, where deg(vi) is the sum of weights of all edges connected to vi. The signless Laplacian matrix Q(G) is defined by D(G) + A(G). We denote by 0 = λ1(G) ≤ λ2(G) ≤ · · · ≤ λn(G) the eigenvalues of L(G), and by μ1(G) ≤ μ2(G) ≤ · · · ≤ μn(G) the eigenvalues of Q(G). We order the degrees of the vertices of G as d1(G) ≤ d2(G) ≤ · · · ≤ dn(G). Various bounds for the Laplacian eigenvalues of unweighte...

We consider critical dense polymers L(1, 2). We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including some examples of the indecomposable structure of the transfer matrix in the continuum limit. Inte...

Let G=(V,E), $V={v_1,v_2,ldots,v_n}$, be a simple connected graph with $%n$ vertices, $m$ edges and a sequence of vertex degrees $d_1geqd_2geqcdotsgeq d_n>0$, $d_i=d(v_i)$. Let ${A}=(a_{ij})_{ntimes n}$ and ${%D}=mathrm{diag }(d_1,d_2,ldots , d_n)$ be the adjacency and the diagonaldegree matrix of $G$, respectively. Denote by ${mathcal{L}^+}(G)={D}^{-1/2}(D+A) {D}^{-1/2}$ the normalized signles...

Let π1, π2 be cuspidal automorphic representations of PGL2(R) of conductor 1 and Hecke eigenvalues λπ1,2 (n), and let h > 0 be an integer. For any smooth compactly supported weight functions W1,2 : R → C and any Y > 0 a spectral decomposition of the shifted convolution sum

Eigenvalue of a graph is the eigenvalue of its adjacency matrix. The energy of a graph is the sum of the absolute values of its eigenvalues. In this note we obtain analytic expressions for the energy of two classes of regular graphs.

The energy E of a graph is defined to be the sum of the absolute values of its eigenvalues. Nikiforov in “V. Nikiforov, The energy of C4-free graphs of bounded degree, Lin. Algebra Appl. 428(2008), 2569–2573” proposed two conjectures concerning the energy of trees with maximum degree ∆ ≤ 3. In this short note, we show that both conjectures are true.

Using the improved lower bound on the sum of the eigenvalues of the Dirichlet Laplacian proved by A. D. Melas (Proc. Amer. Math. Soc. 131 (2003) 631-636), we report a new and sharp estimate for the dimension of the global attractor associated to the complex Ginzburg-Landau equation supplemented with Dirichlet boundary conditions.

Aiming at the link between confinement and chiral symmetry the Polyakov loop represented as a spectral sum of eigenvalues of the Dirac operator was subject of recent studies. We analyze the volume dependence as well as the continuum behavior of this quantity for quenched QCD using staggered fermions. Furthermore, we present first results using dynamical configurations.

Abstract We show that compact Kähler manifolds have the rational cohomology ring of complex projective space provided a weighted sum lowest three eigenvalues curvature operator is positive. This follows from more general vanishing and estimation theorem for individual Hodge numbers. also prove an analogue Tachibana’s manifolds.

The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. In the paper, we characterize the graphs with minimal energy in the class of bipartite unicyclic graphs of a given (p, q)–bipartition, where q ≥ p ≥ 2.