CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS

Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

Thinking about Value Realization of Ecological Products under the Background of Urban-rural Integration in Chengdu“Western Control”Area

Chengdu's development strategy of“western control”has laid a solid ecological background for 8 western districts,cities and counties and cultivated good ecological resources.The integrated urban-rural development in the new era will realize the balanced development of urban and rural areas and give full play to the value of rural ecological resources through the“powerful combination”of urban and rural areas.To realize the urban-rural integration and high-quality rural development in Chengdu“western control”area,it is necessary to enhance the awareness of ecological resources and ecological products,and carry out unified planning of ecological infrastructure,ecological material products and ecological service products in the whole“western control”area.Meantime,ecological restoration must be carried out scientifically,and scene design for value transformation of ecological products should be implemented innovatively.

Why Is an Integral an Accurate Value?

The derivative and integral in calculus are both exact values. To explain this reason, the integration interval can be infinitely subdivided. The difference in area between curved trapezoids and rectangles can be explained by the theory of higher-order infinitesimal, leading to the conclusion that the difference between the two is an infinitesimal value. From this, it can be inferred that the result obtained by integration is indeed an accurate value.

Research on the Value and Strategy of Integrating Music Education and National Music Culture

China’s traditional national music is an art form formed by the working people and art pioneers to express their emotions during thousands of years of productive labor.National music not only contains emotional stories that are capable of evoking praises and tears,but also has a profound understanding of the lives of sages.In summary,integrating college music education with national music culture can allow students to deeply discover music,thereby stimulating students’enthusiasm for learning music,improving students’learning quality,mastering the core parts of music learning,and helping students to go a long way in music.This article mainly focuses on the characteristics and educational value of national music culture,and its effective integration with music education in colleges and universities.This article can help relevant workers in college music education and promote the sustainable development of music education in colleges and universities in China.

Precise integration method for a class of singular two-point boundary value problems

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.

Consistency and Stability Issues in the Numerical Integration of the First and Second Order Initial Value Problem

In this note we consider some basic, yet unusual, issues pertaining to the accuracy and stability of numerical integration methods to follow the solution of first order and second order initial value problems (IVP). Included are remarks on multiple solutions, multi-step methods, effect of initial value perturbations, as well as slowing and advancing the computed motion in second order problems.

Integration of Individualized Management Systems （MSs） as an Aggregating Factor of Sustainable Value for Organizations An Overview Through a Review of the Literature

Nowadays, there exist various standards for individual management systems （MSs）, at least, one for each stakeholder. New ones will be published. An integrated management system （IMS） aims to integrate some or all components of the business into one coherent and efficient MS. Maximizing integration is more and more a strategic priority in that it constitutes an opportunity to eliminate and/or reduce potential factors of destruction of value for the organizations and also to be more competitive and consequently promote its sustainable success. A preliminary investigation was conducted on a Portuguese industrial company which, over the years, has been adopting gradually, in whole or in part, individualized management system standards （MSSs）. A research, through a questionnaire, was performed with the objective to develop, in a real business environment, an adequate and efficient IMS-QES （quality, environment, and safety） model and to potentiate for the future a generic IMS model to integrate other MSSs. The strategy and research methods have taken into consideration the case study. It was obtained a set of relevant conclusions resulting from the statistical analyses of the responses to the survey. Globally, the investigation results, by themselves, justified and prioritized the conception of a model of development of the IMS-QES and consequent definition and validation of a structure of an IMS-QES model, to be implemented at the small- and medium-sized enterprise （SME） where the investigation was conducted.

A Study on the Integration of the Confucian Culture and the Core Values of China

Core value is an important guarantee for building a harmonious socialist society and the ideological and moral basis of the unity of the people of all ethnic groups in our country.In recent years,the cultivation and practice of core values have become more and more popular;the main thoughts of core values derive fromtraditional culture.In retrospect of our traditional culture,Confucian culture is not allowed to be ignored.Therefore,in the process of fostering and practicing the core values,we need to analyze the combination between Confucian culture and core values,and ingeniously fuse the Confucian culture into the core values,so that the connotation of the core values would more abundant.

NEW BREAKTHROUGH OF HEAVY OIL UPGRADING TECHNOLOGY——INTEGRATION PROCESSES OF VRFCC/RMC FOR PRODUCTION OF HIGH VALUE PRODUCTS AND STEAM CRACKING FEED

An integration process of vacuum residue FCC(VRFCC)and moderate pressure hydro cracking(RMC),developed by RIPP and BDI,opens a new route for maximizing production of both high value products and the feed for steam cracking(SC).VRFCC technology has been put on stream at Yanshan Petrochemical Co (YPC)since November 1998.A 79 2%(mass percent)high value product(LPG+GSL+LCO)was surprisingly made on the test run from a resid feedstock of 85 0%(mass percent)Daqing crude VR content.No facility coking was found during the operation.RMC is a renovating moderate pressure hydrocracking technology,the end point of the heavy VGO feed is as high as 534 ℃,and the RMC catalyst performance shows high hydrodenitrogenation activity and high ring opening selectivity.The process highlights the flexibility of product slates——maximum premium mid distillates yield(38 0%(mass percent))and/or maximum hydro unconverted bottoms(Hydro BTMs)yield(50%～70%(mass percent)).Over 30%(mass percent)ethylene was produced from SC process based on Hydro BTMs feed. The application of VRFCC/RMC integration at YPC not only covers the shortages of SC feed for 660 kt/a ethylene production capacity,but also increases the total yield of premium fuel products.

FRACTIONAL ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL

In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.

Landslide susceptibility mapping using an integrated model of information value method and logistic regression in the Bailongjiang watershed,Gansu Province,China

Bailongjiang watershed in southern Gansu province, China, is one of the most landslide-prone regions in China, characterized by very high frequency of landslide occurrence. In order to predict the landslide occurrence, a comprehensive map of landslide susceptibility is required which may be significantly helpful in reducing loss of property and human life. In this study, an integrated model of information value method and logistic regression is proposed by using their merits at maximum and overcoming their weaknesses, which may enhance precision and accuracy of landslide susceptibility assessment. A detailed and reliable landslide inventory with 1587 landslides was prepared and randomly divided into two groups,(i) training dataset and(ii) testing dataset. Eight distinct landslide conditioning factors including lithology, slope gradient, aspect, elevation, distance to drainages,distance to faults, distance to roads and vegetation coverage were selected for landslide susceptibility mapping. The produced landslide susceptibility maps were validated by the success rate and prediction rate curves. The validation results show that the success rate and the prediction rate of the integrated model are 81.7 % and 84.6 %, respectively, which indicate that the proposed integrated method is reliable to produce an accurate landslide susceptibility map and the results may be used for landslides management and mitigation.

Second Order Periodic Boundary Value Problems Involving the Distributional Henstock-Kurzweil Integral

We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is a general intergral, which contains the Lebesgue and Henstock-Kurzweil integrals. And the distributional derivative includes ordinary derivatives and approximate derivatives. By using the method of upper and lower solutions and a fixed point theorem, we achieve some results which are the generalizations of some previous results in the literatures.

THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN C^(2)

k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel.Furthermore,the integral representation for the solution is obtained.

Valuing options to renew at future market value:the case of commercial property leases

In this study,we develop and empirically test a valuation model for a commonly encountered option in office leases:a tenant’s option to renew at future market rent(a fair market value)with lease termination as the maturity date.The model integrates decision analysis with real options analysis and market risk with private risks.“Option value”is defined as the private value of the option to either party pre-contract,while“option price”assumes a fair agreement between transacting parties and can be positive(rental premium paid)or negative(rental discount offered).Without manifest expectations,an analysis of a sample of office leases supports the model’s logic with price estimates in a practical range.The tenants’option price/value is shown to have a negative relationship with the original/renewal lease term;conversely,the landlords’option value is positively related to the original/renewal term.Comparative analyses show that transaction costs have a positive effect on tenants’option value and on prices,while vacancy costs and the vacancy period are both positively related to the landlords’option value and negatively related to price.Market rent is found to have a negative relationship with option price.Overall,this study provides a theoretical analysis and empirical tests of the value of a real option that allows option holders to renew/extend their contracts at a fair market value.

VQT:value cardinality and query pattern based R-schema to XML schema translation with implicit referential integrity

In this paper,we propose a new relational schema (R-schema) to XML schema translation algorithm, VQT, which analyzes the value cardinality and user query patterns and extracts the implicit referential integrities by using the cardinality property of foreign key constraints between columns and the equi-join characteristic in user queries. The VQT algorithm can apply the extracted implied referential integrity relation information to the R-schema and create an XML schema as the final result. Therefore, the VQT algorithm prevents the R-schema from being incorrectly converted into the XML schema, and it richly and powerfully represents all the information in the R-schema by creating an XML schema as the translation result on behalf of the XML DTD.

Extrapolation Method for Cauchy Principal Value Integral with Classical Rectangle Rule on Interval

In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.

A∞ weight estimates for vector-valued commutators of multilinear fractional integral

In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained.

Value Source of Integrated Refining/Chemical Plant

Based on an integrated refining/chemical plant processing 15 Mt/a of crude and manufacturing 1.0 Mt/a of ethylene under the guideline of＂engaging in refining, olefins and aromatics by whatever appropriate means＂ to maximize the overall value of the integrated refining/chemical plant, it is necessary to concentrate on working on the flow diagram and the solution for mutual supply of materials between the refinery and ethylene plant. After analyzing the feedstock slate, the composition and properties of products, it is proposed to optimize the integrated refming/chemical plant in order to reduce investment and operating cost to realize maximization of the value of the integrated plant.

An Equivalent Condition for （K） Integrability of Fuzzy-valued Mappings

In this paper, we first discuss the relationship between the McShane integral and Pettis integral for vector-valued functions. Then by using the embedding theorems for the fuzzy number space E^1, we give a new equivalent condition for （K） integrabihty of a fuzzy set-valued mapping F ： [a, b] → E^1.

BMO BOUNDEDNESS FOR BANACH SPACE VALUED SINGULAR INTEGRALS

In this paper, we consider a class of Banach space valued singular integrals. The Lp boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundedness for the classic g-function and the Marcinkiewicz integral. Some known results are improved.