The nonlinear pde $$ \partial_t^2\phi-\partial_x^2\phi+\lambda\phi^3=0 $$ has the exact solution $$ \phi(x,t)=\mu\left(\frac{2}{\lambda}\right)^\frac{1}{4}{\rm sn}(p_0t-p\cdo …

How can I transform the following proposition that is gotten in $real$ space into the corresponding one used in the $complex$ space? Proposition: Let $A\in R^{n\times n}$ be a ma …

Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville : “The big experts in the field had already tried to make this approach …

Let $P,Q$ be $n$ by $n$ invertible matrices. Suppose further that $P$ and $Q$ satisfies the following equation : $$(P^{-1})^T \circ P = (Q^{-1})^T \circ Q$$ where $\circ$ denotes …

I have tried to understand and program CGT algorithms though I am a beginner still. But I never get to hear Computational Ring Theory. Even GAP largely supports Groups Theory. Is t …

Given that we can never proof the consistency of a theory for the foundations of mathematics in a weaker system, one could seriously doubt whether any of the commonly used foundati …

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Wikipedia is a widely used resource for mathematics. For example, there are hundreds of mathematics articles that average over 1000 page views per day. Here is a list of the 500 mo …

SO Prime III. ABC Conjecture PROOF http://www.one-zero.eu/resources/Z-ABC.pdf

I am unsure which is the right spelling (if there even is a ‘right’ spelling), but maybe native speakers can enlighten me: When should I use fixed point fixed-point fixedpoint …

The following problem arises in the analysis of Bloom filters. Consider $m$ bins and $N=nk$ balls placed uniformly at random into the bins. A query chooses $k$ bins uniformly at …

In Gromov's famous book ,it says "simplical volume of every oriented surface of genus $ \ge 1$ satisfies${\left\| {\left[ S \right]} \right\|_\Delta } = 4g - 4 = - 2\chi \left( S …

Let $X$ be a smooth projective algebraic variety over a field of characteristic zero. Let $U$ be the complement in $X$ of a simple normal crossings divisor $D$. For each degree $k$ …

It is commonplace to consider applications of mathematics to other fields, especially the exact sciences. But what I would like to know about is the converse topic, namely: Wha …

Hi. Consider a a sequence of non-negative functions $(f_n)_n$, bounded in $L^1([-1,1])$ and weakly$-\star$ converging in $\mathscr{M}^1([-1,1])$ to some $f\in L^1([-1,1])$. What I …