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Critical Groups of Simplicial Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacian operators, generalizing the construction of the critical ...
Art M. Duval +2 more
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Eigenvalues and critical groups of Adinkras
Advances in Applied Mathematics, 2023 Adinkras are signed graphs used to study supersymmetry in physics. We provide an introduction to these objects, and study the properties of their signed adjacency and signed Laplacian matrices. These matrices each have exactly two distinct eigenvalues (of equal multiplicity), making Adinkras closely related to the notions of strongly regular graphs. We
Iga, Kevin +3 more
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Journal of the Australian Mathematical Society, 1966 The concept of critical group was introduced by D. C. Cross (as reported byG. Higman in [5]): a finite group is calledcriticalif it is not contained in the variety generated by its proper factors. (Thefactorsof a groupGare the groups H/K where KH ≦G, and H/K is aproper factorofGunlessH = GandK=1).
Kovacs, L. G., Newman, M. F.
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A multiplicity theorem for parametric superlinear (p,q)-equations [PDF]
Opuscula Mathematica, 2020 We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition.
Florin-Iulian Onete +2 more
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Advances in Nonlinear Analysis, 2020 We consider a nonlinear elliptic equation driven by the (p, q)–Laplacian plus an indefinite potential. The reaction is (p − 1)–superlinear and the boundary term is parametric and concave.
Papageorgiou Nikolaos S., Zhang Youpei
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Numerical renormalization group at criticality [PDF]
Physics Letters A, 1996 5 pages, LaTeX, 5 figures available upon ...
Nishino, T., Okunishi, K., Kikuchi, M.
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A Remark on Critical Groups [PDF]
Journal of the Australian Mathematical Society, 1969 Problem 24 of Hanna Neumann's book [3] reads: Does there exist, for a given integer n > 0, a Cross variety that is generated by its k-generator groups and contains (k+n)-generator critical groups? In such a variety, is every critical group that needs more than k generators a factor of a k-generator critical group, or at least of the free group of ...
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Cyclic Critical Groups of Graphs [PDF]
Australas. J Comb., 2015 In this note, we describe a construction that leads to families of graphs whose critical groups are cyclic. For some of these families we are able to give a formula for the number of spanning trees of the graph, which then determines the group exactly. We also pose several open questions related to this work.
Ryan Becker, Darren B. Glass
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Constant sign and nodal solutions for nonlinear Robin equations with locally defined source term
Mathematical Modelling and Analysis, 2020 We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood
Nikolaos S. Papageorgiou +2 more
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Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth
Electronic Journal of Qualitative Theory of Differential Equations, 2021 In this paper we consider a class of second order Hamiltonian system with the nonlinearity of linear growth. Compared with the existing results, we do not assume an asymptotic of the nonlinearity at infinity to exist. Moreover, we allow the system to be
Guanggang Liu
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