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Critical Groups of Simplicial Complexes [PDF]
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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Abstract We define and investigate the property of being “exponent-critical” for a finite group. A finite group is said to be exponent-critical if its exponent is not the least common multiple of the exponents of its proper non-abelian subgroups. We explore properties of exponent-critical groups and give a characterization of such groups.
Simon R. Blackburn +3 more
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Mothers’ groups during critical processes around birth
The article describes a clinical experience with groups of mothers of newborns who are ill and must stay in neonatology. This report tries to reflect on single session therapy within support-groups and also on psychologist ́s role when coping with ...
Alicia Mercado
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Multiplicity results for the Kirchhoff type equation via critical groups
In this paper, we will compute critical groups at zero for the Kirchhoff type equation using the property that critical groups are invariant under homotopies preserving isolatedness of critical points.
Zhenting Wang +3 more
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Eigenvalues and critical groups of Adinkras
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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A multiplicity theorem for parametric superlinear (p,q)-equations [PDF]
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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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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A Critical Mathematics Education for Climate Change [PDF]
Climate change is an urgent global challenge. Responding to climate change requires significant critical mathematical understanding on the part of all citizens.
Barwell, Richard, Hauge, Kjellrun Hiis
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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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Numerical renormalization group at criticality [PDF]
5 pages, LaTeX, 5 figures available upon ...
Nishino, T., Okunishi, K., Kikuchi, M.
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