The Hjek-Rnyi Inequlity For Banach Space Valued Random Variable Sequences and Its Application

In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.

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.

Integrate SMEs into the Global Value Chain

We have talked about inclusiveness in many occasions in the SMEs taskforce working group.The starting point for our discussion is how to incorporate more people,more SMEs,morewomen and more young entrepreneurs into global economic development.SMEs shall be involved in the global trade platform along a certain value chain.If this can be achieved,

ON THE ERROR OF QUADRATURE FORMULAE FOR CAUCHY PRINCIPAL VALUE INTEGRALS BASED ON PIECEWISE INTERPOLATION

We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the estimates where quadrature error) is determined for fixed i and which means that not only the. order, but also the coefficient of the main term of is determined. The behaviour of these error constants is compared -with the corresponding ones obtained for the. method of subtraction of the singularity. As it turns out, these error constants have, in general, the same asymptotic behaviour.

The Rectangle Rule for Computing Cauchy Principal Value Integral on Circle

The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.

Developmetn stage threshold of watershed Landforms in Loess Plateau and separation of erosion mechanism

Threshold is a limit and marginal point when a qualitative change takes place. Since threshold principle was firstly used in landform research by S.A.Schumm in the 1970s, the quantitative research on watershed landform development stage has come true. Davis proposed a three-stage model on landform evolution: young, mature and old stages. Thereafter Strahler quantified this model by hypsometric analysis method. The authors thought that the material movement stage cannot be expressed by hypsometric method in watershed landform at development stage, because of the uncertainty on stage delimitation. To meet this shortcoming, this paper presents an integral erosion value method. A clear delimitation on landform development stage in the Loess Plateau region has been tested by this method. The result shows that gullied loessial hilly area is at the mature stage, and gullied loessial tableland area is at the young stage. It is estimated that from the point of erosion related sediment yield, natural erosion accounts for 70% of the total erosion amount, and artificial accelerating erosion is 30%. Therefore soil and water conservation is very crucial for the Loess Plateau.

A critical analysis of environmental evolutionin the loess-plateau area

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Peano Derivatives and Singular Integrals of Arbitrary Order

The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established.

Integrating Human Rights Conflicts in COVID-19 Pandemic Prevention and Control

In the fight against the COVID-19 pandemic, conflicts between the right to life and health and the rights to freedom, economy and equality are inevitable exploring conflicts of human rights and responding solutions will directly influence the success of the battle against the coronavirus From the perspective of human rights’ subjects, the conflicts are between young and elder COVID-19 patients, COVID-19 and non-COVID-19 patients, citizens from epidemic center areas and non-epidemic areas In terms of the content of these rights, the conflict between the right to life and health and the right to econom ic freedom should be resolved based on four principles: priority, the limit of costs, baseline equality, and resto ration of justice on the value side, the relationship between social order and freedoms should be clarified in five aspects: life, market, security, news, and speech to build a good governance model that can stabilize the order of epidemic preven tion & control order and maintain social vitality.

The Symmetric Banzhaf Value for Fuzzy Games with a Coalition Structure

In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp case.Furthermore,we study the symmetric Banzhaf values for two special kinds of fuzzy games,which are called fuzzy games with multilinear extension form and a coalition structure,and fuzzy games with Choquet integral form and a coalition structure,respectively.

POSITIVE SOLUTIONS TO AN INTEGRAL BOUNDARY VALUE PROBLEM WITH DELAY

In this paper, we study a second order integral boundary value problem with delay. By the Krasnoselskii fixed point theorem, we obtain sufficient conditions for the existence of at least one or two positive solutions to the problem.

POSITIVE SOLUTIONS TO A COUPLED SYSTEM OF FRACTIONAL INTEGRAL BOUNDARY VALUE PROBLEM WITH DELAY

In this paper, we study the existence of positive solutions to an integral boundary value problem with delay for a coupled system of fractional differential equations. By using the Krasnoselskii fixed point theorem, we obtain sufficient conditions for the existence of at least one or two positive solutions to the problem under some weaker conditions.

POSITIVE SOLUTIONS TO A FIRST ORDER IMPULSIVE INTEGRAL BOUNDARY VALUE PROBLEM ON TIME SCALES

In this paper, we are mainly concerned with the existence and multiplicity of positive solutions to a frst order integral boundary value problem with impulsive efects on time scales. Under some conditions concerning the frst eigenvalues corresponding to the relevant linear operators, we obtain the main results by Krasnoselskii-Zabreiko fxed point theorem.

ITERATIVE POSITIVE SOLUTIONS FOR SINGULAR RIEMANN-STIELTJES INTEGRAL BOUNDARY VALUE PROBLEM

By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f（t,u） is non-increasing respect to u.

SOLVABILITY FOR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION BOUNDARY VALUE PROBLEMS AT RESONANCE

The paper deals a fractional functional boundary value problems with integral boundary conditions. Besed on the coincidence degree theory, some existence criteria of solutions at resonance are established.

Globalization and the Evolution and Characteristics of Spatial Distribution of Transnational Organizations in Guangzhou(1949–2012)

Transnational organizations refer to governmental and non-governmental organizations engaged in transnational behaviors,which are important carriers of political globalization.Given the wave of world city studies sweeping the academia worldwide,transnational organizations have attracted increasing attentions.Through a review of existing research,an analysis of historical archive and interviews,and the application of space syntax,this paper examines the development process and characteristics of spatial distribution of transnational organizations in Guangzhou since the founding of P.R.China.It divides the development process of transnational organizations in Guangzhou into three stages: budding period,starting period,and developing period.In this process,the number of organizations and related types increased sharply,and the business was much extended.Along with the eastward shift of the city center,the distribution center of transnational organizations consequently moved to the east,indicating their location characteristics of geographical centrality and proximity to major globalized spaces.The spatial distribution of transnational organizations shows: proximity to city center or high-level transportation center; demands for security,communication,and notability of geographical position; locations of different types of organizations owning different levels of integration value; organizations of specific functions prefer urban districts with related functions.

MULTIPLICITY OF NONNEGATIVE SOLUTIONS TO SECOND-ORDER SINGULAR DIFFERENTIAL EQUATION WITH INTEGRAL BOUNDARY CONDITIONS IN BANACH SPACES

This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].

ON THE CONVERGENCE OF PROJECTOR-SPLINES FOR THE NUMERICAL EVALUATION OF CERTAIN TWO-DIMENSIONAL CPV INTEGRALS

Focuses on a study that proposed product formulas based on projector-splines for the numerical evaluation of two-dimensional Cauchy principal value integrals. Preliminaries; Convergence of quadrature rules using projector-splines; Numerical results.