Related papers: Elementary closed-forms for non-trivial divisors

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

Let P be an elementary closed semi-algebraic set in R^d, i.e., there exist real polynomials p_1,...,p_s such that P= \{x \in R^d : p_1(x) \ge 0, >..., p_s(x) \ge 0 \}; in this case p_1,...,p_s are said to represent P. Denote by $n$ the…

Every fraction is a union of points, which are trivial regular fractions. To characterize non trivial decomposition, we derive a condition for the inclusion of a regular fraction as follows. Let $F = \sum_\alpha b_\alpha X^\alpha$ be the…

We have used recent integral representations of the derivatives of the Bessel functions with respect to the order to obtain closed-form expressions in terms of generalized hypergeometric functions and Meijer-$G$ functions. Also, we have…

I relate some coefficients encountered when computing the functional determinants on spheres to the central differentials of nothing. In doing this I use some historic works, in particular transcribing the elegant symbolic formalism of…

Let $G$ be a finite almost simple group with socle $G_0$. A (nontrivial) factorization of $G$ is an expression of the form $G=HK$, where the factors $H$ and $K$ are core-free subgroups. There is an extensive literature on factorizations of…

Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…

We develop a manifest supertwistor space formalism for three dimensional $\mathcal{N}=1, 2,3,4$ superconformal field theories. This formalism simultaneously makes manifest the supersymmetry, conformal invariance and conservation. We solve…

We give a deterministic algorithm that, given a composite number $N$ and a target order $D \ge N^{1/6}$, runs in time $D^{1/2+o(1)}$ and finds either an element $a \in \mathbb{Z}_N^*$ of multiplicative order at least $D$, or a nontrivial…

Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear…

It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of…

We introduce the family of trimmed serendipity finite element differential form spaces, defined on cubical meshes in any number of dimensions, for any polynomial degree, and for any form order. The relation between the trimmed serendipity…

The prime-counting function $\pi(x)$ which returns the number of primes smaller or equal to a given number is a topic of interest in number theory. An algorithm based on a cyclic group isomorphic to $Z/nZ$, the so-called $Z$-functions, was…

For a positive integer $n$, we denote by $F(n)$ the distance from $n$ to the nearest prime number. We prove that every sufficiently large positive integer $N$ can be represented as the sum $N=n_1+n_2$, where $$ F(n_i) \geqslant (\log…

Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of squares of rational functions modulo the vanishing ideal I(X). From the point of view of applications, such as polynomial optimization, we…

We compute the spectrum of anomalous dimensions of non-derivative composite operators with an arbitrary number of fields $n$ in the $O(N)$ vector model with cubic anisotropy at the one-loop order in the $\epsilon$-expansion. The complete…

We study the arithmetic circuit complexity of threshold secret sharing schemes by characterizing the graph-theoretic properties of arithmetic circuits that compute the shares. Using information inequalities, we prove that any unrestricted…

We present a novel method for deciding whether a given n-dimensional ellipsoid contains another one (possibly with a different center). This method consists in constructing a particular concave function and deciding whether it has any value…

A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations…

We establish a canonical normal form for the iterates of a curved differential in curved differential algebras (CDA). This operator calculus clarifies the underlying algebraic structure of CDAs and bypasses the need for complex…