相关论文: A Combinatorial Method for Computing Steenrod Squa…

The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some…

In this paper we present a comprehensive study on the multi-objective optimization of two-dimensional porous phononic crystals (PnCs) in both square and triangular lattices with the reduced topology symmetry of the unit-cell. The fast…

A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…

A central problem of algebraic topology is to understand the homotopy groups $\pi_d(X)$ of a topological space $X$. For the computational version of the problem, it is well known that there is no algorithm to decide whether the fundamental…

The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing…

A panel structure on a topological space is just a locally finite family of closed subspaces. A space together with a panel structure is called a space with faces. In this paper, we introduce a notion of polyhedral product over a space with…

This article gives an account on various aspects of stochastic calculus in the plane. Specifically, our aim is 3-fold: (i) Derive a pathwise change of variable formula for a path indexed by a square, satisfying some H\"older regularity…

We determine the Hochschild cohomology algebras of the square-free monomial complete intersections. In particular, we provide a formula for the cup product which gives the cohomology module an algebra structure and then we describe this…

Let $G$ be a simple and simply connected algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p>0$. We establish an isomorphism of $G$-modules between a direct sum of modules $\text{St} \otimes \text{St}$ and a…

The purpose of this paper is to give an explicit description of the trivial and alternating components of the irreducible representation decomposition of the bigraded module obtained as the tensor square of the coinvariant space for…

This paper discusses the development of synthetic cohomology in Homotopy Type Theory (HoTT), as well as its computer formalisation. The objectives of this paper are (1) to generalise previous work on integral cohomology in HoTT by the…

In 1999, Reg Wood conjectured that the quotient of Q[x_1,...,x_n] by the action of the rational Steenrod algebra is a graded regular representation of the symmetric group S_n. As pointed out by Reg Wood, the analog of this statement is a…

Nanostructured surfaces usually exhibit complicated morphologies that cannot be described in terms of Euclidean geometry. Simultaneously, they do not constitute fully random noise fields to be characterized by simple stochastics and…

We find conditions such that cup products induce isomorphisms in low degrees for extensions between stable polynomial representations of the general linear group. We apply this result to prove generalizations and variants of the Steinberg…

In this paper we study "discrete polynomial blending," a term used to define a certain discretized version of curve blending whereby one approximates from the "sum of tensor product polynomial spaces" over certain grids. Our strategy is to…

Using the recent work of Frankland and Spitzweck, we define Steenrod operations $P^{n}$ on the mod $p$ motivic cohomology of smooth varieties defined over a base field of characteristic $p$. We show that $P^{n}$ is the $p$th power on…

Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multi-field data, topological analysis requires simultaneous advances both mathematically…

We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…

For a given twisted cartesian products of simplicial sets, we construct the corresponding twisted tensor product in the sense of Brown, with an explicit twisting function whose formula is simple without using inductions. This is done by…

Macdonald polynomials are orthogonal polynomials associated to root systems, and in the type A case, the symmetric kind is a common generalization of Schur functions, Macdonald spherical functions, and Jack polynomials. We use the…