Expression Definition and 999 Threads

Using differential expressions for the generator, verify the commutator expression for ##[J_{\mu\nu},P_{\rho}]=i(\eta_{\mu\rho}P_{\nu}-\eta_{\nu\rho}P_{\mu})## in Poincare group Generator of translation: ##P_{\rho}=-i\partial_{\rho}## Generator of rotation...

I tried to understand proof of this identity from electromagnetics. but I was puzzled at the last expression. why is that line integral of dV = 0 ? In fact, I'm wondering if this expression makes sense.

This seems rather straight forward, but I can't figure out the details... Generally speaking and ignoring prefactors, the Fourier transformation of a (nicely behaved) function ##f## is given by $$f(x)= \int_{\mathbb{R}^{d+1}} d^{d+1}p\, \hat{f}(p) e^{ip\cdot x} \quad\Longleftrightarrow \quad...

I have some dimensionless numbers commonly used in fluid mechanics and I want to express a certain expression in terms of these dimensionless numbes If I, after defining my dimensionless numbers, enter the command : simplify(*expression*) where the expression is a function of variables that...

Here this is my attempt : Reference Textbook : Zangwill's Modern Electrodynamics I stuck at the last step , I really have no idea what to do next.

Let $a,\,b,,c \in \mathbb R$ such that $ab+bc+ca=0$ and $abc\ne 0$. Evaluate $\dfrac{a^5+b^5+c^5-1}{abc}$.

Given an Exponentially Distributed Random Variable $X\sim \exp(1)$, I need to find $\mathbb{E}[P_v]$, where $P_v$ is given as:$$ P_v= \left\{ \begin{array}{ll} a\left(\frac{b}{1+\exp\left(-\bar \mu\frac{P_s X}{r^\alpha}+\varphi\right)}-1\right), & \text{if}\ \frac{P_s X}{r^\alpha}\geq P_a,\\ 0...

Hi I need help I'm lost Assignment: A function given by a logical expression Y = A.B.D + A.not (C) .D + A.not (B) .C.D + A.D write in the truth table.

All I'm reallly confused on this problem is what the expression for the emitted field is. As long as I've got that, I'm good to go, but I just don't know what to use. I've tried looking for an expression for the emitted field but I've had no luck. Would appreciate any ideas or someone telling me...

I don't know how to start with the factorization. $$\frac{(-1)^{2/9} + (-3/2 - \frac{i}{2} \sqrt{3})^{(1/3)}}{(-1)^{2/9}- (-3/2 - \frac{i}{2} \sqrt{3})^{(1/3)}}$$ Any hints would be nice. Thank you.

I have an Energy harvesting expression something like the following $R = \tau B \log\Big(1 + \frac{E h^2}{\tau r^\alpha\sigma^2} \Big)$ $E = \tau(2^{R/\tau B}-1 )\frac{r^\alpha\sigma^2}{h^2}$ Let all constant terms as $a$ to simplify the expression into : $E = a\frac{1}{h^2}$ $E$ is a random...

I just don't know what equations I should use, or what exactly I need to do. I just need some guidelines, thank you!

Hi All, If p is a prime, the p-adic valuation, ## v_p(n) ##, of a positive natural number is defined as the highest power of p that divides n. For instance, ##v_3(45) = 2##. My question is: Is there a mathematical expression for ##v_p(n)## ?

For example, $$Sin(15)= \frac {(\sqrt 6 - \sqrt 2)} 4$$ and $$Sin(3)=\frac {(\sqrt 6 (\sqrt 5 -1)(3+\sqrt 3)} {48} -\frac {\sqrt 3 (3-\sqrt 3 )\sqrt{ 5+\sqrt 5 }} {24}$$ What about ##Sin(1)##?

I came across a rather strange thing in an introductory class I still don't understand. There was a statement that $$lim_n (2+ \sqrt(2))^n $$ is an integer. I recalled that I never understood this and just recently tried to take the limit but just get that the expression diverge? Which I think...

Source: paper When the cells were transfected with miRNA-mimic it increased the miRNA expression. Is this increase due to the activity of RNA-dependent RNA polymerase, which generates secondary miRNAs?

I know that it will take 3 washings to reach the desired purity of sand, and that "N-1" is an exponent in the general expression, but I am stuck beyond that.

The apparent length of a rod is determined to be$$\tilde{L}(x_0) = \gamma L + \beta \gamma \sqrt{D^2 + (\gamma x_0 - \frac{L}{2})^2} - \beta \gamma \sqrt{D^2 + (\gamma x_0 + \frac{L}{2})^2}$$I am trying to determine expressions for ##\tilde{L}(x_0)## when ##x_0 \rightarrow -\infty## and ##x_0...

Let: equation 1 : sin A + sin B = 1 equation 2 : cos A + cos B = 0 Squaring both sides of equation 1 and 2 then add the result gives me: cos (A - B) = -1/2 Then how to proceed? Thanks

I was studying how to compute an unpolarized cross-section (QFT Mandl & Shaw, second edition,https://ia800108.us.archive.org/32/items/FranzMandlGrahamShawQuantumFieldTheoryWiley2010/Franz%20Mandl%2C%20Graham%20Shaw-Quantum%20Field%20Theory-Wiley%20%282010%29.pdf) and came across the following...

Hi, I 'm trying to find the Laplace transform of the following expression. I used the following conversion formulas. I think "1" is equivalent to unit step function who Laplace transform is 1/s. I ended up with the following final Laplace transform. Is my final result correct? Thank you...

I was wondering if someone could check my answer and see if it is correct. The resistance in series is Req= R+ R= 2R The voltage across 2R is the terminal voltage V. The expression I get is: Can I also use this formula P=I^2*R? When using it I get: Current through the resistors is The...

Hello everyone, I recently derived an arithmetic expression in the following form: aπ² + bπ² ± cπ / dπ² = 1, Φ³ (4.23606797...) I have two question about this: i. Does this equation/form resemble anything known in physics/math? (it looks like a psuedo-quadratic to me, but unsure) ii. Is...

I wanted to clear something up, if I wanted to express the Pol-Gag Proteins of HIV-1 in two different viruses would it be expressed by simply putting a promoter into front of the genes? Let's say I had a pseudo-typed HIV-1 Vector's genes and T4 structural genes would the T4 structure express...

I am familiar with the hessian matrix having the square in the numerator and a product of partial derivatives in the denominator: $Hessian = \frac{\partial^2 f}{\partial x_i \partial x_j}$ However, I have come across a different expression, source...

Summary: circuit diagram from minimize expression I am drawing a circuit diagram from a minimize expression. I have come up with two circuit diagrams that give same result. I am not sure which of the circuit diagram (1) or (2) is correct. Are both my diagram correct? Need help

Example done in class: The problem and my solution: My solution seems incorrect because if I try to plug in 0, I don't get the initial condition given in the problem. Does anyone see what I've done wrong along the way? Thanks.

Here's what I have done: Let t1 be the time taken for the ball to reach the ground after the first bounce, and ux be the initial speed in the horizontal direction of ball. Also, let v be the speed after the bounce. For horizontal, $$\dfrac {4}{3}H=U_{x}t_{1} $$ For vertical, $$H=\dfrac...

I'm not sure if I'm doing this right as far as coming up with the equation they are asking for. I feel the question is poorly worded and the formatting makes their equation notation difficult to understand. Any insight would be very helpful. This is my work so far:

Homework Statement: A quantity of ideal gas initially at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat and work...

A bicycle wheel rolls at a constant speed along a circular path on a horizontal surface. The wheel has a constant angle of inclination to the vertical direction and the distance from its center of mass G to the fixed Z axis is R. Determine the relationship between the angular velocity w1 around...

Well ##\cup_{i} E_i## is just the event that at least one color is not used, so its probability is given by ##1- (1/N)^N##. Now if I is a subset of {1,...,N} where ##\left | I \right | = l## then ##Pr(\cap_{i\in I} E_i) = (1-l/N)^N## (I'm guessing this is where I'm making a mistake?). So then we...

Attempt:

Part f. is the only expression I am unsure of what steps to take to get the correct answer. Would anyone be willing to give me an idea?

I see that when n is an even number, the product can be represented as ## \frac {2n} {(n+1)} ##. When n is an odd number, the denominator seems to be changing and I am not able to define an expression for it. How should I go about solving this? Thanks

So I think I do understand how to do this, but the thing is my answers are always incorrect. Will need some guidance/help on this. ##B =\frac{\mu_{0}I}{4\pi}\int\frac{dysin\theta}{r^2} ## ##y = Rtan\phi## ##dy = Rsec^2\phi d\phi## ##B = \frac{\mu_{0}I}{4\pi}\int\frac{dysin\theta}{r^2} =...

I have been attempting this physics problem for a while now. I am not sure how to begin to attempt this problem with the equations of motion formulas.

So far the best I've been able to come up with is to use ##\vec{B} = \mu_0 \vec{H}## which gives me i_c = H 2\pi r j_c = \frac{H 2\pi r}{\pi r^2} = \frac{2H}{r} \therefore B = \mu_0 \frac{r j_c}{2} I'm fairly confident this is just terrible math and physics on my behalf but I'm struggling to...

Summary: I have trouble to define the y distance in my coordinatesystem I need to find an expression for the shear stress on the I figure, where the green parabola illustrates the function. I made a cut, where I defined the length from the start of figure I to the cut as z1. The formula for...

Hello, I’m having difficulties understanding logical relations “A implies B” and “A if and only if” using Boolean expressions and Venn diagrams, there is something where I’m wrong, but I could not find it out. Please, be benevolent and tell me where I’m wrong. Thanks Note : Obviously I’m...

As I said before, I really have no idea on how to proceed.

Problem Statement: What is the correct way of computing the argument of the following equation? Relevant Equations: I am trying to compute the argument ##\Phi## of the equation $$\frac{r-\tau\exp\left(i\varphi\right)}{1-\tau r\exp\left(i\varphi\right)} \tag{1}$$ which using Euler's equation...

Hi, I'm trying to find an expression or phenomenon where a certain quantity is proportional to force squared or power squared. For example, we have Force ∝ acceleration and Power ∝ I². I'm not sure if my question is a legit. I was trying to understand something and this question came to my...

Helping my daughter with her math and hit this one and not sure how to advise. All help welcome(x-2y10)3 / (x-4yz4)-5 This one throws me off because I don't know how to deal with the z, as only on the right side of the divide

##P(T=1|W=w)=\frac{P(\{T=1\}\cap\{W=w\})}{P(W=w)}=\frac{\binom {n-2} {w-1} p^{w-1}(1-p)^{(n-2)-(w-1)}}{\binom n w p^w (1-p)^{n-w}}=\frac{(n-2)!}{(w-1)!(n-w-1)!}\frac{w!(n-w)!}{n!}\frac{1}{p(1-p)}=\frac{w(n-w)}{n(n-1)}(p(1-p))^{-1}##. I cannot seem to get the terms with ##p## out of my expression.

So for part (a), I used the fact that 1/N = the period = T. I solved for the velocity, where i got v=2πRN. I plugged that v into F=(m v^2)/R, which is the centripetal force, but also the force of friction. My answer to part (a) is 4(π^2)mR(N^2). I'm a bit confused on part (b). I know that...

My idea was straight forward calculation: $$\begin{align*}\bar { \psi }' ( x' ) \gamma ^ { \mu } \partial _ { \mu }' \psi ( x' ) &= \psi^\dagger\gamma^{0\dagger}\gamma^0\gamma^\mu \partial_\mu'\gamma^0\psi = \bar\psi\underbrace{\gamma^0\gamma^\mu\gamma^0}_{=\gamma^{\mu\dagger}=-\gamma^\mu}...

Homework Statement A 5.21 kg block is sliding down a slope at an angle of 4.22° to the horizontal. The block is initially moving down the slope at a speed of 1.45 m s−1 and the coefficients of friction between the block and slope are, μs = 0.500, and μk = 0.100. Find an expression for the...

<< Mentor Note -- Poster has been reminded to use the Template when starting new schoolwork threads >> Two particles of identical mass m interact with each other via central potential energy Vcentral(r) = -V0(1-|r|/a), if 0 <= |r| <= a 0, if a < |r| Constants are V0 > 0...