Related papers: Frobenius Splittings

This is a survey of Frobenius splitting techniques in commutative algebra, based on the first author's lectures at the introductory workshop for the special year in commutative algebra at MSRI in fall 2012.

Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner…

We introduce the concept of protometric and present some properties of protometrics.

We compute the Frobenius number for sequences of triangular and tetrahedral numbers. In addition, we study some properties of the numerical semigroups associated to those sequences.

We give a new, shorter computation of Frobenius push-forwards of line bundles on toric varieties.

In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations…

In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…

Two classical rings of invariants are shown to be Frobenius split: for the special linear group acting on the direct sum of several copies of the defining representation and several copies of the dual of the defining representation; and for…

We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers.

We show that, under mild conditions, the (normalized) Frobenius splitting numbers of a local ring of prime characteristic are lower semicontinuous.

Integration by parts is used to reduce scalar Feynman integrals to master integrals.

This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future…

In the present paper, we deal with Fourier-transformation of Frobenius-Euler polynomials. We shall give its applications by using infinite series. Our applications possess interesting properties which we state in this paper.

This is a survey for the 2015 AMS Summer Institute on Algebraic Geometry about the Frobenius type techniques recently used extensively in positive characteristic algebraic geometry. We first explain the basic ideas through simple versions…

A Compact Introduction to Fractional Calculus is presented including basic definitions, fractional differential equations and special functions.

In this paper we compute the Frobenius number of certain {\em Fibonacci numerical semigroups}, that is, numerical semigroups generated by a set of Fibonacci numbers, in terms of Fibonacci numbers.

We present here the concept of Dominated Splitting and give an account of some important results on its dynamics.

A formulation of the Maxwell equations in terms of the split octonions is presented.

We describe the construction of the slice fibration of a given one.

We study the fBm by use of convolution of the standard white noise with a certain distribution. This brings some simplifications and new results.