0
votes
0answers
8 views

Relation of $\mathbb P \{X|\mathcal A\}$ and $\mathbb P \{X|Y=y\}$

Consider a probabilty space $(\Omega ,\mathcal F, \mathbb P$) and two measurable random variables $X,Y:\Omega \rightarrow S$. Define $\mathcal A :=\sigma(Y)\subset \mathcal F$ and $\mathcal B ...
0
votes
0answers
3 views

For which of seventeen wallpaper patterns do the group of symmetries act on the lattice group?

For which of the seventeen wallpaper patterns can coordinates be chosen so that the group $G$ (the group of symmetries) operates on the lattice $L$ (the 2D lattice coordinate points)? Please help. ...
0
votes
0answers
11 views

compute the grades over $\mathbb{Q}$

Let $p_{1}$ $\neq$ $p_{2}$ $\neq$ $p_{3}$ prime numbers. Compute the grades over $\mathbb{Q}$ of the extension fields $\mathbb{Q} ( \sqrt{p_{1}}, \sqrt{p_{2}})$ and $\mathbb{Q} ( \sqrt{p_{2}}, ...
1
vote
0answers
5 views

Preimage surfaces.

Let $U\subset\mathbb{R}^{m+n}$ open set, $f:U\longrightarrow\mathbb{R}^n$, $f\in C^{k}$, and $c\in\mathbb{R}^n$. Set: $$M=\{p\in U; f(p)=c\textrm{ and ...
0
votes
0answers
6 views

Accurate numerical integration for “data times an analytical function”

The Question is as follows: I have an algorithm/data that provides me the value of a function $f(x,y,z)$ on the points of a grid. On the other hand I have an analytical function ...
0
votes
1answer
16 views

Argument for $(a+bi)^2$

I found out the modulus for $(a+bi)^2$, which is $$a^2+b^2$$ but I am unable to find the argument. I found out that $$\theta = \frac{2ab}{(a-b)(a+b)}$$ I don't know how to simplify further! Please ...
0
votes
0answers
4 views

Parametrization of the split orthogonal group O(n,n)

I would like to find or construct an explicit parametrization of the $2m$-by-$2m$ matrix representation of the real indefinite orthogonal group $O(m,m)$ associated to the bilinear form with matrix ...
0
votes
0answers
8 views

Zeros of a differential equation

Is the part highlighted in green correct? Could there not be infinitely many zeros in the region $x<N$?
0
votes
0answers
12 views

May somebody help me prove the following limit solution?

$$\lim_{n\to\infty}\frac{1^n+2^n+3^n+\ldots+n^n}{n^{n+1}}$$ I have tried to solve thise several times ,but with no results.I have tried using lema stolz cezaro and managed to find a general formula ...
0
votes
1answer
37 views

Evaluate $\lim_{x\rightarrow \infty}(1+\frac{1}{\sqrt{x}})^{\sqrt{x}}$. Euler's Limit

Evaluate $\lim_{x\rightarrow \infty}(1+\frac{1}{\sqrt{x}})^{\sqrt{x}}$. Can I get some help? I am thinking that the limit does not exist. If you approach it from the left and then from the right, I ...
0
votes
0answers
21 views

How can I calculate Distance of line?

I have a picture. I want to measure of $P_{1}$ to $P_{4}$ distance. Also I know $P_{1}$ to $P_{2}$ to real distance. and $P_{2}$ to $P_{3}$ real distance $P_{1}-P_{2}$ real distance = $100$ mm ( ...
0
votes
0answers
28 views

Prove vector space identities

Let V be a vector space, and let $x,y,z\in V$. Prove that a) $x-(y-z)=x-y+z$ b) $0x=0$ c) $(-1)x=0-x$ I think I'm making these more complex than they need to be, but could someone show me the ...
0
votes
0answers
4 views

How is an ODE a consistency condition?

I was reading a text on Optimal Control Theory by E. Todorov, when I came accross this passage (on page 10): An ODE is a consistency condition which singles out specific trajectories without ...
0
votes
0answers
16 views

Prove: $\int_a^b e^{z_0t}dt=\frac{1}{z_0}e^{z_0t}|_a^b$

From a complex variables online course, and I need to prove that $$\int_a^b e^{z_0 t}dt=\frac{1}{z_0} e^{z_0 t}|_a^b$$ For every $0\neq z_0\in \mathbb{C}$ and for every $a,b\in\mathbb{R}$. Do I need ...
0
votes
0answers
20 views

How to show this infinite sum converges uniformly?

Let $f_k$ be a real numbers such that $\sum_{k=1}^\infty f_k < \infty$. For each $R > 0$, define the convergent sum $$v(R) = \sum_{k=1}^\infty f_k(b_k(R)e^{-ky} - c_k(R)e^{ky})$$ where $0 \leq y ...
0
votes
0answers
24 views

What is the fastest algorithm for 4x4 matrix multiplication?

I was wondering wich is the faster algorithm for multiplication of 2 4x4 matrices. I read about Strassen but before implementing it (as is costly) I want to be sure I'm not leaving better ones ...
0
votes
0answers
47 views

Why can't we differentiate constants like variables?

I understand why we the derivative of $x$ is $1$. Similarly, the derivative of a constant function $y=a$ is $0$, because it's slope is flat, since for every $x$, $y=a$. But can you please tell me why ...
0
votes
0answers
4 views

How to find the number of transitions, after which the stationary distribution could be found in Markov chain?

Say I have the initial state space vector S = [1 0 0]. and I know both the transition matrix, P and final stationary distribution, S' = [0.3 0.5 0.2]. If I was asked to calculate after how many ...
1
vote
0answers
15 views

Context Free Grammer

I'm working on the exercises in "Problem Soluing in Automata, Languages, and Complexity" and I've run into the below problem. The question asks to construct a CFG for the language , and I just can't ...
1
vote
2answers
28 views

Determinant of a 5x5 matrix

I have a little problem with a determinant. Let $A = (a_{ij}) \in \mathbb{R}^{(n, n)}, n \ge 4$ with $$a_{ij} = \begin{cases} x \quad \mbox{for } \,i = 2, \,\, j \ge 4,\\ d \quad \mbox{for } ...
1
vote
2answers
12 views

Factorising ideals in the ring of integers of a quadratic field

In an undergraduate algebraic number theory course, I was given the question "If $K = \mathbb Q(\sqrt{-33})$ Factorise the ideal $(1+\sqrt{-33})\subset \mathcal O_K$ into a product of prime ideals." I ...
0
votes
0answers
17 views
0
votes
2answers
18 views

Solution set of inequality

This is the question: $$\frac{1-2x-3x^2}{3x-x^2-5} \gt 0$$ What I did : I got the answer as $$\left(x-3\right)\left(x+1\right) \gt 0$$ giving me the solution set : $x \in (-\infty,-1 ...
0
votes
2answers
17 views

Can step functions approximate trigonometric functions?

I have read a notion from a number of different sources simply stating that a step function can approximate any trigonometric function. I am not convinced by simply reading this notion, for example ...
-5
votes
1answer
29 views

limit of a function raised to another function

Find the limit $\lim_{t\to3} (1+\sin(t-3))^{\frac1{t-3}}$. I'm not sure if the answer is supposed to be the natural number $e$ but if it is, can you show me how to arrive at this answer?
2
votes
0answers
11 views

Dual graph of a tree

It is stated here that: For any connected embedded planar graph G define the dual graph G* by drawing a vertex in the middle of each face of G, and connecting the vertices from two adjacent ...
0
votes
1answer
23 views

Taylor series and Maclaurin series problems

Im currently working on these two problems, and Im getting really confused with them. Can someone walk me through them? I will post the work I have so far. http://imgur.com/qXj7zC1 Here is my ...
0
votes
0answers
9 views

Estimation of the population variance

Let $X_1,X_2,...$ be uncorrelated random variables each with mean $\mu$ and variance $\sigma^2$. If $\overline{X}=n^{-1}(X_1+X_2+...+X_n)$, how do I show that ...
0
votes
3answers
17 views

Loci of Complex Equation

How does the loci of the equation $|z-(i+1)| = |1 + i|$ look like? I can't seem to visualise any points on the complex plane satisfying the above except the 2 obvious ones (2,2) and (0,0)... Is that ...
0
votes
0answers
6 views

maximum principles for beam and higher order equations

It is well known that the inequality $u_t<u_{xx}$ meets the maximum principle: Maximum of function $u(x,t)$ is attained at $t=0$ or on the boundary $x=0$ or $x=L$. Do we have maximum principles or ...
0
votes
1answer
16 views

Inner Product Space and Linear Mapping Theorem

I'm having some trouble proving the following theorem: Let $($$X$,$\langle\cdot | \cdot\rangle$$)$ be an inner product space and $f: X \to \mathbb{R}$ a linear mapping. Prove that there exists a ...
0
votes
0answers
8 views

Question about convergence in distribution.

Consdier exponential dist with location parameter $\mu$ and scale parameter $\sigma$ (pdf is $\frac {1} {\sigma}$$e^-\frac{x-\mu} {\sigma}$ $I_{[\mu,\infty]} (x)$ where $\sigma$>0 and -$\infty$ ...
0
votes
0answers
9 views

Is this formulation of Plancherel's Theorem correct?

Let $G$ be a finite group, $u,v\in \mathbb{C}[G]$ where $u = \sum u(g)g, v = \sum v(g)g$, and $\rho_{i}: G\rightarrow GL(W_{i})$ be irreducible representations and $\tilde{\rho_{i}}: ...
0
votes
0answers
8 views

Evaluating a likelihood predictor

Imagine you have a weather predictor which, each day, tells you the probability that it will rain on the following day. Then, that day, it either rains, or it doesn't (binary outcome). Is there a ...
1
vote
0answers
21 views

Div, grad, curl in curvilinear coordinates

I've a lot of different formulas for div, grad, curl, and laplacian in different coordinate systems. How are these formulas derived? What's the general procedure for finding the formula of say the ...
0
votes
1answer
17 views

Time between arrivals Distribution

I am simulating a hair parlor queue with m number of queues and 3 different types of services (queues). I was doing the time between arrival with a uniform distribution with a min value and a max ...
-2
votes
0answers
23 views

Prove that $P(a|a,b)=1$, where $a$ and $b$ are events [on hold]

Prove using first principles that $P(a|b,a) = 1$. State any probability axioms used.
0
votes
0answers
9 views

How to calculate full width half max of this curve

I'm trying to calculate the full width half max of this function and I keep receiving non-sense answers. The function is $F(ω)=A_0 (\frac{\frac{1}{τ}}{(\frac{1}{τ^2})+(ω_0 - ω)^2})$ and I then have ...
1
vote
3answers
20 views

Find third point to make isosceles triangle with a specific area

Using points A(1,2) and B(-2,-2), find a third point, with a positive y-value, that makes ABC an isosceles triangle with area 10 units${^2}$. I have found AB to be 5 and used this as $r^2$ below.. ...
0
votes
0answers
17 views

Prove every bounded sequence in the real numbers has a convergent subsequence using cauchy

Prove that every bounded sequence in $\mathbb{R}$ has a convergent subsequence. I am going to use the Cauchy sequence property to do this. Proof: Let $A_n$ be a bounded sequence in $\mathbb{R}$. ...
0
votes
1answer
14 views

Nature of acceleration from $x$ vs $t$ graph

The figure approximately shows the $x$-coordinate of a particle as a function of time. How can we decide whether the accelerations at time $t_1,t_2,t_3$ are positive or negative?
0
votes
0answers
15 views

There is an estimation of a $ \sum_{x\in\mathbb{F}_p} \left(\frac{a_{n}x^n+a_{n-1}x^{n-1}+…a_0}{p} \right) \le (n-1)\sqrt{p}$

Where can I find a proof of the following inequality? ( $n$ is odd) $$ \sum_{x\in\mathbb{F}_p} \left(\frac{a_{n}x^n+a_{n-1}x^{n-1}+...a_0}{p} \right) \le (n-1)\sqrt{\vphantom{d}p} $$ I read that ...
0
votes
1answer
18 views

How many poker hands have exactly two pairs?

I found an interesting solution to the combinatorial question of "How many poker hands have exactly two pairs?" and I cannot figure out (or find) the reasoning of the solution. The answer I found in ...
0
votes
2answers
39 views

Factoring a 5 term polynomial

I am struggling to factor $n^4 + 4n^3 + 8n^2 + 8n +4$. I have tried grouping the terms a couple of times, but got nowhere. What am I missing?
0
votes
1answer
16 views

Does $\sigma$ -compact imply separable?

Let $D$ be a metric space. If $D$ is $\sigma$-compact, does this imply that $D$ is separable? I thought I had a proof, but I think it is wrong. my proof: Let $K_n$ the compact sets such that $K_n ...
1
vote
1answer
35 views

Cohomology Group of $CP^2 \wedge CP^2$

Calculate the cohomology group of $CP^2 \wedge CP^2$ To do this, at first I am trying to calculate the homology group and then use Universal Coefficient Theorem. To do this, at first I have ...
6
votes
1answer
40 views

If $\lim_{n\to\infty} (a_{n+1}-a_n)=0$ and $|a_{n+2}-a_n|<\frac{1}{2^n}$ then $(a_n)$ converges

Let $(a_n)$ be a sequence such that $\lim_{n\to\infty} (a_{n+1}-a_n)=0$ and $|a_{n+2}-a_n|<\frac{1}{2^n}$ for all $n$. I have to decide whether or not $(a_n)$ converges. My attempt: I think it ...
2
votes
0answers
13 views

Example of a domain where all irreducibles are primes and that is not a GCD domain

One has the following relations for a domain $R$: $R$ GCD domain $\Rightarrow$ All irreducible elements are prime $R$ PID $\Rightarrow$ $(R$ GCD domain $\land$ $R$ statisfies ACCP$)$ $R$ UFD ...
4
votes
0answers
17 views

What is the equation to evenly distribute circles in a spiral?

What is the equation to evenly distribute circles in a spiral? I have attached a picture to show what I am trying to achieve and need to know what the equation is for this.
0
votes
1answer
7 views

What is a good source for learning fourier transformations as an application

I'm an undergraduate physics major and for my research I need to start learning and understanding fourier transformations for my research. Does anyone know good resources for doing this. I don't need ...

15 30 50 per page