On the properties of solutions for NTU communication situations<Superscript>1</Superscript>

We consider the model of cooperative games in which the agents can restrict the communication, because agents are sometimes divided into subgroups in a natural way, for example by their political affinities or by the companies that employ them. More particularly we focus on cooperative games with non-transferable utility, where the communication restrictions are represented by a graph defined on the set of agents. For this class of games we consider two solutions that are modifications of the Shapley value. We axiomatically characterize these two solutions and study their relation to the strong core.The authors acknowledge the financial support of El Ministerio español de Ciencia y Tecnología, FEDER and Xunta de Galicia through projects BEC2002-04102-C02-02 and PGIDIT03PXIC20701PN. We would also like to thank Dr. Jo Dee Anderson for her linguistic support.     

On the Convexity of Precedence Sequencing Games

In this paper we study a class of cooperative sequencing games that arise from one-machine sequencing situations in which chain precedence relations are imposed on the jobs. We show that these sequencing games are convex if the initial order of the jobs is a concatenation of chains. F. Klijn's research is supported by a Ramón y Cajal contract of the Spanish Ministerio de Ciencia y Tecnología. The main part of F. Klijn's work was supported by a Marie Curie Fellowship of the European Community programme “Improving Human Research Potential and the Socio-economic Knowledge Base” under contract number HPMF-CT-2001-01232, carried out at the Departament d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona. His work is also partially supported by Research Grant BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and by the Barcelona Economics Program of CREA     

Splitting graphs when calculating Myerson value for pure overhead games

A communication situation consists of a coalitional game and a graph, the nodes of the graph corresponding to the players of the game. To calculate the Myerson value for such situations, we obtain results which extend those well known for trees and cycle-complete graphs. On the other hand, in order to reduce the associated calculus for communication situations with a pure overhead game, the possibility of splitting the graph in several subgraphs is analyzed. For each fixed decomposition of the graph, a subspace of games compatible with this decomposition is given.     

Approach to accuracy assessment of the glass-electrode potentiometric determination of acid-base properties

Thermodynamic data are suitable subject for investigating strategies and concepts for the evaluation of complete measurement uncertainty budgets in situations where the measurand cannot be expressed in a mathematical formula. Some suitable approaches are the various forms of Monte Carlo simulations in combination with computer-intensive statistical methods that are directed to an evaluation of empirical distribution curves for the uncertainty budget. Basis of the analysis is a cause-and-effect diagram. Some experience is available with cause-and-effect analysis of thermodynamic data derived from spectrophotometric data. Another important technique for the evaluation of thermodynamic data is glass-electrode potentiometry. On basis of a newly derived cause-and-effect diagram, a complete measurement uncertainty budget for the determination of the acidity constants of phosphoric acid by glass-electrode potentiometry is derived. A combination of Monte Carlo and bootstrap methods is applied in conjunction with the commercially available code SUPERQUAD. The results suggest that glass-electrode potentiometry may achieve a high within-laboratory precision because major uncertainty contributions become evident via interlaboratory comparisons. This finding is further underscored by analysing available literature data.     

A core-allocation family for generalized holding cost games

Inventory situations, introduced in Meca et al. (Eur J Oper Res 156: 127–139, 2004), study how a collective of firms can minimize its joint inventory cost by means of co-operation. Depending on the information revealed by the individual firms, they analyze two related cooperative TU games: inventory cost games and holding cost games, and focus on proportional division mechanisms to share the joint cost. In this paper we introduce a new class of inventory games: generalized holding cost games, which extends the class of holding cost games. It turns out that generalized holding cost games are totally balanced.We then focus on the study of a core-allocation family which is called N-rational solution family.It is proved that a particular relation of inclusion exists between the former and the core. In addition, an N-rational solution called minimum square proportional ruleis studied. This work was partially supported by the Spanish Ministry of Education and Science, and the Generalitat Valenciana (grants MTM2005-09184-C02-02, CSD2006-00032, ACOMP06/040). The author thanks Javier Toledo, Josefa Cá novas, and two anonymous referees for helpful comments.     

走进真实情境的初中化学教学——溶液的形成

“溶液的形成”是初中化学学习物质的多样性的典型性内容。通过“制奶茶—探奶茶—品奶茶”3个环节使学生设计实验,运用手持数字化实验、模型示意图等多种手段,观察、比较、分类、推理,从多角度认识溶液,建构溶液的宏观特征与微观本质的关联。在真实的生活情境中转变实验策略,改变学习方式,完成具有挑战性的任务,逐步加深对溶液这一核心知识的理解和迁移应用。在“做中学”“用中学”中领悟学科观念、方法和价值。     

Weak consistency of the Support Vector Machine Quantile Regression approach when covariates are functions

This paper deals with a nonparametric estimation of conditional quantile regression when the explanatory variable X takes its values in a bounded subspace of a functional space X and the response Y takes its values in a compact of the space Y?R. The functional observations, X₁,…,X_n, are projected onto a finite dimensional subspace having a suitable orthonormal system. The X_i’s will be characterized by their coordinates in this basis. We perform the Support Vector Machine Quantile Regression approach in finite dimension with the selected coefficients. Then we establish weak consistency of this estimator. The various parameters needed for the construction of this estimator are automatically selected by data-splitting and by penalized empirical risk minimization.     

The stability of learners’ choices for real-life situations to be used in mathematics

One of the efforts to improve and enhance the performance and achievement in mathematics of learners is the incorporation of life-related contexts in mathematics teaching and assessments. These contexts are normally, with good reasons, decided upon by curriculum makers, textbook authors, teachers and constructors of examinations and tests. However, little or no consideration is given to whether students prefer and find these real-life situations interesting. There is also a dearth of studies dealing explicitly with the real-life situations learners prefer to deal with in mathematics. This issue was investigated and data on students’ choices for contextual issues to be used in mathematics were collected at two time periods. The results indicate that learners’ preferences for contextual situations to be used in mathematics remained fairly stable. It is concluded that real-life issues that learners highly prefer are not normally included in the school mathematics curriculum and that there is a need for a multidisciplinary approach to develop mathematical activities which take into account the expressed preferences of learners.     

A logic‐mathematical point of view of the truth: Reality,perception, and language

In this article, the authors propose a theory of the truth value of propositions from a logic‐mathematical point of view. The work that the authors present is an attempt to address this question from an epistemological, linguistic, and logical‐mathematical point of view. What is it to exist and how do we define existence? The main objective of this work is an approach to the first of these questions. We leave a more thorough treatment of the problem of existence for future works. © 2014 Wiley Periodicals, Inc. Complexity 20: 58–67, 2015     

A REGULARIZED CONJUGATE GRADIENT METHOD FOR SYMMETRIC POSITIVE DEFINITE SYSTEM OF LINEAR EQUATIONS

AbstractA class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.