Function Definition and 1000 Threads

If f(x) is the function of the "ground": My first assumption is that in a certain $$\bar{x}$$, $$f''(\bar{x})=0$$, and from that point I will analyse the situation. The object has initial energy $$E_0=\frac{mv^2}{2}+mgf(x),$$ then $$v=\sqrt{\frac{2}{m}}\sqrt{E_0-mgf(x)}.$$ In each point the...

I know how to solve each of those problems. For the set one, I look at the output of the S and try to match it with the input of T and then take the pair (input_of_S, output_of_T), and I do that for each pair. As for the formula one, I just plug in x = g(y). My confusion lies in trying to...

TL;DR Summary: I want to find a function with f'>0, f''<0 and takes the values 2, 2^2, 2^3, 2^4,..., 2^n Hello everyone. A professor explained the St. Petersburgh paradox in class and the concept of utility function U used to explain why someone won't play a betting game with an infinite...

Would a leaf blower see a different load (in terms of back pressure and flow) depending on whether the outlet tube ends in, say a 1" nozzle, versus a flared out horn of 6" diameter? I am not thinking of viscosity effects here, but rather of Bernoulli type considerations. In the case of the...

I have just finished reading Ballentine Chapter 7.2 and I am positively baffled, perhaps because Ballentine is being sloppy for the first time. I attach the discussion in Ballentine at the end of this post if it helps, though I hope my writing will be independent thereof. This question is...

Evaluate the definite integral $$\int_0^\infty \frac{x^2 + 1}{x^4 + 1}\, dx$$

What is the very common culprit component and what is its function within SMPS having weak current, far weaker than its rating while its voltage is always perfect?

Hello, guys! I have a question. How can I prove the behavior of a particle subjected to an infinite potential? Will the wave function exist?

Where did they get the equation in circled in red from? It does not seem that it can be derived from the graph below. Many thanks

The implementations for the two filters in simulink are as follow: For the first filter: For the second one: The obtained results have values of 10^-12, while the expected results should be between 10^-3 - 10. Since it's the first time when I try t implement a tf with variable coefficients I...

Sakurai, in ##\S## 5.7.3 Constant Perturbation mentions that the transition rate can be written in both ways: $$w_{i \to [n]} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \rho(E_n)$$ and $$w_{i \to n} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \delta(E_n - E_i)$$ where it must be understood that this expression is...

In "QED, The Strange Theory of Light And Matter" Richard Feynman describes the probability path of a single photon emitted from a source, reflected from a mirror surface, and finally reflected to a probe detector. This path is the least time path relative to the probe/viewer, determined by the...

the first method is this : I think I can create a surjective function f:[0,1]^n→S^n in this way : [0,1]^n is omeomorphic to D^n and D^n/S^1 is omeomorphic to S^n so finding a surjective map f is equal to finding a surjective map f':D^n →D^n/S^n and that is quotient map. Now if I take now a...

Can someone please tell me where I am wrong. I am learning how to write ##a^{2} + bx + c## in this form ##f(x)= a(X-X_0)^{2} +Y_0##. The method used in my textbook is a reduction to the perfect square. And it goes like this: ##f(x)=ax^2+bx+c## ##=a[x^2+\frac{b}{a}x]+c## ##=a\left [...

Mentor note: For LaTeX here at this site, don't use single $ characters -- they don't work at all. See our LaTeX tutorial from the link at the lower left corner of the input text pane. I have a function dependent on 4 variables ##f(r_1,r_2,q_1,q)##. I'm looking to minimize this function in the...

I can get the domain, but getting the range seems impossible. Domain $$x-5=0$$ $$x =5$$ $$\therefore x \in (- \infty ,5) \cup (5, + \infty)$$ Range  I can simplify the function to the form below, but I don't know how to go from there. $$ f(x)= x + 5 + \frac {1}{x-5}$$  

Let ##F:[0,2\pi] --> Complex## ##F## is integrable riemman. show for all ##\epsilon>0## you can find a ##g##, continuous and periodic ##2\pi## s,t: ##||f-g||_2<\epsilon## What I tried ( in short ), which is nothing almost, but all I know: because g in continuous and periodic, according to...

Hello All : as i read about solid state physics , reading about crystals and structures , is it possible to create PZE electrodes and put them on kidney to create some vibrations patterns to help in filtration of blood reducing the need to kidney dialyses , as kidney problem is filtration...

TL;DR Summary: I attempt to find the derivative of uv with respect to x using non standard analysis, hyperreals, and the standard part function st; I take u to be a function of x, and I also take v to be a function of x. Hello everyone! I've been learning about non standard analysis concepts...

##f\left(x\right)=\begin{cases}\sqrt{\left|xy\right|}sin\left(\frac{1}{xy}\right)&xy\ne 0\\ 0&xy=0\end{cases}## I showed it partial derivatives exist at ##(0,0)##, also it is continuous as ##(0,0)## but now I have to show if it differentiable or not at ##(0,0)##. According to answers it is not...

I see this written or talked about so often. Pop-sci for sure. But, whatever the wave function is, and whatever might collapse it, can we agree consciousness is not required to collapse it? I.E., the moon was there before "conscious" beings, on this planet or elsewhere, viewed it? Is at...

Why on Earth does anyone, let along Roger Penrose, think gravity might be what causes the wave function to collapse? The most basic experiment in quantum physics, the double slit experiment, shows that collapse is most closely analogous to whether or not the item at issue (for example, an...

I don't really know how I am supposed to approach that. In general, I know how to show that a function is linear, which is to show that ##f(\alpha \cdot x) = \alpha \cdot f(x)## and ##f(x_1 + x_2) = f(x_1) + f(x_2)##. However, for this specific function, I have no idea, since there is nothing...

I've been given the proof, but don't understand; to calculate the limit of ##f## when ##x## tends to zero it's enough to see that if ##\{x_n\}_{n=1}^\infty## is a sequence that tends to ##0##, then...

For this problem, How did they get that formula shown? My working is, All the solutions wrote was, Many thanks!

Like this one: ##f(x)=3x^3 -18x^2 +36x##.Is there any way to find the inverse of this function without using the general solution to cubic equation?

Hi, Unfortunately I am not getting anywhere with task three, I don't know exactly what to show Shall I now show that from ##S(T,V,N)## using Legendre I then get ##S(E,V,N)## and thus obtain the Sackur-Tetrode equation?

function I=main_simpson(a,b,tol) f = @(x) sin(1./x); SO = 0; N = 10; S = 1; while (abs(S-SO)>tol) SO = S; h = (b-a)/(2*N); i = 0:N-1; xi = a+2*i*h; xi1 = a+2*(i+0.5)*h; xi2 = a+2*(i+1)*h; S = (h/3)*sum(f(xi)+4*f(xi1)+f(xi2)); N = 2*N; end end <Moderator's note...

I am wondering if someone can look over my proof, and point out any mistakes I might have made.There is no value of m such that x^3 - 3x + m = 0 has two distinct roots on the interval 0 <= x <= 1. Proof. Let f(x) = x^3 - 3x + m. Suppose, to the contrary, that there is a value of m such that f...

I was wondering if a periodic function could have 2 different fundamental periods? If so, could you give an example? And If not, how can I prove that?

##8 \sin^4u = 3-4\cos 2u+\cos 4u## ##8 \sinh^4u = 3-4(1+2\sinh^2 u)+ \cosh ( 2u+2u)## ##8 \sin^4u = 3-4-8\sinh^2 u+ \cosh 2u \cosh 2u + \sinh 2u \sinh 2u## ##8 \sinh^4u = 3-4+1-8\sinh^2 u+ 4\sinh^2u +4\sinh^4 u + 4\sinh^2 u + 4\sinh^4 u## ##8 \sinh^4u = -8\sinh^2 u+ 8\sinh^2u +8\sinh^4 u##...

Normalize function f(r) = Nexp{-alpha*r} Where alpha is positive const and r is a vector I was just wondering if the fact that we have a vector value in our equation changes anything about the solution

This graph shows ##H## as a function of time related to the L-CDM model. Do we (@Jorrie) have similar graphs e.g. for ##\Lambda=0##; ##k=-1## critical, ##\Lambda=0##; ##k=0## open, ##\Lambda=0##; ##k=+1## closed? That would be great, thanks in advance.

##Z = \sum_{-i}^{i} = e^{-E_n \beta}## ##Z = \sum_{0}^j e^{nh\beta} + \sum_{0}^j e^{-nh\beta}## Those sums are 2 finites geometric series ##Z = \frac{1- e^{h\beta(i+1)}}{1-e^{h\beta}} + \frac{1-e^{-h\beta(i+1)}}{1-e^{-h\beta}}## I don't think this is ring since from that I can't get 2 sinh...

I understand that S (Ssys) is a state function but I can't understand why Ssurr and Suniv (or Stot) are a path function.

I have plotted the function for ##T=15## and ##\tau=T/30## below with the following code in Python: import numpy as np import matplotlib.pyplot as plt def p(t,T,tau): n=np.floor(t/T) t=t-n*T if t<(2*np.pi*tau): p=np.sin(t/tau) else: p=0 return p...

Hi I posted this differential equation to WolframAlpha https://www.wolframalpha.com/input?i2d=true&i=Power[\(40)Divide[a,1+b*cos\(40)y\(40)x\(41)\(41)]\(41),2]*y'\(40)x\(41)=c but no solution , " Standard computation time exceeded... Try again with Pro computation time " Should I ( buy and )...

I study particle physics with “Particles and Nuclei” / Povh et al. and “Modern particle physics” / Mark Thomson and I am currently at “Deep-Inelastic scattering”. After introducing several scattering equations, such as Rosenbluth, that all include terms for electric AND magnetic scattering, i.e...

I found some interesting equations on cosmology and I was wondering how to introduce the integral in an excel sheet: "Paste ( .443s^3+1)^(-1/2) in for the integrand, type in s for the variable and 1 to 2 for the limits. Press submit, then change 2→3→4→5 and repeat." (from the thread...

I am refreshing on this; ..after a long time... Note that i do not have the solution to this problem. I will start with part (a). ##f(u)= 3u-\dfrac{3u^2}{2k}## with limits ##0≤u≤k## it follows that, ##3k - \dfrac{3k}{2}=1## ##\dfrac{3k}{2}=1## ##k=\dfrac {2}{3}## For part (b)...

Hello! I have some experimental data points ##(z_i,dz_i)## and I know that in the most general case this variable can be written in terms of 2 other variables as ##z_i = ay_i+bx_i##. Beside ##z_i## I can also measure, for each point, ##x_i## (we can assume that the uncertainty in ##x_i## is...

Hey all, I was wondering if there was an equivalent closed form expression for ##\Gamma(\frac{1}{2}+ib)## where ##b## is a real number. I came across the following answer...

I have a cubic lattice, and I am trying to find the partition function and the expected value of the dipole moment. I represent the dipole moment as a unit vector pointing to one the 8 corners of the system. I know nothing about the average dipole moment , but I do know that the mean-field...

The problem goes as follows: Let ##M, N## be sets and ##f : M \rightarrow N##. Further let ##L \subseteq M## and ##P \subseteq N##. Then show that ##L \subseteq f^{-1}(f(L))## and ##f^{-1}(f(P)) \subseteq P##. Obviously, I would simply use the definition of a functions inverse to obtain...

Hi, First of all, I'm not sure to understand what he Kramers-kronig do exactly. It is used to get the Real part of a function using the imaginary part? Then, when asked to add a peak to the parity at ##\omega = -\omega_0##, is ##Im[\epsilon_r(\omega)] = \delta(\omega^2 - \omega_0 ^2)## correct...

Question: There is a function ##f##, it is given that for every monotonic sequence ##(x_n) \to x_0##, where ##x_n, x_0 \in dom(f)##, implies ##f(x_n) \to f(x_0)##. Prove that ##f## is continuous at ##x_0## Proof: Assume that ##f## is discontinuous at ##x_0##. That means for any sequence...

For ##R<0##, the antiderivative is just a constant, since then ##R-|x|## is negative for all values of ##x##, which in turn implies ##\Theta(R-|x|)## is zero for all values of ##x##. For ##R\geq 0##, and by inspection apparently, the antiderivative is ##(R+x)\Theta(R-|x|)+2R\Theta(x-R)+C.##...

$$H = - J ( \sum_{i = odd}) \sigma_i \sigma_{i+1} - \mu H ( \sum_{i} \sigma_i ) $$ So basically, my idea was to separate the particles in this way:: ##N_{\uparrow}## is the number of up spin particles ##N_{\downarrow}## "" down spin particles ##N_1## is the number of pairs of particles close...

What should I do when the f(x, y) function's second derivatives or Δ=AC-B² is zero? When the function is f(x) then we can differentiate it until it won't be a zero, but if z = some x and y then can I just continue this process to find what max and min (extremes) it has? What I've done is...

I am refreshing on this; of course i may need your insight where necessary...I intend to attempt the highlighted...this is a relatively new area to me... For part (a), We shall let ##f(x)=\dfrac{1}{x(2-x)}##, let ##g(x)## be the even function and ##h(x)## be the odd function. It follows...