相关论文: The Conway function of a splice

We obtain bounds on hyperbolic volume for periodic links and Conway sums of alternating tangles. For links that are Conway sums we also bound the hyperbolic volume in terms of the coefficients of the Jones polynomial.

The multivariable Conway function is generalized to oriented framed trivalent graphs equipped with additional structure (coloring). This is done via refinements of Reshetikhin-Turaev functors based on irreducible representations of…

In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour…

Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…

We derive simple formulas connecting the generalized Wigner functions for $s$-ordering with the density matrix, and vice-versa. These formulas proved very useful for quantum mechanical applications, as, for example, for connecting master…

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are ({\alpha},m)-convex.

This note investigates the relation between squeezing function and its generalizations. Using the relation obtained, we present an alternate method to find expression of generalized squeezing function of unit ball corresponding to the…

We analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.

We establish Conway's thrackle conjecture in the case of spherical thrackles; that is, for drawings on the unit sphere where the edges are arcs of great circles.

In this paper, we introduce the Levy density function as the limit of a generalized Mittag-Leffler density function. The fractional integral equation for the generalized Mittag-Leffler density function is also given. And the role of the…

Given a finite group $G$ and a prime $p$, we establish the sieve formula, which is a congruence containing as summands numbers of chains of $p$-subgroups of $G$ of certain orders. This generalises the Theorem of Sylow-Frobenius, using…

In this paper, we establish a connection between Dunkl analysis and slice analysis in the setting of Clifford algebras. Specifically, we show that a Clifford algebra-valued function is slice if, and only if, it belongs to the kernel of the…

We show how Conway's multivariable potential function can be constructed using braids and the reduced Gassner representation. The resulting formula is a multivariable generalization of a construction, due to Kassel-Turaev, of the…

We introduce generalized Schur functions and generalized positive functions in setting of slice hyperholomorphic functions and study their realizations in terms of associated reproducing kernel Pontryagin spaces

If a knot K bounds a genus one Seifert surface F in the 3-sphere and F contains an essential simple closed curve alpha that has induced framing 0 and is smoothly slice, then K is smoothly slice. Conjecturally, the converse holds. It is…

This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises…

This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results…

All squigonometric functions admit derivatives that can be expressed as polynomials of the squine and cosquine. We introduce a general framework that allows us to determine these polynomials recursively. We also provide an explicit formula…

In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative $^*$-algebra $A$ over $\mathbb{R}$. These recently introduced function theories generalize to higher dimensions…

The aim of the present paper is to give extensions of the cosine-sine functional equation.