<p style="text-indent:20px;">We consider some system of complex vector fields related to the semi-classical Witten Laplacian, and establish local subellipticity this basing on condition <inline-formula><tex-math id="M1">\begin{document}$ (\Psi) $\end{document}</tex-math></inline-formula>.</p>

The Kirchoff Matrix Tree Theorem states that the number of spanning trees in a graph G is equal to the absolute value of any cofactor of the Laplacian matrix of G. As the theory of simplicial complexes is a generalization of the theory of graphs one would suspect that there is a generalization of the notion of spanning trees to simplicial complexes, such that the number of spanning trees in a g...

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and eigenvectors is a theoretical challenge. In this paper, we study the Laplacian spectra and their corresponding eigenvectors of a class of deterministically growing ...

in this paper, we establish some results on the existence of at least three weak solutions for adirichlet problem involving p-laplacian using a variational approach.

The connection zeta function of a finite abstract simplicial complex G is defined as zeta_L(s)=sum_x 1/lambda_x^s, where lambda_x are the eigenvalues of the connection Laplacian L defined by L(x,y)=1 if x and y intersect and 0 else. (I) As a consequence of the spectral formula chi(G)=sum_x (-1)^dim(x) = p(G)-n(G), where p(G) is the number of positive eigenvalues and n(G) is the number of negati...

this work concerns the study of existence and uniqueness to heat equation with fractional laplacian dierentiation in extended colombeau algebra.

We study spectrum inclusion regions for complex Jacobi matrices that are compact perturbations of the discrete laplacian. The condition sufficient for the lack of discrete spectrum for such matrices is given.

The Laplace transform of |ζ( 1 2 +ix)| is investigated, for which a precise expression is obtained, valid in a certain region in the complex plane. The method of proof is based on complex integration and spectral theory of the non-Euclidean Laplacian.

The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle this problem have been made and all focus on either the controllability or synchronisability of the network — usually analyzed by way of the master stability f...