We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from an antiferromagnetic to a spin-glass state. The eigenvalues associated with replica-symmetric perturbations are in general complex. The natural generalization of the usual stability condition is to require the real part of these eigenvalues to be p...

This paper addresses the exponential stability problem for a class of discrete-time switched linear positive systems (DSLPSs) with time-delay. Firstly, an exponential stability criterion for a non-switched delay positive system is proposed. Then, by constructing a suitable co-positive type Lyapunov–Krasovskii functional, an exponential stability criterion for switched delay positive systems is ...

An alternate approach to the analysis of a Takagi-Sugeno (T-S) fuzzy model is dealt with in this paper. The proposed approach is employed to search for eigenvalues of a T-S fuzzy model in any mixed weighting cases. This effective method is developed by a well-known Routh stability criterion as well as the root locus method to judge the stability of the nonlinear system approximated by a T-S fuz...

The Stieltjes constants γk(a) are the expansion coefficients in the Laurent series for the Hurwitz zeta function about its only pole at s = 1. We present the relation of γk(1) to the ηj coefficients that appear in the Laurent expansion of the logarithmic derivative of the Riemann zeta function about its pole at s = 1. We obtain novel integral representations of the Stieltjes constants and new d...

The paper indicates a number of approaches to checking the roots of a polynomial to detmmine whether they have negative real parts. Interrelations between the various approaches are discussed, and the stability criterion in terms of Marlcov determinants is related to the Hemite criterion vith the aid of Lyapunov theory. $1

We present several asymptotic analyses for quantities associated with the Riemann and Hurwitz zeta functions. We first determine the leading asymptotic behavior of the Stieltjes constants γk(a). These constants appear in the regular part of the Laurent expansion of the Hurwitz zeta function. We then use asymptotic results for the Laguerre polynomials Ln to investigate a certain sum Sγ(n) involv...

In this note, we consider the modified Gram-Schmidt algorithm with reorthogonalization applied on a numerical nonsingular matrix, we explain why the resulting set of vectors is orthogonal up to the machine precision level. To establish this result, we show that a certain L-criterion is necessarily verified after the second reorthogonalization step, then we prove that this L-criterion implies th...

The famous Popov criterion is used for absolute stability analysis of uncertain nonlinear systems. Uncertainty is assumed to exist in the linear subsystem in terms of coefficient perturbations in complex plane discs. Existing results, which are based on strict positive realness (SPR) conditions, are generalized so as to cover a wider spectrum of systems. All the results are then restated using ...

This paper investigates a compartmental pest management model which divides the pest population into a susceptible and an infective class, while also including a class of pathogenic viruses. The model is age-structured, in the sense that it accounts for the differences in the amounts of pathogenic viruses released by infective pests at various infection ages. First, the asymptotic behavior of t...

This note presents closed-form formulas for determining the critical points of general ndimensional differential equations. The formulas do not require commutating the eigenvalues of the Jacobian of a system. Based on the Hurwitz criterion, explicit necessary and sufficient conditions are obtained. Particular attention is focused on Hopf and double Hopf bifurcations. A model of induction machin...