动态多人递阶决策问题——结构、非光滑性及必要条件

利用非光滑分析、集值映射和微分包含理论，分析了动态递阶决策问题的结构、性质，给出了解决这类问题的一个通用性结构化模型。

非光滑动态多人优化与决策问题Nash解的必要条件研究

本文利用非光滑分析、微分包含等理论详细研究了非光滑非合作动态多人优化和决策问题，给出其Ｎａｓｈ解存在的必要条件，并予以严格的数学证明。

求解非线性互补问题的一类光滑牛顿算法

主要研究一类光滑函数法求解非线性互补问题。基于Fischer-Burmeister(FB)互补函数的光滑形式,将非线性互补问题转化为一类光滑的非线性方程组问题。为了求解该光滑非线性方程组问题,提出一类的全局收敛光滑牛顿算法。讨论了方程算子的雅克比矩阵的非奇异性。应用所提出的牛顿方法求解一类互补问题,得到相应的数值结果。

非光滑方程组牛顿法的全局收敛性分析(英文)

通过定义一种新的 * -微分 ,本文给出了局部 L ipschitz非光滑方程组的牛顿法 ,并对其全局收敛性进行了研究 .该牛顿法结合了非光滑方程组的局部收敛性和全局收敛性 .最后 ,我们把这种牛顿法应用到非光滑函数的光滑复合方程组问题上 。

函数mid(·)的一个光滑化函数及其性质

介绍了函数mid(·)可以把混合互补问题转化为一个等价的非光滑的方程组 ,由于其非光滑性 ,难以直接用光滑Newton法求解 ,光滑化就显得尤为重要 .文中采用熵摄动来光滑化函数mid(·) ,讨论了得到的光滑化函数的一些性质 .

Cement Grinding System Status of Roller Press

The working principle of cement roller press and current development of wear resistance on the cement grinding system status at home and abroad was described. The main improvement of previous research on the wear resistance of roller press was proposed from three aspects of wear-resistant material, roller press roller structure, and surface morphology.

PIECEWISE LINEAR NCP FUNCTION FOR QP FREE FEASIBLE METHOD

In this paper, a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems. The new NCP functions are piecewise linear-rational, regular pseudo-smooth and have nice properties. This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions, by using the piecewise NCP functions. This method is implementable and globally convergent without assuming the strict complementarity condition, the isolatedness of accumulation points. Purr thermore, the gradients of active constraints are not requested to be linearly independent. The submatrix which may be obtained by quasi-Newton methods, is not requested to be uniformly positive definite. Preliminary numerical results indicate that this new QP-free method is quite promising.

A New Successive Approximation Damped Newton Method for Nonlinear Complementarity Problems

In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global convergence result of the proposed algorithms. Some numerical results are also reported.

A novel smooth and discontinuous oscillator with strong irrational nonlinearities

In this paper,we propose a novel nonlinear oscillator with strong irrational nonlinearities having smooth and discontinuous characteristics depending on the values of a smoothness parameter.The oscillator is similar to the SD oscillator,originally introduced in Phys Rev E 69(2006).The equilibrium stability and the complex bifurcations of the unperturbed system are investigated.The bifurcation sets of the equilibria in parameter space are constructed to demonstrate transitions in the multiple well dynamics for both smooth and discontinuous regimes.The Melnikov method is employed to obtain the analytical criteria of chaotic thresholds for the singular closed orbits of homoclinic,homo-heteroclinic,cuspidal heteroclinic and tangent homoclinic orbits of the perturbed system.

PROPER HOLOMORPHIC MAPPINGS BETWEEN SOME NONSMOOTH DOMAINS

The authors charaCterize the existence of proper holomorphic mapping between a kind of nonsmooth Reinhardt domains defined as

Skin friction reduction characteristics of variable ovoid non-smooth surfaces

The use of bionic non-smooth surfaces is a popular approach for saving energy because of their drag reduction property. Conventional non-smooth structures include riblets and dimples. Inspired by sand dunes, a novel variable ovoid non-smooth structure is proposed in this study. The body of the variable ovoid dimple was designed based on three size parameters, the radius, semimajor, and depth, and a 3D model was created based on UG software. The constructed variable dimples were placed in a rectangular array on the bottom of a square tube model. Following ANSYS meshing, the grid model was imported into FLUENT, where the flow characteristics were calculated. Results of skin friction reduction were achieved and the effect of the design parameters on different variable ovoid dimples was obtained by orthogonal testing. Various aspects of the skin friction reduction mechanism were discussed including the distribution of velocity vectors, variation in boundary layer thickness, and pressure distribution.

DELAY DIFFERENTIAL EQUATIONS UNDER NONLINEAR IMPULSIVE CONTROL AND APPLICATIONS TO NEURAL NETWORK MODELS

In this paper, a class of delay differential equations with nonlinear impulsive control is discussed. Based on the nonsmooth analysis, criteria of stability are obtained for delay differential equations with nonlinear impulses control under certain conditions. These criteria can be applied to some neural network models. At the end of the paper, two examples are provided to illustrate the feasibility and effectiveness of the proposed results.

Effects of a Kind of Non-smooth Blade on the Performance of an Axial Fan

This paper presents an experimental investigation of effects of a kind of streamwise-grooved blade on the performance of an axial-flow fan. The flow field at 25% chord downstream from the trailing edge at hub was measured using a 5-hole pressure probe at different mass-flow conditions. The fan performance of the groove blades was compared with that of the smooth blades. The measurement results indicate that： （ 1 ） the non-smooth blades increase mass flow of the fan at the same throttle conditions except a near stall condition; （2） the non-smooth blades reduce the relative total pressure loss in the rotor passage and increase the fan＇s total pressure rise at the test mass-flow conditions except the near stall condition; （3） Negative benefits are obtained at a near stall condition when the smooth blades are replaced by the non-smooth ones. The fan mass flow decreases 0.9% while the total-pressure rise decreases 2.4% at the near stall condition.

Bionic surface design of cemented carbide drill bit

The development of a high-performance cemented carbide drill bit is of great significance to the reduction of rock drilling-cost. The non-smooth features of a biological surface provide an insight into how they can obtain low friction and good wear resistance with evolving surface morphology. By analyzing the mechanism of the surface of a dung beetle for reducing soil wear and adherence, we design a cemented carbide drill bit with a bionic surface, which is expected to have superior anti-wearing and anti-sticking properties for drilling the soft coal seam. Inspired from the characteristics of the head and pronotum surface of the dung beetle, optimized non-smooth surface of the drill bit was constructed. The working performance of this innovative drill was experimentally tested. With comparative experiments under the identical drilling conditions, the wear rates, drilling times of conventional drills and bionic drills were measured. Compared with the conventional counterpart, the drill designed exhibits better performance in reducing wear and sticking drilling-breaks, therefore achieving higher levels of efficiency. The diameter of the dome and pit on the bit surface is in the range of 0.8–1.2 mm, and the bionic drill bits could get better performance with preferable drilling speeds and wear rates.

SUFFICIENCY AND DUALITY FOR NONSMOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS INVOLVING GENERALIZED UNIVEX FUNCTIONS

In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems axe also derived for Mond-Weir type multiobjective dual programs.

New Monotonicity Formulae for Semi-linear Ellipti and Parabolic Systems

The authors establish a general monotonicity formula for the following elliptic system △ui＋fi（x,ui,…,um）=0 in Ω,where Ω belong to belong to R^n is a regular domain, （fi（x, u1,... ,um）） = △↓F（x,→↑u）, F（x,→↑u ） is a given smooth function of x ∈ R^n and →↑u = （u1,…,um） ∈ R^m. The system comes from understanding the stationary case of Ginzburg-Landau model. A new monotonicity formula is also set up for the following parabolic systemδtui-△ui-fi（x,ui,…,um）=0 in（ti,t2）×R^n,where t1 〈 t2 are two constants, （fi（x,→↑u ） is given as above. The new monotonicity formulae are focused more attention on the monotonicity of nonlinear terms. The new point of the results is that an index β is introduced to measure the monotonicity of the nonlinear terms in the problems. The index β in the study of monotonieity formulae is useful in understanding the behavior of blow-up sequences of solutions. Another new feature is that the previous monotonicity formulae are extended to nonhomogeneous nonlinearities. As applications, the Ginzburg-Landau model and some different generalizations to the free boundary problems are studied.

Interior Hlder and gradient estimates for the homogenization of the linear elliptic equations

H61der and gradient estimates for the correctors in the homogenization are presented based on the translation invariance and Li-Vogelius＇s gradient estimate. If the coefficients are piecewise smooth and the homogenized solution is smooth enough, the interior error of the first-order expansion is O（e） in the HSlder norm; it is O（e） in W1,∞ based on the Avellaneda-Lin＇s gradient estimate when the coefficients are Lipschitz continuous. These estimates can be partly extended to the nonlinear parabolic equations.

Nonsmooth Semi-Infinite Minmax Programming Involving Generalized(Φ, ρ)-Invexity

This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the necessary and sufficient optimality conditions for a class of nonsmooth semi-infinite minmax programming problems, where set of restrictions are indexed in a compact set. Utilizing the sufficient optimality conditions, the authors formulate three types of dual models and establish weak and strong duality results. The results of the paper extend and unify naturally some earlier results from the literature.

COMPLEXITY ANALYSIS OF NETWORK-BASED DYNAMICAL SYSTEMS

This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.

Local Existence of Smooth Solutions to the FENE Dumbbell Model

The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b > 2.