## Question on my interpretation of logical notation relating to alphabets, theoretical comp sci. February 13

$\exists x \: \Sigma^* (t=xs)$Have I interpreted the above into words correctly?:"There exists a symbol 'x', which is a member of the set which contains all possible strings of alphabet sigma, where sigma contains string 't', which is a concatenation

## Representing Several IF statements inside a FOR loop in Math Notation February 13    1

I wish to correctly represent several IF statements within a for loop in math notation.The FOR loop can be represented as:∀i∈ {0,-,n-1} . (Conditional IF statements) The IF statements apply ...

## Quick question on my interpretation of logical notation relating to alphabets, theoretical comp sci. February 13

$\exists x \: \Sigma^* (t=xs)$Have I interpreted the above into words correctly?:"There exists a symbol 'x', which is a member of the set which contains all possible strings of alphabet sigma, where sigma contains string 't', which is a concatenation

## Why are probabilities needed for stochastic differential equations February 13

A SDE has the form :$\mathrm{d} X_t = \mu(X_t,t)\, \mathrm{d} t + \sigma(X_t,t)\, \mathrm{d} B_t$By fixing $w$ it becomes :$\mathrm{d} X_t(w) = \mu(X_t(w),t)\, \mathrm{d} t + \sigma(X_t(w),t)\, \mathrm{d} B_t(w)$So for each $w$ we have an equation

## Basic topology question regarding the complex plane. February 13    3

Prove that the Complex plane is closed, open and perfect.My intuition is destroyed by the fact that a set can be open and closed at the same time. The following is my understanding.open: If all points in set $E$ is interior to $E$, then $E$ is open.I

## Some questions regarding open sets and its complement. February 13    1

Let $E^o$ be the set of all interior points of the set $E$.I was able to prove that $E^o$ is always open and $E$ is open iff $E = E^o$.Now I am asked to prove that $(E^o)^c = \overline {E^c}$.Intuitively it is very clear, but I am not sure if my proo

## An Eigenvalue of $A^3$ is an Eigenvalue of $A$ February 13    1

Let $A^3$ be a matrix who has a Jordan Normal Form of the following: $$\left(\begin{matrix}8 & 1 & 0\\0 & 8 & 0\\0 & 0 & 1 \end{matrix}\right)$$Calculating the characteristic polynomial of this matrix:$P_x=(\lambda-1)(\lambda-8)^2$

## Why is the set of all integers not open February 13    1

A point $p$ is an interior point of a set $E$ if there exists a neighborhood $N_r(p)$ such that $N_r(p)\subseteq E$, and a set is open if all of its points are interior points. Now my question is that since $r\in \mathbb{R^+}$ then why can't we take

## Finding the multiplicative inverses of fields February 13

Lets say I have the field $F_{11}$ Why does 2 have the multiplicative inverse 6?In some of the examples I have lets say we are looking $F_5$ why are values up to only 2 considered? So in the example of $F_5$, values $1$, $2$, then $-2$, $-1$ are cons

## Stability criterion for eigenvalues of an AR(2) process. February 13

This is pretty much a question on linear algebra stemming from time series analysis.Essentially I want to find a stationarity criterion for an AR(2) process. It is easy to reduce this to the convergence of the matrix powers (by transformation to a VA

## the set of integers is not open or is open February 13

Baby rudin give the example of the set of all integers being not open if it is a subset of R^2 (I forgot how to code the symbols on this site)If we consider the set of integers in R, is this set also not open? I can find a neighborhood which will con

## Finding the multiplicative inverses of the field $F_11$ February 13

Lets say I have the field $F_11$ Why does 2 have the multiplicative inverse 6?In some of the examples I have lets say we are looking $F_5$ why are values up to only 2 considered? So in the example of $F_5$, values $1$, $2$, then $-2$, $-1$ are consid

## Solve $KA-BK=0$, for a $1 \times n$ dimension row vector $K$, where $A$ is known $n \times n$ matrix and $b$ is known scalar February 13

The above equation with mentioned dimensions is to be solved. How can I find the value (or approximate value) of row vector $K$. Please help.

## Pointwise or Uniform convergence February 13

Consider the functions f_n :[-1,1] to the reals defined by f_n(x):= x/(x^2 + 1/n)^1/2 and determine whether the convergence is uniform or pointwise. I can see that this will converge to x/|x|, however, I can't prove that this is the case, or that thi

## Use of Legendre's equation. February 13    2

For some weeks have been studying Legendre polynomial as a solution to this equation. $$(1-x^2)\frac{d^2}{dx^2}f(x)-2x\frac{d}{dx}f(x)+n(n+1)f(x)=0.$$I've found them very interesting to learn from purely mathematical perspective but I haven't come a

## Orthogonal trajectorieswhy is it neccessary to isolate the parameter February 13

For orthogonal trajectory, I realized that I need to express the parameter of the given family of curves in terms of x and y, in order to get the right answer. e.g. y = kx, k is the parameter I was talking about in the preceding sentence above.1) If

## Find the coordinate of a tetrahedron knowing all side lengths February 13

I know the coordinates of three points {x1, y1, z1}, {x2, y2, z2} and {x3, y3, z3}.Now I need to localize a fourth point {x4, y4, z4}. I therefore get all the distances d41, d42, d43. Off course the distances d31, d21 and d32 are known(or easily calc

## Metric space $(X,d)$ with distance $D(x,S)=\inf\{d(x,y)y\in S\}$ for $S$ subset of $X$ February 13

Let $(X,d)$ be a metric space with $S$ a non-empty subset of $X$. For $x\in X$ we define the distance $D$ between $x$ and $S$ as $D(x,S)=\inf\{d(x,y)|y\in S\}$.1 How do I prove that $\overline{S}$ is the set of all $x\in X$ such that $D(x,S)=0$?2 How

You Might Also Like
• $\log_3x^3 + {3\over \log_3x} =4$Ok, the way the computer has put it makes it look weird.But it is :log to b ...
• Let $(X,\Omega,\mu)$ be a measure space. If $1 < p < \infty,$ $f\in L_p$ and $\varepsilon >0$ then ...
• I am working with a matrix A relatively large (200k x 200k), and I want to compute the eigenvectors of the L ...
• $\bf{(1)}::$ Let $\bf{X}$ be the non-empty set and $\bf{P(X)}$ be the set of all subsets of $\bf{X}\;,$ for ...
• What is the definition of rate of convergence of a sequence of random variables? i.e. what does it mean that ...
• What I'm looking for is the trigonomery equations to calculate the x, y and z components of a 3D vector. Wha ...
• Consider the Lattice $\mathbb{Z}^2$ and an in ...
• A square matrix A is called nilpotent is $A^k=0$ for some positive integer k.Let A and B be square matrices ...
• Let $D$ be an $m$-dimensional distribution on an $n$-dimensional manifold $M$. Let $U\subset M$ be an arbitr ...
• I've seen some proofs but I don't really get it..I find it hard to understand..I've done this so far:\begin{ ...