EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo＇s derivative{C0D^δtu（t）=g（t,u（t））,0〈t〈1,1〈δ〈2,u（0）α≠0,u（1）=β≠0.

Measuring Recreational Value of World Heritage Sites Based on Contingent Valuation Method:A Case Study of Jiuzhaigou

World heritage possesses various kinds of use value and non-use value. Measuring the recreational value of world heritage sites is a key issue in the heritage tourism. This paper employs Contingent Valuation Method (CVM), which is an evaluation instrument on the basis of tourists′ attitude and preference, to measure the recreational value of Jiuzhaigou, one of the World Natural Heritage sites in China, and analyzes the biases in the survey. The results show that: 1) In 2009, Jiuzhaigou′s recreational value was 3.46×108 yuan (RMB), and the per capita Willingness to Pay (WTP) was 137.31 yuan by CVM. Compared with the results of other methods, this result is significantly low. 2) Among the factors that influence Jiuzhaigou tourists′ WTP, psychological perception factors have the greatest effect while demographic and socio-economic characteristics have a small effect on WTP. 3) The virtuality in CVM creates biases both from CVM itself and in the procedures that CVM was implemented. The former includes hypothetical bias, information bias, protest response bias, and strategic bias; and the latter includes the questionnaire design, population and sample definition, sampling and data processing. The paper analyses those biases and illustrates their potential in-fluences on the accuracy of CVM measurement. 4) Although there are various defects in CVM measurement, it is still an effective valuation method.

EXISTENCE OF SOLUTION FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.

Optimal b value of diffusion-weighted imaging on a 3.0T magnetic resonance scanner in Crohn's disease

AIM: To determine the optimal b value of diffusion-weighted imaging for detecting active inflammation in Crohn’s disease.

Assessment of self- and cross-absorbed SAF values for HDRK-man using GEANT4 code: internal photon and electron emitters

The ultimate need to account for the partial amount of energy deposited in target tissue/organ resulting from internal inhalation,ingestion,and injection intakes of radionuclides,defined by the Medical Internal Radiation Dosimetry committee as the specific absorbed fraction(SAF),has become obvious.In this study,we assessed the SAF values for self-and cross-absorption,which were calculated for a uniform distribution of monoenergetic photon and electron emitters with energies ranging from 15 keV to 3 MeV.The voxelized human phantom‘‘High-Definition Reference Korean-man’’(HDRK-man),which was implemented using the Monte Carlo simulation code GEANT4(version 10.1),was used for several combinations of target–source organs.The results were compared to those of the International Commission on Radiological Protection Reference(ICRP133)and Zubal phantoms.It was found that the SAF values of the three models have a similar trend.However,the SAF values for the HDRK-man phantom were higher than those of the other two models,with a relatively good agreement with those for the ICRP133 phantom(differences of 13.9±2.8 and 12.1±3.2 for photon and electron emitters,respectively).To analyze the differences in SAF values,we calculated the chord length distributions(CLDs)for selected target–source combinations.The parameters of organ mass(or volume)and CLDs,in addition to the adopted computational procedures,mainly cause such discrepancies.For realistic radionuclide emission spectra,an overall overestimation was observed when computing the S values for three radiopharmaceuticals studied(I-131,In-111,and Lu-177)and for liver–spleen intra-and inter-organ absorption when compared with published data.The new arrangement of S and SAF values is expected to add value for multidisciplinary research and clinical communities.

Davis's Inequalities for Two-Parameter Banach Space Valued Strong Martingales and Geometrical Properties of Banach Spaces

In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach spaces.

Q value of anelastic S-wave attenuation in Yunnan region

The study of seismic attenuation property is a major subject in seismology. Seismic waves recorded by seismic stations （seismographs） contain source effect, seismic wave propagation effect, site response of seismic stations and instrumental response. The path effect of seismic wave propagation, site response of seismic stations and instrumental response must be taken out in the study of source property with seismic data. The path effect of seismic wave propagation （seismic attenuation） involves an important influential factor, the anelastic attenuation of medium, which is measured with quality factor Q, apart from geometric attenuation with the distance. As a basic physical parameter of the Earth medium, Q value is essential for quantitative study of earthquakes and source property （e.g. determination of source parameters）, which is widely used in earthquake source physics and engineering seismology.

On Accelerated Singular Value Thresholding Algorithm for Matrix Completion

An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT to O(1/N2), where N is the number of iterations. In this paper, we show that it is the same as the Nemirovski’s approach, and then modify it to obtain an accelerate Nemirovski’s technique and prove the convergence. Our preliminary computational results are very favorable.

BOREL'S DIRECTIONS AND SHARED VALUES

In this article, we study the problems of Borel＇s directions of meromorphic func- tions concerning shared values and prove that if two meromorphie functions of infinite order share three distinct values, their Borel＇s directions are same.

Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .

Resolution of Grandi’s Paradox as Extended to Complex Valued Functions

Grandi’s paradox, which was posed for a real function of the form 1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function 1/(1+ ex ) . Grandi-type complex valued functions such as 1/(i + x) are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.

Existence of Positive Solutions of Three-point Boundary Value Problem for Higher Order Nonlinear Fractional Differential Equations

In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.

The Value of Saudi Arabia Industrial Firms Between the Modigliani-Miller＇s and Gordon＇s Models： An Empirical Study on Cement Companies in Saudi Arabia

The most important target of the financial management is to develop the values of the foundation and develop the wealth of shareholders （wealth of the owners）, which is the primary target of the qualified and successful financial management. This target, developing the value of the foundation, depends on the total profit that could be achieved by the company and counting the profit per share, but undoubtedly, the financial management should consider the other targets such as social responsibility and exchange between risk and revenue and others. This research, with its both theoretical and practical aspects, aims at illuminating the value of some foundations in Saudi Arabia, which are already registered in the stock market, by comparing the value of each foundation using two models namely the model of Modigliani-Miller （M＆M） and the model of Gordon. In spite of the difficulties found in the usage of both models, especially Gordon＇s model, we will use both of them to explain the aspects of imperfection in each model. This research will depend on a sample of Sandi industrial companies by getting financial data of these companies over a past decade and the usage of these data, in other words, to measure the value of Saudi companies against the market.

Unified Equation of Fundamental Forces’ Coupling Values, and the Existence of Subsequent, Fifth and Other, Forces

This paper provides an equation to entangle all known fundamental forces by employing their coupling constants, i.e., strong (αs), electromagnetic (α), weak (αw), and gravitational (αg) interaction coupling values. The constant coupling formulation is further indicative of many other fundamental forces with significantly weaker coupling values. As an example, the fifth fundamental force, Kashi’s Force, is found to have a coupling constant of 10-1446, which is significantly smaller than the smallest known fundamental force, gravitational force, with an approximate coupling constant value of 10-38. Additionally, the paper finds the sum of all fundamental forces based on the equation proposed is equal to 0.118065, which is within the range of effective world value of the strong coupling constant αs(M2z).

A Cross-Cultural Analysis on Guasha Treatment from Hofstede's Value Dimensions

Nowadays,with the irresistible trend of globalization and more increasing cultural exchanges among different cultures,there are more and more contacts and collisions from different cultural backgrounds.People can derive a lot from different cultures through communication.But if people cannot understand other cultures'customs,religions,habits,and so on very well,people will be faced with cultural clashes.Guasha Treatmen is Zheng Xiaolong's classical movie,which tells us a judicial conflict owing to red scars on a boy's back.In the movie,because the boy catches a cold,Chinese immigrates performs Guasha treatment to cure the boy while American people believes that the boy is treated badly.For the Chinese family in the movie,Guasha treatment is only a traditional medical therapy,but American people assume that it is an illegal act as they cannot understand Chinese medical culture.Hence,there exists misunderstanding and cultural conflicts because of cultural differences.This paper will be analyzed from the perspective of Greet Hofstede's three value dimensions so as to help people face the contradiction and conflicts in the process of cross-cultural communication and improve the ability of intercultural communication.

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.

Well-posedness of the time-varying linear electromagnetic initial-boundary value proble

The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday＇s law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss＇s formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.

Absolute Reference Values of the Real Gas

With his publication in 1873 [1] J. W. Gibbs formulated the thermodynamic theory. It describes almost all macroscopically observed properties of matter and could also describe all phenomena if only the free energy U - ST were explicitly known numerically. The thermodynamic uniqueness of the free energy obviously depends on that of the internal energy U and the entropy S, which in both cases Gibbs had been unable to specify. This uncertainty, lasting more than 100 years, was not eliminated either by Nernst’s hypothesis S = 0 at T = 0. This was not achieved till the advent of additional proof of the thermodynamic relation U = 0 at T = Tc. It is noteworthy that from purely thermodynamic consideration of intensive and extensive quantities it is possible to derive both Gibbs’s formulations of entropy and internal energy and their now established absolute reference values. Further proofs of the vanishing value of the internal energy at the critical point emanate from the fact that in the case of the saturated fluid both the internal energy and its phase-specific components can be represented as functions of the evaporation energy. Combining the differential expressions in Gibbs’s equation for the internal energy, d(μ/T)/d(1/T) and d(p/T)/d(1/T), to a new variable d(μ/T)/d(p/T) leads to a volume equation with the lower limit vc as boundary condition. By means of a variable transformation one obtains a functional equation for the sum of two dimensionless variables, each of them being related to an identical form of local interaction forces between fluid particles, but the different particle densities in the vapor and liquid spaces produce different interaction effects. The same functional equation also appears in another context relating to the internal energy. The solution of this equation can be given in analytic form and has been published [2] [3]. Using the solutions emerging in different sets of problems, one can calculate absolutely the internal energy as a function of temperature-dependent, phase-specific volumes and vapor pressure.

Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems

In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.

Godunov＇s method for initial-boundary value problem of scalar conservation laws

This paper is concerned with Godunov＇s scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov＇s scheme, which satisfies the boundary entropy condition, was given. By use of the scheme, numerical simulation for the weak entropy solution to the initial-boundary value problem of scalar conservation laws is conducted.