Institute of Mathematics AS CR, v. v. i.
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The covariety of perfect numerical semigroups with fixed Frobenius number
No full textsummary:Let be a numerical semigroup. We say that is an isolated gap of if A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by the multiplicity of a numerical semigroup . A covariety is a nonempty family \scr {C} of numerical semigroups that fulfills the following conditions: there exists the minimum of \scr {C}, the intersection of two elements of \scr {C} is again an element of \scr {C}, and S\backslash \{{\rm m}(S)\}\in \scr {C} for all S\in \scr {C} such that S\neq \min (\scr {C}). We prove that the set \scr {P}(F)=\{S\colon S is a perfect numerical semigroup with Frobenius number is a covariety. Also, we describe three algorithms which compute: the set \scr {P}(F), the maximal elements of \scr {P}(F), and the elements of \scr {P}(F) with a given genus. A -semigroup (or -semigroup) is a perfect numerical semigroup that in addition is an Arf numerical semigroup (or saturated numerical semigroup), respectively. We prove that the sets is a -numerical semigroup with Frobenius number and is a -numerical semigroup with Frobenius number are covarieties. As a consequence we present some algorithms to compute and ${\rm Psat}(F).
Left EM rings
No full textsummary:Let be the polynomial ring over a ring with unity. A polynomial is referred to as a left annihilating content polynomial (left ACP) if there exist an element and a polynomial such that and is not a right zero-divisor polynomial in . A ring is referred to as left EM if each polynomial is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions. Moreover, several extensions of EM rings are investigated, including polynomial rings, matrix rings, and Ore localizations
A note on the -property of some subgroups of finite groups
No full textsummary:Let be a subgroup of a finite group . We say that satisfies the -property in if for any chief factor of , is a -number. We obtain some criteria for the -supersolubility or -nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the -property
Highly robust training of regularizedradial basis function networks
Get PDFsummary:Radial basis function (RBF) networks represent established tools for nonlinear regression modeling with numerous applications in various fields. Because their standard training is vulnerable with respect to the presence of outliers in the data, several robust methods for RBF network training have been proposed recently. This paper is interested in robust regularized RBF networks. A robust inter-quantile version of RBF networks based on trimmed least squares is proposed here. Then, a systematic comparison of robust regularized RBF networks follows, which is evaluated over a set of 405 networks trained using various combinations of robustness and regularization types. The experiments proceed with a particular focus on the effect of variable selection, which is performed by means of a backward procedure, on the optimal number of RBF units. The regularized inter-quantile RBF networks based on trimmed least squares turn out to outperform the competing approaches in the experiments if a highly robust prediction error measure is considered
A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations
No full textsummary:We multiply both sides of the complex symmetric linear system by to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method
On the least almost-prime in arithmetic progressions
No full textsummary:Let denote a positive integer with at most prime factors, counted according to multiplicity. For integers , such that , let denote the least in the arithmetic progression . It is proved that for sufficiently large , we have This result constitutes an improvement upon that of J. Li, M. Zhang and Y. Cai (2023), who obtained $\mathcal P_{2}(q,a)\ll q^{1.8345}.
Perturbations of real parts of eigenvalues of bounded linear operators in a Hilbert space
No full textsummary:Let be a bounded linear operator in a complex separable Hilbert space , and be a selfadjoint operator in . Assuming that belongs to the Schatten-von Neumann ideal we derive a bound for , where are the eigenvalues of . Our results are formulated in terms of the ``extended'' eigenvalue sets in the sense introduced by T. Kato. In addition, in the case we refine the Weyl inequality between the real parts of the eigenvalues of and the eigenvalues of its Hermitian component
A note on average behaviour of the Fourier coefficients of \lowercase {th} symmetric power -function over certain sparse sequence of positive integers
No full textsummary:Let be a given integer. Let be the set of all normalized primitive holomorphic cusp forms of even integral weight for the full modulo group . For , denote by the th normalized Fourier coefficient of th symmetric power -function () attached to . We are interested in the average behaviour of the sum where is sufficiently large, which improves the recent work of A. Sharma and A. Sankaranarayanan (2023)
