# Search results

1. ### How does the phase noise of the LO effect IF accuracy?

Many thanks! I have looked into phase noise, and now I understand that I should calculate the total rms phase error, which describes the "average" deviation of the system. And here comes the problem: how to calculate this? I have found various tutorials on manufacturers' website, most of them is...
2. ### How does the phase noise of the LO effect IF accuracy?

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...
3. ### A Combinatorial optimization problem

Thanks for the immediate reply! I have heard about this one, actually already tried a basic version. I am wondering if there are other methods? B & B is an "art" for me, not sure what is the most efficient way for bound estimation, that's why I am asking.
4. ### A Combinatorial optimization problem

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...
5. ### Frequency measurement -- how to choose sampling ?

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...
6. ### Complex Numbers problem

First you should solve the equation for 'a'. After that, you can calculate the argumentum and the abs. value of 'a', resulting in a = r*(cos(theta) + i* sin(theta)). Finally, apply De Moivre for calculating a^2011.
7. ### MRI technology

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...
8. ### Infinite square well solution

You have thought it right, 'A' can be complex indeed. In fact, A=\sqrt\frac 2 a\,e^{i\phi} satisfies the the normalization constraint for any real \phi. Mind that the phase of the wave function is arbitrary.
9. ### Good thermal conductor but insulator

Good idea, but unfortunatelly this won't solve my problem. I'll use it as a sample holder at 4 K, and it'll be subjected to AC magnetic fields. The aim is to get rid of the eddy currents and for this I need the bulk to be an insulator as well.
10. ### Good thermal conductor but insulator

Thank you very much for your help, I'll look into the hints!
11. ### Good thermal conductor but insulator

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.
12. ### Clarifications regarding definitions of Taylor, Laurent etc. series

Here are some crucial differences: 1. A Laurent series is convergent on an annulus in the complex plane, whereas the Taylor series is on a disk. 2. EVERY function that is holomorphic on r < | z - a | < R has a unique, convergent Laurent series (defined on this disk. The exact values of the...
13. ### Clarifications regarding definitions of Taylor, Laurent etc. series

Here are some crucial differences: 1. A Laurent series is convergent on an annulus in the complex plane, whereas the Taylor series is on a disk. 2. EVERY function that is holomorphic on r < | z - a | < R has a unique, convergent Laurent series (defined on this disk. The exact values of the...
14. ### Designing a microwave cavity

Thank you, I'll look into it! Just out of curiosity: do you know any open source alternative?
15. ### Designing a microwave cavity

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...
16. ### Calculate the following limit ( not sure if possible!)

Thank you for your efforts! I've tried that, but I think it won't help, because m won't be an integer. I also tried to approximate with an intergral using Stirling's formula for n!, but the resulting intergral seems too complicated. I'm also considering to use somehow the residue theorem, but so...
17. ### Calculate the following limit ( not sure if possible!)

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...
18. ### Do Hilbert Space Isomorphism Map Dense Sets to Dense Sets?

It is true. Suppose, that A(X) is not dense. Then let V be a non-empty open set in K \ A(X). The pullback of V by A is open (A is bounded) and not empty (A is isomorphism), and by definition it is not in X, which contradicts the fact, that X is dense in H.
19. ### Spinons vs. psinons

Sorry guys, wrong link. It is actually in the third part: http://arxiv.org/abs/cond-mat/0008018 Here are some more articles, conserning this topic: http://prb.aps.org/abstract/PRB/v66/i5/e054405 http://prb.aps.org/abstract/PRB/v62/i22/p14871_1
20. ### Reaction between photon and proton !

So the reaction is: p^+ + ph \rightarrow pion + n^0 The energy of the left handside must not be less, than that of the right handside, so you'll just have to look up the energies of the neutron and pion (zero velocity).
21. ### Tricky Logical Problem

The statement is true, because if you choose z to be less or equal to x, then (x < z) is a false statement, so (x < z ) -> A is always true, regardless of "A".
22. ### Spinons vs. psinons

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...
23. ### Difficult expectation

It is finite of course , but I was wrong with the pi^2 / 3. If i got time for tomorrow, I'll give it a try.
24. ### Simplified Maxwell's Equation Proof

Check this: http://en.wikipedia.org/wiki/Electromagnetic_wave_equation
25. ### How to solve where a maclaurin series intersects a graph

Because the series is infinite, you cannot treat it as a polynomial equation. However, the left side is just cos (2x), so you need to solve cos(2x)=2x^3. This cannot be solved (as far as I know) analytically, the approx. solution is 0.58236.
26. ### Difficult expectation

but exp(x)/(1+exp(x))^2 is symmetric... and just to make it cleaner: in 3. you must do some algebra before expanding: 1/(1+exp(x))=exp(-x) * 1/(1+exp(-x)), and now you can expand the latter term
27. ### Computation of this integral

Basically any software that can do numerics for you, e.g. Wolfram Mathematica, Matlab, or you can write a C code as well (using GSL).
28. ### Difficult expectation

I haven't worked this out fully, but the following might work: 1. the function you integrate is symmetric, so write it as 2* integrate from 0..infinity 2. notice, that exp(x)/(1+exp(x))^2 is just the derivative of -1/(1+exp(x)), and integrate by parts 3. you will end up with something...
29. ### Eigenfunction expansions

Of course, there is an analogy: a matrix can be thought of as a linear map from a finite dimensional vector space to an other one. A linear operator is "the same", in the sense, that it is a map from an (infinite) vector space to an other one. But this is not, what you need know. What you use...
30. ### Mathematics in 10 levels.

To be honest, I see no reason to make this categorization... Of course, if you learn math e.g. at a university, you will have different subjects, like algebra, linear algebra, analysis, etc. However, after learning enough, you will see, that everything is connected with almost everything in...