Solution with Singularity of Order One for Singular Integral Equation with Hilbert Kernal

The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.

SINGULAR INTEGRAL EQUATIONS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.

Assessing Suitability of Rural Settlements Using an Improved Technique for Order Preference by Similarity to Ideal Solution

Land suitability assessment is a prerequisite phase in land use planning; it guides toward optimal land use by providing information on the opportunities and constraints involved in the use of a given land area. A geographic information system-based procedure, known as rural settlement suitability evaluation(RSSE) using an improved technique for order preference by similarity to ideal solution(TOPSIS), was adopted to determine the most suitable area for constructing rural settlements in different geographical locations. Given the distribution and independence of rural settlements, a distinctive evaluation criteria system that differed from that of urban suitability was established by considering the level of rural infrastructure services as well as living and working conditions. The unpredictable mutual interference among evaluation factors has been found in practical works. An improved TOPSIS using Mahalanobis distance was applied to solve the unpredictable correlation among the criteria in a suitability evaluation. Uncertainty and sensitivity analyses obtained via Monte Carlo simulation were performed to examine the robustness of the model. Daye, a resource-based city with rapid economic development, unsatisfied rural development, and geological environmental problems caused by mining, was used as a case study. Results indicate the following findings: 1) The RSSE model using the improved TOPSIS can assess the suitability of rural settlements, and the suitability maps generated using the improved TOPSIS have higher information density than those generated using traditional TOPSIS. The robustness of the model is improved, and the uncertainty is reduced in the suitability results. 2) Highly suitable land is mainly distributed in the northeast of the study area, and the majority of which is cultivated land, thereby leading to tremendous pressure on the loss of cultivated land. 3) Lastly, 12.54% of the constructive expansion permitted zone and 8.36% of the constructive expansion conditionally permitted zone are situated in an unsuitable area, which indicates that the general planning of Daye lacks the necessary verification of suitability evaluation. Guidance is provided on the development strategy of rural settlement patches to support decision making in general land use planning.

SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by this article contain special cases discussed before.

HIGHER ORDER ASYMPTOTIC SOLUTION OF MODE Ⅰ CRACK GROWTH IN ELASTIC-PERFECTLY PLASTIC MEDIA

A higher order asymptotic solution of near-tip field is studied for plane-atrain Mode-Ⅰ quasi-static steady crack growth in the incompressible (v=1/2) elastic perfectly-plastic media.The results show that the near-tip stress and strain are fully continuous,and the strain possesses In (A/r) singularity at the crack tip.The expressions of the stress,strain and velocity in each region are also given.

Existence of Ordered Solutions to Quasilinear Schrodinger Equations with General Nonlinear Term

In this paper, the existence of a pair of ordered solutions for the following class of equations in ?(1)?was studied. A bounded (PS) (Palais-Smale) sequence was constructed and the related variational principle was used to prove the existence of the positive solution. The existence of the ordered solutions is finally found.

PIECEWISE SMOOTH SOLUTION OF THE FIRST ORDER SEMILINEAR HYPERBOLIC SYSTEMS IN HIGHER SPACE DIMENSION

It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for

EQUATION OF MATHEMATICAL PHYSICS AND OTHER AREAS OF APPLICATION: A CLASSICAL INTEGRABLE SYSTEM AND THE INVOLUTIVE REPRESENTATION OF SOLUTIONS OF THE HIGHER ORDER KAUP-NEWELL EQUATION

Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.

SOLUTIONS OF THE BENJAMIN-ONO EQUATION IN FRACTIONAL ORDER SOBOLEV SPACES

We show for the Benjamin-Ono equation an existence uniqeness theorem in Sobolev spaces of arbitrary fractional order s greater-than-or-equal-to 2, provided the initial data is given in the same space.

FINITE SPEED OF PROPAGATION OF SOLUTIONS FOR SOME QUASILINEAR HIGHER ORDER PARABOLIC EQUATIONS WITH DOUBLY STRONG DEGENERATION

Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.

Ordered Sn distribution adjacent to the precipitate-matrix interface in a Mg-9.8wt.%Sn alloy

The major interface betweenβ-Mg_(3)Sn precipitate plate and theα-Mg matrix in a Mg-9.8wt.%alloy has been investigated using aberrationcorrected scanning transmission electron microscopy and first-principles calculations.It is found that Sn atoms orderly distribute in the single layer of theα-Mg matrix immediately adjacent to the broad surface ofβat the early stage of ageing.These Sn atoms substitute Mg atoms located at the centers of equilateral triangles constituted by three Mg columns in the outmost layer ofβ.First-principles calculations suggest that the ordered Sn distribution is energetically favored and it not only decreases the interfacial energy of theβ-matrix interface but also hinders the occurrence of 1/3<01■0>αshear that thickens theβplate.

Periodic Solutions of a Cooperative System with State Feedback Control

In this paper, we propose a semi-continuous dynamical system to study the cooperative system with feedback control. Based on geometrical analysis and the analogue of Poincare criterion, the existence and stability of the positive order one periodic solutions are given. Numerical results are carried out to illustrate the feasibility of our main results.

Spatial-temporal Evolution Analysis on Land Use Multifunctionality in the China-Vietnam Border Area

Exploring the spatial and temporal evolution characteristics of the border land use multifunctionality(LUMF)provides insights for taking advantage of border land use and optimizing border land use policies.Based on the improved Technique for Order Preference by Similarity to an Ideal Solution(TOPSIS)mode,this study identifies and evaluates the LUMFs in the China-Vietnam border area between 2000 and 2018 from the perspectives of agricultural production,social security,ecological service,landscape recreation,and national security.The results show that:1)The comprehensive land use functions in most counties and cities continued to be improved.2)The comprehensive land use function exhibits remarkable spatial divergence and aggregation characteristics.The high-value area of the agricultural production function and social security function evolves from the east to the west.In addition,the spatial evolution of ecological service function is complicated,without an obvious spatial divergence and aggregation pattern.The landscape recreation function shows different spatial differentiation characteristics in the early and middle stage,and forms a large cluster in the later stage.Finally,the spatial evolution pattern of the national security function is significant.3)Designing differentiated border land policies,improving border land use security,and establishing a long-term mechanism for ecological protection and ecological compensation can aid in optimizing the LUMF level in the border area.

An Evaluation of the Critical Success Factors in Sustainable Food Supply Chains in Developing Countries

Food is one of the biggest industries in developed and underdeveloped countries. Supply chain sustainability is essential in established and emerging economies because of the rising acceptance of cost-based outsourcing and the growing technological, social, and environmental concerns. The food business faces serious sustainability and growth challenges in developing countries. A comprehensive analysis of the critical success factors (CSFs) influencing the performance outcome and the sustainable supply chain management (SSCM) process. A theoretical framework is established to explain how they are used to examine the organizational aspect of the food supply chain life cycle analysis. This study examined the CSFs and revealed the relationships between them using a methodology that included a review of literature, interpretative structural modeling (ISM), and cross-impact matrix multiplication applied in classification (MICMAC) tool analysis of soil liquefaction factors. The findings of this research demonstrate that the quality and safety of food are important factors and have a direct effect on other factors. To make sustainable food supply chain management more adequate, legislators, managers, and experts need to pay attention to this factor. In this work. It also shows that companies aiming to create a sustainable business model must make sustainability a fundamental tenet of their organization. Practitioners and managers may devise effective long-term plans for establishing a sustainable food supply chain utilizing the recommended methodology.

基于组合赋权-TOPSIS模型的机场运行效率评价

为提高机场运行效率评价结果的科学性和全面性,提出了一种基于组合赋权-TOPSIS(technique for order performance by similarity to ideal solution)模型的机场运行效率评价方法。从机位运行效率、旅客登机效率、飞机滑行效率和协同效率4个维度出发,构建了由航班靠桥率、廊桥周转率、机位变更比例等11个指标组成的机场运行效率评价体系;利用G1法、熵权法分别计算评价指标主观和客观权重,以最小化主客观加权属性偏离程度为目标计算组合权重;使用TOPSIS计算待评价机场综合评价指数。利用该模型分析国内3类共8家机场的运行效率,可以得到各评价对象的运行效率等级和综合排名。结果表明:该模型能够有效探明影响机场运行效率的主要因素,具有一定的参考价值。

数字贸易发展水平测度及影响因素分析——以浙江省为例

随着数字经济的快速发展,数字贸易已成为影响经济发展的重要力量。在数字经济背景下探讨数字贸易内涵,从信息网络基础设施、数字技术水平、产业数字化贸易、数字产业化贸易和贸易潜力5个维度构建数字贸易发展评价指标体系,运用相对熵的TOPSIS(technique for order preference by similarity to an ideal solution)法对浙江省2010—2018年数字贸易发展水平进行测度。结果表明:2010-2018年浙江省数字贸易发展总体呈上升趋势;进一步基于TOE(technology-organization-environment,技术-组织-环境)框架和灰色关联度模型探讨了数字贸易发展水平的影响因素。实证研究发现:信息化水平、产业结构、政府支持力度、经济发展水平、对外贸易开放水平均能促进浙江省数字贸易发展,其中信息化水平影响最为显著,而对外贸易开放水平的影响最小。

我国三级公立医院绩效考核指标评分方法分析

基于某市三级公立医院绩效考核实践,指出用加权逼近理想解排序法及全国三级公立医院绩效考核评分办法参考说明中推荐的评分方法进行考核存在的问题与不足,并提出改进和优化评分方法的思路,为构建更加科学公正的绩效考核体系提供新的思路和方法。

Dynamic Target Wireless Network Selection Technique Using Fuzzy Linguistic Variables

Even though various wireless Net- work Access Technologies （NATs） with dif- ferent specifications and applications have been developed in the recent years, no single wireless technology alone can satisfy the any- time, anywhere, and any service wire- less-access needs of mobile users. A real seamless wireless mobile environment is only realized by considering vertical and horizontal handoffs together. One of the major design issues in heterogeneous wireless networks is the support of Vertical Handoff （VHO）. VHO occurs when a multi-interface enabled mobile terminal changes its Point of Attachment （PoA） from one type of wireless access technology to another, while maintaining an active session. In this paper we present a novel multi-criteria VHO algorithm, which chooses the target NAT based on several factors such as user preferences, system parameters, and traf- tic-types with varying Quality of Service （QoS） requirements. Two modules i.e., VHO Neces- sity Estimation （VHONE） module and target NAT selection module, are designed. Both modules utilize several ＂weighted＂ users＇ and system＇s parameters. To improve the robust- ness of the proposed algorithm, the weighting system is designed based on the concept of fuzzy linguistic variables.

Extension of TOPSIS for fuzzy multi-attribute decision making problem based on experimental analysis

This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.

Quasiperiodic Solutions for Nonlinear Differential Equations of Second Order with Symmetry

In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.