Related papers: Frobenius Splittings
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
We present a summary of recent and older results on Bessel integrals and their relation with zeta numbers.
We narrow in on the number of graphical partitions for which there is no known generating function by manipulating the well known generating function for Frobenius partitions.
We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…
The aim of this paper is to represent any polynomial in terms of the degenerate Frobenius-Euler polynomials and more generally of the higher-order degenerate Frobenius-Euler polynomials. We derive explicit formulas with the help of umbral…
This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.
In this paper we explore Kruyswijk's method and show how to obtain congruences for cubic partition. That apart we also examine inequalities for a(n) and provide upper bound for it in the fashion of the classic partition function p(n).
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
We obtain some new inequalities of Chebyshev Type.
The quantum Frobenius map and it splitting are shown to descend to corresponding maps for generalized $q$-Schur algebras at a root of unity. We also define analogs of $q$-Schur algebras for any affine algebra, and prove the corresponding…
Let G be a simply connected semisimple algebraic group over an algebraically closed field k of positive characteristic. We will untwist the structure of G-modules by a newly found splitting of the Frobenius endomorphism on the algebra of…
In this work we discuss the connection between Feynman integrals and Fox functions. Illustrative examples are given.
In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author described periods and sometimes precise form of…
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
We present a procedure to enumerate the whole set of numerical semigroups with a given Frobenius number F, S(F). The methodology is based on the construction of a partition of S(F) by a congruence relation. We identify exactly one…
We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to a suitable loop algebra we recover a generalized Drinfeld-Sokolov reduction. This gives a way to construct new examples of algebraic Frobenius manifolds.
In a previous article, we obtained data on the distribution of traces of Frobenius of non-hyperelliptic genus $3$ curves over small finite fields. In the present one, we give a heuristic explanation of these data, by extrapolating from…
We introduce a collection of polynomials $F_N$, associated to each positive integer $N$, whose divisibility properties yield a reformulation of the Goldbach conjecture. While this reformulation certainly does not lead to a resolution of the…
Generalizations of Bell polynomials, Bell numbers, and Stirling numbers of the second kind have been introduced and their generating functions were evaluated.
Experimental results on hadronic structures are discussed in view of our physics understanding. Achievements and challenges are noted.