Related papers: Quantifying singularities with differential operat…

In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the…

For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds…

This is a survey article on $F$-singularities and their applications.

A non-negative integer invariant, estimating from below the number of geometrically different critical points of a smooth function $f$ defined in the 2-disk, $f:\mathbb{B}^{2}\rightarrow\mathbb{R}$, is considered. (We denote it by…

In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…

The polynomial-time computability of the permanent over fields of characteristic 3 for k-semi-unitary matrices (i.e. square matrices such that the differences of their Gram matrices and the corresponding identity matrices are of rank k) in…

We compute some numerical invariants of local cohomology of the ring of invariants by a finite group, mainly in the modular case. Also, we present some applications. In particular, we study Cohen-Macaulay property of modular invariants from…

Let $X$ be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) $f$. Integral expressions for the c.f.\ of the r.v.'s $\max(0,X)$ in terms of $f$ are given, as well as other related results. Applications…

If two G-manifolds are G-cobordant then characteristic numbers corresponding to the fixed point sets (submanifolds) of subgroups of G and to normal bundles to these sets coincide. We construct two analogues of these characteristic numbers…

For any fixed globally F-regular projective variety X over an algebraically closed field of positive characteristic, we study the F-signature of section rings of X with respect to the ample Cartier divisors on X. In particular, we define an…

We establish a criterion for the strong $F$-regularity of a (non-Gorenstein) Cohen-Macaulay reduced complete local ring of dimension at least $2$, containing a perfect field of prime characteristic $p$. We also describe an explicit…

We introduce the notion of semi-characteristic polynomial for a semi-linear map of a finite- dimensional vector space over a field of characteristic p. This polynomial has some properties in common with the classical characteristic…

Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…

The signed permutation modules are a simultaneous generalization of the ordinary permutation modules and the twisted permutation modules of the symmetric group. In a recent paper Dave Benson and Peter Symonds defined a new invariant…

Hironaka's characteristic polyhedron is an important combinatorial object reflecting the local nature of a singularity. We prove that it can be determined without passing to the completion if the local ring is a G-ring and if additionally…

Corrected versions of the numerically invariant expressions for the affine and Euclidean signature of a planar curve proposed by E.Calabi et. al are presented. The new formulas are valid for fine but otherwise arbitrary partitions of the…

Let $p$ be a prime number. We consider diagonal $p$-permutation functors over a (commutative, unital) ring $\mathsf{R}$ in which all prime numbers different from $p$ are invertible. We first determine the finite groups $G$ for which the…

It is shown that 'non-quantum systems', with anomalous statistical properties, would carry a distinctive experimental signature. Such systems can exist in deterministic hidden-variables theories (such as the pilot-wave theory of de Broglie…

Let G < SL(V) be a finite group, V is finite dimensional over a field F, p=char F and S(V) is the symmetric algebra of V. We determine when the subring of G-invariants S(V)^G is a polynomial ring. As a consequence, we classify, if F is…

We know that for a finite field $F$, every function on $F$ can be given by a polynomial with coefficients in $F$. What about the converse? i.e. if $R$ is a ring (not necessarily commutative or with unity) such that every function on $R$ can…