相关论文: Selection rules of canonical differential equation…

This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate…

We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix…

This work introduces a canonical structure for a broad class of unconstrained first-order algorithms that admit a Lur'e representation, including systems with relative degree greater than one, e.g., systems with delayed gradient feedback.…

The task of this survey is to present various results on intersection patterns of convex sets. One of main tools for studying intersection patterns is a point of view via simplicial complexes. We recall the definitions of so called…

Differential equations are a powerful tool for evaluating Feynman integrals. Their solution is straightforward if a transformation to a canonical form is found. In this paper, we present an algorithm for finding such a transformation. This…

We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…

The properties of the intersection algebra of two principal monomial ideals in a polynomial ring are investigated in detail. Results are obtained regarding the Hilbert series and the canonical ideal of the intersection algebra using methods…

In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into canonical form, their solution in terms of special functions is straightforward. Recently,…

A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the…

Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficients. First, we show that matrices constructed in this way…

We introduce the notion of residual intersections of modules and prove their existence. We show that projective dimension one modules have Cohen-Macaulay residual intersections, namely they satisfy the relevant Artin-Nagata property. We…

We compute log canonical thresholds of reduced plane curves of degree $d$ at points of multiplicity $d-1$. As a consequence, we describe all possible values of log canonical threshold that are less than $2/(d-1)$ for reduced plane curves of…

We propose '$\mathrm{d} \mathcal{E}$-forms' as fundamental building blocks of canonical integrands for elliptic Feynman integrals, which lead to Kronecker-Eisenstein $\omega$-form symbol letters. Built upon pure elliptic multiple…

We study the axiomatisability of the iteration-free fragment of Propositional Dynamic Logic with Intersection and Tests. The combination of program composition, intersection and tests makes its proof-theory rather difficult. We develop a…

The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…

We consider the canonical fundamental systems of solutions of linear homogeneous Caputo fractional differential equations with continuous variable coefficients. Here we gained a series-representation of the canonical fundamental system by…

In this paper, a generic intersection theorem in projective differential algebraic geometry is presented. Precisely, the intersection of an irreducible projective differential variety of dimension d>0 and order h with a generic projective…

The purpose of this paper is to point out a relation between the canonical sheaf and the intersection complex of a singular algebraic variety. We focus on the hypersurface case. Let $M$ be a complex manifold, $X\subset M$ a singular…

We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equations include classical path-dependent SDEs containing running…

Optimal designs are required to make efficient statistical experiments. D-optimal designs for some models are calculated by using canonical moments. On the other hand, integrable systems are dynamical systems whose solutions can be written…