Year 2022

• Multi-Criteria Simulation-Optimization Analysis of Usage of Automated Parcel Lockers: A Practical Approach

  Publication

  • B. Sawik
  • A. Serrano-Hernandez
  • A. Muro
  • J. Faulin

  - Mathematics - Year 2022

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Year 2021

• Isolation Number versus Domination Number of Trees

  Publication

  • M. Lemańska
  • M. J. Souto-Salorio
  • A. Dapena
  • F. Vazquez-Araujo

  - Mathematics - Year 2021

  If G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G)....

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• Progress on Roman and Weakly Connected Roman Graphs

  Publication

  • J. Raczek
  • R. Zuazua

  - Mathematics - Year 2021

  A graph G for which γR(G)=2γ(G) is the Roman graph, and if γwcR(G)=2γwc(G), then G is the weakly connected Roman graph. In this paper, we show that the decision problem of whether a bipartite graph is Roman is a co-NP-hard problem. Next, we prove similar results for weakly connected Roman graphs. We also study Roman trees improving the result of M.A. Henning’s A characterization of Roman trees, Discuss. Math. Graph Theory 22 (2002)....

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Year 2020

• Characterization of the Functionally Graded Shear Modulus of a Half-Space

  Publication

  • V. Zelentsov
  • P. Lapina
  • B. Mitrin
  • V. Eremeev

  - Mathematics - Year 2020

  In this article, a method is proposed for determining parameters of the exponentialy varying shear modulus of a functionally graded half-space. The method is based on the analytical solution of the problem of pure shear of an elastic functionally graded half-space by a strip punch. The half-space has the depth-wise exponential variation of its shear modulus, whose parameters are to be determined. The problem is reduced to an integral...

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• Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree

  Publication

  • Z. Dzedzej
  • T. Gzella

  - Mathematics - Year 2020

  Consider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...

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