Related papers: Frobenius Splittings
We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject. Among the applications, we use new methods to compute…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
We show that for a Frobenius split variety, there are only finitely many closed subvarieties which are compatibly-split.
Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. These carry the structure of a Frobenius algebra on each tangent space, but…
We provide an introduction to mathematical theory of scattering resonances and survey some recent results.
We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The…
We develop a method for calculating Riemann sums using Fourier analysis.
In this short paper we review and extract some features of the Fredholm Alternative problem .
In an earlier paper we introduced the notion of 'bifurcating continued fractions' in a heuristic manner. In this paper a formal theory is developed for the 'bifurcating continued fractions'.
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…
We generalize the work of Erdos-Pomerance and Fiori-Shallue on counting Frobenius pseudoprimes from the cases of degree one and two respectively to arbitrary degree. More specifically we provide formulas for counting the number of false…
We describe a method to compute Hurwitz-Hodge integrals.
We classify Frobenius forms, a special class of homogeneous polynomials in characteristic $p>0$, in up to five variables over an algebraically closed field. We also point out some of the similarities with quadratic forms.
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how…
In this article, a sequel to "Global Frobenius Liftability I" (math:1708:03777v2), we continue the development of a comprehensive theory of Frobenius liftings modulo $p^2$. We study compatibility of divisors and closed subschemes with…
We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most…
We present a brief overview of fractional analytic QCD, basically following the results recently obtained in Refs. [1,2].
Fractional $q$-extensions of some classical $q$-orthogonal polynomials are introduced and some of the main properties of the new defined functions are given. Next, a fractional $q$-difference equation of Gauss type is introduced and solved…
This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper…