# analysis

1. ### Implications of unitary matrix with sub-blocks of matrices

If we consider some unitary operator in matrix form given by $U = \left[ {\begin{array}{cc} P_{00} & P_{01} \cdot \cdot & P_{0J} \\ P_{10} & \\ \cdot &\\ \cdot\\ P_{J0} \cdot\cdot\cdot& & P_{JJ} \\ \end{array} } \right]$ Where each $P_{nm}$ are matrices (sub-blocks of...
2. ### Fourier-Series, where is my mistake?

Hello, I've got a piecewise defined, 4-periodic function . I have calculated the coefficients as seen in the pictures . The problem is, when I plot the Fourier series , it seems not to be correct, as you can see in this picture (blue: Fourier series, black: actual function): I am looking...
3. ### Numerical Analysis

Hi , Can anyone check for me if I'm doing correctly calculations based on 2 equations? Especially an integral because I don't really know how should I compute it. I'm calculating it in microsoft office excel (I've got those equations from scientific paper, and I don't really know if there is a...
4. ### Prove: If f(A-B) = f(A)-f(B), then f is injective.

Book: Mathematical Analysis by Apostol Theorem 2.2:(a,b) = (c,d) \iff a = c \text{ and } b = d. A - B = \{ x: x\in A, \text{ but } x \notin B\} Let f: X \rightarrow Y. Prove that if f(A-B) = f(A) - f(B) \text {for all } A,B \subseteq X \text{, then } f \text{ is injective.} My...
5. ### Help understanding this proof: E is a subset of f^(-1)(f(E))

\text{Let } f: X\rightarrow Y, \text{ where } X \text{ and } Y \text{ are sets.} \text{Prove that }E \subseteq f^{-1}(f(E)) \text{ } \forall E \subseteq X. PROOF: \text{Let } x \in E. \text{Then, }y = f(x) \in f(E), \text{ so } x \in f^{-1}(f(E)). \text{ Hence } E \subseteq f^{-1}(f(E)) How...
6. ### Complex analysis- residue theorem

Is it possible to solve the above using residue theorem? if yes then how to start?
7. ### Numerical analysis- fixed point iteration method

Q. Compute by the method of fixed point iteration a real root of the equation x^3 + x^2 - 1 =0 correct up to two decimal places. In the above problem if we take f(x)=0, then to solve it we can write f(x) in the form of x=g(x). Now g(x) can take three different forms. i) 1/sqrt(1+x) ii)...

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9. ### Analysis: show xn is a null sequence

Prove that x_{n+1}-1/2x_n\to 0 \Rightarrow x_n\to 0. My approach: Let \varepsilon>0. Then there exists an N\in \Bbb N s.t. \forall n\geq N, |x_{n+1}-1/2x_n|<\varepsilon. It follows that -\varepsilon\leq -\varepsilon+1/2x_n<x_{n+1}<\varepsilon \leq \varepsilon+1/2x_n. Then for any n\geq N, we...
10. ### Interval of Convergence for differing odd/even coefficients of power series

Hello, I am studying for a midterm this week. One of the practice problems is to find the radius of convergence of \sum_{n=0}^{\infty} a_n x^n where a_n = 5^n if n is odd and a_n = 1/3^n if n is even. It took me a while to hazard a guess that I take the smaller of the two radii? Then a =...
11. ### Complex Analysis Singularities

I've found that the singularities for the complex function $\frac{1}{cos(1-\frac{1}{z})}$ are $z=0$ and $z=\frac{2}{2-(2k+1)\pi}$ where $k\in\mathbb{C}$ but how do you know what kind of singularity they are? (i.e. poles, removable singularities or essential singularities) Any help would be much...
12. ### Power analysis for sample size that measures heterogeneity

Hi I hope someone can help me with this question here. I would like to do a power analysis for sample size, but I am unsure how to approach it because I am measuring heterogeneity in my dataset. Here are the details: I have two different types of cell lines and I am measuring the growth of...
13. ### Reading the periodogram of spectral analysis

Hello! I want to test if there is cyclical component in Imports and Exports, so I used Spectral Analysis. I am not sure if I am reading the periodogram correctly, so I will welcome any opinion of yours. From my understanding if the periodogram has similar to this shape /\, then there is...
14. ### error analysis Question

Hello Everyone So I am doing an error analysis but my instructor said " Go online and figure it out, come back to me and show me what you found, once you have done that, I will show you " I don't have anyone that can assist me. I tried locating the Math tutoring center but their appointments...
15. ### Error analysis Question

Hello Everyone So I am doing an error analysis but my instructor said " Go online and figure it out, come back to me and show me what you found, once you have done that, I will show you " I don't have anyone that can assist me. I tried locating the Math tutoring center but their appointments...
16. ### Numerical Analysis

I need a way to approach this problem. I saw this problem in chapter 3, section 3.4 of numerical analysis. I appreciate any help on any idea that may help me start out with this problem. Show that the following method has third order convergence for computing R1/2 Xn+1= Xn(X2n+3R)/(3X2n+R)...
17. ### Bayesian Analysis

Hi Guys I read an interesting stat yesterday that said people that play fantasy football are 67% more likely to watching live content compared to if they were not in a fantasy league. I am trying to figure out how much increased viewership in the NFL has been caused by people that play fantasy...
18. ### Principal factor analysis

Hello everyone: I have a statistical problem I've been trying to solve for quite a while without any success. I'm not sure if I am right here for my question but maybe someone can help me. I want to recreate a measure for earnings smoothing used in literature but I don't fully understand how...
19. ### Aggregated data analysis

Hi, I would like to know how it would be possible to make a t-test with aggregated data on SPSS or R. My dataset looks like this: Region......Question.....%positive.......%negative......n 1..............15...............20...................45............2956...
20. ### SARIMA forecasting time series analysis

Hello, This is a forecasting problem for an seasonal SARIMA(0,0,1)X(1,0,0)_4 model in time series analysis. I'll be very appreciated if you help me..Thanks.