Related papers: Some new classes of (almost) perfect $c$-nonlinear…
In this paper we describe a class of codes called {\it permutation codes}. This class of codes is a generalization of cyclic codes and quasi-cyclic codes. We also give some examples of optimal permutation codes over binary, ternary, and…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by…
The notion off-ideals is recent and has been studied in the papers[1] [2], [5], [10], [11], [12], [13], [14] and [15]. In this paper, we have generalized the idea off-ideals to quasi f-ideals. This extended class of ideals is much bigger…
Power functions with low $c$-differential uniformity have been widely studied not only because of their strong resistance to multiplicative differential attacks, but also low implementation cost in hardware. Furthermore, the…
We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…
This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
We prove that the commutator is stable in permutations endowed with the Hamming distance, that is, two permutations that almost commute are near two commuting permutations. Our result extends to $k$-tuples of almost commuting permutations,…
We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if $u\circ f$ is quasi-nearly subharmonic for all quasi-nearly…
We introduce an upper semi-continuous function that stratifies the highest multiplicity locus of a hypersurface in arbitrary characteristic (over a perfect field). The blow-up along the maximum stratum defined by this function leads to a…
We consider quasiconformal deformations of $\mathbb{C}\setminus\mathbb{Z}$. We give some criteria for infinitely often punctured planes to be quasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$. In particular, we characterize the…
We formulate conjectures regarding percolation on planar triangulations suggested by assuming (quasi) invariance under coarse conformal uniformization.
In this article, we obtain quasiconformal extensions of some classes of conformal maps defined either on the unit disc or on the exterior of it onto the extended complex plane. Some of these extensions have been obtained by constructing…
In this paper, we mainly investigate on the finite order transcendental entire solutions of two Fermat types delay-differential and one Fermat type c-shift equations, as these types were not considered earlier. Our results improve those of…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…
The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of centralizers each having…
In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact…