Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 32

Nonlinear diffusion (heat) equation

Good day to all!Let me consider equation$$frac{partial u}{partial t}=frac{partial }{partial x}left(f(u)frac{partial u}{partial x}right)+g(u)$$where $tin(0,+infty),xin [a,b]$ and $f(u),g(u)$ are smooth bounded functions. In addition,...

Asked on 12/20/2021 by Vertum

0 answer

What is the difference between a semiconnected graph and a weakly connected graph?

These are the definitions I have found: Semiconnected: if, and only if, for any pair of nodes, either one is reachable from the other, or they are mutually reachable. Weakly...

Asked on 12/20/2021 by Maximilian Levine

2 answer

For $pin (0, 1)$ and $nrightarrow infty$, how do I evaluate a general term in the binomial expansion of $(p+1-p)^n$?

This may be a slightly trivial question but I got stuck on it for a while and would be grateful if someone can point out the catch to me. The...

Asked on 12/20/2021

2 answer

If $|{z}|=maxbig{|{z}+2|,|{z}-2|big}$, then which is true: $|zpm bar{z}|=2$ or $|zpm bar{z}|=1/2$?

If $|{z}|=maxbig{|{z}+2|,|{z}-2|big}$, then (a) $|{z}-bar{z}|=1 / 2$. (b) $|{z}+overline{{z}}|={2}$. (c) $|{z}+overline{{z}}|=1 / 2$. $({d})|{z}-overline{{z}}|={2}$.My approach $|z|=|z+2|$$Rightarrow {zoverline{z}}=({z}+2)(overline{{z}}+2)$ $Rightarrow {z}+{overline{z}}=-2 Rightarrow|{z}+{overline{z}}|=2$...

Asked on 12/18/2021

2 answer

Is there an explicit solution to $a^x+b^x=1$?

Is there an explicit solution to $a^x+b^x=1$? Where $a, b in [0, 1]$ and $a+b le 1$. I've been playing around with this equation, but I...

Asked on 12/18/2021

4 answer

Let $Acup B$ be open, disconnected in $Bbb{R}^2$ where $A,B$ are non-empty, disjoint. Are both $A,B$ open in $Bbb{R}^2$?

I have tried it in the following manner-Assume $A$ is not open. Then $exists xin A$ such that $xnotin A^circ$ i.e. $forall epsilon>0, B(x,epsilon)notsubset A$...

Asked on 12/18/2021 by MathBS

2 answer

How do we apply the dominated convergence theorem to conclude the proposed claim?

Definition Let ${f_{lambda}:lambdainLambda}$ be a collection of functions in $L^{1}(Omega,mathcal{F},mu)$. Then for each $lambdainLambda$, by the dominated convergence theorem and the integrability of $f_{lambda}$,begin{align*}...

Asked on 12/18/2021 by user0102

2 answer

$G$ acts faithfully on $Omega$, $Aleq G$, $A$ transitive on $Omega$. Then $|C_G(A)|$ is a divisor of $|Omega|$.

$G$ acts faithfully on $Omega$, $Aleq G$, $A$ transitive on $Omega$. Then $|C_G(A)|$ is a divisor of $|Omega|$. If in addition $A$...

Asked on 12/18/2021 by stf91

1 answer

Kirby and Siebenmann obstruction for $D neq 5$?

In 1984 old Book "Instantons_And_Four-Manifolds_Instantons and 4-Manifolds" in p.1 by Dan Freed and Karen Uhlenbeck: it says "In 1968 Kirby and Siebenmann determined that for a topological manifold M of...

Asked on 12/18/2021

0 answer

CDF approximation - L'Hopital's rule

The following CDF,begin{equation}F_{y}(x) = 1- Big( frac{ (1-phi) x}{phi (k-1)}+1Big)^ {1-k} e^{- frac{x}{phi y}}end{equation} is approximated for $k rightarrow infty$ as follows...

Asked on 12/18/2021 by Mina Kay Nak

2 answer

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