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 …

Ground field $\Bbb{C}$. Algebraic category. Elliptic surfaces are those surfaces endowed with a morphism onto some smooth curve, with generic fiber an elliptic curve. Suppose $E$ …

I have a convex optimization problem of finding a function Q(x,y) as below: Minimize $\int{k(x,y)Q(x,y)dxdy}$ subject to a list of constraints which are not relevant to the questi …

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 …

I have four solutions which are termed: A1, A2, A3, A4. These are actually the results of a searching algorithm. I know that A1 is the best solution, A2 is next to A1, A3 is next t …

Let $R$ be a ring, $\Sigma$ be a multiplicatively closed subset of $R$. $M$ is an $R$-module. Denote the injective hull of $M$ by $E(M)$. $M$ is $\Sigma$-torsion if for any $m$ …

A knot in S^3 is small if its complement does not contain a closed incompressible surface. Is it a generic property for knots, meaning that among all knots with less than $n$ cross …

In algebraic geometry weighted projective spaces (WPS) are very popular ! In algebraic topology , WLS have been (cohomologically at least) studied. Roughly speaking , a WPS is a …

PART I (Initial version) Let   $P$   be the set of all primes   $2\ 3\ \ldots$.   Let $$P_d\ \ :=\ \ \{\ p\in P\ :\ \exists_{q\in P}\ \ 0 < |p-q|\le d\ \}$ …

I am interested in examples of hypersurfaces $X, Y$ defined by polynomials $F(x_1, \cdots, x_n), G(x_1, \cdots, x_n)$ respectively, so that the intersection $X \cap Y$ has a singul …

We know if x/y =y/z and if the straight line length for x and y are given, then how many different geometric construction methods are there to draw the straight line equals to z …

Suppose we are given a commutative ring R with unit-element. Now we have a composition of R as the direct product of two rings $R\cong R_1\times R_2$. It is now straight forward, …

Let G={(a,b) in ZxZ|a= b mod10}. Proof that G is a Finitely-generated abelian group. Find a basis of G.

$M$ is a finitely generated $A$-module of dimension $d$ such that $G(M)$ is eqidimensional and $M$ does not have any embedded prime. Given $x\in I$ where $I$ is an ideal of $A$ an …

Hello! I have a question about the relationship between numerical integration and the solution of ordinary differential equations (ODE). Suppose I want to evaluate the integral $I …