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summary:Libuše Hozová (1939-2024). Vzpomínkové odpoledne a seminář ke 100. výročí narození profesora Miloše Zlámala

Classification of irreducible representations of near-group fusion algebras

summary:We explicitly classify the irreducible representations of the near-group fusion algebra associated with a finite group over a field with arbitrary characteristic

Stabilizability of multi-agent systems over finite fields via fully actuated system approaches

summary:The problem of stabilizability of high-order fully actuated (HOFA) multi-agent systems over finite fields is considered in this paper. The necessary and sufficient conditions for the stabilizability of HOFA multi-agent systems are presented, which indicates the stabilizability is closely related to the interaction topology among agents. Using the full-actuation property of HOFA models, a stabilization control protocol with neighbor interaction is given for HOFA multi-agent systems. Additionally, when the multi-agent system is stabilizable, the time for the system to reach a stable state can be determined through the control protocol. Finally, the results are employed to solve the formation control problem, and some sufficient and/or necessary conditions are proposed. Numerical examples are presented to demonstrate the effectiveness of the proposed results

Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies

summary:We investigate a class of Kirchhoff-type equations characterized by critical growth within Orlicz-Sobolev spaces. The main result establishes the existence of infinitely many solutions with negative energy. Using an adapted concentration-compactness principle and advanced variational methods, we overcome key challenges such as non-compactness and non-differentiability to the associated functionals. This work extends existing results to more general functional spaces, offering new insights into nonlocal nonlinear equations

The Korean Suneung Exam

summary:Článek uvádí ukázky úloh z matematiky, které byly součástí přijímací zkoušky na vysoké školy v Jižní Koreji v roce 2023. Řešení uvedených úloh jsou od autora tohoto článku, což nevylučuje že existují  lepší řešení těchto úloh

Weakly SS-2-absorbing ideals

summary:Let $R$ be a commutative ring with identity. The notion of $S$-$2$-absorbing ideal was introduced by G. Ulucak, Ü. Tekir, S. Koç (2020) as a generalization of $2$-absorbing ideal. We introduce $a$ weaker version of 2-absorbing ideals by defining the concept of weakly-$S$-2-absorbing ideal. Let $S\subseteq R$ be a multiplicatively closed subset of $R$. A proper ideal $I$ of $R$ disjoint with $S$ is called a weakly $S$-2-absorbing ideal of $R$ if whenever $abc\in I$ for $a,b,c\in R$ then there exists $s\in S$ such that $sab\in I$ or $sbc\in I$ or $sac\in I$. We investigate many properties and characterizations of weakly $S$-2-absorbing ideals

Sufficient conditions to determine the linear dependency of two meromorphic functions

summary:We comprehensively explore the generalized concept of sharing sets to establish conditions for the linear dependency of two meromorphic functions. By applying this approach, we significantly extend and enhance the existing results related to URSM (unique range set of meromorphic functions). It is well known that URSMs can be represented as zeros of specific polynomials. However, our findings demonstrate that the concept of URSM can be understood from a broader perspective, where it can be characterized as a special case of the zero sets of two interconnected polynomials. Such investigations have not been conducted before, thus the text breaks the barriers of the traditional definition of URSM

Global weak solutions to a 3D self-consistent chemotaxis-Stokes system with nonlinear resource consumption

summary:We study the self-consistent chemotaxis-fluid system with nonlinear resource consumption $$\begin {cases} n_{t}+u\cdot \nabla n=\Delta n^m -\nabla \cdot (n \nabla c)+\nabla \cdot (n\nabla \phi ), & x\in \Omega ,\ t>0, \\ c_{t}+u\cdot \nabla c=\Delta c-n^\alpha c, & x\in \Omega ,\ t>0, \\ u_t+ \nabla P=\Delta u-n\nabla \phi +n \nabla c,& x\in \Omega ,\ t>0,\\ \nabla \cdot u=0,& x\in \Omega ,\ t>0,\\ \end {cases}$$ under no-flux boundary conditions in a bounded domain $\Omega \subset \mathbb {R}^3$ with smooth boundary. It is proved that this system possesses a global weak solution provided $m>1$ and $\alpha > \frac {4}{3}$

Generalized semidirect sums of Lie algebras and their modules

summary:Generalized semidirect sums of Lie algebras and their modules are introduced, which are not necessarily (non)-Abelian extensions and may be applied to construct Lie algebras from modules. Some properties of generalized semidirect sums are described. In particular, it is shown that finite dimensional non-solvable Lie algebras can be realized as generalized semidirect sums. The complete classification up to isomorphism of all generalized semidirect sums of $\mathfrak {sl}_2$ and its finite-dimensional irreducible modules is given

Hybrid algorithms for fixed charge transportation problem

summary:In this paper, we consider the fixed-cost transportation problem. This problem is known to be NP-hard. Therefore, various heuristic and metaheuristic approaches have been proposed to find an approximate optimal solution. In this paper, we propose three hybrid algorithms that combine the ideas of metaheuristic and heuristic approaches in different ways. Two of the proposed algorithms consist of the sequential implementation of metaheuristic and heuristic algorithms, while the third one is a full hybrid algorithm designed by completely intertwining these two approaches. Experimental results on medium-size problems show that our proposed full hybrid algorithm provides approximately a