geometry books which you might like to read while youre waiting for my dg book to be written. Apr 21, 2017 this book is the second part of a twovolume series on differential geometry and mathematical physics. This book is a monographical work on natural bundles and natural operators in differential geometry and this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry. Riemannian geometry is a fundamental area of modern mathematics, and the subdiscipline of geodesics shortest paths is of particular significance. The variational theory of geodesics paperback august 1, 1983. Before going to riemannian geometry, the author pre sents a more general theory of manifolds with a linear con nection. Differential geometry and mathematical physics springerlink. Earlier we had seen the problem book on differential geometry and topology by these two authors which is the associated problem book for this course.
Postnikov has written a wellstructured and readable book with a. The author successfully combines the coordinate and invariant approaches to differential geometry, which give the reader tools for practical calculations as well as a theoretical understanding of the subject. The aim of this textbook is to give an introduction to di erential geometry. I only read the first edition, but i thought it was written fairly well and did a good job of developing geometric intuition because of the number of pictures. Elementary differential geometry by barrett oneill is another good book. For my tastes the book uses coordinate arguments too much, probably trying to avoid abstract methods which could scare a. He was on the mechanics and mathematics faculty of moscow state university. Similarly, they say kreyszigs book, with the coordinate p. There is a new book by jeffrey lee called manifolds and differential geometry in the ams graduate studies series. Postnikov m m abebooks abebooks shop for books, art. The book is devoted to the study of the geometrical and topological structure of gauge theories. Oct 21, 2010 differential geometry can be successfully used in many areas of study from special relativity to image processing. Postnikov, the variational theory of geodesics 1967 pages 2235, 7579, 8587. Nov, 2019 within the larger context of riemannian mathematics, the active subdiscipline of geodesics shortest paths in riemannian spaces is of particular significance.
Oct 22, 2016 in this post we will see a course of differential geometry and topology a. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. Postnikovs lectures on geometry 3 and 4, this is really the most coherent book ive read. This book is a direct continuation of the authors previous book and is akin to it in being a nearly faithful record of the lectures delivered by the author in the second semester of the first year at the mathematicsmechanics faculty of moscow state university named after m.
The original russian edition of this book is the fifth in my series lectures on geometry. Get free shipping on an introduction to differential geometry by t. We thank everyone who pointed out errors or typos in earlier versions of this book. Lectures on differential geometry mathematical association of. I can honestly say i didnt really understand calculus until i read. The variational theory of geodesics dover books on. Linear algebra and differential geometry, semester iii. Differential geometry has always been one of my favorite subjects. The author successfully combines the coordinate and invariant approaches to differential geometry, giving the reader tools for practical calculations as well as a theoretical understanding of the subject. Youtube, youtube channel, video marketing, youtuber, igtv, erika vieira, video, instagram hatecast clint taylor. Buy products such as differential geometry of curves and surfaces ebook at walmart and save. Discover delightful childrens books with prime book box, a subscription that delivers new books every 1, 2. Within the larger context of riemannian mathematics, the active subdiscipline of geodesics shortest paths in riemannian spaces is of particular significance. It consists of the following three building blocks.
Postnikovs lectures on geometry 3 and 4, this is really the most coherent book i ve read. Taimanov modern geometric structures and fields the book is about manifolds, differential geometry and topology, algebraic topology and application of all this machinery to theoretical physics. Singer and thorpe are well known mathematicians and wrote this book for undergraduates to introduce them to geometry from the modern view point. Fine copies without previous owners names or markings. What book a good introduction to differential geometry. The author successfully combines the coordinate and invariant approaches to differential. Soviet mathematician mikhail mikhailovich postnikov 19272004 worked primarily in algebraic and differential topology. This book developed from taimanovs undergraduate lecture course at novosibirsk. Free differential geometry books download ebooks online. Open library is an open, editable library catalog, building towards a web page for every book ever published. This book treats that part of riemannian geometry related to more classical topics in a very original, clear and solid style. Lomonosov to mathematical students a course in linear algebra and analytic geometry. The classical roots of modern di erential geometry are presented in the next two chapters.
The course in linear algebra and analytic geometry is just a part of a single twoyear course in geometry, and much in this book is accounted for, as regards the choice of the material and its accentuation, by orientation to the second year devoted to the differential geometry of manifolds. Geometry and topology of fibre bundles, clifford algebras, spin structures and dirac operators, gauge theory. Applied differential geometry a modern introduction vladimir g ivancevic defence science and technology organisation, australia tijana t ivancevic the university of adelaide, australia n e w j e r s e y l o n d o n s i n g a p o r e b e i j i n g s h a n g h a i h o n g k o n g ta i p e i c h e n n a i. If you prefer something shorter, there are two books of m. Postnikov author see all formats and editions hide other formats and editions. Do carmo, topology and geometry for physicists by cha. Riemannian geometry encyclopaedia of mathematical sciences v. Differential geometry of curves and surfaces, and 2.1140 531 217 1645 809 1047 836 712 1422 99 1642 921 254 885 797 192 486 1122 1087 490 522 185 860 1504 365 1327 423 722 829 361 1223 877 1487 1334 749 1351 1183 200
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https://www.mathsisfun.com/geometry/hyperbola.html
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math
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Did you know that the orbit of a spacecraft can sometimes be a hyperbola?
A spacecraft can use the gravity of a planet to alter its path and propel it at high speed away from the planet and back out into space using a technique called "gravitational slingshot".
If this happens, then the path of the spacecraft is a hyperbola.
(Play with this at Gravity Freeplay)
A hyperbola is two curves that are like infinite bows.
Looking at just one of the curves:
any point P is closer to F than to G by some constant amount
The other curve is a mirror image, and is closer to G than to F.
In other words, the distance from P to F is always less than the distance P to G by some constant amount. (And for the other curve P to G is always less than P to F by that constant amount.)
As a formula:
|PF − PG| = constant
- PF is the distance P to F
- PG is the distance P to G
- || is the absolute value function (makes any negative a positive)
Each bow is called a branch and F and G are each called a focus.
Have a try yourself:
Try moving point P: what do you notice about the lengths PF and PG ?
Also try putting point P on the other branch.
There are some other interesting things, too:
On the diagram you can see:
- an axis of symmetry (that goes through each focus)
- two vertices (where each curve makes its sharpest turn)
- the distance between the vertices (2a on the diagram) is the constant difference between the lengths PF and PG
- two asymptotes which are not part of the hyperbola but show where the curve would go if continued indefinitely in each of the four directions
And, strictly speaking, there is also another axis of symmetry that goes down the middle and separates the two branches of the hyperbola.
You can also get a hyperbola when you slice through a double cone.
The slice must be steeper than that for a parabola, but does not
So the hyperbola is a conic section (a section of a cone).
By placing a hyperbola on an x-y graph (centered over the x-axis and y-axis), the equation of the curve is:
x2a2 − y2b2 = 1
One vertex is at (a, 0), and the other is at (−a, 0)
The asymptotes are the straight lines:
- y = (b/a)x
- y = −(b/a)x
(Note: the equation is similar to the equation of the ellipse: x2/a2 + y2/b2 = 1, except for a "−" instead of a "+")
Any branch of a hyperbola can also be defined as a curve where the distances of any point from:
- a fixed point (the focus), and
- a fixed straight line (the directrix) are always in the same ratio.
This ratio is called the eccentricity, and for a hyperbola it is always greater than 1.
The eccentricity (usually shown as the letter e) shows how "uncurvy" (varying from being a circle) the hyperbola is.
On this diagram:
- P is a point on the curve,
- F is the focus and
- N is the point on the directrix so that PN is perpendicular to the directrix.
The eccentricity is the ratio PF/PN, and has the formula:
e = √(a2+b2)a
Using "a" and "b" from the diagram above.
The Latus Rectum is the line through the focus and parallel to the directrix.
The length of the Latus Rectum is 2b2/a.
The reciprocal function y = 1/x is a hyperbola!
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https://www.encyclopediaofmath.org/index.php/Universal_behaviour_in_dynamical_systems
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math
|
Universal behaviour in dynamical systems
In the late 1970's, P. Coullet and C. Tresser [a6] and M. Feigenbaum
independently found striking, unexpected features of the transition from simple to chaotic dynamics in one-dimensional dynamical systems (cf. also Routes to chaos). By the example of the family of quadratic mappings acting (for ) on the interval , the period-doubling scenario is recalled here. For , has periodic points of every (least) period. Let be the infimum of parameter values for which has a periodic orbit of least period . Then
For , the dynamics of is described by statements i)–iii) below.
i) has precisely one periodic orbit of (least) period for each , and no other periodic orbits;
ii) any pair of adjacent points in is separated by a unique point in ;
iii) with the exception of the (countably many) orbits which land on some , , and stay there, every -orbit tends asymptotically to .
For (when is sometimes called the Feigenbaum mapping), statement i) holds, but with ranging over all non-negative integers, and ii) holds for each ; furthermore, the following analogue of iii) holds:
iv) (for ) the closure of the orbit of the turning point is a Cantor set , which is the asymptotic limit of every orbit not landing on one of the periodic orbits , . The restricted mapping is a minimal homeomorphism (the "adding machine for chaos in a dynamical systemadding machine" ).
Finally, is the threshold of "chaos" , in the following sense:
v) for , has infinitely many distinct periodic orbits, and positive topological entropy.
Many features of this "topological" , or combinatorial picture were understood by early researchers in this area, specifically P.J. Myrberg [a12] and N. Metropolis, M.L. Stein and P.R. Stein [a13]. They recognized as well that the combinatorial structure of the periodic orbits is rigidly determined by the fact that is unimodal (cf. [a14]). In essence, the statements above can be formulated for any family of unimodal mappings (cf. ). In fact, the (weak) monotonicity of the 's, together with the fact that if , then must have periodic orbits of least period for (some ) and no others, follows for any family of continuous mappings on the line from Sharkovskii's theorem [a16], [a2]; recent work has yielded a more general understanding of the combinatorial structure of periodic orbits for continuous mappings in dimension (cf. [a1]).
Coullet, Tresser and Feigenbaum added to the topological picture described above a number of analytic and geometric features:
vi) the convergence is asymptotically geometric:
vii) the periodic orbits scale: let denote the orbit for ; then
These statements, formulated for the particular family of quadratic mappings, are technically interesting, but not so striking. However, they observed that v)–vii) hold for a very broad class of unimodal one-parameter families, subject only to trivial "fullness" conditions (essentially that has only finitely many periodic orbits while has positive entropy) and smoothness (essentially that is and each has a non-degenerate critical point). And, sensationally, the constants and are independent of the family .
In [a6] and
these assertions were reduced, using ideas from renormalization theory, to certain technical conjectures concerning a doubling operator acting on an appropriate function space. O. Lanford
(cf. also [a3], [a5]) gave a rigorous, computer-assisted proof of the basic conjecture, that has a saddle-type fixed point with one characteristic multiplier (the same as in vi)) and stable manifold of codimension . D. Sullivan [a17] showed the uniqueness of this fixed point in the space of "quadratic-like" mappings. The final conjecture, concerning transversality of the stable manifold with certain bifurcation submanifolds, remains unproved. Recently, Sullivan , introducing a number of new ideas, has circumvented this difficulty and provided a rather complete theory of universal features for families of unimodal mappings. In particular, the asymptotic geometry of the Cantor set (for ) and of analogous sets appearing at other "threshold" parameter values (the "infinitely renormalizable mappings of bounded type" ) is universal; for example, the set always has Hausdorff dimension . Full expositions of this theory are provided in [a18] and [a7].
These ideas have been applied as well to circle diffeomorphisms [a10],
and area-preserving planar diffeomorphisms [a4], .
|[a1]||Ll. Alsedà, J. Llibre, M. Misiurewicz, "Combinatorial dynamics and entropy in one dimension" (to appear)|
|[a2]||L. Block, J. Guckenheimer, M. Misiurewicz, L.-S. Young, "Periodic points and topological entropy of one dimensional maps" Z. Nitecki (ed.) C. Robinson (ed.) , Global theory of dynamical systems (Proc. Northwestern Univ., 1979) , Lect. notes in math. , 819 , Springer (1980) pp. 18–34 MR0591173 Zbl 0447.58028|
|[a3]||M. Campanino, H. Epstein, D. Ruelle, "On the existence of Feigenbaum's fixed point" Comm. Math. Phys. , 79 (1981) pp. 261–302 MR612250|
|[a4]||P. Collet, J.-P. Eckmann, H. Koch, "On universality for area-preserving maps of the plane" Physica , 3D (1981) pp. 457–467 MR0631180 Zbl 1194.37050|
|[a5]||P. Collet, J.-P. Eckmann, O. Lanford, "Universal properties of maps on an interval" Comm. Math. Phys. , 76 (1980) pp. 211–254 MR0588048 Zbl 0455.58024|
|[a6]||P. Coullet, C. Tresser, "Itérations d'endomorphismes et groupe de rénormalisation" J. Phys. , C5 (1978) pp. 25–28 MR0512110|
|[a7]||W. de Mello, S. van Strien, "One-dimensional dynamics" (to appear)|
|[a8a]||M. Feigenbaum, "Quantitative universality for a class of non-linear transformations" J. Stat. Phys. , 19 (1978) pp. 25–52 MR501179|
|[a8b]||M. Feigenbaum, "The universal metric properties of a non-linear transformation" J. Stat. Phys. , 21 (1979) pp. 669–706 MR555919|
|[a9a]||L. Jonker, D. Rand, "Bifurcations in one dimension" Invent. Math. , 62 (1981) pp. 347–365 MR0608525 MR0604832 Zbl 0475.58015|
|[a9b]||L. Jonker, D. Rand, "Bifurcations in one dimension" Invent. Math. , 63 (1981) pp. 1–16 MR0608525 MR0604832 Zbl 0475.58015|
|[a10]||L. Jonker, D. Rand, "Universal properties of maps of the circle with -singularities" Comm. Math. Phys. , 90 (1983) pp. 273–292 MR714439|
|[a11a]||O. Lanford, "A computer-assisted proof of the Feigenbaum conjectures" Bull. Amer. Math. Soc. , 6 (1982) pp. 427–434 MR0648529 Zbl 0487.58017|
|[a11b]||O.E. Lanford, "Computer assisted proofs in analysis" A.M. Gleason (ed.) , Proc. Internat. Congress Mathematicians (Berkeley, 1986) , Amer. Math. Soc. (1987) pp. 1385–1394 MR0934342 Zbl 0676.65039|
|[a12]||P.J. Myrberg, "Sur l'iteration des polynomes réels quadratiques" J. Math. Pures Appl. , 41 (1962) pp. 339–351 MR0161968 Zbl 0106.04703|
|[a13]||N. Metropolis, M.L. Stein, P.R. Stein, "On finite limit sets for transformations on the unit interval" J. Comb. Theory , 15A (1973) pp. 25–44 MR0316636 Zbl 0259.26003|
|[a14]||W. Thurston, "On iterated maps of the interval" J.C. Alexander (ed.) , Dynamical Systems (Proc. Maryland, 1986–7) , Lect. notes in math. , 1342 , Springer (1988) pp. 465–563 MR0970571 Zbl 0664.58015|
|[a15a]||D. Rand, "Universality and renormalization in dynamical systems" T. Bedford (ed.) J. W. Swift (ed.) , New directions in dynamical systems , Cambridge Univ. Press (1987) pp. 1–56|
|[a15b]||D. Rand, "Global phase space universality, smooth conjugacies and renormalisation: the case." Nonlinearity , 1 (1988) pp. 181–202 MR928952|
|[a16]||A.N. Sharkovskii, "Coexistence of cycles of a continuous map of the line into itself" Ukrain. Mat. Zh. , 16 (1964) pp. 61–71 (In Russian) MR1415876 MR1361914|
|[a17]||D. Sullivan, "Quasiconformal homeomorphisms in dynamics, topology and geometry" A.M. Gleason (ed.) , Proc. Internat. Congress Mathematicians (Berkeley, 1986) , Amer. Math. Soc. (1987) pp. 1216–1228 MR0934326 Zbl 0698.58030|
|[a18]||D. Sullivan, "Bounds, quadratic differentials, and renormalization conjectures" , Centennial Publ. , 2 , Amer. Math. Soc. (1991) MR1184622 Zbl 0936.37016|
Universal behaviour in dynamical systems. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Universal_behaviour_in_dynamical_systems&oldid=24587
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| 8,211 | 44 |
http://www.docstoc.com/docs/127021724/electricity
|
math
|
What do you think?
• Complete the following statements.
1. “Electricity is…”
2. “Electricity comes from…”
What is it?
• It is NOT just the flow of electrons
– That is one instance of electricity.
• It IS the flow of charged particles.
– Protons (if you can get them by themselves)
– Ions (very common)
• Do electrons flow
• Do positive atoms flow
– When you stick your hand in a light socket
– Inside batteries
• The most common way to “make”
electricity is to boil water.
• This boiled water is steam that turns
• Turning those turbines moves magnets.
• Conserve electricity?
– Electricity is not renewable nor nonrenewable
– The stuff use to generate electricity is.
• We convert other types of energy
(gravitational potential energy, chemical
energy, mechanical energy) into electrical
• Spin magnets inside a coil of wire and you
have electricity (or spin the coil).
– It’s that easy!
• The tough part is making it spin fast and
• The top fuel to boil the water is coal
– Nearly 50% of electricity generated in the US is by
coal power stations.
– Natural gas
– Falling water
– Nuclear fission
Now we have to move it
• It’s very hard to
• We must move it from
the power plant to
• William Stanley –
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https://vestnik-mmi.syktsu.ru/en/vestnik-8-2008/
|
math
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I. Balakin S.V. Runs characteristics in a ternary Marcov Chain
A ternary Markov chain is considered. There are functionals concerned with a number of events and a number of runs. Probability generating functions for joint distributions of this functionals are obtained. Precise formulas for expectations, variances and covariations are founded.
II. Vechtomov E.M., Chuprakov D.V. Congruences on semirings of continious functions and F-spaces
The congruences of semirings of non-negative continuous functions on topological space are investigated. In terms such congruences new algebraic characterizations of F-spaces and P-spaces are received.
III. Mekler A.A. On positive integer characteriyation of regular variyng quasi-concave modulars
The initiated in study of the correspondence between quasi-concave modulars and sequences of positive integers is continued. In the presented paper are examenated especially regularly variying quasi-concave modulars. It is stated in Theorems 9, that a sequence of positive integers corresponds to a fast variyng quasi-concave modular (that means the case of regularity index α=0) iff it is equivalent to a integer sequence which tends to +∞. In Theorem 8 is proved that the sequence of positive integers corresponds to a slow variyng modular (the case of regularity index α=1) iff it is equivalent to a sequence of the form 211•••1211•••121••• •••••• where the lengths of blocks of units tends to +∞. In Theorem 5 the case of intermediate value of regularity index α: 0<α<1 is investigated.
IV. Savelev L.J. Extension of a measure up to integral
In this paper the task about a bend of cylindrical panel under effect of normal load is considiered. The normal load are distributed on field, simular to middle surface of a panel. The bend of panel on register of transversal shears by S.P.Timoshenko’s model is described. The mechanism of dependence of a moments for transversal shears is confirmed – the graphics of moments for change of curvature of middle surface and for change of transversal shears are be in anti-phases in fields of a maximal absolute values.
V. Belyaeva N.A. The structural models of deformation processes
Mathematical models of flow and deformation processes of materials with evolutionarizating structure are presented. The problems spread to wide sphere of structure-sensitive objects – from powder systems to polymer materials and composites. This models allow to define change of deformation, temperature and structure characteristics of varried systems in the various processing-hardening, non-Newtonian flow, solid-state extrusion.
VI. Nikitenkov V.L. Basic property of the optimal integer-valued solving of the linear cutting problem
It was proved that basic solution of the some modification linear cutting problem is optimal integer-valued solving of the integer cutting problem.
VII. Sakovnich D.Y. Singularity in the format cutting problem
In scope of format cutting problem the problem of minimization winder adjustments is considered. It was offered the method for getting the most singular solution if the problem.
VIII. Kluchnikov E.A. SOA data store and search system
The author consider SOA data store and search system written in Java. SOA approach makes such systems scalable and easy to integrate as basis of enterprise infrastructure. Java technology makes it easier to use the full power of modern servers.
IX. Simakov A.V. Parallel compression of huge images
In this paper we describe an efficient algorithm for parallel compression of huge images. The algorithm is based on wavelet transform. The article is focused on practical implementation and evaluation of this compression method. As a result, all described features are implemented in software library written in C language. This library and compression program is freely available through the Internet and distributed with full source code under the terms of Open Source GNU GPL license.
X. Poroshkin A.G., Popova L.A. Remark about the outer measures geneated by measures
It is proved that outer measures generated by measures in sense of Halmos, Vuklikh, Poroshkin are lower continuous, however the outer measure of Lebesque in R is not continuous from above and not exhaustive.
XI. Tarasov V.N., Andryukova V.Yu. On stability and supercritical behavior of a spherical shell
The problem of the spherical shell experiencing external normal pressure is considered. A precise formula is used for the calculation of the work of external forces. In the work a variational approach is applied. Cubic splines are used for the finite-dimensional approximation of displacements. The influence of nonlinear terms on the amount of the critical force is investigated.
XII. Tulubenskaya E.V., Kargin R.V. The stability of the longitudinally compressed shank with unconstant rigidity at the border of two Winkler’s ambiences
The stability of the longitudinally compressed shank with unconstant rigidity at the border of two Winkler’s ambiences is investigated. The algorithm is based on the local search variants.
XIII. Jakovlev V.D. On one way of introducing integrals in the high school mathematics
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| 5,180 | 25 |
https://www.geogebra.org/m/vjyE3xFr
|
math
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The Princess and the Key
- Judah L Schwartz
A beautiful princess is locked in a tower. The lock to the tower can only be opened from the inside. The princess’ lover has the key but he is outside the tower. Talking to one another through a window they decide that he should toss the key up to her. There are many windows along the height of the tower – some are taller windows and some are shorter windows. They are trying to decide which window she should lean out and how fast he should throw the key up. • Use the Princess and the Key environment to compile a table of at least three possibilities of combinations of window size, window height and initial speed that will enable the princess to grab the tossed up key. For each combination, indicate when and for how long the key is just outside the window. • What strategy would you advise to maximize the possibility of the key being caught? • Knowing that the time in seconds for which the height of the key is a maximum is initialspeed / 9.8 write an expression for the height of the key as a function of time.
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CC-MAIN-2019-13
| 1,076 | 3 |
https://swmm5.org/2018/06/12/dynamic-wave-routing-options-in-infoswmm-and-swmm5-2/
|
math
|
Dynamic Wave Routing Options
The Dynamic Wave page of the Simulation Options dialog, shown below, sets several parameters that control how the dynamic wave flow routing computations are made. These parameters have no effect for the other flow routing methods.
Contents of this simulation option dialog page are described below:
|Inertial Terms||Indicates how the inertial terms in the St. Venant momentum equation will be handled.
|Variable Time Step||Indicates whether or not a variable time step should be used. The variable step is computed for each time period so as to satisfy the Courant stability criterion for each conduit and to prevent an excessive change in water depth at each node. The Routing Time Step Summary Report is available for checking statistics about how InfoSWMM is altering the timestep.
|Time Step for Conduit Lengthening||This is a time step, in seconds, used to artificially lengthen conduits so that they meet the Courant stability criterion under full-flow conditions (i.e., the travel time of a wave will not be smaller than the specified conduit lengthening time step). As this value is decreased, fewer conduits will require lengthening. A value of 0 means that no conduits will be lengthened. The roughness value of the conduit will also be artificially lowered so that the same velocity and flow are maintained after lengthening. Also note that the conduit slope reported in the output will reflect a numerically smaller slope due to a longer conduit length.
Conduit Lengthening in InfoSWMM H2OMap SWMM InfoSWMM SA
If you use the conduit lengthening option in InfoSWMM H2OMap SWMM InfoSWMM SA then your short conduits will be lengthened based on the CFL or explicit time step criterion. Any conduits in which the Length Factor or the courant time step link length over the original length is greater than 1 will be lengthened and will have its roughness lowered so that the conduit is hydraulically the same at full conduit depth. The full area, full width and full hydraulic radius stay the same in the modified link – only the length, slope and roughness are altered.
|Minimum Surface Area||This is a minimum surface area used at nodes when computing changes in water depth. If 0 is entered, then the default value of 12.566 ft2 (i.e., the area of a 4-ft diameter manhole) is used.|
|Use Normal Flow Limit||Selects which condition is used to make InfoSWMM H2OMap SWMM InfoSWMM SA limit the flow in a conduit to the normal flow computed from the Manning equation:
The effect of these three options is on the value of sigma for the nonlinear term in the St Venant Equation; a sigma value of 1 means that the whole term is used, a value of 0 means that the nonlinear term is not used for that time step.
|Force Main Equation||Choose the head loss equation to be used to model force mains
|Maximum Number of Iterations||Allows you to control the maximum number of iterations in the solution. The number of iterations range from 2 to a possible 20 iterations.
|Stopping Tolerance||Controls the Stopping tolerance (internal units of feet) for node iterations.
Two new parameters and a modified table in the output starting in InfoSWMM 11 and v10 that does the following:
1. Allows you to control the maximum number of iterations in the solution,
2. Controls the Stopping tolerance (internal units of feet) for node iterations, and
3. Shows not only the percent continuity error at a node but the error in million gallons (Mgal)
If you have a high continuity error or want to reduce your existing continuity error then you can increase the number of iterations or lower the stopping tolerance so that at each time step there is less continuity error.
|
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| 3,683 | 19 |
http://www.ask.com/web?q=Is+Pi+a+Rational+or+Irrational+Number%3F&o=2603&l=dir&qsrc=3139&gc=1
|
math
|
In the 18th century, Johann Heinrich Lambert proved that the number π (pi) is
irrational: that is, ... Then Lambert proved that if x is non-zero and rational then
this expression must be irrati...
Because 22 7 isn't pi. The definition of an irrational number is that it cannot be
expressed as a ...
Jun 30, 2015 ... pi is an irrational number Rational numbers are all numbers expressible as p/q
for some integers p and q with q != 0. pi is not expressible as p/q ...
Nov 26, 2015 ... Why (22/7) is a rational number and (π) is irrational number. please explain. Edit:
How can you say that 22 / 7 = π , when one number if rational ...
Nov 8, 2013 ... You might remember the terms rational and irrational numbers from math class.
As a refresher, numbers like 3, 0.5, 0.333…., -10, -1/2, or 1/7 ...
Mar 27, 2016 ... Pi (π) is an irrational number, meaning it represents a real number with a ... Both
rational and irrational numbers are infinite in that they “can't be ...
Pi is a real number, as all numbers that exist on a number line are real. Real
numbers include all rational and irrational numbers; pi is defined as an irrational..
Therefore, it's irrational. Note that from here, you can say that since the square
root of any irrational number is still irrational, pi itself is also ...
What's the difference between a rational number and an irrational number? ...
and -3030 are integers, but numbers like 1/2, 4.00032, 2.5, Pi, and -9.90 are not.
Aug 31, 2014 ... We will prove that pi is, in fact, a rational number, by induction on the number ...
without loss of generality, does not make an irrational number.
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| 1,624 | 21 |
https://oneclass.com/class-notes/us/uc-irvine/econ/econ-1/2685337-econ-1-lecture-13.en.html
|
math
|
ECON 1 Lecture Notes - Lecture 13: Gdp Deflator, Interest Rate, Nominal Interest RatePremium
Course CodeECON 1
This preview shows half of the first page. to view the full 3 pages of the document.
ECON 1 - Lecture 13 - Measuring the Cost of Living
Look for the answers to these questions
● What is the Consumer Price Index (CPI)?
○ How is it calculated? What is it used for?
● What are the problems with the CPI? How serious are they?
● How does the CPI differ from the GDP deflator?
● How can we use the CPI to compare dollar amounts from different years? Why would we
want to do this anyway?
● How can we correct interest rates for inflation?
The Consumer Price Index
● Consumer price index (CPI)
○ Measure of the overall level of prices
○ Measure of the overall cost of goods and services
■ Brought by a typical consumer
● Computed and reported every month by the Bureau of Labor Statistics
1. Fix the basket
● The Bureau of Labor Statistics (BLS) surveys consumers to determine what’s in
the typical consumer’s “shopping basket”
2. Find the prices
● The BLS collects data on the prices of all the goods in the basket
3. Compute the basket’s cost
● Use the prices to compute the total cost of the basket
4. Chose a base year and compute the CPI
● Cost of basket of goods and services in current year divided by cost of basket in
● Times 100
5. Compute the inflation rate
● The percentage change in the CPI from the preceding period
𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 = 𝐶𝑃𝐼 𝑡ℎ𝑖𝑠 𝑦𝑒𝑎𝑟 − 𝐶𝑃𝐼 𝑙𝑎𝑠𝑡 𝑦𝑒𝑎𝑟
𝐶𝑃𝐼 𝑙𝑎𝑠𝑡 𝑦𝑒𝑎𝑟 ×100
Problems with the CPI
● Substitution Bias
○ Over time, some prices rise faster than others
○ Consumers substitute toward goods that become relatively cheaper, mitigating
the effects of price increases
○ The CPI misses this substitution because it uses a fixed basket of goods
○ Thus, the CPI overstates increases in the cost of living
● Introduction of New Goods
You're Reading a Preview
Unlock to view full version
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https://www.revisioncentre.co.uk/gcse/maths/numbers.html
|
math
|
Types of Numbers
Integers are whole numbers (both positive and negative, including
zero). Natural numbers are positive integers.
A rational number is
a number which can be written as a fraction where
numerator and denominator are integers (where the top and bottom of the fraction
are whole numbers). For example 1/2, 4, 1.75 (=7/4).
numbers are numbers which cannot be written as fractions, such as pi and Ö2. In decimal form these numbers go on
forever and the same pattern of digits are not repeated.
numbers are numbers which can be obtained by multiplying another number by
itself. E.g. 36 is a square number because it is 6 x 6 .
numbers left written as Ön , where n is
positive but not a square number. E.g. Ö2 (see 'surds').
Prime numbers are numbers above 1
which cannot be divided by anything (other than 1 and itself) to give an
integer. The first 8 prime numbers are: 2, 3, 5, 7, 11, 13, 17,
Real numbers are all the numbers which you will have come
across (i.e. all the rational and irrational numbers). All real numbers can be
written in decimal form (such as 3.165).
Prime Factor Decomposition
An important fact is that any number can be written as the product
(multiplication) of prime numbers in one way. For example, 20 = 5 x 2 x 2 . This
is the only way of writing 20 as the product of prime numbers. Writing a number
in this way is called prime factor decomposition.
Find the prime factor decomposition of 36.
We look at 36 and try to find numbers which we can divide it by. We can see
that it divides by 2.
36 = 18 x 2
2 is a prime number, but 18 isn't. So we need to split 18 up into prime
numbers. We can also divide 18 by 2.
18 = 9 x 2
and so 36 = 18 x 2 = 9 x
2 x 2
But we haven't finished, because 9 is not a prime number. We know that 9
divides by 3.
9 = 3 x 3.
Hence 36 = 9 x 2 x 2 = 3 x 3 x 2 x 2.
This is the answer, because both 2 and 3 are prime numbers.
LCM and HCF
The lowest common multiple (LCM) of two or more numbers is the smallest
number into which they evenly divide. For example, the LCM of 2, 3, 4, 6 and 9
The highest common factor (HCF) of two or more numbers is the highest
number which will divide into them both. Therefore the HCF of 6 and 9 is 3.
If the side of a square field is given as 90m, correct to the nearest
The smallest value the actual length could be is 85m (since this is the
lowest value which, to the nearest 10m, would be rounded up to 90m). The largest
value is 95m.
Using inequalities, 85£ length <95.
Sometimes you will be
asked the upper and lower bounds of the area. The area will be smallest when the
side of the square is 85m. In this case, the area will be 7725m². The largest
possible area is 9025m² (when the length of the sides are 95m).
When simplifying an expression such as 3 + 4 × 5 - 4(3 + 2), remember to work
it out in the following order: brackets, of (/indices),
division, multiplication, addition, subtraction.
So do the thing in the brackets first, then any division, followed by
multiplication and so on. The above is: 3 + 20 - 4 × 5 = 3 + 20 - 20 = 3 .
You mustn't just work out the sum in the order that it is
Copyright © Matthew Pinkney 2003
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CC-MAIN-2019-35
| 3,141 | 59 |
http://www.topix.com/forum/news/weird/T9QUH2OMJGJK10DEH/p3329
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math
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And you just proved your ignorance. Anyone who says the phrase "just a theory" or its equivalent, does not know what a scientific theory is.<quoted text>Science thinks the Big Bang created everything.....that's absurd! In human terms it makes sense. In the scope of understanding infinite space...its a theory, nothing more.
By the way what evidence do you have that space is infinite? That is not a mistake that scientists will make. Without evidence they will not claim that space is infinite or bounded. In fact that is one question that they are still studying.
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CC-MAIN-2017-22
| 565 | 2 |
https://www.assignmentexpert.com/homework-answers/engineering/civil-and-environmental-engineering/question-167473
|
math
|
Determine the location from the surface of a vertical square so that the center of pressure will be acting 80mm below its center of gravity. Calculate as well the hydrostatic force exerted by oil. One side of the gate measures 2m.
The location from the surface will be at the center.
The hydrostatic force exerted by oil is: 80mm/2m
Therefore the answer is 40
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CC-MAIN-2023-40
| 359 | 4 |
https://content.sciendo.com/browse?pageSize=10&sort=relevance&t=EN-01-02
|
math
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A characteristic feature of the description of physical phenomena formulated by an appropriate boundary or initial-boundary value problem and occurring in microstructured materials is the investigation of the unknown field in the form of decomposition referred to as micro-macro hypothesis. The first term of this decomposition is usually the integral average of the unknown physical field. The second term is a certain disturbance imposed on the first term and is represented in the form of a finite or infinite number of singleton fluctuations. Mentioned expansion is usually referred to as a two-scale expansion of the unknown physical field. In the paper, we purpose to apply two-scale expansion in the form of a certain Fourier series as a result of an applying Surface Localization of the unknown field. The considerations are illustrated by two examples, which results in analytical approximated solutions to the Effective Heat Conduction Problem for periodic composites, including the full dependence on the microstructure length parameter.
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CC-MAIN-2019-35
| 1,048 | 1 |
https://www.physicsforums.com/threads/integration-and-forces.871663/
|
math
|
The question is pretty long and wordy so apologies in advance!
Inside the Earth the gravitational field falls off linearly as one approaches the centre. An accurate description of motion in a very deep hole would therefore be to use Newton’s law, f = ma, but with the force being
f = −gmx/R
where m is the object’s mass, x is the distance of the object from the centre of the Earth, R is the radius of the Earth, and g is the usual acceleration due to gravity measured at the surface.
- (i) Suppose that a parcel destined for Australia is dropped from rest at ground level into a hole that goes through the centre of the Earth. Derive an equation for the speed of the subsequent motion v(x) (where v = x ̇). [Hint: Use x ̈ = vdv/dx.]
- (iii) Find an expression for the parcel’s position, x(t).
- (iv) Using the θ ≪ 1 approximation, cosθ ≈ 1 − θ2 + ..., show that when the displacement is small, (R − x) ≪ R, your expression for x(t) gives the usual result, x ≈ R − gt2/2 .
- (v) Show (using the approximations for R and g in (ii)) that it takes about an hour for the parcel to arrive in Australia.
The Attempt at a Solution
1) I tried -gmx/R = mx.. = mvdv/dx
I then separated the variables and integrated
-gm/R∫xdx = mvdv with the limits of x from 0-->2R and the limits for v 0-->v
this gave me -4gmR = mv2
Rearranging for v (I'm not sure about the sign) v = 2√gr
2) Assuming the above equation is correct (which I'm fairly cercain it isn't!) I then simply integrated with respect to time to get x = 2t√gr. This is obviously wrong as it doesn't work in the next part parts.
I'd really appreciate any help, thanks!
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662573053.67/warc/CC-MAIN-20220524142617-20220524172617-00359.warc.gz
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CC-MAIN-2022-21
| 1,646 | 16 |
https://www.ventureline.com/accounting-glossary/C/cap-definition/
|
math
|
CAP is a series of European interest rate call options used to protect against rate moves above a set strike level.
DISCOUNT HOUSE is a company that specializes in discounting bills of exchange, Treasury bills and short-dated government bonds.
LEASE RATE FACTOR is the periodic lease or rental payment expressed as a percentage (or decimal equivalent) of equipment cost. Used to calculate payments given the cost of equipment (e.g. A lease rate factor of 0360 on an equipment cost of $5,000.00 requires a monthly payment of $180.00 (0360x$5,000.00=$180.00).
Enter a term, then click the entry you would like to view.
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CC-MAIN-2018-09
| 616 | 4 |
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