GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

A Non-Monotone Trust Region Method with Non-Monotone Wolfe-Type Line Search Strategy for Unconstrained Optimization

In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our algorithm utilizes non-monotone Wolfe line search to get the next point if a trial step is not adopted. Thus, it can reduce the number of solving sub-problems. Theoretical analysis shows that the new proposed method has a global convergence under some mild conditions.

Lyapunov function and global st ability for a two-strain SEIR model with bilinear and non-monotone incidence

In this paper,we study a multi-strain SEIR epidemic model with both bilinear and nonmonotone incidence functions.Under biologically motivated assumptions,we show that the model has two basic reproduction numbers that we noted R0,1 and R0,2;and four equilibrium points.Using the Lyapunov method,we prove that if R0,1 and R0,2 are less than one then the disease-free equilibrium is Globally Asymptotically Stable,thus the disease will be eradicated.However,if one of the two basic reproduction numbers is greater than one,then the strain that persists is that with the larger basic reproduction number.And finally if both of the two basic reproduction numbers are equal or greater than one then the total endemic equilibrium is globally asymptotically stable.A numerical simulation is also presented to illustrate the influence of the psychological effect,of people to infection,on the spread of the disease in the population.This simulation can be used to determine the status of different diseases in a region using the corresponding data and infectious disease parameters.

Global Regularity of Solutions for a One-dimensional Nuclear Fluid with Non-monotone Pressure

We consider a one-dimensional continuous thermal model of nuclear matter, which is described by a compressible Navier-Stokes-Poission system with a non-monotone equation of state owing to the effective Skyrme nuclear interaction between particles. We prove the global existence of solutions in H^4 space for a free boundary value problem with a possible destabilizing influence of the pressure which is not always positive,provided a sufficient thermal dissipation is present and first obtain the existence of classical solutions.

Traveling Waves for Nonlocal and Non-monotone Delayed Reaction-difusion Equations

We study the existence of traveling wave solutions for a nonlocal and non-monotone delayed reaction-diffusion equation. Based on the construction of two associated auxiliary reaction diffusion equations with monotonicity and by using the traveling wavefronts of the auxiliary equations, the existence of the positive traveling wave solutions for c 〉 c. is obtained. Also, the exponential asymptotic behavior in the negative infinity was established. Moreover, we apply our results to some reactiondiffusion equations with spatio-temporal delay to obtain the existence of traveling waves. These results cover, complement and/or improve some existing ones in the literature.

Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters

In this paper,we consider a singularly perturbed convection-diffusion prob-lem.The problem involves two small parameters that gives rise to two boundary lay-ers at two endpoints of the domain.For this problem,a non-monotonefinite element methods is used.A priori error bound in the maximum norm is obtained.Based on the a priori error bound,we show that there exists Bakhvalov-type mesh that gives optimal error bound of O(N-2)which is robust with respect to the two perturbation parameters.Numerical results are given that confirm the theoretical result.

A Regularization Semismooth Newton Method for P_(0)-NCPs with a Non-monotone Line Search

In this paper,we propose a regularized version of the generalized NCPfunction proposed by Hu,Huang and Chen[J.Comput.Appl.Math.,230(2009),pp.69–82].Based on this regularized function,we propose a semismooth Newton method for solving nonlinear complementarity problems,where a non-monotone line search scheme is used.In particular,we show that the proposed non-monotone method is globally and locally superlinearly convergent under suitable assumptions.We test the proposed method by solving the test problems from MCPLIB.Numerical experiments indicate that this algorithm has better numerical performance in the case of p=5 andθ∈[0.25,075]than other cases.

Global Exponential Periodicity of a Class of Recurrent Neural Networks with Non-Monotone Activation Functions and Time-Varying Delays

The stability of a periodic oscillation and the global exponential class of recurrent neural networks with non-monotone activation functions and time-varying delays are analyzed. For two sets of activation functions, some algebraic criteria for ascertaining global exponential periodicity and global exponential stability of the class of recurrent neural networks are derived by using the comparison principle and the theory of monotone operator. These conditions are easy to check in terms of system parameters. In addition, we provide a new and efficacious method for the qualitative analysis of various neural networks.

具有双密度制约和Non-Monotonic型功能反应的捕食扩散系统的周期解的存在性

利用重合度理论中的延拓定理,研究了一类具有双密度制约和Non-Monoton ic型功能反应的捕食者-食饵扩散系统正周期解的存在性问题。运用分析技巧获得了一个有界开集和至少存在一个周期正解的充分条件。揭示了当食饵群负载容纳量和捕食者种群增长率均足够大时,系统将产生生物性周期振荡现象。

Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems

Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.

具双密度制约和Non-Monotonic型功能反应的捕食系统的周期性与全局稳定性

利用比较原理和重合度理论与Lyapunov函数,研究了一类具有双密度制约和Non-Monotonic型功能性反应食饵-捕食者系统的持久性和全局周期解的存在性及其全局稳定性,得到了周期系统存在唯一全局渐近稳定的正周期解的充分条件.所得结论推广了已有的结果.

Non-Monotonic Lyapunov-Krasovskii Functional Approach to Stability Analysis and Stabilization of Discrete Time-Delay Systems

In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities(LMIs)to study the global asymptotic stability of state-delay systems.Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a p H neutralizing process are provided to demonstrate the efficacy of the proposed method.

A Novel Mechanism in MPLS Network under Adversarial Uncertainty

The advantage of multi-protocol label switching (MPLS) is its capability to route the packets through explicit paths. But the nodes in the paths may be possibly attacked by the adversarial uncertainty. Aiming at this problem in MPLS Network, in this paper, we propose a novel mechanism in MPLS network under adversar-ial uncertainty, making use of the theory of artificial intelligence, at first, we find the initialized label switching paths (LSPs) using the A* arithmetic, and secondly, during the process of data transmission, we switch the transmission path duly by taking advantage of the non-monotone reasoning mechanism. Com-pared to the traditional route mechanism, the experimental results show that it improves the security if data transmission remarkably under our novel mechanism in MPLS network.

具有Smith增长和双密度制约的捕食扩散系统的周期正解

利用重合度理论中的延拓定理,研究了一类具有Smith增长和双密度制约以及HollingⅣ型功能性反应的捕食者-食饵扩散系统正周期解的存在性问题,运用分析技巧获得了一个有界开集和至少存在一个周期正解的充分条件.

Electromechanical responses and instability of electro-active polymer cylindrical shells

Based on the theories of finite deformation elasticity, electromechanical responses and instability of an incompressible electro-active polymer （EAP） cylindrical shell, which is subjected to an internal pressure and a static electric field, are studied. Deformation curves and distribution of stresses are obtained. It is found that an internal pressure together with an electric field may cause the unstable non-monotonic deforma- tion of the shell. It is also shown that a critical thickness for the shell exists, and the shell may undergo the unstable deformation if its thickness is less than this critical value. In addition, the effects of the electric field, axial stretch, thickness, and internal pressure on the instability of the shell are discussed.

Research of recognizing intelligence based on commanding decision-making

In commanding decision-making, the commander usually needs to know a lot of situations（intelligence） on the adversary. Because of the military intelligence with opposability, it is inevitable that intelligence personnel take some deceptive information released by the rival as intelligence data in the process of intelligence gathering. Since the failure of intelligence is likely to lead to a serious aftereffect, the recognition of intelligence is a very important problem. An elementary research on recognizing military intelligence and puts forward a systematic processing method are made. First, the types and characteristics of military intelligence are briefly discussed, a research thought of recognizing military intelligence by means of recognizing military hypotheses are presented. Next, the reasoning mode and framework for recognizing military hypotheses are presented from the angle of psychology of intelligence analysis and non-monotonic reasoning. Then, a model for recognizing military hypothesis is built on the basis of fuzzy judgement information given by intelligence analysts. A calculative example shows that the model has the characteristics of simple calculation and good maneuverability. Last, the methods that selecting the most likely hypothesis from the survival hypotheses via final recognition are discussed.

ATMS Based Information Fusion Target Recognition Method

The non-monotonic problem exited in information fusion systems is solved. Through the introducing of non-monotonic reasoning method, which was realized with ATMS, into the information fusion system, it gains the ability to process insufficient information with flexibility and non-monotonic behavior. In the simulation test of our system, our system manifests its ability of dealing the insufficient and contradictory information, which partly solves the decision dilemma brought out by the insufficient information in battle situations. The information fusion target recognition system can process the information in battle situation fast and with flexibility.

Asymptotic behavior of an SIQR epidemic model driven by Lévy jumps on scale-free networks

To investigate the effect of information transmission,Levy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic,a stochastic SIQR epidemic model with non-monotone incidence rate and Levy jumps on scale-free networks is constructed.At first,the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov functions.Then the stochastic model is made in accordance with the ecological significance,the existence and uniqueness of the global positive solution of the stochastic SIQR model is manifested.Next,by constructing suitable stochastic Lyapunov functions and applying Ito formula with jump,the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is checked.At last,the correctness of the analytical results is verified by numerical simulations.

Novel Non-monotonic Lyapunov-Krasovskii Based Stability Analysis and Stabilization of Discrete State-delay System

This paper proposes a novel less-conservative non-monotonic Lyapunov-Krasovskii stability approach for stability analysis of discrete time-delay systems.In this method,monotonically decreasing requirements of the Lyapunov-Krasovskii method are replaced with non-monotonic ones.The Lyapunov-Krasovskii functional is allowed to increase in some steps,but the overall trend should be decreasing.The model of practical systems used for stability analysis usually contain uncertainty.Therefore,firstly a non-monotonic stability condition is derived for certain discrete time-delay systems,then robust non-monotonic stability conditions are proposed for uncertain systems.Finally,a novel stabilization algorithm is derived based on the introduced non-monotonic stability condition.The Lyapunov-Krasovskii functional and the controller are obtained by solving a set of linear matrix inequalities(LMI)or iterative LMI based nonlinear minimization.The proposed theorems are first evaluated by some numerical examples,and then by simulation and implementation on the pH neutralizing process plant.

Numerical study of the flow in the Yellow River with non-monotonous banks

A 2-D depth averaged RNG k- ε model is developed to simulate the flow in a typical reach of the Upper Yellow River with non-monotonic banks. In order to take account of the effect of the secondary flow in a bend, the momentum equations are modified by adding an additional source term. A comparison between the numerical simulation and the field measurements indicates that the improved 2-D depth averaged RNG k- ε model can improve the accuracy of the numerical simulation. An arc spline interpolation method is developed to interpolate the non-monotonic river banks. The method can also be reasonably applied for the 2-D interpolation of the river bed level. Through a comparison of the water surface gradients simulated in the seven bends of the studied reach, some analytical formulae are improved to reasonably calculate the longitudinal and transverse gradients in meandering river reaches. Furthermore, the positions of the maximum water depth and the maximum velocity in a typical bend are discussed.