The Frontiers and Future Landscape of Research and Education on Value Rationality in Contemporary China

The importance of conducting in-depth research and education on value rationality in the new era is increasingly recognized.Therefore,it is essential to systematically grasp the themes,frontiers,and trends of research in this field,organizing the knowledge system to provide references for future studies.This necessitates clarifying the research achievements of scholars from different disciplines and institutions.Using the CiteSpace visualization analysis method,we can analyze,summarize,and synthesize research networks,hotspots,and knowledge structures,thereby forming a direction for advancing research.Through literature review methods and knowledge graph software analysis,it is believed that value rationality and instrumental rationality represent the rational attitudes individuals adopt when contemplating issues and putting them into practice.They are merely methods and should not be subjected to excessive value judgments.The relationship between value rationality and instrumental rationality is a focal point of societal concern,involving complex interdisciplinary issues with significant theoretical value and practical implications.In the future,the academic community needs to strengthen research collaboration,enhance the expansion of value rationality in various social practice fields,and conduct empirical studies to build consensus for the construction of Chinese society.

Analysis on Value Rationality of Traditional Farm Tools in the Taomin Area

This paper introduces the types of traditional farm tools,and analyzes the value rationality of these traditional farm tools:on the one hand,these farm tools have witnessed the farming culture,and they are also a manifestation of local culture in the Taomin area,representing the cultural characteristics and civilization progress of this area.

The value rationality and tool rationality of Health Priority

Health Priority is increasingly becoming a human need and an international consensus.In addition to the basic value judgment and direction-leading function,Health Priority also has a clear,practical meaning and distinct tool attributes.The text adheres to the organic unity of regularity and purpose,follows the modern medical model and the philosophy of system theory,combines the characteristic facts,and discusses the value rationality and tool rationality of Health Priority based on the whole process management,and tries to refine the Health Priority governance model with Chinese characteristics,so as to provide a reference for global health governance.

MATRIX ALGORITHMS AND ERROR FORMULA FOR BIVARIATE THIELE-TYPE RECTANGULAR MATRIX VALUED RATIONAL INTERPOLATION

A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.

Werner-Type Matrix Valued Rational Interpolation and Its Recurrence Algorithms

In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fraction form to rational function form of the interpolants, an efficient forward recurrence algorithm is obtained.

THE NOTE ON MATRIX-VALUED RATIONAL INTERPOLATION

In [3], a kind of matrix-valued rational interpolants (MRIs) in the form of Rn(x) = M(x)/D(x) with the divisibility condition D(x) | ‖M(x)‖2, was defined, and the characterization theorem and uniqueness theorem for MRIs were proved. However this divisibility condition is found not necessary in some cases. In this paper, we remove this restricted condition, define the generalized matrix-valued rational interpolants (GMRIs) and establish the characterization theorem and uniqueness theorem for GMRIs. One can see that the characterization theorem and uniqueness theorem for MRIs are the special cases of those for GMRIs. Moreover, by defining a kind of inner product,we succeed in unifying the Samelson inverses for a vector and a matrix.

Rational solutions of Painlevé-Ⅱequation as Gram determinant

Under the Flaschka-Newell Lax pair,the Darboux transformation for the Painlevé-Ⅱequation is constructed by the limiting technique.With the aid of the Darboux transformation,the rational solutions are represented by the Gram determinant,and then we give the large y asymptotics of the determinant and the rational solutions.Finally,the solution of the corresponding Riemann-Hilbert problem is obtained from the Darboux matrices.

On the Coalitional Rationality and the Inverse Problem for Shapley Value and the Semivalues

In cooperative game theory, a central problem is to allocate fairly the win of the grand coalition to the players who agreed to cooperate and form the grand coalition. Such allocations are obtained by means of values, having some fairness properties, expressed in most cases by groups of axioms. In an earlier work, we solved what we called the Inverse Problem for Semivalues, in which the main result was offering an explicit formula providing the set of all games with an a priori given Semivalue, associated with a given weight vector. However, in this set there is an infinite set of games for which the Semivalues are not coalitional rational, perhaps not efficient, so that these are not fair practical solutions of the above fundamental problem. Among the Semivalues, coalitional rational solutions for the Shapley Value and the Banzhaf Value have been given in two more recent works. In the present paper, based upon a general potential basis, relative to Semivalues, for a given game and a given Semivalue, we solve the connected problem: in the Inverse Set, find out a game with the same Semivalue, which is also coalitional rational. Several examples will illustrate the corresponding numerical technique.

Generalized Inverse Vector Valued Osculatory Rational Interpolation and Its Error Formula

In this paper, osculatory rational functions of Thiele-type introduced by Salzer (1962) are extended to the case of vector valued quantities using tile t'ormalism of Graves-Moms (1983). In the computation of the osculatory continued h.actions, the three term recurrence relation is avoided and a new coefficient algorithm is introduced, which is the characteristic of recursive operation. Some examples are given to illustrate its effectiveness. A sutficient condition for cxistence is established. Some interpolating properties including uniqueness are discussed. In the end, all exact interpolating error formula is obtained.

PROBLEMS AND METHODS IN MATRIX VALUED RATIONAL INTERPOLATION

A variety of matrix rational interpolation problems include the partial realizationproblem for matrix power series and the minimal rational interpolation problem for generalmatrix functions.Several problems in circuit theory and digital filter design can also be re-duced to the solution of matrix rational interpolation problems[1—4].By means of thereachability and the observability indices of defined pairs of matrices,Antoulas,Ball,Kang and Willems solved the minimal matrix rational interpolation problem in[1].On

On the Coalitional Rationality of the Shapley Value and Other Efficient Values of Cooperative TU Games

In the theory of cooperative transferable utilities games, (TU games), the Efficient Values, that is those which show how the win of the grand coalition is shared by the players, may not be a good solution to give a fair outcome to each player. In an earlier work of the author, the Inverse Problem has been stated and explicitely solved for the Shapley Value and for the Least Square Values. In the present paper, for a given vector, which is the Shapley Value of a game, but it is not coalitional rational, that is it does not belong to the Core of the game, we would like to find out a new game with the Shapley Value equal to the a priori given vector and for which this vector is also in the Core of the game. In other words, in the Inverse Set relative to the Shapley Value, we want to find out a new game, for which the Shapley Value is coalitional rational. The results show how such a game may be obtained, and some examples are illustrating the technique. Moreover, it is shown that beside the original game, there are always other games for which the given vector is not in the Core. The similar problem is solved for the Least Square Values.

一类微分-差分多项式的值分布及分担有理函数的唯一性

本文利用Nevanlinna值分布理论,研究了零级超越亚纯函数条件下的一类微分-差分多项式的值分布问题,以及两个零级超越亚纯的微分-差分多项式在极点相同(不计重数)的条件下CM分担一个有理函数的唯一性问题,得到了两个定理及三个推论,所得结果改进或推广了陈文杰等人以及赵秋霞等人的相关结果.

Estimating Sums of Convergent Series via Rational Polynomials

Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained by taking the asymptotic limit of the rational polynomial. A rational function with second-degree polynomials both in the numerator and denominator is found to produce excellent results. Sums of series with different characteristics such as alternating signs are considered for testing the performance of the proposed approach.

Non-use value assessment for wetland ecosystem service of Hongxing National Nature Reserve in northeast China

By the contingent value method, we studied the non-use value of wetland ecosystem service of Hongxing National Nature Reserve （HNNR） in Heilongjiang Pro- vince, northeast China. The proportion of respondents willing to pay （WTP） for protection of HNNR was 63 %. The WTP ratio was affected by geographical area, contact nature, personal preferences, and familiar degree of the respondents. The WTP value was affected by age, education level and career of the respondents. The mainly reasons for people rejecting to pay for protecting HNNR were ＂I am not familiar to HNNR＂ and ＂I had no capacity for additional spending because of low income＂. Weighted average individual WTP value was CNY 59.26 Yuan ind.^-1 year^-1 for all the respondents with WTP. The total non-use ecosystem service value of HNNR was CNY 1430 million Yuan in 2013. The heritage value was highest followed by existence value and option value. From the high ecosystem service value in HNNR, it is very important to construct nature reserve for protecting natural ecosystems and human sustainable use of natural resources.

VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.

Three-Dimensional Generalized Inverse Matrix Rational Interpolation

In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.

Two Dual Expansions for Generalized Bivariate Thiele-Type Matrix Valued Interpolating Continued Fractions

A new method for the construction of bivariate matrix valued rational interpolants on a rectangulargrid is introduced. The rational interpolants are expressed in the continued fraction form with scalardenominator. Tile matrix quotients are based oil the generalized inverse for a matrix, Which is found to beeffective in continued fraction interpolation. In this paper, tWo dual expansions for bivariate matrix valuedThiele-type interpolating continued fractions are presented, then, tWo dual rational interpolants are definedout of them.

Should a Rational Person With Risk-Averse Attitude Gamble？ A Case Study of Mark Six in Hong Kong

Contrary to the conventional wisdom which suggests that a perfectly rational subject with risk-averse attitude should never gamble, this paper provides a vivid example in our real economy for people to expect a positive return to gamble Within the existing literature, scholars have proposed different reasons to explain why an original risk-averse person would start to gamble, with the implicit assumption that the expected payoff of a bet is always lower than its cost. In contrast, our paper discusses when and why a risk-averse person could bet strategically with a positive expected return; in particular, we used field data in Hong Kong to illustrate a vivid scenario for positive expected return in gambling.

论预防性治理中价值-工具双重理性关系的平衡

预防性治理作为风险或纠纷源头治理的重要方式,在我国治理现代化进程中发挥着重要作用。重大决策社会稳定风险评估机制、矛盾纠纷排查机制和社会治安综合治理机制等是预防性治理的重要载体。这些机制内含价值-工具双重理性。受传统社会管理模式等因素影响,预防性治理机制中的价值理性和工具理性之间会产生紧张关系。具体表现为,作为治理目的的“人”未得到应有尊重,多元价值位阶倒置影响预防性治理效果,以及治理主导主体的治理权缺乏有效规范等。为此应当进行必要的调整或采取相应措施,包括明确“人”作为预防性治理的首要目的,重置预防性治理所维护的多元价值位阶,以及规范治理主导主体治理权的使用等,以平衡好预防性治理中价值-工具双重理性的关系,实现良好治理。

A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.