Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 65

Half-SAT/ Half-Satisfiability

Is the following satisfiability problem hard? Given a set of clauses over boolean variables in conjunctive normal form, decide whether there is an assignment of truth values to the variables...

Asked on 11/29/2021 by F.U.A.S.

1 answer

Derivative of vectorized function wrt to a Cholesky decompositiion

Let $Sigma$ be a symmetric, positive definite $ptimes p$ covariance matrix, and let $f(Sigma)$ be it's Cholesky factor. That is, $f(Sigma)$ is a lower triangular ...

Asked on 11/29/2021 by user802652

1 answer

Simplification of division of integral of standard normal distribution

I'm integrating two standard normal distributions and, for numerical problems, I would like to simplify the expresion below, since the only difference between the numerator and denominator is the upper...

Asked on 11/29/2021 by Ga13

0 answer

How does integration affect the spectrum of a vector outer product?

Start with a general eigenvalue problem. We have the following matrix: $$M(t) = a(t) a(t)^T$$Where the notation $a(t)$ denotes that the vector $a$ is a function...

Asked on 11/29/2021

1 answer

Condition number - eigenvalues

I have the following matrix begin{bmatrix} 15.52 & 0.00 & -14.52 \ -11.05 & 1.00 & 11.05 \-0.01 & 0.00 & 0.01end{bmatrix} I am supposed...

Asked on 11/29/2021 by Felipe Ca

0 answer

Is there a general form for the relation between $df(x)$ and $dx$?

Let's say that $f(x)$ is a function and $dx$ is a slight change in the input, $x$. It has been used here as standard calculus notation and...

Asked on 11/26/2021

3 answer

Solve second order DE: $sin^2 xfrac{d^2y}{dx^2} = 2y$

Solve:$$sin^2 x frac{d^2y}{dx^2} = 2y $$So what I did was separation of variables, it got me $$frac{y''} {2y}= csc^2 x$$ and integrating both sides will give...

Asked on 11/26/2021

1 answer

Spiral equation

Considering concentric arcs, of equal developed length, whose start point is aligned: ...

Asked on 11/26/2021

1 answer

If $exists$ a surjection from nonempty set $A$ onto $mathcal{P}(mathbb{Z_+})$, then $A$ is uncountable

I wanted to show this to use it in some other proofs. I believe it holds. My questions are, if this proposition is true and if the proof...

Asked on 11/26/2021

0 answer

How to show that $ int_0^1frac{sin(frac{1}{x})}{x^2}dx$ diverges?

I'm trying to prove that the following integral diverges:$$int_0^1frac{sin(frac{1}{x})}{x^2}dx$$I tried to use Dirichlet theorm but without any success. How can I show it without using...

Asked on 11/26/2021 by abuka123

1 answer

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