Delta Definition and 1000 Threads

Hi again, another question. Please see the schematic below. It shows a wye-wye(n) with a delta tertiary winding. So this delta winding is inserted here so that we can achieve amp-turn balance with the zero sequence currents flowing on the secondary side. I know that zero sequence currents...

Homework Statement Find the uncertainty ∆y in y as a function of the uncertainties ∆u and ∆v in u and v for the following functions: y = 1/2(u+v) Homework Equations : Error propagation formula[/B] The Attempt at a Solution Don't know where to begin even. Help?[/B]

Homework Statement Homework Equations Power Triangle and 3-phase equations (listed in my solutions) The Attempt at a Solution Here are the instructor solutions: The instructor solutions just go straight into using equations, but I like to use the power triangle because it is more...

I made a few paper airplanes. I noticed that the common paper airplane (shown below) https://i.ytimg.com/vi/v29M7Oa1l-A/hqdefault.jpg flies much further/better than paper planes that look like standard 747s. Any know why ? I expected 747 like plane to be very efficient at generating the lift...

Currently, I am reading this article which introduces electromagnetism. It gives a function for the charge density as: $$\rho = q\delta(x-r(t))$$ The paper states that "the delta-function ensures that all the charge sits at a point," but how does it do that? Also, if ##r(t)## is the trajectory...

Hi, Consider this definition of the Dirac delta: $$\delta (x-q)=\lim_{a \rightarrow 0}\frac{1}{a\sqrt \pi}e^{-(x-q)^2/a^2}$$ First, this would make a normalized position eigenfunction $$\psi (x)=\lim_{a \rightarrow 0}\frac{1}{\sqrt{a\sqrt \pi}}e^{-x^2/2a^2}$$ right? If that is so, why do...

Homework Statement Prove the following '()( − ) = −′() ∫-∞∞δ'(x)*f(x-a) = -f'(a) Homework Equations ∫-∞∞δ'(x-a)*f(x) = f(a) The Attempt at a Solution [/B] ∫-∞ ∞δ'(x)*f(x-a) = ∫δ(x)*f(x-a)dx-∫f'(x-a)*δ(x)dx = f(-a) - f'(-a) Went from 1st to second by integration by parts Used...

Hey, everyone! I'm helping a friend through his calculus course and we've come across something that has stumped me (see: the title). When I learned calculus, our treatment of the epsilon-delta definition of the limit was, at best, brief. Anyway, here is the problem: Given ##\lim_{x \rightarrow...

Homework Statement I need to integrate this expression : P(k, w) = A * δ(w-k*v) * f(k, w) A is constant and δ, Dirac Delta.Homework Equations [/B] There is double integration : I = ∫0∞ dk ∫0∞ P(k,w) dw = A ∫∫0∞ δ(w-k*v) * f(k, w) dw dk The Attempt at a Solution [/B] I'm confused with...

Homework Statement Ultimately, I would like a expression that is the result of an integral with the sin(nx)/x function, with extra terms from the expansion. This expression would then reconstruct the delta function behaviour as n goes to infty, with the extra terms decaying to zero. I...

Is the square of a Dirac delta function, ##(\delta(x))^2##, still a Dirac delta function, ##\delta(x)##? A Dirac delta function peaks at one value of ##x##, say 0. If it is squared, it still peaks at the same value, so it seems like the squared Dirac delta function is still a Dirac delta...

Homework Statement Calculate ##\int_{r=0}^\inf δ_r (r -r_0)\,dr## Homework Equations ##\int_V \delta^3(\vec{r} - \vec{r}') d\tau = 1## The Attempt at a Solution $$\int_V \delta^3(\vec{r} - \vec{r}') d\tau = \int_V \frac {1}{r^2 sinθ}\delta_r(r-r_0) \delta_θ (θ-θ_0) \delta_Φ (Φ-Φ_0) r^2...

Homework Statement Homework Equations Continuity: $$\vert x-c \vert < \delta~\Rightarrow~\vert f(x)-f(c) \vert < \epsilon$$ $$\delta=\delta(c,\epsilon)$$ The Attempt at a Solution $$\vert f(x)-f(c) \vert <\frac{1}{2}f(c)~\Rightarrow~\vert x-c \vert < \delta_1$$ So i have this δ1 but what...

Homework Statement find a δ for a given ε for f(x)=x3 around c=5: $$\vert x-5\vert<\delta~\Rightarrow~\vert x^3-5^3 \vert < \epsilon$$ Homework Equations Continuity: $$\vert x-c \vert < \delta~\Rightarrow~\vert f(x)-f(c) \vert < \epsilon$$ $$\delta=\delta(c,\epsilon)$$ The Attempt at a...

I just want to make sure that I am understanding the Dirac Delta function properly. Is the following correct?: For two variables ##x## and ##y##: \begin{equation} \begin{split} \delta(x-y) f(x) &= f(y) \end{split} \end{equation} And: \begin{equation} \begin{split} \delta(x-x) f(x) &=...

Homework Statement I have a 2D integral that contains a delta function: ##\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\exp{-((x_2-x_1)^2)+(a x_2^2+b x_1^2-c x_2+d x_1+e))}\delta(p x_1^2-q x_2^2) dx_1 dx_2##, where ##x_1## and ##x_2## are variables, and a,b,c,d,e,p and q are some real...

Homework Statement definition of εijk εijk=+1 if ijk = (123, 231, 312) εijk = −1if ijk = (213, 321, 132) , (1.1.1) εijk= 0,otherwise . That is,εijk is nonzero only when all three indices are different. From the definition in Eq. (1.1.1), show that...

I'm an undergraduate student, so I understand that it may be difficult to provide an answer that I can understand, but I have experience using both the Dirac delta function and residue calculus in a classroom setting, so I'm at least familiar with how they're applied. Whether you're integrating...

So if I have a logistic regression: ##log (\hat {odds})=\hat{\beta_{0}}+\hat{\beta_{1}}x##. How would I find a confidence interval for x if I am given ##odds=5## This is going in reverse, where if I have the outcome, I try to do inference on the predictor. We know that ##\hat{\vec{\beta}}##...

Trying to narrow down what type and size radiator and flow of both the water and air I should be looking at that would give me my best heat exchange efficiencies, if I want to input 50F water into a radiator that will have 100F air (60% RH) blowing through it and my goal here is the cooling down...

Homework Statement Homework EquationsThe Attempt at a Solution So cts approx holds because ##\frac{E}{\bar{h}\omega}>>1## So ##\sum\limits^{\infty}_{n=0}\delta(E-(n+1/2)\bar{h} \omega) \approx \int\limits^{\infty}_{0} dx \delta(E-(x+1/2)\bar{h}\omega) ## Now if I do a substitution...

Homework Statement In this problem we shall consider the scattering from repulsive δ-function potentials. We have already considered a single such potential. If the strength of the potential is V0, the transmitted and reflected fluxes may be represented by the transmission and reflection...

Homework Statement I just have a quick question about the delta function, I'm pretty confident in most other cases but in this simple one I'm not so sure. $$\int_{-\infty}^{\infty} \phi (x)\delta (-x)dx$$ Homework EquationsThe Attempt at a Solution [/B] $$\int_{-\infty}^{\infty} \phi...

Hi. I understand that in 1-D when E< V(minimum) there exist no physically acceptable solution to the Schrodinger Equation. I have been looking at delta potentials using Griffiths book. I follow his working for the delta potential well but when it comes to the potential barrier I don't understand...

TL;DR: My professor asked me to graph the probability that a particle would be excited from the ground state to a stationary state with a certain energy E (y-axis) verse the energy of that new state (x-axis). I need help finding this probability as a function of E. Probability=|<ΨE|P|Ψg>|2 P is...

Homework Statement True/False: If a particular delta has been constructed as a suitable response to a particular epsilon challenge, then any smaller positive delta will also suffice. Homework EquationsThe Attempt at a Solution The submitted solution is as follows: However, when I read this...

Thereis no proof for anything in us other than matter(and energy). Thermodynamics works everywhere. I think we live upto the time our system's Delta G (Gibbs free enery) remains negative. Please friends tell me if my undrstanding is justified.

I'm trying to use the Animate function on Mathematica to show a gaussian wave packet passing through a delta potential. I'm quite new to Mathematica and this is by far the hardest thing I've had to do so please bear with me. I effectively want to solve the integral: ## \phi_k(x) = \left\{...

so, continuous signals as sums of weighted delta functions can be represented like this: if you switch order of some variables you get ∫x(τ)δ(-τ+t)dτ, and since,I presume, Dirac delta "function" is even I can write it like this ∫x(τ)δ(-(-τ+t))dτ=∫x(τ)δ(τ-t)dτ=x(t) and we got ourselves a...

The width of Δ resonances is around 110...120 MeV. All four of them. With modest differences. The difference in width between Δ0 and Δ++ is estimated from 5 to 9 MeV. Why? Δ+ and Δ0 resonances have two options to decay. Δ+→p+π0 Δ+→n+π+ and correspondingly Δ0→p+π- Δ0→n+π0 In contrast, Δ++ and Δ-...

Homework Statement \begin{equation} \int_V (r^2 - \vec{2r} \cdot \vec{r}') \ \delta^3(\vec{r} - \vec{r}') d\tau \end{equation} where: \begin{equation} \vec{r}' = 3\hat{x} + 2\hat{y} + \hat{z} \end{equation} Where d $\tau$ is the volume element, and V is a solid sphere with radius 4, centered...

Is square root of delta function a delta function again? $$\int_{-\infty}^\infty f(x) \sqrt{\delta(x-a)} dx$$ How is this integral evaluated?

I've come across the equation $$\int_0^1 dx \frac{dA(x)}{dx} + B = C = \text{finite}$$ in my readings on a certain topic in physics and, in both articles i have read, the following step is taken $$\int_0^1 dx \left( \frac{dA(x)}{dx} + (B-C)\delta(1-x) \right) = \text{finite}$$ For the...

I am quite new here, and was wondering if anybody knows how this 2D integral is evaluated. $$ \int_{-\infty}^\infty \int_{-\infty}^\infty \delta(k_1 x-k_2y)\,dx\,dy$$Any help is greatly appreciated! Thanks!

Homework Statement Using the equations given, show that the wave function for a particle in the periodic delta function potential can be written in the form ##\psi (x) = C[\sin(kx) + e^{-iKa}\sin k(a-x)], \quad 0 \leq x \leq a## Homework Equations Given equations: ##\psi (x) =A\sin(kx) +...

I am looking at an explanation of the gradient operator acting on a scalar function ## \phi ##. This is what is written: In the steps 1.112 and 1.113 it is written that ## \frac {\partial x'_k} {\partial x'_i} ## is equivalent to the Kronecker delta. It makes sense to me that if i=k, then...

We know, $$\delta(x) = \begin{cases} \infty & \text{if } x = 0 \\ 0 & \text{if } x \neq 0 \end{cases}$$ And, also, $$\int_{-\infty}^{\infty}\delta(x)\,dx=1$$ Using Fourier Transformation, it can be shown that, $$\delta(x)=\lim_{\Omega \rightarrow \infty}\frac{\sin{(\Omega x)}}{\pi x}$$ Let's...

Homework Statement I am trying to show that ## \int \delta (x-a) \delta (x-c) dx = \delta (-a-c) ## via integeration by parts, but instead I am getting ##\delta (c-a) ## (or ##\delta (a-c)## depending how I go...). Can someone please help me out where I've gone wrong: struggling to spot it...

Homework Statement I have ##\int dx \int dy \delta (x^{2}+y^{2}-E) ## [1] I have only seen expressions integrating over ##\delta## where the ##x## or the ##y## appear seperately as well as in the delta function and so you can just replace e.g ##y^2 = - x^{2} +E## then integrate over ##\int...

I want to calculate $$\langle x|XP|y \rangle$$ where X is the position operator and P the momentum operator, and the states are position eigenstates. But I get two different answers depending on if I insert a complete set of states. First way: $$\langle x|XP|y \rangle=x\langle x|P|y...

Hallo, I have a question which elements are responsible for the increase of tangent delta in a X Capacitor and the reduction of its insulation resistance?

Hi, I am studying transmission lines faults. There was a line that said In case of delta star transformer in transmission line, an Earth fault on star (grounded) side is seen as a line to line fault on delta side. There was no explanation. I tried to google solutions but couldn't find any...

My history of physics is all too rusty. Who first wrote that the work done by a conservative force is the negative of the change in potential energy? Was he/she also the one who first presented the equation?

Q's Let f,g ℝ→ℝ. Suppose that g is bounded. This means that its image is bounded or in other words there exists a positive real number B s.t. |g(x)| ≤ B ∀ x. Prove that if lim x→c f(x) = 0, then lim x→c f(x)g(x) = 0. Work. See the picture. I am really confused I can't seem to understand the idea...

Homework Statement During a .0050 second time period a rocket expels 1.000kg of gas at a velocity of 5000 m/s. Calculate the rockets average Thrust, as well as Impulse. http://imgur.com/a/uE9dVI am going to use this note for reference on a test and want to rock solid about it. 2. Homework...

Homework Statement A wooden pallet carrying a load of 600 kg rests on a wooden floor. (s= .28 and k= .17) a. A forklift driver decides to push it horizontally instead of lifting it. What force must be applied to just get the pallet moving from rest? b. After a bit of time, the driver pushes the...

I would like to evaluate the following integral: ##\displaystyle{\int_{-\infty}^{\infty} dp^{0}\ \delta(p^{2}-m^{2})\ \theta(p^{0})}## ##\displaystyle{= \int_{-\infty}^{\infty} dp^{0}\ \delta[(p^{0})^{2}-\omega^{2}]\ \theta(p^{0})}## ##\displaystyle{= \int_{-\infty}^{\infty} dp^{0}\...

Homework Statement Find Req in the given circuit Homework Equations Series: req = r1+r2... parallel: 1/req = 1/r1 + 1/r2 ... The Attempt at a Solution Without redrawing the circuit I do: 12||60 = 10 10+20 = 30 30 || 30 = 15 15+10 = 25 25||25 = 12.5 12.5+15+5 = 32.5 = Req This is the correct...

Note from mentor: this thread was originally posted in a non-homework forum, therefore it lacks the homework template. I was wondering if the electric charge density ##\rho({\bf{r}})## of a point charge ##q## at position ##{\bf{r}}_{0}## is given by...

Homework Statement Lauryl alcohol is obtained from coconut oil and is used to make detergents. A solution of 5.00 gram of lauryl alcohol in 0.100Kg of benzene freezes at 4.1 degrees Celsius. What is the molar mass of the lauryl alcohol? Kf for benzene = 5.12, Freezing point of benzene is 5.5...