Hi,
I have a roughly 1.1 GHz signal to be downconverted to 100 MHz by mixing it with a 1 GHz local oscillator. I am not sure how to choose the performance of the LO.
In particular: let's assume the LO has a jitter of 100 fs rms. At 1 GHz this corresponds to a frequency error of 100 kHz. Does...
Hi,
I have the following optimization problem. I have a list of tasks that I should be able to perform with my tools. Each tool costs a certain amount of money, and may be used to carry out a finite number of tasks. The goal is to choose an optimal set of tools in such a way that the toolset can...
Hi,
let's say I want to measure the frequency f of a periodic signal. I may take N data points with an arbitrary timestep of T.
The question is how shall I choose T for a fixed N to have the best accuracy? In principle the frequency resolution is 1/(N*T) when taking the Fourier transform...
Hi all,
I am wondering about the actual technological parameters of a modern MRI. In particular I mean sensitivity, i.e. the order of magnitude of the signals to be detected and the noise levels in practice.
Can somebody recommend a good reference about the subject from an engineering...
Hi,
Does anybody know a material which is a good thermal conductor and an insulator at the same time (at temperatures around 4 K) and is "easy" to fabricate? For e.g. sapphire fulfils the first two requirements, but is extrmely hard.
Hi all,
I need a proper software for designing microwave cavities. I intend to use simple base geometries (e.g. closed box) with some modifications, like holes for optical access or for feeding the MW. These modifications however may seriously affect the Q factor, the frequency or might...
Homework Statement
Calculate the following limit for real t -s.
\sum_{n=0}^{∞} exp[i\cdot \sqrt{n + 1}\cdot t] / n!
Homework Equations
None
The Attempt at a Solution
Without the root it's trivial... I am not sure if it is even possible to give a closed form, I am out of ideas...
Hi,
I've recently read an introductory review of Bethe ansatz for antiferromagnetic spin-1/2 Heisenberg chains : cond-mat: 9809163. I understand that the elementary excitations above the ground state in absence of magnetic field are spinons.
The article claims that when a finite magnetic...
Elliptic function -- different definitions
Hi,
I have recently discovered, that the definition of the complete elliptic integral of the first kind in Wolfram Mathematica (EllipticK[m]) is different from the usual (K(m)), given in Abramowitz-Stegun.
Their domains are not the same. In...
Hi,
I need to solve the following system of equations:
qa = fa (qa, qb, qc, qd)
qb = fb (qa, qb, qc, qd)
qc = fc (qa, qb, qc, qd)
qd = fd (qa, qb, qc, qd)
where all the variables and functions are complex. However, there are some additional constraints for the variables, lets call...
Hi,
Does anybody know a nice formula for the capacitance of two metallic wire loops with equal radius R?
(The center of the loops are above each other, their distance is d. The whole system is in vacuum)
Thank you!
latex -- superscript & subscript together
Hi,
I need to use expressions that have arguments, multiple superscript and subscript indices at the same time, e.g
V(ij)_{\sigma_1\sigma_2}^{\tau_1\tau_2}
Is it possible to force latex to make this formula more compact, ie. to put the...
Hi,
I am looking for the operator representing the absolute value of a particle's momentum. In other words: the square root of the laplacian (preferably in 3 dimensions, but 2 would also be fine).
I am aware, that integral formulas exist for this operator, but is it possible to express it...
Graphene -- Green's function technique
Hi,
I am looking for a comprehensive review about using Matsubara Green's function technique for graphene (or at least some hints in the following problem). I have already learned some finite temperature Green's function technique, but only the basics...
Hi,
I need some help to calculate this integral:
\int _0^{2\pi}\frac{x^n}{\sqrt{1-m\cos x}}dx, where 0<m<1.
What I've already tried:
took the binomial series of (1-m cos(x))^(-1/2), this results in integrals like
\int_0^{2\pi} x^n(\cos x)^k dx
After this I've replaced cos(x)^k as a...
Hi,
can anyone explain to me, how the Feynman-Kac formula is used to obtain the following expression for the N-particle canonical partition function of a Bose gas (with interaction potential V)?
Z=1/N!Ʃ_{π\in S_N}Ʃ_{x1,...,xn}E[ exp(-∫_0^β Ʃ_{i<j}V(X_i(s), X_j(s) ds*indicator(X_i(β)=xπ(i)...
Hi,
I need to expand my storage capacity on my notebook. I'm considering 2 options:
1 TB internal 5400 rpm with sata (or sata2 if my notebook is capable of)
or
2 TB external 7200 rpm with usb 2 (the hdd can do usb 3, but I don't have usb 3 port in my computer)
Can you give me...
Hi.
Can somebody recommend a good book (advanced level) dealing with applications of cross correlation functions? I mean what kind of conclusions can be drawn etc?
Hi,
Can anybody recommend an advanced book concerning mechanical vibrations? I'm especially interested in vibrations of a spehere, hemispehere and bell.
Thank you!
Hi,
I was given the following problem, and i couldn't solve it yet:
Give a bijection between the elements of SO(3) and the fractional linear transformations of the form
\varphi_{z,w}\,(u)=\frac{zu+w}{-\bar wu+\bar z}, where u\in \mathbb C\cup \{\infty\};\, z,w\in \mathbb C.
Any ideas...
Hi everybody,
On a probability theory lecture I met an interesting problem:
Let f : [0;1] -> R a bounded, 3 times continously differentiable function. Calculate the following limit
n * \int_0^1 \int_0^1 ... \int_0^1 f(\frac{x_1+...+x_n}n)-f(0.5) dx_1...dx_n while n -> infinity
Any ideas?