0
votes
0answers
3 views

How to realize the simplest agreement protocol

Consider the simplest case: 1 o-----o 2 with x1 = 1 and x2 = 11 The agreement protocol is: I think we can realize it by the discrete case: In this ...
0
votes
0answers
6 views

Is there any general selection criteria for using a probability distribution?

I have learned that Poisson distribution is used often for queues, while exponential are used for the time between events of a queues. I know for small sample sizes to use the student distribution, ...
0
votes
0answers
13 views

How I can refine the proof of $\mathop {\lim }\limits_{(x,y)\, \to \,(3, - 1)} \left( {{x^2} + {y^2} - 4x + 2y} \right) = - \,4$

To prove that $\mathop {\lim }\limits_{(x,y)\, \to \,(3, - 1)} \left( {{x^2} + {y^2} - 4x + 2y} \right) = - \,4$ ; I followed the following process: Because the hypothesis and the definition of ...
0
votes
0answers
5 views

A proof by contraposition problem

Use a direct proof to show that the cube of an odd number is also odd. Proof: Assume that $a$ is odd. Therefore, $a = 2p + 1$, where $p$ is a non-negative integer. Therefore, $a^3 = (2p ...
0
votes
1answer
17 views

Is $\sum_{n=1}^\infty {1\over 3^{\sqrt{n}}}$ convergent?

Is $\sum_{n=1}^\infty {1\over 3^{\sqrt{n}}}$ convergent ? I use it to compare with $1/n^2$, and then I used LHôpitals rule multiple times. Finally , I can solve it. However,I think we have other ...
0
votes
0answers
2 views

Minimzing the generalized dissimilarity measure

I am trying to solve the following problem for quite some time now, but with no progress. Here is the problem. Let $x_1....x_n$ be n samples in d-dimmensional space and let $\Sigma$ be a non ...
1
vote
0answers
6 views

Request for online reference to Hamilton's “The Ricci Flow on Surfaces”

Does anyone know of an online source for Richard Hamilton's paper "The Ricci Flow on Surfaces?" I've searched Google for it and it doesn't seem to give any results.
0
votes
1answer
14 views

Classifying functions that satisfy $|f(x)-f(y)| \leq M|x-y|^{\alpha}$

If $f: [0,1] \to \mathbb{R}$ is a (not necessarily continuous) function satisfying $$ |f(x)-f(y)| \leq M|x-y|^{\alpha} $$ where $M$ and $\alpha$ are fixed real numbers and $\alpha > 1$. Classify ...
0
votes
0answers
3 views

Using a reverse polynomial for a partial fraction decomposition in a recurrence relation problem

I recently asked this question about finding the formula for: $$gn=g_{n−1}+g_{n−2}+n, g_0=1, g_1=2$$ On that question, I was able to get help to the point of generating this partial fraction ...
0
votes
1answer
7 views

Find term for one angle of two in a trig function

In a right angled triangle, I know that tan(x) = 4/z and that tan(x+y) = 12/z I need to find an equation which has only tan(y). The answer is 12/z = [4/z + tan(y)]/[1-(4/z)tan(y)] but I have no ...
0
votes
1answer
13 views

exponential number

I knew e=2.692, but don't know how this has been derived (I am not from maths major, but have genuine interest in mathematics), and how it has been used in solving equation, For expample in solving ...
0
votes
0answers
7 views

Proving there is no set of five distinct points s.t. every three points are the vertices of a right triangle.

We can see that the following proposition is true. Proposition : Each triangle $ABD, ACD, BCD$ is a right triangle for $$A(0,b,0), B(a,0,0), C(0,0,0)\ \ \ (a\gt 0, b\gt 0)$$ $\iff D$ is either ...
0
votes
3answers
13 views

Combinatorics/Probability, Choosing from group of People

I attempted to do this problem and I do have some guesses and trying to see whether they are right. Can you please correct if I'm wrong and explain. would really appreciate it. For a) I have ...
0
votes
0answers
7 views

probability of second highest no in a uniform distribution

Suppose $n$ real no are drawn at random from the uniform distribution over the interval $[0,1]$. For $x$ belongs to $[0,1]$, what is the probability that the second highest number drawn is $<= x$? ...
-2
votes
0answers
7 views

Graph Theory - Lower bounds

I am trying to solve for the following problem: Find (and justify) a lower bound for 0(G) in terms of X'(G) and E|(G)| and alpha'(G). (where alpha'(G) represents the maximum size of a matching in ...
-1
votes
0answers
8 views

ordinary differential equatins

I want to solve the folowing system of equation using bvp4c f'''+ff''-f'^2+m(\lambda-f')+lmbda^2=0 (1) theta''+pr(Nbphi'theta'+Nt theta'^2)=0 (2) phi''+Lefphi'+Nt/Nb theta''= 0 (3) ...
1
vote
1answer
15 views

Continuity and Density

If a function is continuous on an interval $(a,b)$, does it mean that it is dense in the interval $[f(a), f(b)]$? Can I use the continuity of $\sin x$ to show that it is dense in $[0,1]$?
0
votes
0answers
7 views

Show that $B(X)$ is semisimple for a Banach space $X$

Show that $B(X)$ is a semisimple Banach algebra, where $X$ is a Banach space. That is, to show that rad $B(X)=\{0\}$, or equivalently, to show $\sigma(AT)={0} \, \forall T\in B(X)\Rightarrow A=0$ I ...
0
votes
0answers
10 views

Question about Fubini's Theorem for Riemann Integral functions

Let $f: [0,1] \times [0,1] \to \mathbb{R}$ be given such that $$ f(x,y) = \left\{ \begin{array}{lr} 1 & : x \in \mathbb{Q}\\ 2y & : x \notin \mathbb{Q} \end{array} ...
2
votes
2answers
16 views

Transformation on a random variable

Can someone please help me with formatting this question? $Y$ is an exponential random variable with parameter $1$. Let $Z=-Y$, what is the pdf of $Z$? Attempt: $$\Pr(-Y< y)=\Pr(Y>-y) ,$$ ...
1
vote
1answer
11 views

Quantified Logic with miltuple variables

Problem: ∀y¬∃x¬(Fxy ∨ Fyx) ⊢ ∀y∀z(Fyz→Fzy) I don't really understand how to deal with multiple variables in instances like this. So far I have: ...
0
votes
1answer
10 views

Set Theory: Symmetric Relation

If relation S1 is symmetric, prove that S1 circle S1^(-1) is also a symmetric relation. (x,y)inS and (y,x)inS. Thank you for help!
1
vote
1answer
10 views

Proof by contradiction problem on rational numbers

Using proofs by contradiction, show that there is no smallest negative rational number and no largest positive rational number. Assume that there is a smallest negative rational number. Therefore, ...
1
vote
0answers
12 views

How to properly use technology for back-of-the-envelope calculations?

I'm usually quite eager on using technology wherever sensibly applicable, however whenever I make some calculations I still end up using a pen and paper, by now resulting in an entire pile of sheets ...
1
vote
0answers
15 views

differential equation

can anybody help me to solve this equation? \begin{equation} 2r \frac{dR}{dr}+r^2 \frac{d^2 R}{dr^2} - \left[ l(l+1) + r^2 s \left( 1+ \frac{a}{r}\right) ^4\right] R = 0 \end{equation} where $s, l$ ...
0
votes
0answers
11 views

Conditional independence: does $(A\bot B) \mid C$ imply $(A \bot B) \mid C^c$?

I think the answer is no, but cannot construct a counterexample. A,B,C are events, $C^c$ is the complement of C.
0
votes
1answer
6 views

Examples of Regular Graphs that are Not Vertex-Transitive?

I've just been learning about vertex-transitive graphs. I've seen plenty of examples of graphs that are vertex-transitive, but no examples of graphs that are not vertex-transitive and regular. Can ...
0
votes
1answer
10 views

probability, depedence => uncorrelated?

One quick question. Two random variables are dependent, so it must be uncorrelated? Also for the terminalogy, does the term "uncorrelated" means two random variables have a corvariance factor of 0? ...
0
votes
1answer
6 views

Any Straight Line Contained in a Surface is Asymptotic and Hyperbolic “Squares”

I have to prove that "any straight line $\alpha$ contained on a surface $S$ is an asymptotic curve and geodesic (modulo parametrization) of that surface $S$". Can I have hints at tackling this ...
0
votes
0answers
9 views

Question about the frequency domain and the fourier transform

if you have a signal say x(t) in continuous time and you transform it using the Fourier transform for continuous time you get X(w) which is the frequency domain representation of this signal x(t). ...
0
votes
0answers
19 views

A Challenging Question. Eigenvalues of a Special Matrix.

$N\times N$ matrix $L$ can be partitioned into $p\times p$ blocks, ...
0
votes
0answers
17 views

Number of edges of a plane graph isomorphic to its dual

I am having trouble proving the following statement: Suppose that $G$ is a plane graph which is isomorphic to its dual. Prove that $G$ has $2n-2$ edges.
0
votes
0answers
11 views

Linear Algebra: On inner product, projection and maxima-minima

Let $X$ be a set of $d$-dimensional vectors. For all $x \in X$, the components of $x$ are between $0$ and $1$. Let $y$ be another vector with same property. Let $W$ represent a set of weighing ...
0
votes
1answer
15 views

Let $X = \{x_{n}\}_{n=1}^{\infty}$ be a sequence of distinct real numbers. Define a metric $d(x_{m},x_{n}) = |1/m-1/n|$ on $X$.

The question is what is the completion of $X$? My thought: $[-\infty, \infty]$? Not sure...
0
votes
2answers
23 views

Apostol - Analytic Number Theory, Chapter 3 problem 4a

The problem comes from "Introduction to Analytic Number Theory" by Tom M. Apostol, Chapter 3, Problem 4a: Question: Prove $\sum_{n \le x} \mu(n)[ \frac xn]^2 = \frac{x^2}{\zeta(2)} + O(x log(x))$ ...
0
votes
1answer
33 views

Inequality proof, why isn't squaring by both sides permissible?

Suppose $a$ and $b$ are real numbers. Prove that if $0 < a < b$ then $a^2 < b^2$. I understand that the normal way to prove this is to multiply $a < b$ by $a$ and then by $b$ and then ...
1
vote
1answer
22 views

finding vector that isn't a linear combination

Hi can someone help me with this question: Find a vector in $\mathbb{R}^5$ which is not a linear combination of u and v. Verify that your vector is not a linear combination of u and v. Where u = ...
3
votes
4answers
47 views

$\lim_{n\to \infty}\left(1 - \frac {1}{n^2}\right)^n =?$

Can you give any idea regarding the evaluation of the following limit? $\lim_{n\to \infty}\left(1 - \frac {1}{n^2}\right)^n$ We know that $\lim_{n\to \infty}\left(1 - \frac {1}{n}\right)^n = ...
0
votes
0answers
4 views

Inequality of strong $L^p$ and weak $L^p$ norm on a finite set with counting measure

If $X$ is a counting finite set with counting measure. Let $f : X \to \mathbb C$ be a complex valued function. For any $ 0 < p < \infty$, show that $$ ||f||_{ L^p } \le C_p (\log (1 + |X| ...
1
vote
0answers
12 views

Algorithm for determining what order to perform a set of tasks in

Consider a set of $n$ items. Each item has a date $d$ by which it must be completed. Each item also has a priority level of $p$ and takes a time $t$ to complete. Is there an algorithm for determining ...
1
vote
0answers
13 views

When a sort of weak topology is enough to generate vector space topology

Consider a vector space $V$, and some functions $f_\alpha: V \rightarrow \mathbb{C}$ where $\alpha$ ranges over some index set $A$. We can think about the coarsest topology which: a) makes the ...
0
votes
1answer
13 views

Question of Buffon's Needle

I looked at the gif on wikipedia that explains Buffon's needle, but I have two questions. First, why do you only consider $x$ as the distance from the center of the needle to the closest line, so it ...
0
votes
0answers
7 views

Laplace transform, when $s \rightarrow \infty$

I'm reviewing lecture notes on Laplace Transform and there's one step that I don't understand: Find the solution to: $$x y'' + y' + xy = 0, y(0) = 1, y'(0) \mbox{ finite}$$ Taking the Laplace ...
5
votes
4answers
33 views

How to prove continuity of $e^x$.

I simply want a proof that $e^x$ is continuous. I have never really been able to find something satisfying these points: $e$ is defined to be the limit $\lim_{n\to\infty}\left(1+{1\over ...
4
votes
3answers
29 views

How to calculate $\exp\left(t\begin{bmatrix}0 & z\\z^* & 0\end{bmatrix}\right)$?

or, in a more general case: $e^{\begin{bmatrix}0 & v\\w & 0\end{bmatrix}}$, where: $v, w \in \mathbb{C}$
1
vote
1answer
15 views

Graph Theory - Proof

I am need help to Prove the following statement: Let G be a $k$-regular graph with $n$ vertices and $k \geq 1$. Prove that $G$ does not have an independent set of size greater than $\dfrac{n}{2}$. ...
2
votes
3answers
25 views

How do we calculate the Right and Left Hand Limit of 1/x?

I am confused regarding one sided limits and how to calculate it. For Example: $$\lim_{x\to 0}\frac{1}{x}\quad\text{does not exist}$$ How can I validate that $\lim\limits_{x\to 0^+}\frac{1}{x}$ or ...
-1
votes
0answers
10 views

.mat files and functions that do not return values [on hold]

i have a .mat file as shown.the same data is used in different .mat files.but how it is generating variable val with diiferent sizes and different info? function importfile2(fileToRead1) ...
1
vote
1answer
13 views

Probability of at least one card matching when flipping through two separate decks.

Two identical decks consist of 6 white cards and 6 black cards each. The top card of each deck is flipped at the same time. If this is done repeatedly, what is the probability that at least one of the ...
1
vote
1answer
26 views

One-sided Derivative Question

Let's say we define $$D_{+}f(x):=\lim_{h\to 0^+}\frac{f(x+2h)-f(x+h)}{h}$$ to be the "right-handed" derivative. This way the function does not have to exist (or equal what it 'should') at the point ...

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