Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation

In this paper, we discuss the multi-group SEIR and SIR model with random perturbation, allowing random fluctuation around the endemic equilibrium of deterministic SEIR and SIR models. We prove that the endemic equilibriums of the two models are both stochastic asymptotically stable. In addition, the stability condition is obtained by the construction of the Lyapunov function and graph theory. Finally, numerical simulations are presented to illustrate our mathematical findings.     

Asymptotic Lefschetz fixed point theory for ANES(compact) maps

A number of new Lefschetz fixed point theorems are established for ANES(compact) maps. Also compact absorbing contraction maps are discussed.      

On the existence of integrable solutions for a nonlinear quadratic integral equation

In this paper, we investigate the existence of integrable solution to a nonlinear integral equation, which includes many important integral and functional equations that arise in nonlinear analysis and its applications. Our results are obtained under rather general assumptions. In particular, the solvability of the well known Chandrasekhar equation is discussed under appropriate assumptions. Our analysis uses the technique of measures of weak noncompactness and rely on a variant of Schauder’s fixed point theorem.     

Intersection Theorems with Applications in Optimization

In this paper, we establish two intersection theorems which are useful in considering some optimization problems (complementarity problems, variational inequalities, minimax inequalities, saddle point problems).     

Twin Solutions to Singular Dirichlet Problems

The existence of two nonnegative solutions to Dirichlet second order boundary value problems is established in this paper. Our nonlinearity may be singular at y = 0, t = 0, and/or t = 1.     

One-step fabrication of glucose sensors based on entrapment of glucose oxidase within poly(ester-sulfonic acid) coatings

A simple, rapid, reproducible and effective one-step procedure for biosensor construction, based on casting mixed poly(ester-sulfonic acid)-glucose oxidase solutions onto solid electrodes is described. The cation exchanger simultaneously performs the entrapment, charge permselectivity and antifouling functions. The discrimination against potential interferences is accompanied with a fast and sensitive response to glucose. With flow injection operation, 180 samples can be processed per hour, with a detection limit of 3 × 10^?6 M. The effects of numerous experimental variables are explored. These properties of poly(ester-sulfonic acid) ionomers, coupled with their availability as aqueous dispersions, make them attractive and versatile for biosensor work.     

Fixed points and random fixed points for weakly inward approximable maps

In this paper we obtain new fixed point and random fixed point theory for approximable maps.

     

Non-Oscillatory Solutions for Higher Order Dynamic Equations

A new non-oscillatory theory is presented for higher order delayand neutral equations. The results include both singular andnonsingular problems.     

Upper and lower solutions for singular problems with nonlinear boundary data

We obtain via Schauder's fixed point theorem new results for singular boundary value problems when our nonlinear term f is allowed to change sign. Our boundary data include the Sturm Liouville condition , and the Stefan condition .