Related papers: Well-poised basic q-Taylor expansions with complem…
In the paper, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the…
In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of $\ell^p$ regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that…
The classical lemma of Borel reads: any power series with real coefficients is the Taylor series of a smooth function. Algebraically this means the surjectivity of the completion map at a point, $C^\infty(\Bbb{R}^n) \twoheadrightarrow…
We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by…
Products, multiplicative Chern characters, and finite coefficients, are unarguably among the most important tools in algebraic K-theory. Although they admit numerous different constructions, they are not yet fully understood at the…
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…
In a recent paper Ismail, Masson, and Suslov have established a continuous orthogonality relation and some other properties of a $_2\varphi_1$-Bessel function on a $q$-quadratic grid. Dick Askey suggested that the ``Bessel-type…
In this paper, we introduce two focussed sequent calculi, LKp(T) and LK+(T), that are based on Miller-Liang's LKF system for polarised classical logic. The novelty is that those sequent calculi integrate the possibility to call a decision…
The weight systems of finite-dimensional representations of complex, simple Lie algebras exhibit patterns beyond Weyl-group symmetry. These patterns occur because weight systems can be decomposed into lattice polytopes in a natural way.…
We develop a theory of $p$-adic continued fractions for a quaternion algebra $B$ over $\mathbb Q$ ramified at a rational prime $p$. Many properties holding in the commutative case can be proven also in this setting. In particular, we focus…
We derive and study expansions of and over the Askey--Wilson polynomials. We study these expansions and examine some limits to the continuous dual $q$-Hahn, Al-Salam--Chihara, continuous big $q$-Hermite and continuous $q$-Hermite…
We investigate exponential sums over singular binary quartic forms, proving an explicit formula for the finite field Fourier transform of this set. Our formula shares much in common with analogous formulas proved previously for other vector…
We prove that the dual fine Selmer group of an abelian variety over the unramified $\mathbb{Z}_{p}$-extension of a function field is finitely generated over $\mathbb{Z}_{p}$. This is a function field version of a conjecture of…
Building on work of J. Robinson and A. Shlapentokh, we develop a general framework to obtain definability and decidability results of large classes of infinite algebraic extensions of $\mathbb{F}_p(t)$. As an application, we show that for…
Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 10-phi-9 transformation. From this result, we deduce new multivariable terminating 10-phi-9 transformations, 8-phi-7…
The classical summation and transformation theorems for very well-poised hypergeometric functions, namely, $_{5}F_4(1)$ summation, Dougall's $_{7}F_6(1)$ summation, Whipple's $_{7}F_6(1)$ to $_{4}F_3(1)$ transformation and Bailey's…
For a finite field $\mathbb{F}_q$ of characteristic $p\geq 5$ and $K=\mathbb{F}_q(t)$, we consider the family of elliptic curves $E_d$ over $K$ given by $y^2+xy - t^dy=x^3$ for all integers $d$ coprime to $q$. We provide an explicit…
We show how to develop an expansion of nearly oblate systems in terms of a set of potential-density pairs. A harmonic (multipole) structure is imposed on the potential set at infinity, and the density can be made everywhere regular. We…
We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson $q$-exponential of the sum of two non-$q$-commuting operators as an (in general) infinite product of $q$-exponential operators involving repeated…
We prove a formula for the Taylor series coefficients of a zero of the sum of a complex-exponent polynomial and a base function which is a general holomorphic function with a simple zero. Such a Taylor series is more general than a Puiseux…