Terms Definition and 1000 Threads

Homework Statement S = 1+ x/1! +x2/2! +x3/3! +...+xn/n! To find S in simple terms. Homework Equations None The Attempt at a Solution I tried with Taylor's expansion, coshx and sinhx expansions. But cannot see consequence.

The Helmholtz function differential form for a reversible process is: dF = -SdT - PdV, as for a reversible process δW (by system/here an (ideal) gas) = PdV and dS = δQ/T. Therefore, for a reversible isothermal process, dT = 0 and hence dF = -PdV. Therefore, the work done by the system is W =...

Hi. The induced emf is given by -d/dt ∫B.dS but when the time derivative is taken inside the integral sign this becomes -∫ ∂B /∂t.dS . Why isn't B.dS differentiated using the product rule giving an extra term inside the integral sign ? For some reason the integral sign is appearing as a small...

Homework Statement https://imgur.com/DUdOYjE The problem (#58) and its solution are posted above. Homework Equations I understand that I can approach this two different ways. The first way being the way shown in the solution, and the second way, which my professor suggested, being a Direct...

Homework Statement u and v are two vectors in the same plane. Vector OM = u+2v Vector OP = 6u+v Vector OQ = 5u +2v Vector OR =2(VecOM) +v Given that ZPQM is a parallelogram, express Vector OZ in terms of u and v.Homework EquationsThe Attempt at a Solution First they wanted me to find Vectors...

Hi, first of all I am aware of the fact that QUICK SCHEME used in computational fluid dynamics has consistent slope at the sides of node elements (for instance at the left side of node 3 in my attachment same slopes exist) as you can see in my picture/attachment. But I must express that I can...

Homework Statement A scalar is given by It is controlled by With step time h = 0.2 s 1. Find the discrete equivalent model 2. Check the stability of closed loop (K = +1) 3. Obtain the via the Bode plot Homework EquationsThe Attempt at a Solution So for question 1. This is where I'm...

I am doing a project on stabilizer code, and I keep running into a term about qubits and leakage. What does leakage mean?

Homework Statement Taking derivative of 3 term product. ## \frac{d}{dx} (3x^3 y^2 y'^2) ## Homework Equations I read that (abc)' = (ab)c' + (bc)a' + (ca)b' The Attempt at a Solution ## 9x^2(y^2y'^2) + 6x^3yy'^2 + 6x^3y^2y' ## is this correct ?

Homework Statement Hello there are two types of pens expensive and cheap. The ratio of the prices of the two is 3:7 The total cost for 30 of the cheaper pens and 10 of the expensive pens is $1568. I am asked to derive an expression for the cost of ONE of the expensive pens which i will...

I'm trying to understand what exactly it means in terms of the voltage of a battery. I know that the voltage in a battery is just the potential difference between the two terminals. But, is the negative terminal used as a relative point and seen as 0? If that's the case does 12V mean that the...

The Hamiltonian of the Qi, Wu, Zhang model is given by(in momentum space): ## H(\vec{k})=(sink_x) \sigma_{x}+(sink_y) \sigma_{y}+(m+cosk_x+cosk_y)\sigma_{z} ## . What is the physical meaning of each component of this Hamiltonian? Note: for the real space Hamiltonian(where maybe the analysis of...

Homework Statement I have the following integral, $$\frac{1}{\sigma \sqrt{2\pi} t} \int_{-\infty}^{0} \exp[\frac{-1}{2\sigma ^2} (\frac{x-x_0}{t} - p_0)^2]dx$$ that I wish to write in terms of the error function, $$erf(x) = \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-g^2}dg$$ However, I can't seem...

Hello community I was hoping someone could help me with the following problem. I am trying to understand what a middle Ordinate is in terms of geometry (I know it has a versine along a chord).Given the diagram below:- The Blue line is an arc of some radius. AB & CB are both tangent to...

Why does Google limit its searches with 32 terms? I think other search engines seems to not limit but adding more terms for some reasons such as filtering does not work, for example in Yahoo. Thank you.

Time can be divided three ways Time in the future Time in the present Time in the past We are living in the 'present'. My question: how 'big' is this present time? It might help if you think of a pen placed on a white sheet of paper. The pen represents our present time. The white space above...

Hi there, I hold an engineering degree and I was just reviewing a page on Wikipedia. This image specifically demonstrates the impossibility of two theoretical heat engines having different efficiencies between two heat reservoirs. The full Wikipedia page can be found...

Dear Members, I was going through some video lecture (Quantum Mechanics) when I encountered a definition of momentum as shown in the attached picture. I do not understand how iota and ħ is ignored ? There are some negligible terms after plus sign. What are those ? In short how they have...

How do I express ex,ey,ez in terms er,eθ,eZ? r=(x^2+y^2)^1/2,θ=arctan(y/x),Z=z A(r,θ,z) ∂A/∂x=x/(x^2+y^2)^1/2er+(-y)/(x^2+y^2)eθ=cosθer-(sinθ/r)eθ ex=(∂A/∂x)/|∂A/∂x| I should get ex as cosθer-sinθeθ, but I don't get ex correctly. am i doing this wrong?

The Hong-Ou-Mandel experiment is one of many examples where the amplitudes associated with two histories cancel out, leaving us with a reduced range of possible outcomes. Obviously, the total probability of those outcomes has to be unity. My question relates to the fact that these processes are...

Homework Statement Find the Taylor series for: ln[(x - h2) / (x + h2)] Homework Equations f(x+h) =∑nk=0 f(k)(x) * hk / k! + En + 1 where En + 1 = f(n + 1)(ξ) * hn + 1 / (n + 1)! The Attempt at a Solution ln[(x - h2) / (x + h2)] = ln(x-h2) - ln(x + h2) This is as far as I have been able to...

I'm trying to make an approximation to a series I'm generating; the series is constructed as follows: Term 1: \left[\frac{cos(x/2)}{cos(y/2)}\right] Term 2: \left[\frac{cos(x/2)}{cos(y/2)}-\frac{sin(x/2)}{sin(y/2)}\right] I'm not sure yet if the series repeats itself or forms a pattern...

Not a homework problem, just something I came across in my book that makes sense but not fully. Homework Statement Factor: ##a^4-b^4## Homework EquationsThe Attempt at a Solution [/B] The book's solution: ##a^4-b^4## ##=a^4-a^3b+a^3b-a^2b^2+a^2b^2-ab^3+ab^3-b^4##...

Homework Statement Basic projectile motion if you throw from ground level, to obtain a max distance in the x you'd want to throw at a 45° angle right? So as your initial height increases, your throwing angle will decrease and my guess is as your initial velocity increases your angle increases...

how total internal reflection of light takes place in terms of quantum world?

If there is a massive object floating in space and I tap the side of it with a relatively small force it will move said object a very small amount. If I tried the same thing on Earth the object would not move because of gravity. I'm inferring (perhaps erroneously) that this means the object is...

I've often wondered at the "resolution" of the human visual system but it's not at all clear from what I've read whether this question even makes sense. As a sort of general position, many of the articles I've read suggest that the human eye, over the full field of vision, delivers around...

When mapping out re-combinations of a crossed trihybrid you have to account for the proportion of the offspring who do not share parental genotypes. Of the 8 possible genotypes stemming from this mating, 6 will be recombinant and two will be of parental genotypes. Your idea is to Map out the...

Firstly I know how to do this with first derivatives in differential equations - for example say we had ##\frac{dy}{dx}=4y^2-y##, and we're also told that ##y=1## when ##x=0##. ##\frac{dy}{dx}=4y^2-y## ##\frac{dx}{dy}=\frac{1}{4y^2-y}=\frac{1}{y\left(4y-1\right)}=\frac{4}{4y-1}-\frac{1}{y}##...

Hello and thank you for trying to help. In spite of the fact that this seems a very simple problem, I do not find myself able to get a solution. Here it goes: Let $$f(x)=\displaystyle \sum_{k=3}^\infty a_k \frac{x^k}{k(k-1)(k-2)}$$ and $$g(x)=\displaystyle \sum_{k=0}^\infty a_k x^k$$. Express...

I bought this book "Idiot's Guide to Quantum Physics" I bought it because I know I am an idiot in quantum physics. Now I have a question about the contents. It says that: "The four fundamental forces in nature (gravity, electromagnetism, plus two more that we'll formally introduce in Chapter...

Homework Statement The board shown below is being held in equilibrium in the vertical plane by three smooth rods at A, B, and C Determine the magnitudes of forces at A, B, and C in terms of the weight of the body, W. Homework Equations Moment = f*r Here's a diagram The Attempt at a...

If there are two interaction terms in a single model, does that mess up the interpretation of it? For example, Gender*Weight and Gender*Height. Say the model is Y~Weight+Height +Gender +Gender*Weight+Gender*Height. Would I simply interpret it as usual? That is, "The difference in mean...

Hello. I came across a Quadratic Equation that looks like this. 5x2 + 4x + 9 = 0. The '5' in the above equation is called Quadratic Coefficient. The '4' in the above equation is called Linear Coefficient. The '9' in the above equation is called Constant. The 'x' in the above equation is called...

Hey guys, this is a rather silly question, but does anyone know how to pronounce 1. Kac in Kac-Moody algebras 2. Henneaux in Brown Henneaux central charge? Don't want to make a fool of myself when talking to people.

Factor the expression. (a - a^2)^3 + (a^2 - 1)^3 + (1 - a)^3 (a - a^2)(a - a^2)(a - a^2) + (a^2 - 1)(a^2 - 1)(a^2 - 1) + (1 - a)(1 - a)(1 -a) Is this the right approach thus far?

Homework Statement How close is x to x_0 (x_0 \neq 0) so that 2. Homework Equations The Attempt at a Solution I tried to use absolute value properties:- \epsilon \lt \frac{\sqrt{x_0^2+1}}{x_0^3} - \frac{\sqrt{x^2+1}}{x^3} \lt \epsilonBy adding in the three sides, we...

What is the procedure for finding the unknown term(end value in this scenario) in a series? For example \sum_{r=1}^{n}{2r+3} My Attempt was to simply state the first four terms and then simply add the nth term as it is: 2(1)+3=5 2(2)+3=7 2(3)+3=9 2(4)+3=11 2(n)+3=2n+3...

The general Ampere force law equation given by Maxwell is: According to Maxwell, all terms containing function ##Q(r)## will vanish after closed integration w.r.t. ##s'## because they will get reduced to functions of ##r## and the upper and lower integration limits will be same since the...

Homework Statement Express the gravitational force equation in terms of density. Homework Equations F(Gravity) = ((GravitationalConstant)(Mass1)(Mass2))/radius^2 Density = mass/volume The Attempt at a Solution Based on the original equation for gravitational force, there are two masses...

I'm fairly new to QFT and I'm currently trying to understand perturbation theory on this context. As I understand it, when one does a perturbative expansion of the S-matrix and subsequently calculates the transition amplitude between two asymptotic states, each order in the perturbative...

Let's say we have a proposition (or state, if we prefer) ##P\equiv \psi \equiv AB^\perp + e^{j \theta} A^\perp B## where, e.g., ##A^{\perp}## indicates some ket that is orthogonal to ##A##. We also have an operator ##\hat{O}## . Without reference to a physical context, is there a test to say...

Homework Statement Consider the free real scalar field \phi(x) satisfying the Klein-Gordon equation, write the Hamiltonian in terms of the creation/annihilation operators. Homework Equations Possibly the definition of the free real scalar field in terms of creation/annihilation operators...

Does anyone know how I can prove the following equation? ##\displaystyle \frac 1 {d-1}-\int_0^1 \frac{dy}{y^d} \left( \frac 1 {\sqrt{1-y^{2d}} }-1\right)=-\frac{\sqrt \pi \ \Gamma(\frac{1-d}{2d})}{2d \ \Gamma(\frac 1 {2d})} ## Thanks

How do i get an idea, or a 'feel' of the components of the acceleration in polar coordinates which constitute the component in the eθ direction? from what i know, a= (r¨−rθ˙^2) er + (rθ¨+ 2r˙θ˙) eθ ; (where er and eθ are unit vectors in the radial direction and the direction of increase of the...

Hi, I'd like to use Switch with an integer partition of a number. For example, if n=4, then I define the partition as: monodromyTypes = IntegerPartitions[n]; this gives: monodromyTypes={{4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}}. I'd then like to set up a Switch depending on what the...

In 2D, if we define exchange statistics in terms of the phase change of the wavefunction of two identical particles when there are exchanged via adiabatic transport (https://arxiv.org/abs/1610.09260), we would discover that this phase can be arbitrary due to the topology of relative...

Hi, I have a question about taylor polynomials. https://wikimedia.org/api/rest_v1/media/math/render/svg/09523585d1633ee9c48750c11b60d82c82b315bfI was looking for proof that why every lagrange remainder is decreasing as the order of lagnrange remainder increases. so on wikipedia, it says, for a...

https://en.wikipedia.org/wiki/List_of_English_terms_of_venery,_by_animal Lists lots of animals. Clearly people made up some of these things when it was clear nobody really knew if it was correct or not. Heck, we can do that! So let's see what we can come of with: How about a slime of...

Homework Statement "Prove: ##∀n∈ℕ,7|[3^{4n+1}-5^{2n-1}]##" Homework EquationsThe Attempt at a Solution (1) "We take the trivial case: ##n=1##, and notice that ##3^5-5=238## and ##7|238## because ##7⋅(34)=238##." (2) "Now let ##n=k## for some ##1<k∈ℕ##. Then we assume that...