Related papers: Octal Bent Generalized Boolean Functions
In these notes we study several categorical generalizations of the M\"obius function and discuss the relations between the various approaches. We emphasize the topological and geometric meaning of these constructions.
We construct a family of BC_n-symmetric biorthogonal abelian functions generalizing Koornwinder's orthogonal polynomials, and prove a number of their properties, most notably analogues of Macdonald's conjectures. The construction is based…
We introduce a new type of multiple zeta functions, which we call bilateral zeta functions, analogous to the Barnes zeta functions. The bilateral zeta function is a periodic function and shares certain basic properties of Barnes zeta…
In this article a procedure to construct bent functions from $\F_{p^n}$ to $\F_p$ by merging plateaued functions which are bent on ($n-2$)-dimensional subspaces of $\F_{p^n}$ is presented. Taking advantage of such classes of plateaued…
In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
In this paper we define generalizations of boson normal ordering. These are based on the number of contractions whose vertices are next to each other in the linear representation of the boson operator function. Our main motivation is to…
We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized…
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…
The notion of o-polynomial comes from finite projective geometry. In 2011 and later, it has been shown that those objects play an important role in symmetric cryptography and coding theory to design bent Boolean functions, bent vectorial…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boolean function, depending on internal structures, with…
Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a…
We study the twisted q-zeta functions and twisted q-Bernoulli polynomials
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…
We prove three sharp estimates for the generalized Zalcman coefficient functional: one for the Hurwitz class, another for the Noshiro-Warschawski class, and yet another for the functions in the closed convex hull of convex univalent…
Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group $(\gf(2^{2m}), +)$, have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective…
We consider and provide an accurate study for the fractional Zernike functions on the punctured unit disc, generalizing the classical Zernike polynomials and their associated $\beta$-restricted Zernike functions. Mainly, we give the…