Corrections to the scaling of the second-order structure function in isotropic turbulence

The approach of Obukhov assuming a constant skewness was used to obtain analytical corrections to the scaling of the second order structure function, starting from Kolmogorov＇s 4/5 law. These corrections can be used in model applications in which explicit expressions, rather than numerical solutions are needed. The comparison with an interpolation formula proposed by Batchelor, showed that the latter gives surprisingly precise results. The modification of the same method to obtain analytical corrections to the scaling law, taking into account the possible corrections induced by intermittency, is also proposed.

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson＇s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler＇s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material （FGM） hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.

Multi-symplectic method for the generalized(2+1)-dimensionalKdV-mKdV equation

In the present paper, a general solution involv- ing three arbitrary functions for the generalized （2＋1）- dimensional KdV-mKdV equation, which is derived from the generalized （1＋1）-dimensional KdV-mKdV equa- tion, is first introduced by means of the Wiess, Tabor, Carnevale （WTC） truncation method. And then multi- symplectic formulations with several conservation laws taken into account are presented for the generalized （2＋1）- dimensional KdV-mKdV equation based on the multi- symplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from thegeneral solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent 1：o the Preissmann scheme. From the results of the numerical experiments, we can con- clude that the multi-symplectic schemes can accurately sim- ulate the periodic wave solutions of the generalized （2＋1）- dimensional KdV-mKdV equation while preserve approxi- mately the conservation laws.

Chung’s functional law of the iterated logarithm for the Brownian sheet

In this paper,we investigate functional limit problem for path of a Brownian sheet,Chung’s functional law of the iterated logarithm for a Brownian sheet is obtained.The main tool in the proof is large deviation and small deviation for a Brownian sheet.

FUNCTIONAL LAW OF ITERATED LOGARITHM FOR ADDITIVE FUNCTIONALS OF REVERSIBLE MARKOV PROCESSES

Using the forward-backward martingale decomposition and the martingale limit theorems, we establish the functional law of iterated logarithm for an additive functional (At) of a reversible Markov process, under the minimal condition that σ~2(A)= tim BA_t~2/t exists in R. We extend also t →∞ the previous remarkable functional central limit theorem of Kipnis and Varadhan.

Normative Effect of Fine Family Values Clauses in the Marriage and Family Section of China's Civil Code

The fine family values incorporated into China's Civil Code can effectively resolve the contradiction between the Marriage and Family Law's specific socialization requirements and the relatively insufficient socialization theypresent after they have been incorporated into the Civil Code of the People's Republic of China.The fine family values clauses can reflect the ethics of Marriage and Family Law by introducing the family's subject position in identity law,by specifying the scope and source of public order for judging behavior legitimacy in family relations,and by checking and balancing the tendency of turning Marriage and Family Law into Property Law.The clauses'normative effect includes the organizational effect aimed at regulating family power,social power and state power,and the advisory effect for promoting moral education.However,its core lies in its behavior normative effect for guiding the judicial process and its adjudicative normative effect.In terms of specific application,we should focus on realizing the normative function of the fine family values clauses.This function includes proving the relationship between a guardian's“lack of control and education”and external damage caused by family members,balancing family stability and personal freedom value,1limiting seeking improper property interests by means of identity behavior and creating independent legal interests.

Educational Function of the Family Property Legal System in China's Civil Code-Research on the Core Socialist Values

The educational function of law is to inherently and positively standardize and institutionalize core ideologies and values by directly affecting those ideologies,incorporating the outlook on values,ethics,life and honor and disgrace.The purpose of the Legislative Revision Plan of Integrating the Core Socialist Values into the Construction of Rule of Law,adopted by China's central government in 2018,is to comprehensively strengthen the educational function of law under the guidance of the socialist core values within the entire socialist legal system,to consolidate a solid socialist ideological foundation,and to improve ideology and ethics across China.As a family is the cell of a society and the first classroom of life,family value is not only at the core of a family but also an essential part of a society.The legal system relating to family property,based on the family property system and spousal inheritance right,can rationally adjust the family property relationship;this system can combine,cultivate and carry forward socialist core values,guide and cultivate ethics,and promote family values,family culture and family traditions.Moreover,it can educate people to formulate an appropriate outlook on life,values and money and sense of honor.Today,the legal system of family property,such as the joint possession of marital incomes and the unlimited right to spousal inheritance,has shown a negative effect on educational function,since it was born during the period of the relative shortage of family property in the past.Therefore,the Civil Code should follow the socialist core values,and update and innovate the family property legal system and thereby provide an effective and efficient path to rectify the hitherto negative effect on educational function of the family property legal system.

Prediction of Forming Limit Diagrams for Materials with HCP Structure

The forming limit diagram（FLD） is an important tool to be used when characterizing the formability of metallic sheets used in metal forming processes. Experimental measurement and determination of the FLD is timeconsuming and therefore the analytical prediction based on theory of plasticity and instability criteria allows a direct and efficient methodology to obtain critical values at different loading paths, thus carrying significant practical importance.However, the accuracy of the plastic instability prediction is strongly dependent on the choice of the material constitutive model [1–3]. Particularly for materials with hexagonal close packed（HCP） crystallographic structure, they have a very limited number of active slip systems at room temperature and demonstrate a strong asymmetry between yielding in tension and compression [4, 5]. Not only the magnitude of the yield locus changes, but also the shape of the yield surface is evolving during the plastic deformation [4]. Conventional phenomenological constitutive models of plasticity fail to capture this unconventional mechanical behavior [4, 6]. Cazacu and Plunkett [6] have proposed generic yield criteria, by using the transformed principal stress, to account for the initial plastic anisotropy and strength differential（SD） effect simultaneously. In this contribution, a generic FLD MATLAB script was developed based on Marciniak–Kuczynski analytical theory and applied to predict the localized necking. The influence of asymmetrical effect on the FLD was evaluated. Several yield functions such as von Mises, Hill, Barlat89, and Cazacu06 were incorporated into analysis. The paper also presents and discusses the influence of different hardening laws on the formability of materials with HCP crystal structures. The findings indicate that the plastic instability theory coupled with Cazacu model can adequately predict the onset of localized necking for HCP materials under different strain paths.

How big are the Csorgo-Revesz increments of two-parameter Wiener processes?

In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.

A Functional LIL for Integrated α Stable Process

Let {X（t）,t ∈ R＋} be an integrated α stable process. In this paper, a functional law of the iterated logarithm （LIL） is derived via estimating the small ball probability of X. As a corollary,, the classical Chung LIL of X is obtained. Furthermore, some results about the weighted occupation measure of X（t） are established.

A Functional LIL for m-Fold Integrated Brownian Motion

Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This extends the classic Chung type liminf result for this process. Furthermore, a result about the weighted occupation measure for Xm（t） is also obtained.

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.