We present an algorithm which explores permutation symmetries to describe the time evolution of agent-based epidemic models. The main idea to improve computation times relies on restricting the stochastic process to one sector of the vector space, labeled by a single permutation eigenvalue. In this scheme, the transition matrix reduces to block diagonal form, enhancing computational performance...

We study the relation between the diameter, the first positive eigenvalue of the discrete p-Laplacian and the `p-distortion of a finite graph. We prove an inequality relating these three quantities and apply it to families of Cayley and Schreier graphs. We also show that the `p-distortion of Pascal graphs, approximating the Sierpinski gasket, is bounded, which allows to obtain estimates for the...

Let L = −∆− W be a Schrödinger operator with a potential W ∈ L n+1 2 (R), n ≥ 2. We prove that there is no positive eigenvalue. The main tool is an L − Lp′ Carleman type estimate, which implies that eigenfunctions to positive eigenvalues must be compactly supported. The Carleman estimate builds on delicate dispersive estimates established in [7]. We also consider extensions of the result to var...

The main purpose of this paper is to describe the extension of the successful modified integral series methods for Schrödinger problems to more general Sturm-Liouville eigenvalue problems. We present a robust and reliable modified Neumann method which can handle a wide variety of problems. This modified Neumann method is closely related to the second-order Pruess method, but provides for higher...

In this paper the Bogdanov-Takens (BT) bifurcation of an 2m coupled neurons network model with multiple delays is studied, where one neuron is excitatory and the next is inhibitory. When the origin of the model has a double zero eigenvalue, by using center manifold reduction of delay differential equations (DDEs), the second-order and third-order universal unfoldings of the normal forms are ded...

The paper is devoted to first-order trace formulas for the iterates of the Fox–Li and related Wiener–Hopf integral operators. Such formulas provide first insight into the asymptotic behaviour of the eigenvalues and can be used to test whether a specific guess for the eigenvalue distribution is acceptable or not. The main technical problem consists in obtaining the asymptotics of a multivariate ...

We consider three parametric relaxations of the 0-1 quadratic programming problem. These relaxations are to: quadratic maximization over simple box constraints, quadratic maximization over the sphere, and the maximum eigenvalue of a bordered matrix. When minimized over the parameter, each of the relaxations provides an upper bound on the original discrete problem. Moreover, these bounds are eec...

In this work, we investigate the eigenvalue intervals of nonlinear boundary value problems involving fractional q -difference equations by means of the properties of the Green function and Guo-Krasnosel’skii fixed point theorem on cones. Furthermore, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are establi...

This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the compactness in the Palais Smale condition and the order of the nonlinearity in the operator. The main result is applied to estimate the asyptotic behav...

mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper the author derives a lower bound for the largest eigen-value and an upper bound for the smallest eigenvalue of Hermitian matrices , based on Weyl's inequalities. Some related results, consequences, applications, and examples...