Conservation Laws of the Differential-Difference KP Equation

An infinite number of semi-discrete and continuous conservation laws for the differential-difference KP equation were obtained by using a solvable generalized Riccati equation.

Influences of Cultural Differences on Translation of Titles of Laws

For whatever kind of literary forms, the first thing that we come into contact with is the title. The title functions as not only the eye catcher but also the summary of the context. Any legal document starts with its title and a good translation of the title lays the foundation for the interpretation of follow- up terms and conditions. However, translating titles of laws is affected by different factors, especially cultural differences, such as history, diction and conventions. Anyway, cultural impact on translation of law titles can be handled tactfully.

A Numerical Simulation of Air Flow in the Human Respiratory System Based on Lung Model

The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.

On the Limiting Behavior of Weighted Partial Sums for B Valued Martingale Difference Sequences

Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.

LARGE TIME STEP GENERALIZATION OF RANDOM CHOICE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC CONSERVATION LAWS

A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.

EXACT SOLUTION OF THE DEGREE DISTRIBUTION FOR AN EVOLVING NETWORK

In this paper we propose a simple evolving network with link additions as well as removals. The preferential attachment of link additions is similar to BA model’s, while the removal rule is newly added. From the perspective of Markov chain, we give the exact solution of the degree distribution and show that whether the network is scale-free or not depends on the parameter m, and the degree exponent varying in （3, 5] is also depend on m if scale-free.

Some Limit Theorems for Weighted Sums of Random Variable Fields

Let{Xn^-,n^-∈N^d}be a field of Banach space valued random variables, 0 〈r〈p≤2 and{an^-,k^-, （n^-,k^-） ∈ N^d × N^d ,k^-≤n^-} a triangular array of real numhers, where N^d is the d-dimensional lattice （d≥1 ）. Under the minimal condition that {｜｜Xn^-｜｜ r,n^- ∈N^d} is {｜an^-,k^-｜^r,（n^-,k^-）} ∈ N^d ×N^d,k^-≤n^-}-uniformly integrable, we show that ∑（k^-≤n^-）an^-,k^-,Xk^-^（L^r（or a,s,）→0 as ｜n^-｜→∞ In the above, if 0〈r〈1, the random variables are not needed to be independent. If 1≤r〈p≤2, and Banach space valued random variables are independent with mean zero we assume the Banaeh space is of type p. If 1≤r≤p≤2 and Banach space valued random variables are not independent we assume the Banach space is p-smoothable.

AN INVESTIGATION ON INTERNAL THERMAL FLOW OF NON-NEWTONIAN FLUID

In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the flow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied. For the flow into mould cavity the constitutive equation of power-law fluid is used as a Theological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid flow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting difference method. The numerical results show that the splitting difference method is suitable for the 2D problem of non-Newtonian fluid. The present application of the splitting diffference method is at first developed by us for non-Newtonian case. For the unsteady flow in the tube the finite difference scheme is given which leads to a tridiagonal system of equations.

A note on strong law of large numbers of random variables

In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker than that in Chung’s theorem. Some convergence theorems for martingale difference sequence such as Lp martingale difference sequence are the particular cases of results achieved in this paper. Finally, the convergence theorem for A-summability of sequence of random variables is proved, where A is a suitable real infinite matrix.

Origin, Alternative Expressions of Newcomb-Benford Law and Deviations of Digit Frequencies

The Newcomb-Benford law, which describes the uneven distribution of the frequencies of digits in data sets, is by its nature probabilistic. Therefore, the main goal of this work was to derive formulas for the permissible deviations of the above frequencies (confidence intervals). For this, a previously developed method was used, which represents an alternative to the traditional approach. The alternative formula expressing the Newcomb-Benford law is re-derived. As shown in general form, it is numerically equivalent to the original Benford formula. The obtained formulas for confidence intervals for Benford’s law are shown to be useful for checking arrays of numerical data. Consequences for numeral systems with different bases are analyzed. The alternative expression for the frequencies of digits at the second decimal place is deduced together with the corresponding deviation intervals. In general, in this approach, all the presented results are a consequence of the positionality property of digital systems such as decimal, binary, etc.

The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws:An Alternative Technique

To solve conservation laws,efficient schemes such as essentially nonoscillatory(ENO)and weighted ENO(WENO)have been introduced to control the Gibbs oscillations.Based on radial basis functions(RBFs)with the classical WENO-JS weights,a new type of WENO schemes has been proposed to solve conservation laws[J.Guo et al.,J.Sci.Comput.,70(2017),pp.551–575].The purpose of this paper is to introduce a new formulation of conservative finite difference RBFWENO schemes to solve conservation laws.Unlike the usual method for reconstructing the flux functions,the flux function is generated directly with the conservative variables.Comparing with Guo and Jung(2017),the main advantage of this framework is that arbitrary monotone fluxes can be employed,while in Guo and Jung(2017)only smooth flux splitting can be used to reconstruct flux functions.Several 1D and 2D benchmark problems are prepared to demonstrate the good performance of the new scheme.

Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors

Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.

Numerical simulation of hydraulic fracture propagation in laminated shale reservoirs

The main area of the Jiaoshiba anticline of the Fuling shale gas field was taken as the research object,laboratory rock mechanical experiments and direct shear experiments were conducted to clarify the mechanical anisotropy characteristics and parameters of rock samples with rich beddings.Based on the experimental results,a 3D fracture propagation model of the target reservoir taking mechanical anisotropy,weak bedding plane and vertical stress difference into account was established by the discrete element method to analyze distribution patterns of hydraulic fractures under different bedding densities,mechanical properties,and fracturing engineering parameters(including perforation clusters,injection rates and fracturing fluid viscosity).The research results show that considering the influence of the weak bedding plane and longitudinal stress difference,the interlayer stress difference 3–4 MPa in the study area can control the fracture height within the zone of stress barrier,and the fracture height is less than 40 m.If the influence of the weak bedding plane is not considered,the simulation result of fracture height is obviously higher.Although the opening of high-density bedding fractures increases the complexity of hydraulic fractures,it significantly limited the propagation of fracture height.By reducing the number of clusters,increasing the injection rate,and increasing the volume and proportion of high-viscosity fracturing fluid in the pad stage,the restriction on fracture height due to the bedding plane and vertical stress difference can be reduced,and the longitudinal propagation of fractures can be promoted.The fracture propagation model was used to simulate one stage of Well A in Fuling shale gas field,and the simulation results were consistent with the micro-seismic monitoring results.

AN ADAPTIVE VERSION OF GLIMM'S SCHEME

This article describes a local error estimator for Glimm＇s scheme for hyperbolic systems of conservation laws and uses it to replace the usual random choice in Glimm＇s scheme by an optimal choice. As a by-product of the local error estimator, the procedure provides a global error estimator that is shown numerically to be a very accurate estimate of the error in L1 （R） for all times. Although there is partial mathematical evidence for the error estimator proposed, at this stage the error estimator must be considered ad- hoc. Nonetheless, the error estimator is simple to compute, relatively inexpensive, without adjustable parameters and at least as accurate as other existing error estimators. Numerical experiments in 1-D for Burgers＇ equation and for Euler＇s system are performed to measure the asymptotic accuracy of the resulting scheme and of the error estimator.

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

On the Conservative Finite Difference Scheme for the Generalized Novikov Equation

In this paper, we investigate a numerical method for the generalized Novikov equation. We propose a conservative finite difference scheme and use Brouwer fixed point theorem to obtain the existence of the solution of the corresponding difference equation. We also prove the convergence and stability of the solution by using the discrete energy method. Moreover, we obtain the truncation error of the difference scheme which is .

Differences between Traditional Chinese Family Law and National Law Analysis

Chinese traditional family-based society is the legal basis for political, patriarchal hierarchy and national politics Consistent hierarchy, as represented by the family law civil law is to adjust the traditional social relations, maintaining the main legal norms of social order, Family law as one of the most important traditional Chinese society, the legal system, and the state law regulating social order constitute the dual legal structure. And its fundamental purpose is to maintain social harmony and stability of the feudal rule of order.

Corporate Tax Differences under the New Accounting Standards

The tax differences is the enterprise according to the provisions of accounting standards to calculate the total profit and tax calculated according to the enterprise income tax＇s tax base taxable income differences. Enterprise accounting standards and tax for the same subject for different purposes, leading to both the principle is different, as well as for the same matter measurement and confirmation of different, resulting in tax differences. In this paper, from the aspect of theory to the study of tax differences, from tax differences that the tax law and accounting purposes different proceed with, on the basis of theoretical analysis, design a regression model from empirical research on tax differences. According to the 2009,2010 and201 lthree annual sample data regression results, discussed in the new＂ accounting standards for business enterprises＂ of corporate tax difference change tendency, and according to the tax law and accounting standards caused by the different effects of tax differences for the main project correlation analysis, so as to verify the theoretical expectations.

Spatial Pattern and Evolution of Urbanization in Shandong Province

Based on Arc GIS and SPSS Statistics,authors of this paper used the principal component analysis(PCA) and the analytic hierarchy process(AHP),and selected 6 indicators concerning population,land,and economy to study the spatial pattern of urbanization and regional economic differences in Shandong Province,namely urban population,urban population density,construction land,area of urban districts,disposable income of residents,and added value of the tertiary industry.The development of urbanization in Shandong Province was measured by the proportion of urban population to the total population in 2000,2005,2010,and 2014 respectively.It is hoped that this paper will provide a theoretical basis for building an orderly regional spatial structure and coordinating regional urban decision-making.

著作权法上独创性概念的澄清与重释

由于个性、创造性、智力劳动等概念比较抽象,一部作品是否具有独创性通常取决于预设的私人立场。这种判定模式会不合理地损害著作权保护的预期。从我国的作品定义看,独创性是一部作品区别于其他作品的内在尺度。独创性既表明了特定作品的特有属性,又表达了与其相关的权益归属。这一内涵与著作权法的内外价值一致。依此逻辑,独创性是指作品的相对差异,并暗示作品进入市场的机会与作品价值的二分。按照相对差异标准,作者享有依照著作权法提出保护的应然权利。