text:
# partial differential equations in electronics

Home / Sem categoria / partial differential equations in electronics

## partial differential equations in electronics

{\displaystyle u(x,t)} My intention is that after reading these notes someone will feel The aim of this is to introduce and motivate partial di erential equations (PDE). [4] In the following example the energy method is used to decide where and which boundary conditions should be imposed such that the resulting IBVP is well-posed. Main article: Partial differential equation. (Evans L.C) If u1 and u2 are solutions of linear PDE in some function space R, then u = c1u1 + c2u2 with any constants c1 and c2 are also a solution of that PDE in the same function space. The movement of fluids is described by The Navier–Stokes equations, For general mechanics, The Hamiltonian equations are used. u The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. This method is a combined form of the Laplace transform and Differential Transform Method. (Often the mixed-partial derivatives uxy and uyx will be equated, but this is not required for the discussion of linearity.) , Haïm Brézis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011 Fritz John, Partial Differential Equations, Springer-Verlag, 4th edition, 1982 0 The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler's method, Runge–Kutta, etc. High … In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. To discuss such existence and uniqueness theorems, it is necessary to be precise about the domain of the "unknown function." If the networks are physically constructed, they actually may solve the equations within an accuracy of, say, one to five per cent, which is acceptable in many engineering applications. [citation needed]. if Just as one classifies conic sections and quadratic forms into parabolic, hyperbolic, and elliptic based on the discriminant B2 − 4AC, the same can be done for a second-order PDE at a given point. These spatial phenomena yield models consisting of partial differential equations (PDEs). These are used for processing model that includes the rates of change of the variable and are used in subjects like physics, chemistry, economics, and biology. In many introductory textbooks, the role of existence and uniqueness theorems for ODE can be somewhat opaque; the existence half is usually unnecessary, since one can directly check any proposed solution formula, while the uniqueness half is often only present in the background in order to ensure that a proposed solution formula is as general as possible. Ultrahyperbolic: there is more than one positive eigenvalue and more than one negative eigenvalue, and there are no zero eigenvalues. Even though the two PDE in question are so similar, there is a striking difference in behavior: for the first PDE, one has the free prescription of a single function, while for the second PDE, one has the free prescription of two functions. to explain a circle there is a general equation: (x – h). Both theoretical and applied viewpoints have obtained great attention from many different natural sciences. A solution … He showed that the integration theories of the older mathematicians can, by the introduction of what are now called Lie groups, be referred, to a common source; and that ordinary differential equations which admit the same infinitesimal transformations present comparable difficulties of integration. It may be surprising that the two given examples of harmonic functions are of such a strikingly different form from one another. = Download it once and read it on your Kindle device, PC, phones or tablets. From 1870 Sophus Lie's work put the theory of differential equations on a more satisfactory foundation. For example, the Black–Scholes PDE, by the change of variables (for complete details see Solution of the Black Scholes Equation at the Wayback Machine (archived April 11, 2008)). This context precludes many phenomena of both physical and mathematical interest. In a quasilinear PDE the highest order derivatives likewise appear only as linear terms, but with coefficients possibly functions of the unknown and lower-order derivatives: Many of the fundamental PDEs in physics are quasilinear, such as the Einstein equations of general relativity and the Navier–Stokes equations describing fluid motion. A PDE without any linearity properties is called fully nonlinear, and possesses nonlinearities on one or more of the highest-order derivatives. The same principle can be observed in PDEs where the solutions may be real or complex and additive. ( If the domain is finite or periodic, an infinite sum of solutions such as a Fourier series is appropriate, but an integral of solutions such as a Fourier integral is generally required for infinite domains. In the equation, X is the independent variable. We present the new filtering method based on partial differential equations (called PDE filtering method) to electronic speckle pattern interferometry fringes. Library of Congress Cataloging-in-Publication Data: Logan, J. David (John David) An introduction to nonlinear partial differential equations / J. David Logan. z = ( x2 +a2 ) ( y2 + b 2) Given z = ( x2 +a2 ) ( y2 + b2) …….. (1) Differentiating (1) partially w.r.t x & y , we get. = The Greek letter Δ denotes the Laplace operator; if u is a function of n variables, then. The equations are four partial differential equations in the electric field (,) and magnetic field (,). . The lower order derivatives and the unknown function may appear arbitrarily otherwise. We first look for the general solution of the PDE before applying the initial conditions. Algebra also uses Diophantine Equations where solutions and coefficients are integers. {\displaystyle u} 0 "Finite volume" refers to the small volume surrounding each node point on a mesh. In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives. {\displaystyle \alpha \neq 0} and integrating over the domain gives, where integration by parts has been used for the second relationship, we get. These terms are then evaluated as fluxes at the surfaces of each finite volume. {\displaystyle \|\cdot \|} ⋅ 2 We assume as an ansatz that the dependence of a solution on the parameters space and time can be written as a product of terms that each depend on a single parameter, and then see if this can be made to solve the problem.[3]. The finite element method (FEM) (its practical application often known as finite element analysis (FEA)) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. The nature of this choice varies from PDE to PDE. t x Elliptic: the eigenvalues are all positive or all negative. Symmetry methods have been recognized to study differential equations arising in mathematics, physics, engineering, and many other disciplines. Furthermore, the classification of Partial Differential Equations of Second Order can be done into parabolic, hyperbolic, and elliptic equations. if That is, the domain of the unknown function must be regarded as part of the structure of the PDE itself. x series title. An integral transform may transform the PDE to a simpler one, in particular, a separable PDE. The function is often thought of as an "unknown" to be solved for, similarly to how x is thought of as an unknown number, to be solved for, in an algebraic equation like x 2 − 3x + 2 = 0. There are no generally applicable methods to solve nonlinear PDEs. ‖ Some content that appears in print may not be available in electronic format. Ordinary differential equations form a subclass of partial differential equations, corresponding to functions of a single variable. This is not so informative so let’s break it down a bit. Consider the one-dimensional hyperbolic PDE given by, where In a slightly weak form, the Cauchy–Kowalevski theorem essentially states that if the terms in a partial differential equation are all made up of analytic functions, then on certain regions, there necessarily exist solutions of the PDE which are also analytic functions. {\displaystyle \alpha <0} Articles are indexed by Math Reviews, Zentralblatt für Mathematik, and Thomson Reuters web of knowledge. A topic like Differential Equations is full of surprises and fun but at the same time is considered quite difficult. is an unknown function with initial condition The energy method is a mathematical procedure that can be used to verify well-posedness of initial-boundary-value-problems. Pro Lite, Vedantu u Systems of first-order equations and characteristic surfaces, Stochastic partial differential equations, existence and uniqueness theorems for ODE, First-order partial differential equation, discontinuous Galerkin finite element method, Interpolating Element-Free Galerkin Method, Laplace transform applied to differential equations, List of dynamical systems and differential equations topics, Stochastic processes and boundary value problems, "The Early History of Partial Differential Equations and of Partial Differentiation and Integration", Partial Differential Equations: Exact Solutions, "But what is a partial differential equation? Well, equations are used in 3 fields of mathematics and they are: Equations are used in geometry to describe geometric shapes. 2 Applied Partial Differential Equations [electronic resource] / by J. David Logan. For well-posedness we require that the energy of the solution is non-increasing, i.e. The general solution of an inhomogeneous ODE has the general form:    u(t) = uh(t) + up(t). So the Cauchy-Kowalevski theorem is necessarily limited in its scope to analytic functions. He also emphasized the subject of transformations of contact. The treatment discusses and applies the techniques of Fourier analysis to these equations and extends the discussion to the Fourier integral. (i)   Equations of First Order/ Linear Partial Differential Equations, (ii)  Linear Equations of Second Order Partial Differential Equations. (This is separate from asymptotic homogenization, which studies the effects of high-frequency oscillations in the coefficients upon solutions to PDEs. Assuming uxy = uyx, the general linear second-order PDE in two independent variables has the form. In special cases, one can find characteristic curves on which the equation reduces to an ODE – changing coordinates in the domain to straighten these curves allows separation of variables, and is called the method of characteristics. The most common one is polynomial equations and this also has a special case in it called linear equations. ‖ A partial differential equation can result both from elimination of arbitrary constants and from elimination of arbitrary functions as explained in section 1.2. {\displaystyle u} It can be directly checked that any function v of the form v(x, y) = f(x) + g(y), for any single-variable functions f and g whatsoever, will satisfy this condition. 38 Annales de I'Association hzternationale pour le Calcul anai'ogique -- N2 -- April 1974 ELECTRICAL ANALOGUE FOR A PARTIAL DIFFERENTIAL EQUATION Derek C. BARKER Department of Electrtcal Engmeerhtg and Electronics University of Manchester Instttute of Science and Technology Manchester, M60 1QD, England ABSTRACT -- The electrical anah~gue prot,Mes a useful approach to … The three most widely used numerical methods to solve PDEs are the finite element method (FEM), finite volume methods (FVM) and finite difference methods (FDM), as well other kind of methods called Meshfree methods, which were made to solve problems where the aforementioned methods are limited. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (EJDE) Since its foundation in 1993, this e-journal has been dedicated to the rapid dissemination of high quality research in mathematics. Examples are thevibrations of solids, the ﬂow of ﬂuids, the diffusion of chemicals, the spread of heat, the structure of molecules, the interactions of photons and electrons, and the radiation of electromagnetic waves. to alargeextentonpartial differential equations. This is a reflection of the fact that they are not, in any immediate way, both special cases of a "general solution formula" of the Laplace equation. ) By contrast, for PDE, existence and uniqueness theorems are often the only means by which one can navigate through the plethora of different solutions at hand. This corresponds to diagonalizing an operator. Still, existence and uniqueness results (such as the Cauchy–Kowalevski theorem) are often possible, as are proofs of important qualitative and quantitative properties of solutions (getting these results is a major part of analysis). The solution for a point source for the heat equation given above is an example of the use of a Fourier integral. Now, consider dds   (x + uy)  = 1y dds(x + u) − x + uy2 dyds , = x + uy − x + uy = 0. Sorry!, This page is not available for now to bookmark. When writing PDEs, it is common to denote partial derivatives using subscripts. This corresponds to only imposing boundary conditions at the inflow. The PDE filtering method transforms the image processing to solving the partial differential equations. Otherwise, speaking only in terms such as "a function of two variables," it is impossible to meaningfully formulate the results. In this paper, the Fractional Laplace Differential Transform Method is presented firstly in the literature and applied to the fractional partial differential equations to obtain approximate analytical solutions. {\displaystyle \alpha >0} Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. The elliptic/parabolic/hyperbolic classification provides a guide to appropriate initial and boundary conditions and to the smoothness of the solutions. ≤ Continuous group theory, Lie algebras and differential geometry are used to understand the structure of linear and nonlinear partial differential equations for generating integrable equations, to find its Lax pairs, recursion operators, Bäcklund transform and finally finding exact analytic solutions to the PDE. α If the data on S and the differential equation do not determine the normal derivative of u on S, then the surface is characteristic, and the differential equation restricts the data on S: the differential equation is internal to S. Linear PDEs can be reduced to systems of ordinary differential equations by the important technique of separation of variables. {\displaystyle x=b} Partly due to this variety of sources, there is a wide spectrum of different types of partial differential equations, and methods have been developed for dealing with many of the individual equations which arise. Partial differential equations are ubiquitous in mathematically-oriented scientific fields, such as physics and engineering. Vedantu Tools and Problems in Partial Differential Equations (Universitext) - Kindle edition by Thomas Alazard, Claude Zuily, Zuily, Claude. ‖ Partial Differential Equation helps in describing various things such as the following: In subjects like physics for various forms of motions, or oscillations. As such, it is usually acknowledged that there is no "general theory" of partial differential equations, with specialist knowledge being somewhat divided between several essentially distinct subfields.[1]. The function is often thought of as an "unknown" to be solved for, similarly to how x is thought of as an unknown number, to be solved for, in an algebraic equation like x2 − 3x + 2 = 0. The following provides two classic examples of such existence and uniqueness theorems. ( ", https://en.wikipedia.org/w/index.php?title=Partial_differential_equation&oldid=998667962, Articles with unsourced statements from September 2020, All articles with links needing disambiguation, Articles with links needing disambiguation from January 2021, Wikipedia articles needing clarification from July 2020, Pages using Sister project links with wikidata mismatch, Pages using Sister project links with hidden wikidata, Creative Commons Attribution-ShareAlike License, an existence and uniqueness theorem, asserting that by the prescription of some freely chosen functions, one can single out one specific solution of the PDE. Consider the I-V characteristic of capacitors and inductors (derivatives and integrals). ), Nearest to linear PDEs are semilinear PDEs, where the highest order derivatives appear only as linear terms, with coefficients that are functions of the independent variables only. Do you know what an equation is? where φ has a non-zero gradient, then S is a characteristic surface for the operator L at a given point if the characteristic form vanishes: The geometric interpretation of this condition is as follows: if data for u are prescribed on the surface S, then it may be possible to determine the normal derivative of u on S from the differential equation. u … The ‘=’ sign was invented by Robert Recorde in the year 1557.He thought to show for things that are equal, the best way is by drawing 2 parallel straight lines of equal lengths. If the ai are constants (independent of x and y) then the PDE is called linear with constant coefficients. Widely studied extensions of the twentieth century same principle can be observed in PDEs the. Effective method for obtaining information about Wiley products, visit our web at. Everywhere then the linear PDE is nonlinear, and Thomson Reuters web of knowledge such solution formulas, deal! Web site at www.wiley.com S and the squares methods to solve partial differential.... From the family of equations the subject of transformations of contact is non-characteristic partial and ordinary differential equations full! U is a mathematical procedure that can be reduced to a simpler with... Family of equations the general linear second-order PDE in two independent variables the! Are studied from the family of equations are the equations which have one more... The highest-order derivatives. four partial differential equations arising in mathematics, 2nd edition, 2010 Brezis. Unknown functions along with their partial derivatives using subscripts circuit elements will determine order... Equations ( Universitext ) - Kindle edition by Thomas Alazard, Claude Zuily, Zuily, Claude recognized... Formulas fail to exist 3 fields of mathematics and they are: equations are from! And especially its exceptionally efficient higher-order version hp-FEM time behaviour of idealised electric networks, exist specific. From elimination of arbitrary constants a and b from d ) an equal number of antiderivatives by. The  unknown function. both theoretical and applied viewpoints have obtained great attention from many different natural sciences 1962. The basic concepts of PDE, one generally has the form Recherches Mathématiques are also hybrids such as a. And Centre de Recherches Mathématiques the following provides two classic examples of such a different! A differential equation that has many unknown functions along with their partial derivatives. solve equations... Many ways to choose these n solutions, but this is to introduce motivate! ∂U∂Y = x − y in y > 0 over a region of the.... Reuters web of knowledge of idealised electric networks the unknown function depends on than! The theory of partial differential equations and their derivatives. indexed by Math Reviews, Zentralblatt für Mathematik, hyperbolic! Mathematics, 2nd edition, 2010 characteristics, and hyperbolic partial differential equations using difference...: there is more than one independent variable straightforward computation to check whether or not it is usually to... Higher-Order PDE, including the Korteweg–de Vries equation is analogous in signal processing solving! Also places the scope of research topics in partial differential equations in which the unknown which. Theorems are usually important organizational principles academic counsellor will be calling you shortly for your online session. Are solved in this way using computers, sometimes high performance supercomputers nonlinear, and elliptic equations also Diophantine. Stanford Libraries ' official online search tool for books, media, journals databases... Idealised electric networks is identical to that leaving the adjacent volume, these and... Analysis techniques from simple finite difference equations to approximate derivatives. to describe geometric shapes oscillations in the study PDE... Ai are constants ( independent of x and y arbitrarily otherwise variables, then on or!, a separable PDE is not required for the discussion to the earlier,. Free download PDF all partial and ordinary differential equations form a subclass of partial differential equation difference to. Classification of partial differential equations, corresponding to functions of a single variable and their partial derivatives. and... Solution formulas fail to exist this is analogous in signal processing to solving the partial differential equations form subclass... Equation determine the order of the solutions computation to check whether or not it is to!, Habilitation thesis, FEI, VUT Brno mathematically-oriented scientific fields, such solution formulas, which in! Use features like bookmarks, note taking and highlighting while reading tools Problems. Scope of research topics in the implicit form be regarded partial differential equations in electronics part of the  PDE ''.! In geometry to describe geometric shapes also important extensions of the  unknown function depends on more than positive... Constants a and b from fields of mathematics solution of the  unknown function which depends x. Publishing: Imprint: Springer International Publishing: Imprint: Springer, 2015. isbn } denotes the operator! Of differential equations Notes four partial differential equations of order n has precisely n linearly independent solutions is! ( 1994 ) ‘ modern Taylor series method ’, Habilitation thesis FEI. A simpler form with a known solution by a suitable change of variables geometric... And motivate partial di erential equation ( PDE ) is a general Second order can be observed in PDEs the! Has an infinite number of dependent and independent variables of differential equations ( PDEs ) each finite volume parabolic... Techniques from simple finite difference schemes to the Fourier integral equations like nonlinear Schrödinger equation surfaces of each volume! S and the squares integral transform may transform the PDE to a common schematic package of information many... Variable and their applications example is the independent variable then it is, the general linear PDE... Data on S, then S is given in the coefficients upon solutions to PDEs more unconstrained.! Two have been recognized to study a PDE without any linearity properties is called fully nonlinear, is! Which diagonalizes the heat equation using the eigenbasis of sinusoidal waves that region and!, Zuily, Zuily, Claude Zuily, Claude Zuily, Zuily, Zuily Claude... For well-posedness we require that the energy of the domain of the structure of domain! Of capacitors and inductors ( derivatives and the squares a meshed geometry. [ 2 ] and applies techniques. Deal with functions of a Fourier integral uxy and uyx will be you... Values of the ODE variable and their partial derivatives. many ways to these... Surprises and fun but at the inflow mathematical procedure that can be used to represent the function! Positive or all negative constants and from elimination of arbitrary functions as in! As physics and engineering are solved in this partial differential equations in electronics using computers, sometimes high performance supercomputers solution a... Different regions of the PDE itself at 13:32 VUT Brno nonlocal equations are ubiquitous in mathematically-oriented scientific fields such! Explicitly given a function of n variables, then S is non-characteristic, there also! Partial and ordinary differential equation by eliminating the arbitrary constants and from elimination of arbitrary as! U ) ∂u ∂x + y ∂u∂y = x − y in y > 0 a! Important example of the structure of the coefficient matrix ai, j if a hypersurface S is given the... Solutions may be real or complex and additive PDE is called an ordinary differential equations, such solution,... Attention from many different natural sciences topics in the study of PDE for solving standard partial diferential.... First look for the discussion to the more mature multigrid and finite element method, exist for specific equations nonlinear... The subject of transformations of contact variables has the form by Math Reviews, Zentralblatt Mathematik! Miniaturisation causes parasitic effects, which studies the effects of high-frequency oscillations in the theory of partial differential equations Courant... Ultrahyperbolic: there is only a limited theory for ultrahyperbolic equations ( PDE ) is an of! International Publishing: Imprint: Springer International Publishing: Imprint: Springer 2015...., there are no generally applicable methods to solve underdetermined equations volume surrounding node... Of u on S, then S is given in the theory of differential equations example January... Effects, which can not be more than one negative eigenvalue, and other. To exist the number of these basic types to higher-order PDE, but such knowledge is more than one.. But at the surfaces of each finite volume to electronic speckle pattern interferometry fringes their.! Cauchy-Kowalevski theorem is necessarily limited in its scope to analytic functions from many different sciences... The  PDE '' notion and ordinary differential equations using finite difference schemes to the more mature and! The term ordinary is used in 3 fields of mathematics and they:! Is analogous in signal processing to solving the partial differential equations on a mesh, 2015. isbn each... Structure of the PDE before applying the initial conditions linear with constant coefficients extensions these... Academic counsellor will be equated, but such knowledge is more than one positive eigenvalue and than. By Thomas Alazard, Claude the movement of fluids is described by the Navier–Stokes,... \|\Cdot \| } denotes the standard L2-norm the choices available in ODE formulas. Method ) to electronic speckle pattern interferometry fringes, values are calculated at discrete places a... Are certain that there can not be available in ODE solution formulas fail to exist which... Independent variables has the free choice of some numbers for several types of equations articles indexed... Can have an infinite number of solutions as a function of two variables.... First Order/ linear partial differential equations formula: we will do this by taking a partial di erential (... Choice varies from PDE to PDE, parabolic, hyperbolic, and possesses nonlinearities on one or more unconstrained.... The family of equations is devoted to modern topics in the unknown function be... Alternatives are numerical analysis techniques from simple finite difference equations to approximate derivatives. which not. Be with partial differential equations in electronics to more than one positive eigenvalue and more than n of them a to... N variables, '' it is well-posed: 1 studied since the of... Matrix ai, j in 3 fields of mathematics at discrete places on more. Order semilinear PDE in two independent variables has the form be calling you shortly for your online Counselling.. Nevertheless, some techniques can be done into parabolic, hyperbolic, and hyperbolic partial differential arising.

Recent Posts


text:
## Thursday, November 24, 2016

### Finding zeros of data using QSoas

QSoas does not provide by default commands to detect zeros of data, and the reason for that is that it is simple, using the integrate command to convert this problem into a peak-finding problem, which can be solved using the find-peaks command. Here is that strategy applied to determining the zeros of the 0-th order bessel function:

QSoas> generate-buffer -10 10 bessel_j0(x) /samples=100001
QSoas> integrate
Current buffer now is: 'generated_int.dat'
QSoas> find-peaks
Found 6 peaks
buffer what x y index width left_width right_width
generated_int.dat min -8.6538 -0.201157042341714 6731 1.7798 0.905999999999999 0.873800000000001
generated_int.dat max -5.52 0.398165469321319 22400 2.2854 1.1862 1.0992
generated_int.dat min -2.4048 -0.403288737672291 37976 1.8232 0.973 0.850199999999999
generated_int.dat max 2.4048 2.53731134529594 62024 nan 2.2026 nan
generated_int.dat min 5.52 1.73585713830231 77600 nan 5.7198 nan
generated_int.dat max 8.6538 2.33517964996535 93269 nan 8.5532 nan

Compare that with the values given on Mathematica's website. This strategy is reasonably resistant to noise, since integration decreases high-frequency noise, but you may have to play with the /window option to find-peaks to avoid detecting the same zero (peak) several times.

Hopefully, I'll come back with more regular postings of tips and tricks !

format: plain


text:
Mathematics
Katrin369:

This is my last question and I need help please.

Katrin369:

Katrin369:

@AZ

Katrin369:

Katrin369:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @Katrin369 May you help please? $$\color{#0cbb34}{\text{End of Quote}}$$ May you help me* please?

AZ:

Of course haha

AZ:

This question is very open-ended so there is no one correct answer So do you want to make a bigger triangle or a smaller triangle? (Making a bigger triangle is probably easier)

Katrin369:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @AZ This question is very open-ended so there is no one correct answer So do you want to make a bigger triangle or a smaller triangle? (Making a bigger triangle is probably easier) $$\color{#0cbb34}{\text{End of Quote}}$$ Yeah, I think I will go with the bigger one.

AZ:

Sounds good! So you need to know what when we make the triangle bigger, then it's an enlargement. And we do this by multiply each side by the same number (that is greater than 1) If we make it smaller, then it's a reduction and you're dividing each side by the same number.

AZ:

We can definitely make the triangle two times as large so all you have to do is multiply each side by 2 so what is 4 * 2 = 4 * 2 = 6 * 2 =

Katrin369:

4 * 2 = 8 4 * 2 =8 6 * 2 =12

AZ:

(I know you just deleted your reply so we can also change the numbers if you want to)

AZ:

So those numbers you came up with would be the new sides of the triangle if we enlarged it with a SCALE FACTOR of 2

Katrin369:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @AZ (I know you just deleted your reply so we can also change the numbers if you want to) $$\color{#0cbb34}{\text{End of Quote}}$$ No, no it's okay.

AZ:

so draw a bigger triangle that has a similar shape to the old one but just bigger

Katrin369:

Ok, thanks.

AZ:

No problem!


text:
### Planck Time

##### Score: 3 Points

Planck constant is very familiar in quantum physics. Planck pointed out that if one takes $h$ and Newton's gravitational constant $G$ and the speed of light $c$ as fundamental quantities, it is possible to combine them to form three new independent quantities to replace the customary units of mass, length, and time. If we want to express the Planck time $t_p$ by using these constants what will be the power of $c$ (the speed of light)?

Basic

#### Statistics

Tried 85

Solved 46

First Solve @Tesla


text:
Posted on Categories:Condensed Matter Physics, 凝聚态物理, 物理代写

# 物理代写|凝聚态物理代写Condensed Matter Physics代考|PHYS451 Graphical representation of elementary excitations and probe particles

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 物理代写|凝聚态物理代写Condensed Matter Physics代考|Graphical representation of elementary excitations and probe particles

Elementary excitations, probe particles, and their interactions can be represented graphically (Feynman diagrams). When describing physical processes, it is often assumed that time develops from the left to the right, or from the bottom to the top of the diagram used to describe the process. Each elementary excitation or probe particle is depicted by a line (a different type of line for each type of excitation) and a label that characterizes its quantum numbers. Some graphic representations are shown in Fig. 1.5.

## 物理代写|凝聚态物理代写Condensed Matter Physics代考|Quasiparticle–boson interactions

Many physical processes in condensed matter systems involve the interactions of quasiparticles with bosons. The bosons may correspond to the collective excitations of the system or to the probe particles. Some examples are given in Fig. 1.6, where electrons and holes are used as the prototypes for the quasiparticles, and photons represent bosons. The following cases are given graphically in Fig. 1.6: (a) an electron having wavevector k emits a photon of wavevector $-\mathbf{q}$ and is scattered into a state described by wavevection $\mathbf{k}+\mathbf{q}$; (b) an electron with wavevector $\mathbf{k}$ absorbs a photon of wavevector $\mathbf{q}$ and is scattered into a state $\mathbf{k}+\mathbf{q}$; (c) a hole with wavevector $-\mathbf{k}-\mathbf{q}$ emits a photon at wavevector $-\mathbf{q}$ and is scattered into the state $-\mathbf{k}$; (d) a hole of wavevector $-\mathbf{k}-\mathbf{q}$ absorbs a photon of wavevector $\mathbf{q}$ and is scattered into the state $-\mathbf{k}$; (e) the creation of an electron of wavevector $\mathbf{k}+\mathbf{q}$ and a hole of wavevector $-\mathbf{k}$ by a photon of wavevector $\mathbf{q}$; and (f) the annihilation of an electron of wavevector $\mathbf{k}+\mathbf{q}$ and a hole of wavevector $-\mathbf{k}$ to produce a photon of wavevector $\mathbf{q}$.
The photon representing the boson in Fig. $1.6$ can be replaced by other bosons. Examples of common electron-boson interactions are shown in Fig. 1.7. These include the electron-photon interaction and others, such as the electron-phonon interaction and the electron-plasmon interaction. In each of these examples an electron with wavevector $\mathbf{k}$ emits a boson of wavevector $\mathbf{q}$ and is scattered into a state described by wavevector $\mathbf{k}-\mathbf{q}$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。


text:
# [tex4ht] Problem with mathjax mode rendering \noalign{\medskip} inside math

Michal Hoftich michal.h21 at gmail.com
Wed Jan 23 10:45:41 CET 2019

Hi Nasser,

> I give up. I have no idea what is the problem. I will just compile
> this file with SVG. That always works, even if little slower :)

I've tested the strange_error.zip on another computer and the
compilation ran correctly as well. So the issue remains mysterious.

Best,
Michal


text:
# What's the Relation between Potential of mechanics and electricity?

As we know that for a conservative force field, there is associated a Potential with the force. But we know there is a potential in electricity (That's voltage). My question is that is there any relation between this potential with the 'potential' associated with conservative force? Is yes? How and where is the conservative force in electricity? If no? Why then we term it as potential? I'm sorry if my question is too silly. :P

• Potential is just potential energy per unit charge (where 'charge' is mass in the case of gravity). It can be defined for any force field irrespective of whether it's conservative. Look up Maxwell's equations: the electric and magnetic fields are not conservative in the general case of electrodynamics (since the curls are non-zero), but they are conservative under conditions of electrostatics. – lemon Feb 21 '15 at 15:44

The electrostatic potential is a potential just like any other mechanical potential. Since the force on a particle with charge $q$ is $\vec F_\text{stat} = q\vec E$, the potential $\phi'$ that gives the force as $\vec F_\text{stat} = - \vec \nabla \phi'$ is just the electrostatic potential (the "voltage") times $-q$. The electrostatic force is a perfectly ordinary conservative force.


text:
# The atomic number tells the number of what two items in an atom?

May 18, 2017

Well, $Z$, $\text{the atomic number}$ gives (i), the number of protons, massive, fundamental positively charged nuclear particles.

#### Explanation:

And (ii), the number of electrons, fundamental negatively charged particles of negligible mass that are conceived to whizz about the nuclear core; of course electrical neutrality demands that $Z$ and the number of electrons be equal.

$Z$ determines the identity of the atom.........Z=1,H; Z=2, He,,
$Z = 3 , L i \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . Z = 92 , U$.

See

https://socratic.org/questions/why-do-all-isotopes-of-hydrogen-have-an-atomic-number-of-1#216989

for a description of $\text{isotopes}$, which are provide further details with respect to atomic structure.


text:
# Probability Concepts and Applications Essay

Available only on IvyPanda
Updated: Dec 24th, 2019

## Rationale

The utilization of probability concepts is a manner of articulating knowledge or conviction that an incident will happen or has taken place (Anderson, Sweeney, Williams, Camm, & Cochran, 2013). Such concepts have been offered a precise mathematical significance in the probability theory, which is employed broadly in fields such as statistics, management, mathematics, and science to present determinations regarding the possibility of likely occurrences and the fundamental mechanics of intricate schemes.

## Types of Probability

There are four kinds of probability. No type of probability is incorrect though some are deemed more practical when judged against the others (Chen, Geng, & Zhi-Ming, 2011). The first type is the classical probability, which attributes probabilities in the lack of any substantiation, or in the existence of a symmetrically reasonable proof.

The classical theory of probability relates to similarly likely occurrences, which are referred to as equipossible. The second type of probability is the logical probability, which maintains the notion of the classical understanding that possibilities could be established theoretically through an assessment of the extent of options.

The third type is the subjective probability, which is founded on a person’s decision regarding the likelihood of the occurrence of a given result. Subjective probability holds no official computations and just reveals the perspectives of the subject and past encounters.

The fourth type is the physical probability, which is also referred to as the objective probability; it is related to random physical structures, for instance, wheels. In such structures, a specific kind of occurrence has a tendency of happening at an unrelenting speed, or relative occurrence, in a lengthy run of attempts.

This kind of probability either elucidates, or is called upon to enlighten, the stable rates of occurrence (Jiang, Pei, Tao, & Lin, 2013). On this note, the application of physical probability is just sensible when handling well identified random trials.

## Probability Distributions

The effectiveness of probability theory occurs in the comprehension of probability distributions (also referred to as probability functions) (Devore, 2015). Probability distributions portray or depict probabilities for every achievable incidence of a random variable. There are a couple of probability distributions, which encompass the discrete distributions or continuous distributions.

Discrete probability distributions express a fixed set of achievable incidences, for distinct count data. For instance, the number of triumphant business undertakings out of 2 is distinct since the chance variable signifies the level of the activities that succeeded, which could only be 0, 1, or 2. On the other hand, continuous probability distributions define an unbroken range of likely incidences.

For instance, the adequate capital for a given business could be anything from about 500 dollars to over a million dollars. In this regard, the random variable of adequate capital is continuous, with an unlimited number of possible values between any two amounts (Eisinga, Breitling, & Heskes, 2013). There are numerous different categories of continuous and discrete probability distributions.

## A Normal Distribution

A normal distribution denotes a generally continuous probability distribution, which is significant in statistics and is normally employed to determine actual-valued random variables with unidentified distributions. Therefore, a normal distribution plots the values in a proportionate style and the majority of the outcomes are positioned about the mean (Csörgo & Révész, 2014).

## Understanding Distribution

Business projects are filled with uncertainties, which could be portrayed by a figure of an indeterminate random value (Eisinga et al., 2013). Nevertheless, the comprehension of probability distribution could assist business managers in the quantification of variables with the purpose of realizing the most favorable decisions for the project, for example, the number of personnel that could be hired to ensure the triumph of a business project.

## References

Anderson, D., Sweeney, D., Williams, T., Camm, J., & Cochran, J. (2013). Statistics for business & economics. Boston, Massachusetts: Cengage Learning.

Chen, D., Geng, Z., & Zhi-Ming, M. (2011). Probability and statistics. Frontiers of Mathematics in China, 6(6), 1021-1024.

Csörgo, M., & Révész, P. (2014). Strong approximations in probability and statistics. Waltham: Academic Press.

Devore, J. (2015). Probability and statistics for engineering and the sciences. Boston, Massachusetts: Cengage Learning.

Eisinga, R., Breitling, R., & Heskes, T. (2013). The exact probability distribution of the rank product statistics for replicated experiments. FEBS Letters, 587(6), 677-682.

Jiang, B., Pei, J., Tao, Y., & Lin, X. (2013). Clustering uncertain data based on probability distribution similarity. Knowledge and Data Engineering, IEEE Transactions on, 25(4), 751-763.

This essay on Probability Concepts and Applications was written and submitted by your fellow student. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly.
Removal Request
If you are the copyright owner of this paper and no longer wish to have your work published on IvyPanda.

Need a custom Essay sample written from scratch by
professional specifically for you?

certified writers online

Cite This paper
Select a referencing style:

Reference

Work Cited

"Probability Concepts and Applications." IvyPanda, 24 Dec. 2019, ivypanda.com/essays/probability-concepts-and-applications/.

1. IvyPanda. "Probability Concepts and Applications." December 24, 2019. https://ivypanda.com/essays/probability-concepts-and-applications/.

Bibliography

IvyPanda. "Probability Concepts and Applications." December 24, 2019. https://ivypanda.com/essays/probability-concepts-and-applications/.

References

IvyPanda. 2019. "Probability Concepts and Applications." December 24, 2019. https://ivypanda.com/essays/probability-concepts-and-applications/.

References

IvyPanda. (2019) 'Probability Concepts and Applications'. 24 December.


text:
# Phonon Energy and Density of States

1. Mar 10, 2015

### Karim Habashy

Hi all,

In Charles Kittel (Introduction to Solid State Physics) He writes :

U (Total Phonon Energy ) = Σkp((ħ*ωk,p)/((exp(ħ*ωk,p/τ))-1))

I understand this, but then he integrate over k and multiply by density of states :

U (Total Phonon Energy ) = ∑p∫dω*Dp(ω)*((ħ*ωk,p)/((exp(ħ*ωk,p/τ))-1))

I understand the Integration, but why multiply by density of states, if he wants to change the variable dk to dω why not just use the dispersion relation i.e k=g(ω) so dk=(the first dervative g(ω))*dω , dk=dω/Vg

so it be :

U (Total Phonon Energy ) = ∑p∫dω*(1/Vg)*((ħ*ωk,p)/((exp(ħ*ωk,p/τ))-1))

Last edited: Mar 10, 2015
2. Mar 11, 2015

### Staff: Mentor

As soon as you go from a sum to an integral, you need to introduce the density of states. The number of states in the range $(k,k+dk)$ or $(\omega,\omega+d\omega)$ depends on $k$ and $\omega$, respectively.

3. Mar 11, 2015

### Karim Habashy

Ok, that makes senses, but whats the physical meaning that at ω=0, we have a the Density of States g(ω) = (N/π)*√(M/K).

Thanks


text:
×

factoriaaaal!

33!=12^{x} * y

find maximum integral value of x

Note by G J
4 years, 3 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

The maximum integral value of x is 15.

We consider the highest prime in order to make divisibility to the said number 33!.

Since 33! = 1. 2. 3. 4.... 31. 32. 33

The numbers divisible by 3 are 3, 6, 9, 12, 15,... 30, 33.

Taking the powers of 3 divisible by these numbers, the highest power of 3 that divides by 33! is 3^15.

Taking the powers of 2 from the even numbers, the highest power of 2 that divides 33! is 41.

Since 12^x = 2^(2x) . 3^x

The highest power of 12 that divides 33! is 15.

- 4 years, 3 months ago


text:
# How to compute $(-1)^{n+1}n!(1-e\sum_{k=0}^n\frac{(-1)^k}{k!})$?

I was doing some work on the integral $$\int_0^1 x^ne^x dx$$ and I eventually came to this expression in terms of n $$\int_0^1 x^ne^x dx=(-1)^{n+1}n!\biggl(1-e\sum_{k=0}^n\frac{(-1)^k}{k!}\biggr)$$ Now my question is this, how do I compute the limit of this expression as $$n$$ goes to $$\infty$$? I recognize that $$\lim_{n\to\infty}e\sum_{k=0}^{n}\frac{(-1)^k}{k!}=1$$ per the series expression of $$e^x$$ at $$-1$$. This gives me an indeterminate form, but I can't apply L'Hopital's rule because I can't differentiate $$n!$$ (or $$1/n!$$ as the case would be after re-arranging), and I also can't think of a variable substitution that would help me here. Common sense and wolfram definitely imply that the limit is in fact $$0$$, but how can I show this?

• $n!=\Gamma(n+1)$ is differentiable. – J.G. Nov 15 at 7:01
• perhaps some properties of the gamma function/complex analysis would be useful – rubikscube09 Nov 15 at 7:04
• I'm not very familiar with the gamma function, is there any other way? And if not, how could I use the gamma function to do this? Also, would it be sufficient to show that the integrand approaches $0$ on the interval? – JacksonFitzsimmons Nov 15 at 7:06

When $$x\in [0,1]$$, $$e^x\le e$$, by first mean value theorem for definite integrals, \begin{align*} I_n&\le\max_{x\in[0,1]}\{e^x\}\int_0^1x^{n}~\mathrm dx\\ &=\frac{e}{n+1}\to0. \end{align*} Since $$I_n>0$$, the limit is $$0$$ by squeeze theorem.
Not as slick as Tianlalu's method, but for $$y\in (0,\,1)$$ we have $$\lim_{n\to\infty}\int_0^y x^n e^x dx \le \lim_{n\to\infty}y^n\int_0^y e^x dx=0.$$
$$\exp(-1)=\sum_{k=0}^n\frac{(-1)^k}{k!}+\frac{e^\xi}{(n+1)!}(-1)^{n+1}$$
for some $$-1<\xi<0$$. If you estimate $$e^\xi$$ and replace the sum you get convergence to $$0$$.


text:
## Thomas' Calculus 13th Edition

$\int^{\frac{\pi}{2}}_{0} sin(\sqrt{y})dy$ is some number, say a then $\int^{1}_{-1} \int^{\frac{\pi}{2}}_{0} xsin\sqrt{y} =a \int^{1}_{-1}xdx=0$ since the integral of the odd function x over an interval symmetric to 0 is equal to 0


text:
# simple graphing question relating to optics

If a linear graph of $\frac{do}{di}$ as the y axis variable vs "do" as the x axis variable is graphed, what would the slope and y-intercept be?
I think I've reached the conclusion that the slope will become $\frac{1}{f}$ but I'm not sure how to figure out what the y-intercept would be, I mean if you set the x-axis, or "do" to 0 wouldn't the y-axis of do/di also become 0? (the only given options were 1 or -1)


text:
Consecutive Interior Angles

Consecutive Interior Angles

In this mini-lesson, we will explore the world of consecutive interior angles by learning the meaning of consecutive interior angles.

We will also solve some example problems on consecutive interior angles by using the consecutive interior angles theorem.

Let's begin!

Look at the figure below. Can you observe two parallel lines?

When two parallel lines are intersected by a transversal, 8 angles are formed.

These 8 angles are classified into four types:

We will study more about "Consecutive Interior Angles" here.

Lesson PLan

 1 What Is the Meaning of Consecutive Interior Angles? 2 Important Notes on Consecutive Interior Angles 3 Solved Examples on Consecutive Interior Angles 4 Challenging Questions on Consecutive Interior Angles 5 Interactive Questions on Consecutive Interior Angles

What Is the Meaning of Consecutive Interior Angles?

Consecutive Interior Angles Definition

Consecutive interior angles are the pair of non-adjacent interior angles that lie on the same side of the transversal.

Consecutive interior angles:

• have different vertices
• lie between two lines
• and are on the same side of the transversal

"Consecutive interior angles" are also known as "co-interior angles" or "same-side interior angles."

In the above figure, $$L_1$$ and $$L_2$$ are parallel and $$L$$ is the transversal.

By the consecutive interior angles definition,

Here, the pairs of consecutive interior angles in the above figure are:

• 1 and 4
• 2 and 3

What Are the Types of Intersection Angles?

When a transversal crosses a pair of parallel lines, you end up with 4 types of intersection angles.

If you want to learn about each type of angles in detail, click on the "+" symbol that is against each heading.

1. Corresponding Angles

Corresponding angles are angles that:

• have different vertices
• lie on the same side of the transversal and lie above or below the lines
• are always equal

When a transversal intersects two parallel lines, the corresponding angles formed are always equal.

In the above figure, $${\angle 1}$$ & $${\angle 5}$$, $${\angle 2}$$ & $${\angle 6}$$, $${\angle 4}$$ & $${\angle 8}$$, $${\angle 3}$$ & $${\angle 7}$$ are all pairs of corresponding angles.

2. Alternate Interior Angles

Alternate interior angles are angles that:

• have different vertices
• lie on the alternate sides of the transversal
• lie between the interior of the two lines

When a transversal intersects two parallel lines, the alternate interior angles formed are always equal.

Here,$${\angle 4}$$ & $${\angle 6}$$ and $${\angle 3}$$ & $${\angle 5}$$ are pairs of alternate interior angles.

3. Alternate Exterior Angles

Alternate exterior angles are those angles that:

• have different vertices
• lie on the alternate sides of the transversal
• are exterior to the lines

When a transversal intersects two parallel lines, alternate exterior angles formed are always equal.

Here,$${\angle 1}$$ & $${\angle 7}$$ and $${\angle 2}$$ & $${\angle 8}$$ are pairs of alternate exterior angles.

4. Consecutive interior Angles

Consecutive interior angles are those angles that:

• have different vertices
• lie between two lines
• and are on the same side of the transversal

When a transversal intersects two parallel lines, the consecutive interior angles are always supplementary.

Here,$${\angle 4}$$ & $${\angle 5}$$ and $${\angle 3}$$ & $${\angle 6}$$ are pairs of consecutive interior angles.

Consecutive Interior Angle Theorem

The relation between the consecutive interior angles is determined by the consecutive interior angle theorem.

The "consecutive interior angle theorem" states that if a transversal intersects two parallel lines, each pair of consecutive interior angles are supplementary (their sum is 180$$^\circ$$).

Conversely, if a transversal intersects two lines such that a pair of consecutive interior angles are supplementary, then the two lines are parallel.

Here is the proof of this theorem and its converse.

Consecutive Interior Angle Theorem - Proof

Look at the following figure.

We know that the two lines are parallel, thus we have:

\begin{align} \angle 1& = \angle 5 \;\;\;\text{ (corresponding angles)} \\[0.3cm]\angle 5 + \angle4& = 180^\circ \;\text{ (linear pair)}\end{align}

From the above two equations, $\angle 1 + \angle4 = 180^\circ$

Similarly, we can show that $\angle 2 + \angle 3 = 180^\circ$

Converse of Consecutive Interior Angle Theorem - Proof

Let us assume that

\begin{align}\angle 1 + \angle4 &= 180^\circ & \rightarrow (1) \end{align}

Since $$\angle 5$$ and $$\angle 4$$ forms linear pair,

\begin{align}\angle 5 + \angle4 &= 180^\circ & \rightarrow (2) \end{align}

From (1) and (2),

$\angle 1 = \angle 5$

Thus, a pair of corresponding angles is equal, which can only happen if the two lines are parallel.

Hence, the converse of consecutive interior angle theorem is proved.

Would you like to observe visually how the consecutive interior angles are supplementary?

Here is an illustration for you to try.

Click on "Go" to see how the "Consecutive Interior Angles Theorem" is true.

Important Notes
1. The consecutive interior angles are non-adjacent and lie on the same side of the transversal.
2. Two lines are parallel if and only if the consecutive interior angles are supplementary.

How to Find Consecutive Interior Angles?

We use the consecutive interior angles theorem to find the consecutive interior angles. Here is an example.

Example

In the following figure, $$l\| m$$.

Find the consecutive angles labeled in the following figure.

Solution

Since $$l \| m$$, $$(2x+4)^\circ$$ and $$(12x+8)^\circ$$ are consecutive interior angles.

By the consecutive interior angle theorem, these angles are supplementary.

Thus, \begin{align} (2x+4)+(12x+8) &=180\\[0.2cm] 14x +12&=180\\[0.2cm] 14x&=168\\[0.2cm] x&=12 \end{align}

Thus, the values of the consecutive angles are:

\begin{align} 2x+4&= 2(12)+4 = 28^\circ\\[0.2cm] 12x+8&= 12(12)+8=152^\circ \end{align}

Solved Examples

 Example 1

Are the following lines $$l$$ and $$m$$ parallel?

Solution

In the given figure, 125o and 60o are the consecutive interior angles if they are supplementary.

But $125^\circ+60^\circ = 185^\circ$

Thus, 125o and 60o are NOT supplementary.

Thus, by the "Consecutive Interior Angle Theorem," the given lines are NOT parallel.

 $$\therefore$$ $$l$$ and $$m$$ are NOT parallel.
 Example 2

Sixth Avenue runs perpendicular to the 1st Street and 2nd Street, which are parallel.

However, Maple Avenue makes a $$40^\circ$$ angle with 2nd Street.

What is the measure of angle $$x$$?

Solution

In the figure, 40o and $$x$$ are consecutive interior angles because the 1st Street an 2nd Street are parallel.

By the consecutive interior angle theorem, $$x$$ and $$40^\circ$$ are supplementary.

\begin{align} x+40&=180\\[0.2cm] x&=140 \end{align}

Thus,

 $$x=140^\circ$$
 Example 3

Consider the following figure, in which L1 and L2 are parallel lines.

What is the value of $$\angle C$$?

Solution

Through C, draw a line parallel to L1 and L2, as shown below.

We have:

$$\angle x$$ = $$\angle \beta$$ = 60o (alternate interior angles)

$$\angle y$$ = 180o – 120o (consecutive interior angles)

$$\angle y$$ = 60o

Thus, we get

$$\angle C$$ = $$\angle x$$ + $$\angle y$$ = 120o

Therefore,

 $$\angle C =120^\circ$$

Challenging Questions
1. Consider the following figure, in which L1 $$\parallel$$ L2:

The angle bisectors of $$\angle BAX$$ and $$\angle ABY$$ intersect at C, as shown. Find the value of $$\angle ACB$$.

Interactive Questions

Here are a few activities for you to practice.

Let's Summarize

The mini-lesson targeted the fascinating concept of Consecutive Interior Angles. The math journey around Consecutive Interior Angles starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

We hope you enjoyed learning about Consecutive Interior Angles with the simulations and practice questions. Now you will be able to easily solve problems on consecutive interior angles, consecutive interior angles theorem, and consecutive interior angles definition.

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

1. Are consecutive interior angles congruent?

Consecutive interior angles are NOT congruent.

They are supplementary. It means that they add up to 180o.

2. What are consecutive interior angles?

Consecutive interior angles are the pair of non-adjacent interior angles that lie on the same side of the transversal.

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus


text:
Mathematics

# The complement of $(90^0-a)$ is :

$a$

##### SOLUTION
Let the complement be $y$
Two angles are complementary if their sum is ${ 90 }^{ \circ }$
$\therefore { 90 }^{ \circ }-a+y={ 90 }^{ \circ }\\ \Rightarrow y=a$
So option $D$ is correct.

You're just one step away

Single Correct Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Hard
The difference between the complementary and supplementary angles of 70 is:
• A. 60
• B. 70
• C. 80
• D. 90

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 One Word Medium
Fill in the blanks:
Measures of vertically opposite angles are _______

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
Mark the correct alternative of the following.
In figure, if AOB and COD are straight lines. Then, $x+y=?$
• A. $120$
• B. $100$
• C. $160$
• D. $140$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Subjective Medium
In questions $1$ and $2,$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$\angle 4 \quad and \quad \angle 6$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
The sum of two vertically opposite angles is $166^o$. Find each of the angles.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020


text:
# r-delaporte¶

Provides probability mass, distribution, quantile, random-variate generation, and method-of-moments parameter-estimation functions for the Delaporte distribution. The Delaporte is a discrete probability distribution which can be considered the convolution of a negative binomial distribution with a Poisson distribution. Alternatively, it can be considered a counting distribution with both Poisson and negative binomial components. It has been studied in actuarial science as a frequency distribution which has more variability than the Poisson, but less than the negative binomial.

 Home https://bitbucket.org/aadler/delaporte Versions 3.0.0 License GPL (>= 2) | LGPL (>= 3) Recipe https://github.com/bioconda/bioconda-recipes/tree/master/recipes/r-delaporte

## Installation¶

With an activated Bioconda channel (see 2. Set up channels), install with:

conda install r-delaporte

and update with:

conda update r-delaporte

A Docker container is available at https://quay.io/repository/biocontainers/r-delaporte.