Related papers: Constructing commutative semifields of square orde…
The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.
A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…
New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…
We study almost symmetric semigroups generated by odd integers. If the embedding dimension is four, we characterize when a symmetric semigroup that is not complete intersection or a pseudo-symmetric semigroup is generated by odd integers.…
We construct and describe the basic properties of a family of semifields in characteristic $2.$ The construction relies on the properties of projective polynomials over finite fields. We start by associating non-associative products to each…
We extend the construction of bad fields of characteristic zero to the case of arbitrary prescribed divisible green torsion.
Almost perfect nonlinear (APN) functions on finite fields of characteristic two have been studied by many researchers. Such functions have useful properties and applications in cryptography, finite geometries and so on. However APN…
This is a survey article on the recent developments of semipositivity, injectivity, and vanishing theorems for higher-dimensional complex projective varieties.
Some binary quadratic operads are endowed with anticyclic structures and their characteristic functions as anticyclic operads are determined, or conjectured in one case.
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
In this note, we extend the quasi-projective dimension of finite (that is, finitely generated) modules to homologically finite complexes, and we investigate some of homological properties of this dimension.
Generating functions for plane overpartitions are obtained using various methods such as nonintersecting paths, RSK type algorithms and symmetric functions. We extend some of the generating functions to cylindric partitions. Also, we show…
This paper considers the construction of isodual quasi-cyclic codes. First we prove that two quasi-cyclic codes are permutation equivalent if and only if their constituent codes are equivalent. This gives conditions on the existence of…
In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials.…
Planar functions, introduced by Dembowski and Ostrom, are functions from a finite field to itself that give rise to finite projective planes. They exist, however, only for finite fields of odd characteristics. They have attracted much…
A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of…
Many examples of rank two bundles on ${\bf P}^4$ are constructed in positive characteristic. Construction depends on constructing certain special bundles on ${\bf P}^3$ which is shown to be equivalent to constructing bundles on ${\bf P}^4$…
An involution over finite fields is a permutation polynomial whose inverse is itself. Owing to this property, involutions over finite fields have been widely used in applications such as cryptography and coding theory. As far as we know,…
We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their…
Twistor methods provide a powerful tool in the study of harmonic maps and harmonic morphisms. Indeed, their use has enabled us to produce a variety of examples of harmonic morphisms defined on 4-dimensional manifolds, and a complete…