Some inequalities for geominimal surface areas

The concept of geominimal surface area is first intro- duced, and then, the affine surface area projection inequality is given by Petty. In recent years, associated with geominimal surface area, Lutwak obtained some significant results containing the extended affine projection inequality. In this paper, combining with curvature image and combinations of convex bodies, we get some inequalities for geominimal surface areas. Furthermore, the integral form of geominimal surface area is obtained.     

Synchronization for unified chaotic systems with noise-disturbed parameters by sliding mode control

In this paper,the active sliding mode control method is utilized to study the synchronization for unified chaotic systems with noise-disturbed parameters.Some novet results about the suitable sliding mode surface and the synchronizing control law are derived,which avoid the mistake inequality sC△Ae≤‖△A‖∞ sCe in Ref.[Chaos,Solitons & Fractals 21(2004) 1249].Finally,numerical sireulations are included to show the correctness of our results and the effectiveness of the developed approach.     

On reverses of the <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-Busemann-Petty centroid inequality and its applications

In this paper,the reverse forms of the L p-Busemann-Petty centroid inequality are shown. As the applications of the reverse forms,we obtain the reverse forms of the L p-centroid-affine inequality and an upper bound of the isotropic constant for convex bodies.     

Inequalities for the radial p-th mean bodies

In this paper, we establish an inequality for the volumes of K and its radial p-th mean body R_pK by L_p-dual mixed volume. Further, the Shephard-type problem and a monotonitic inequality of R_pK are shown when p>0 .     

The Polar φ-Brunn-Minkowski Inequalities

A general framework of polar Brunn-Minkowski theory that unifies the Orlicz Brunn-Minkowski inequality, the L_p Brunn-Minkowski inequality for p ∈(0,1) and the logBrunn-Minkowski inequality all for polar bodies is provided. It is shown that this general polar φ Brunn-Minkowski inequality is equivalent to a general polar φ Minkowski mixed volume inequality.     

Stability analysis of BAM neural networks with time-varying delays

Some new criteria for the global asymptotic stability of the equilibrium point for the bi-directional associative memory neural networks with time varying delays are presented. The obtained results present the structure of linear matrix inequality which can be solved efficiently. The comparison with some previously reported results in the literature demonstrates that the results in this paper provide one more set of criteria for determining the stability of the bi-directional associative memory neural networks with delays.     

Stability analysis of BAM neural networks with time-varying delays

Some new criteria for the global asymptotic stability of the equilibrium point for the bi-directional associative memory neural networks with time varying delays are presented. The obtained results present the structure of linear matrix inequality which can be solved efficiently. The comparison with some previously reported results in the literature demonstrates that the results in this paper provide one more set of criteria for determining the stability of the bi-directional associative memory neural networks with delays.     

Dual Orlicz affine surface area

According to the notion of Orlicz mixed volume, in this paper, we extend L_p-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequality for the dual Orlicz affine surface area. Besides, we also get the monotonicity inequality for Orlicz dual affine surface area.     

Principle of Interaction between Plastic Volumetric and Sh ear Strains and the Constitutive Model for Geotechnical Materials

Here is proposed the principle of interaction between plastic volumetric and shear strains,revealing the main origin of generating the complexity and variety of deformations for geotechnical materials．Here are also explained the manners of the interaction between plastic volumetric and shear strains and the conditions of generating shear dilatancy．It is demonstrated that dependency of the stress path exists and is a combination of effects of this interaction．According to this principle,it is theoretically proved that the space critical state line exists,and is unique and independent of the stress history．Based on this principle,the constitutive models that are able completely and accurately to characterize the basic behavior features for geotechnical materials have been constructed within the framework of thermodynamics．What is determined is a general expression of the constitutive relation as well as the inequality of the dissipative potential increment for obeying the second law of thermodynamics．     

Simulation of phase transition process using lattice Boltzmann method

A new lattice Boltzmann model based on SC model, is proposed to describe the liquid-vapor phase transitions. The new model is validated through the simulation of the one-component phase transition process. Compared with the simulation results of van der Waals gas and the Maxwell equal-area construction, the results of the new model have a better agreement with the analytical solutions than those of SC and Zhang models. Since the obtained temperature range and the maximum density ratio in this model are expanded, and the magnitude of maximum spurious current is only between those of SC and Zhang models, it is believed that this new model has better stability than SC and Zhang models. Consequently, the application scope of this new model is expanded compared with the existing phase transition models. According to the principle of the corresponding states in engineering thermodynamics, the simulations of ammonia and water phase transition process were implemented using this new model with different equations of state. Compared with the experimental data of ammonia and water, the results show that the Peng-Robinson is the best equation of state to describe the phase transition process of ammonia and water. Especially, the simulation results of ammonia with Peng-Robinson equation of state have an excellent agreement with its experimental data. Therefore these simulation results have a significant influence on the real engineering applications.     

S_p系统的强收敛性

讨论了一定条件下的φ-混合、ψ-混合随机变量序列是Sp系统,通过建立φ-混合、ψ-混合序列的矩不等式,研究了Sp系统的强收敛性,将独立同分布随机变量的Marcinkiewicz强大数定律推广到了ψ-混合、φ-混合序列.     

ρ混合序列的Hajek-Renyi型不等式

将独立随机变量序列的Hajek-Renyi型不等式推广到ρ混合序列,并应用此不等式研究其强大数定律。     

对偶L_q变换法则

在已有结果的基础上对对偶L_q Brunn-Minkowski理论做了一些推广,主要讨论了对偶L_q Brunn-Minkowski型不等式并得到部分结果.给出统一的处理对偶L_q Brunn-Minkowski型不等式的方法,称此方法为对偶L_q变换法则,通过运用此法则给出了关于对偶混合体积著名的对偶L_q Brunn-Minkowski型不等式的简化证明.     

φ混合序列的几乎处处收敛性

讨论φ^～混合序列级数的收敛性,得到φ^～混合序列的几个几乎处处收敛定理,把文献[2]中ρ^～混合序列的相关收敛性质推广到φ^～混合序列．     

误差为NOD样本下的非参数回归模型估计的相合性

研究了误差为NOD序列时的非参数回归模型未知函数估计量相合性问题,而NOD序列比NA序列要弱。利用NOD序列的C r不等式,Jensen不等式以及权函数相关性质,证明了其弱相合性。     

NA序列和的若干收敛性

利用NA序列的一个矩不等式,讨论了不同分布的NA随机变量序列加权和的完全收敛性,得到了更为一般的完全收敛性.     

一般随机变量序列部分和的不等式

通过研究一般随机变量序列部分和的问题,得到了一般随机变量部分和分布的一个重要不等式,以及非负有界的随机变量的部分和及其相应的条件期望序列部分和的关系．     

Deviation inequality for the number of k -cycles in a random graph

We study the number of k-cycles in a random graph G(n, p). We estimate the probability that a random graph contains more k-cycles than expected. In this case, the usual martingale inequality with bounded difference is not effective. By constructing a variable that approximates to the number of k-cycles in a random graph and using a new and extensive martingale inequality, we get the results in this paper. Foundation item: Supported by the National Natural Science Foundation of China (10571139)     

两两广义NQD列的一些性质

在两两NQD列的基础上定义了两两广义NQD列,并获得了与两两NQD列类似的基本性质、Kolmogorov不等式及一个弱大数定律.     

不同分布ρ混合序列部分和的完全收敛性

讨论不同分布^~ρ混合序列部分和的完全收敛性,利用矩不等式和截尾手法,获得了几乎与独立情形完全一样的Baum和Katz完全收敛定理.