All Questions

1,100,467 questions
5 views

Linear Combinations of Solutions to a Search Problem

Let $P_1=(X_1,U_1)$ be a search problem with the domain of search $$X_1=\{x \in Z_2^n | wt(x)\leq k\}$$ and the set of admissable tests be $U=Z_2^n$ (where $wt(x)$ is the hamming weight of $x$). ...
3 views

Why $\dim(\ker T_z f)=\dim(T_z(f^{-1}(c)))$?

I am studying submanifolds and I have some problems with the proof of a claim about Rank Theorem. Rank Theorem: Let $f: U \subseteq \mathbb{R}^n \rightarrow \mathbb{R}^m$ be a smooth map and each ...
6 views

4 views

13 views

Nature of improper integral following values of $\alpha$

It is asked to study the nature of the improper integral $$\displaystyle\int_0^{+\infty} \dfrac{\ln(\arctan(x))}{x^\alpha} dx$$ At $+\infty$, it seems it converges for $\alpha > 1$ since the ...
22 views

If f (n) and g(n) are injective then show if h(n) = f (n) + g(n) is injective?

Let $f,g:\mathbb Z\to \mathbb Z$. If $f$(n) and $g$(n) are injective then show if $h$(n) = $f$(n) + $g$(n) is injective? Prove or disprove. I think it's true, but I'm having a hard time ...
15 views

Different topologies with the same continuous real maps

For any topological space $(X,\tau)$, denote $C(X,\tau)$ the algebra of all continuous real-valued functions. Is the following true or false : For any set $X$, and topologies $\tau$, $\tau'$ on $X$ ...
24 views

Proper dense open subset of X

$X$ be a topological space and $U$ be a proper dense open subset of $X$. Then pick the correct statement from the following: If $X$ is connected then $U$ is connected. If $X$ is compact then $U$ is ...
12 views

10 views

Total differential to calculate approximately the largest error

I have the following problem: Use the total differential to calculate approximately the largest error at determine the area of a triangle rectangle (right triangle) from the lengths of the cathetus if ...
11 views

Boundary of a hollowed out sphere

If I let M be a manifold such that M is a hollowed out sphere in $\mathbb{R}^3 - \{0\}$, then what is the boundary of $M$? Specifically if I'm integrating a form over M, and I want to use Stokes' ...
12 views

Gaining intuition for Complex Integration by Parts

I'm trying to gain some intuition for integration by parts in the complex case. Suppose we integrate on $[0,1]$ for $f,g : [0,1] \rightarrow \mathbb{C}$ that are differentiable at all points on the ...
48 views

Find all integers a and b such that $2a + 2b = ab$ .

Find all integers $a$ and $b$ such that $2a + 2b = ab$.
9 views

Recursive functions and recursive sets

Given the definition of recursive function as below, I need to prove that: i)Prove that a function N → N is recursive if and only if its graph is a recursive subset of $N^2$. (ii) Now we ask about ...
7 views

7 views

Poisson process example

My question is about an example involving Poisson process inter arrival times. First some background: A Poisson process refers to the number of arrivals at time $t$ denoted by $N_t$. The $n^{th}$ ...
The cylinder has the equation $y^2 + z^2 = 25$ The point is $(2,9,12)$ How do I find the coordinates of the closest point on the cylinder to the point $(2,9,12)$ using lagrange multipliers?