一般形式线性分式规划解集的结构与求法

使用多面集的分解定理,导出一般形式线性分式规划解集的结构,并基于有效的算法,给出解的唯一性条件以及当唯一性条件不满足时确定解集的计算步骤.同时附有数值例子.

一道分式方程增根的溯源及应用

本文由一道教材习题引出对分式方程产生增根的原因进行剖析,进而归纳出这类方程的一般形式,然后在这种思想的指导下,进行推广应用成编制分式方程的理论依据.

关于等价无穷小代换的推广

等价无穷小代换是计算0/0型极限的重要方法,但在实际应用中还存在一些不足之处。通过研究该方法,得到了函数乘除极限形式下可直接代换的结论,并讨论分析了加减法极限情况下的等价代换。

Theoretical framework for distributed reduction in concept lattice

In order to reduce knowledge reasoning space and improve knowledge processing efficiency, a framework of distributed attribute reduction in concept lattices is presented. By employing the idea similar to that of the rough set, the characterization of core attributes, dispensable attributes and unnecessary attributes are described from the point of view of local formal contexts and virtual global contexts. A determinant theorem of attribute reduction is derived. Based on these results, an approach for distributed attribute reduction is presented. It first performs reduction independently on each local context using the existing approaches, and then local reducts are merged to compute reducts of global contexts. An algorithm implementation is provided and its effectiveness is validated. The distributed reduction algorithm facilitates not only improving computation efficiency but also avoiding the problems caused by the existing approaches, such as data privacy and communication overhead.

Fault Diagnosis of Cylindrical Grinding Machine

Based on experiment modal analysis(EMA) and operation modal analysis(OMA), the dynamic characteristics of cylindrical grinding machine were measured and provided a basis for further failure analysis.The influences of grinding parameters on dynamic characteristics were studied by analyzing the diagnostic signals extracted from racing and grinding experiments.The significant frequency of 38 Hz related to grinding wheel spindle speed of 2 307 r/min showed that the wheel spindle system was in a state of imbalan...

Operator Methods in High Order Partial Differential Equation

For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals, explicit solutions are obtained with an integral form of a given function.

Stewart formula and some inequalities for a simplex

Problems on Stewart formula and inequalities for the areas of the bisection planes of the dihedral angles of a simplex are studied with the theory and method of distance geometry. Stewart formula and some inequalities for the areas of the bisection planes of the dihedral angles of a simplex in nE are established.

Environmental regulation and trade pattern:a case of China

As a growing number of countries, including both developed and developing countries, have in recent yearstaken environmental regulation at different levels, a question of great concern has been raised: can the regulation alterthe existing trade volume and trade pattern, and ultimately drive pollution-intensive industries to countries with low-levelregulations or even those without regulations at all? Starting from the three different propositions concerning therelationship between environmental regulation and trade pattern, this paper applies cointegration analysis and errorcorrection model to empirically testing the relationship between environmental regulation and trade in China during theperiod of 1985-2005. Our empirical results indicate that in the short run the collection of pollution discharge fees bearsa positive impact on the export share of clean products of total exports. Thus, higher pollution discharge fees raise theratio of clean products exports to total exports. This further indicates that more stringent environmental regulationpromotes the exports of clean products. In the long run pollution discharge fees are positively correlated with the exportshare of clean products but negatively associated with their import share. Such correlations imply that environmentalregulation tends to facilitate the international specialization in line with comparative advantages.

The Degenerate Form of the Adomian Polynomials in the Power Series Method for Nonlinear Ordinary Differential Equations

In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable nonlinearities. We establish efficient algorithms for the degenerate Adomian polynomials. Next we compare the results by the Adomian decomposition method using the classic Adomian polynomials with the results by the Rach-Adomian-Meyers modified decomposition method incorporating the degenerate Adomian polynomials, which itself has been shown to be a confluence of the Adomian decomposition method and the power series method. Convergence acceleration techniques including the diagonal Pade approximants are considered, and new numeric algorithms for the multistage decomposition are deduced using the degenerate Adomian polynomials. Our new technique provides a significant advantage for automated calculations when computing the power series form of the solution for nonlinear ordinary differential equations. Several expository examples are investigated to demonstrate its reliability and efficiency.

Absorbing Boundary Conditions for Hyperbolic Systems

This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.

On Generalizations of a Kind of Hilbert’s Integral Inequality

In this paper, we generalize the equivalent form of Hilbert's integral inequality by introducing parameters p,q,a,b and t.

Spectral self-affine measures on the planar Sierpinski family

The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The previous researches on this subject have led to the problem within the possible fifteen cases.We shall show that among the fifteen cases,the nine cases correspond to the spectral measures,and reduce the remnant six cases to the three cases.Thus,for a large class of such measures,their spectrality and non-spectrality are clear.Moreover,an explicit formula for the existent spectrum of a spectral measure is obtained.We also give a concluding remark on the remnant three cases.

On Radon-Penrose transformation and k-Cauchy-Fueter operator

It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an explicit Radon-Penrose type integral formula to realize this correspondence:given a -closed(0,1)form f with coefficients in the(-k-2)th power of the hyperplane section bundle H-k-2,there is an integral representation Pf such that ι*(Pf) is a solution to the k-Cauchy-Fueter equations,where ι is an embedding of the quaternionic space Hn into C4n.

Liouville theorems for an integral system with Poisson kernel on the upper half space

We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（|x- y|n）dx, y ∈?R+n,where n 3, ωn is the volume of the unit ball in Rn. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Hang et al.（2008）.With natural structure conditions on f and g, we classify the positive solutions of the above system based on the method of moving spheres in integral form and the inequality mentioned above.

China＇s Choice of Analytical Models for Its Anti-Monopoly Law

Modem analytical models for anti-monopoly laws are a core element of the application of those laws. Since the Anti-Monopoly Law of the People＇s Republic of China was promulgated in 2008, law enforcement and judicial authorities have applied different analytical models, leading to divergent legal and regulatory outcomes as similar cases receive different verdicts. To select a suitable analytical model for China＇s Anti-Monopoly Law, we need to consider the possible contribution of both economic analysis and legal formalism and to learn from the mature systems and experience of foreign countries. It is also necessary to take into account such binding constraints as the current composition of China＇s anti-monopoly legal system, the ability of implementing agencies and the supply of economic analysis, in order to ensure complementarity between the analytical model chosen and the complexity of economic analysis and between the professionalism of implementing agencies and the cost of compliance for participants in economic activities. In terms of institutional design, the models should provide a considered explanation of the legislative aims of the law＇s provisions. It is necessary, therefore, to establish a processing model of behavioral classification that is based on China＇s national conditions, applies analytical models using normative comprehensive analysis, makes use of the distribution rule of burden of proof, improves supporting systems related to analytical models and enhances the ability of public authorities to implement the law.

Conformal vector fields on some Finsler manifolds

We study conformal vector fields on a Finsler manifold whose metric is defined by a Riemannian metric, a 1-form and its norm. We find PDEs characterizing conformal vector fields. Then we obtain the explicit expressions of conformal vector fields for certain spherically symmetric metrics on R^n.

Lie Symmetries,Conservation Laws and Explicit Solutions for Time Fractional Rosenau–Haynam Equation

Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.

PREDICTING SUBCHLOROPLAST LOCATIONS OF PROTEINS BASED ON THE GENERAL FORM OF CHOU＇S PSEUDO AMINO ACID COMPOSITION： APPROACHED FROM OPTIMAL TRIPEPTIDE COMPOSITION

Chloroplasts are organelles found in plant cells that conduct photosynthesis. The subchloroplast locations of proteins are correlated with their functions. With the availability of a great number of protein data, it is highly desired to develop a com- putational method to predict the subchloroplast locations of chloroplast proteins. In this study, we proposed a novel method to predict subchloroplast locations of proteins using tripeptide compositions. It first used the binomial distribution to optimize the feature sets. Then the support vector machine was selected to perform the prediction of subchloroplast locations of proteins. The proposed method was tested on a reliable and rigorous dataset including 259 chloroplast proteins with sequence identity ≤ 25%. In the jack-knife cross-validation, 92.21% envelope proteins, 93.20% thylakoid mem- brane, 52.63% thylakoid lumen and 85.00% stroma can be correctly identified. The overall accuracy achieves 88.03% which is higher than that of other models. Based on this method, a predictor called ChloPred has been built and can be freely available from http：//cobi.uestc.edu.cn/people/hlin/tools/ChloPred/. The predictor will provide important information for theoretical and experimental research of chloroplast proteins.

AUTOMATED DERIVATION OF THE CONSERVATION LAWS FOR NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS

Based on Wu＇s elimination method and ＂divide-and-conquer＂ strategy, the undetermined coefficient algorithm to construct polynomial form conservation laws for nonlinear differential-difference equations （DDEs） is improved. Furthermore, a Maple package named CLawDDEs, which can entirely automatically derive polynomial form conservation laws of nonlinear DDEs is presented. The effective- ness of CLawDDEs is demonstrated by application to different kinds of examples.

A weak form of beyond endoscopic decomposition for the stable trace formula of odd orthogonal groups

We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace formula, when r is the standard or the second fundamental representation of the dual group, and show that they satisfy a similar kind of beyond endoscopic decomposition. The results are consequences of Arthur's works(2013) on endoscopic classification of automorphic representations, together with known results concerning a class of Langlands L-functions for special odd orthogonal groups.