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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue

Vol 16 - Issue 2 (March 2025)

Advances in Pure and Applied Mathematics


List of Articles

On the index of regularity of additive decompositions of forms
Edoardo Ballico

Let f be a degree d form in n+1 variables x0,,xn. Any additive decomposition of f is associated to a finite set A\subset ℙ^n with \#A the number of non-proportional addenda. We study the index of regularity \rho(A) of A, i.e. the first integer t such that h^1(\mathcal{I}_A(t)) = 0, of the finite subset A\subset ℙ^n associated to the additive decompositions of degree d forms in n+1 variables. Obviously \rho(A)\le d. We prove that \rho(A)\ge d-k if A spans ℙ^n and k is the maximal integer such that x_0^k divides at least one monomial of f. If f essentially depends on less variables, but A spans ℙ^n, then \rho(A)=d. We give examples (but with \#A bigger that the rank of f) in which we have \rho(A)=d.


Metrical Weyl almost automorphy and applications
S. Abbas, M. Kostić

In this paper, we reconsider and slightly generalize various classes of Weyl almost automorphic functions ([29], [33]). More precisely, we consider here various classes of metrically Weyl almost automorphic functions of the form F : {\mathbb R}^{n} \times X \rightarrow Y and metrically Weyl almost automorphic sequences of the form F : {\mathbb Z}^{n} \times X \rightarrow Y, where X and Y are complex Banach spaces. The main structural characterizations for the introduced classes of metrically Weyl almost automorphic functions and sequences are established. In addition to the above, we provide several illustrative examples, useful remarks and applications of the theoretical results.


Classifying symplectic metric Jordan superalgebras
Ahmad Alghamdi, Amir Baklouti, Warda Bensalah

This paper complements the description of finite-dimensional Jordan symplectic metric superalgebras on algebraically closed fields of characteristic zero. We discuss the graduation of the metric and the symplectic structures and use a new type of generalized double extension by two-dimensional Jordan superalgebras.