In this paper, some inequality relations between the Laplacian/signless Laplacian H-eigenvalues and the clique/coclique numbers of uniform hypergraphs are presented. For a connected uniform hypergraph, some tight lower bounds on the largest Laplacian H+-eigenvalue and signless Laplacian H-eigenvalue related to the clique/coclique numbers are given. And some upper and lower bounds on the clique/...

We prove first that for the Barycentric refinement G1 of a finite abstract simplicial complexG, the Gauss-Bonnet formula χ(G) = ∑ xK (x) holds, where K(x) = (−1)(1−χ(S(x))) is the curvature of a vertex x with unit sphere S(x) in the graph G1. This curvature is dual toK −(x) = (−1) for which GaussBonnet is the definition of Euler characteristic χ(G). Because the connection Laplacian L′ = 1+A′ of...

We study details of geometry noncommutative de Sitter space: we determine the Riemann and Ricci curvature tensors, energy Laplacian. find, in particular, that fuzzy space is an Einstein space, $R_{ab}=-3\zeta\,\eta_{ab}$. The Laplacian, defined frame formalism, not hermitian gives nonunitary evolution. When symmetrically ordered, it has usual quadratic form $\Delta=\Pi_a\Pi^a$ (when acting on f...

For a graph G with vertex set V(G) = {v1, v2, . . . , vn}, the extended double cover G∗ is a bipartite graph with bipartition (X, Y), X = {x1, x2, . . . , xn} and Y = {y1, y2, . . . , yn}, where two vertices xi and yj are adjacent if and only if i = j or vi adjacent to vj in G. The double graphD[G] of G is a graph obtained by taking two copies of G and joining each vertex in one copy with the n...

Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier transform and then transpose signal processing operations to graphs by implementing them in the spectral domain. Here, we build on recent work that generalized Slepian functions to ...

We compute the asymptotic determinant of the discrete Laplacian on a simply-connected rectilinear region in R2. Specifically, for each > 0 let H be the subgraph of Z2 whose vertices lie in a fixed rectilinear polygon U . Let N (H ) denote the number of vertices of H and B(H ) the number of vertices on the boundary (the outer face). Then the log of the determinant of the Laplacian on H has the f...

The positive-definiteness of the Hamiltonian operator for Yang–Mills theory in four dimensions is studied by using the Coulomb gauge. It was indeed well known that the Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P built from infinitely many inverse powers of the Laplacian. If space-time is replaced by a compact Riemannian four-manifold without boundary, on w...

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources" (2015). This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, u t t − ∆ p u − ∆u t = f (u), in a bounded domain Ω ⊂ R 3 and subject to Dirichlét boundary conditions. The operator ∆ p , 2 < p < 3, denotes the classical p-Laplacian. The nonlinear term f (u) is a source feedback t...

We consider a class of generalized nonlocal $p$ -Laplacian equations. find some proper structural conditions to establish version Harnack inequalities weak solutions such problems by using the expansion positivity and energy estimates.