Terms Definition and 1000 Threads

Although I have a good understanding of how to do calculations in gauge field theory, I am still dissatisfied with my understanding of why we use them in the first place. From a philosophical point, it should be possible to characterize a gauge theory in terms of observables only. I suppose one...

This is not only a question strictly about mathematics, but in science or any other quantitative field in which there is an integration - or a summation that is like a discrete integration. [ A ] the parameter that is considered the input variable for the integration/summati - i.e., the x of dx...

Homework Statement The instantaneous force F acting on a particle, as measured in frame S, is Use the formula for the linear momentum () in and the definition of the acceleration a to show that The Attempt at a Solution The professor said that this required use of programs such...

Homework Statement [/B] Calculate \widehat{Y^{2}} (i.e., the mean of the square of Y. Homework Equations Y=\sum_{k=0}^{N-1}y_{k} where y_{k}=e^{-\gamma t}e^{\gamma \tau k}G_{k} and t=N\tau The quantities y_{k} (or G_{k}) are statistically independent. The Attempt at a Solution...

This question mostly pertains to how looking at affine independence entirely in terms of linear independence between different families of vectors. I understand there are quite a few questions already online pertaining to the affine/linear independence relationship, but I'm not quite able to...

Homework Statement For each of the following functions find the first few terms of each of the Laurent series about the origin, that is, one series for each annular ring between singular points. Find the residue of each function at the origin. The function is... 1/(z*(z-1)(z-2)^2) Homework...

I have been given a task to create an interpolating/extrapolating programme. I have completed the programme for linear interpolation (2 points) but now must make it usable for 3 or more points, ie a polynomial of n points. I think I have the equation in general for a polynomial as it is an...

Homework Statement (4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0[/B]Homework Equations (4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0 The Attempt at a Solution i expanded it as 4x^3y^3dx-2xydx+3x^4y^2dy-x^2dy=0 next we have to take the common such that there will be m(X)(xdy+ydx)[/B] m(x) is the common onee

Hello, PF! Recently, while reading chapter 10 (microscopic energy balances) of the second edition of BSL, I found a minor discrepancy which is confusing me, especially when considering the mathematical analogies of heat and mass transfer. In section 10.1, the authors introduce Newton's law of...

1. Homework Statement Express the beam energy loss in the accelerator in terms of the change in the beam momentum. It is taken from one paper, where \begin{equation} \Delta T = \left( \frac{1+\gamma}{\gamma}\right) \frac{T_0 \Delta p}{p_0} \end{equation}expression is used for transition from...

I was wondering if anyone knows of what type of law is involved with the terms of service of internet discussion forums. Is it possible through terms of service for a discussion forum to legally own poster's posts? Thanks!

Hi, Suppose I have a function on a graph with a vertical axis is Force and the horizontal axis is distance. Then the area under the curve is given by F*d = Work = Energy, correct? If so, then what would the slope of the curve represent? F/d = ? Thank you.

Homework Statement Find consensus (redundant) terms for the minimal SOP solution for the following function (inputs A,B,C,D and output F): Σm(1,3,4,5,7,10,11,12,14,15) Homework Equations n/a The Attempt at a Solution I find the minimal SOP solution is F=A'D + AC + BC'D' Then it seems like...

For this function f(x)=x^2/(1-5x). The interval of convergence is (-1/5) < x < (1/5). I tried to differentiate, but got it wrong. Could someone please help?

Why is the nominal capacity of power plants given in terms of power and not in terms of energy?

Homework Statement Express the vector R in terms of A, B, C, D (VIEW IMAGE ATTACHED) Homework EquationsThe Attempt at a Solution R=B-D OR R=A+C In this problem, I figured that because of the way the arrows are pointing R+D=B which you can then simplify to R=B-D. However, this is not an answer...

I am confused about the algebraic process of finding a limit. Let us take ##\frac{x^2 -1}{x - 1}##. In trying to find ##\lim_{x\rightarrow 1}\frac{x^2 -1}{x - 1}##we do the following: ##\displaystyle\lim_{x\rightarrow 1}\frac{(x+1)(x-1)}{x - 1}## ##\displaystyle\lim_{x\rightarrow 1}x+1##...

I need to show that the following expression, $$a^3b-a^3c+a^3z+a^3x+a^3y-a^2bx+a^2by+a^2cx-a^2cy-a^2zx+a^2zy-a^2x^2+a^2y^2-abcz-abcx-aczx-acx^2+b^2c^2+2bc^2x+c^2x^2-b^2c-2bcx-cx^2,$$ is positive given that: $1.$ $\ a,b,c,x,y,z$ are positive real numbers $2. \ \ a>b+x$ $3. \ \ c<b+y$ I...

Would it be possible to write the torsion tensor in terms of the metric? I know that a symmetric Christoffel Symbol can be written in terms of the partial derivatives of the metric. This definition of the christoffel symbols does not apply if they are not symmetric. Is it possible to write a...

Homework Statement ## L (v^2 + 2 \pmb{v} \cdot \pmb{ \epsilon } ~ + \pmb{ \epsilon} ^2)##, where ## \pmb{\epsilon}## is infinitesimal and ##\pmb{v}## is a constant vector (## v^2 ## here means ## \pmb{v} \cdot \pmb{v} ## ), must be expanded in terms of powers of ## \pmb{\epsilon} ## to give...

I was receiving help for the following problem... The 2.0 kg wood box in the figureslides down a vertical wood wall while you push on it at a 45 ∘ angle. The coefficient of kinetic friction of wood on wood is μk = 0.200. What magnitude of force should you apply to cause the box to slide down at...

All I know is that Lagrangian is kinetic energy- potential energy and Hamiltonian is kinetic energy + Potential energy. Why do we calculate the lagrangian or hamiltonian?

I just want to know how do I determine the number of terms will be in this summation. The answer to this 2N+1 terms. I can only arrive at preliminary steps of solving this. can you tell why 2N+1 is the number of terms? I know that the magnitude of complex exponential function squared would...

Hi all, I was unsure where to put this thread as I read the main topic title in the topology/analysis forums and decided to post it here. I am looking for a chart/graph/website that helps me understand the basic terms such as: -neighborhoods -Boundary points -Singularity points - "Function is...

skills? If you got a B.S. in Math, you probably know some programming, but not enough to qualify you for a software engineering job; some statistics, but not enough to qualify you to be an actuary; and some data science-type stuff, but not enough to qualify you for a data analysis or database...

Homework Statement Is there any difference between these 2 terms, if yes how are they different? \begin{align}(\nabla\cdot\nabla\vec A)\vec B &= (\nabla\vec A\cdot\nabla)\vec B\end{align} Homework Equations From what i know about dot product, it is commutative, so does this property apply here?

could it be possible, to make a, for example, and lens that has a special texture, or colour and putting it on would make the pictures more saturated? or maybe make a pair of glasses for people who can't produce as much cones as others? my questions is because i can't really think of it, but...

See these equations: \left | \frac{d \vec{f}}{d \vec{r}} \right | = \left | \frac{d(f_1,f_2)}{d(x,y)} \right | = \frac{\partial f_1 \wedge \partial f_2}{\partial x \wedge \partial y} = \left | \begin{bmatrix} \frac{\partial f_1}{\partial x} & \frac{\partial f_1}{\partial y} \\ \frac{\partial...

The Theoretical Minimum: Quantum Mechanics - https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20 Sakurai Modern Quantum Mechanics - http://www.amazon.com/dp/0201539292/?tag=pfamazon01-20 I want to know, which book covers more in depth? And Sakurai's book is more advanced than Leonard...

In a geometric mean equation, say 2 x 8 = 16, or a x b = c, what are the words we would use to describe the numbers or terms? Specifically, if you know 'a' and 'c', what do you call 'b'? For example, in a normal multiplication, a x b = c, 'a' is the multiplicand, 'b' is the multiplier, and 'c'...

Hello everyone, What does it means first and second order of pressure measurement value? Whats the main difference?

(Again, I am sorry for the simplicity of these questions. I am a mechanical engineer learning this stuff late in life.) I have read the following terms or phrases: group algebra group algebra the algebra of a group an algebra group an algebraic group a group of algebras So... could someone...

Ran out of room for my title - not sure how to say it concisely, or if there is a better place to put this question...lets say this is "financial engineering"... I am looking for a formula what will give me the number of terms that will be compounded in a given length of time. Say: Principle =...

Homework Statement Homework Equations PV=nRT The Attempt at a Solution not sure if this is the right approach plugging into -ρg gives us -PMg/RT = dP/dy now we have to integrate both sides to find P?

Homework Statement (4a/a+4)+(a+2/2a) Homework Equations Just combine and then factor out The Attempt at a Solution It's actually fairly simple, but I'm having difficulty at the end. /multiply each term by opposite denominator 4a(2a)/a+4(2a) + a+2(a+4)/2a(a+4) /combine 4a(2a)+(a+2)(a+4) /...

Homework Statement Suppose x-2,x and x+6, where x is an integer, are consecutive terms in a geometric sequence S Determine x Homework Equations r=x/(x-2)=(x+6)/x The Attempt at a Solution x/(x-2)=(x+6)/x cross multiply x(x)=(x-2)(x+6) x^2=x^2+4x-12 x^2-x^2+4x-12/4=0 4x=12 x=3

Homework Statement QUESTION ADDED AS ATTACHMENT AS NEED TO SEE GRAPH. Homework Equations C = (12NkBπ4/5)(T/θD)3 for T<<θD C = 3NkB for T>>θD The Attempt at a Solution a.)[/B] So I assume the expression for the specific heat as a function of temperature that the question must want: C =...

I work a good deal better when the equation is in x and y form, is it possible to set up a trig expression like 5Cos(x)/(Sin(x)-1)and substitute the proper x or y equivalent so long as I remember to replace the trig identities later when the problem is finished? Or can you just not solve these...

I am a beginer. I have read that any given signal whether it simple or complex one,can be represented as summation of orthogonal basis functions.Here, what the terms orthogonal and basis functions denote in case of signals? Can anyone explain concept with an example?Also,what are the physical...

Homework Statement Finding Vout in terms of Vin Vs=5sin(10t)mV Assuming an ideal op-amp Homework Equations V=IR Nodal Analysis The Attempt at a Solution I am able to caluclate V(pi) and therefore,the value of the current source. However, I am not sure how the current flows after that...

Hi, I have been studying general relativity using Hobson's lately, particularly about the FRW universe. I know that for a matter universe with curvature, H^2 = \left( \frac{\dot a}{a} \right)^2 = \frac{8\pi G}{3} \rho_m -\frac{kc^2}{a^2} Another expression I came across is also 1 = \Omega_m +...

Homework Statement Write ##\int_{0}^{1}x^2(ln\frac{1}{x})^3 dx## in terms of the gamma function 2. Relevant equation ##\Gamma(p+1)=p\Gamma(p)## The Attempt at a Solution Say ##x=e^{-u}## one would eventually obtain the integral ##\int_{-\infty}^{0} u^3 e^{-u} du## STEPS: ##x=e^{-u}##...

Homework Statement Determine values for beta the constant of proportionality for a semiconductor. Homework Equations Given below. The Attempt at a Solution Im struggling with line 2 to line 3 of the solution. The problem I'm having is I can't see where the squared exponential term has...

The way I have interpenetrated this phenomena without technical jargon is that: Light is basically waves or ripples of the + and - charges of the electromagnetic field which permeates the entire universe. This is very similar to sound rippling through a field of air molecules. These waves can...

In the derivation of the boundary conditions we apply the integral form of maxwell's equations, but once we take a very small volume we find that some terms disappear like the displacement current as well as the time derivative of the magnetic field. Why do these terms disappear? For reference...

Write the piecewise function \[ f(t) = \begin{cases} 2t, & 0\leq t < 3 \\ 6, & 3 \le t < 5 \\ 2t, & t \ge 5 \\ \end{cases} \] in terms of unit step functions. So here is what i;ve got just guessing , I don't think I'm correct. I really need some help. But I got...

We all know that the system loss in transmission line is i^2R. So, in order to reduce the loss we diminish the current flow through the line by means of transformer. My question is i can also calculate system loss by the formula v^2/R where v is the potential across transmission line. So...

I'm having some trouble with the terminology used in calculus. My book states: "Fortunately we don't need to solve an equation for Y in terms of X in order to find the derivative of Y. Instead we can use the method of implicit differentiation. This consists of differentiating both sides of the...

I found the following identity in a paper: ## \sum_{l=1}^{\infty}exp(-\pi\alpha l^2)=(\frac{1}{2\sqrt{\alpha}}-\frac{1}{2})+\frac{1}{\sqrt{\alpha}}\sum_{l=1}^{\infty}exp(\frac{-\pi l^2}{\alpha}) ## Someone please let me give some hints on how to prove this.

Show that Planck's law expressed in terms of the frequency f is: u(f) = (8πf2/c3)(hf/(ehf/kT - 1)) from the equation: u(λ) = (8πhcλ-5)/(ehc/λkT - 1) When I do this algebraically by simply plugging in λ = c/f, I get: u(f) = (8πhc-4)/(f-5(ehf/kT - 1) which clearly doesn't involve the correct...