The median procedure in cluster analysis and social choice theory

Classical approachs for fitting and aggregation problems, specially in cluster analysis, social choice theory and paired comparisons methods, consist in the minimization of a remoteness function between relational data and a relational model. The notion of median, with its algebraic, metric, geometrical and statistical aspects, allow a unified treatment of many of base problems. Properties of median procedures are organized according to four directions: stabilities and axiomatic characterizations; Arrow-like properties; combinatorial properties; effective computational possibilities. Finally, interesting mathematical problems, related to the notion of median are surveyed.     

变动供给下的多物品拍卖

变动供给下的多物品拍卖是在线拍卖的形式之一，但对这一问题的相关研究未能真正地解决销售商如何确定待拍商品的数量和价格问题。本就变动供给下的多物品拍卖问题，建立了一个新的决策分析模型，与已有的模型相比，它不仅能同时确定待售商品的数量与价格，而且能有效地避免替代性商品间的外部性损失，为销售商的决策提供参考。     

The multiple judge,multiple criteria ranking problem: A fuzzy set approach

This paper investigates the problem of selecting, from a set of issues, those which best satisfy a collection of criteria. A group of judges have fuzzy sets defined over the issues, for each criterion, whose values lie in a finite linearly ordered set $\text{L}$. These judges also have fuzzy sets defined over the set of criteria. The paper discusses methods of aggregating all the fuzzy sets into one fuzzy set μ, defined on the issues, so that μA?L gives the final ranking for issue A.     

A Mössbauer study of octahedral site symmetries in systems Co x Mn3−x−y Fe y O4 and Ni x Mn3−x−y Fe y O4

A Mössbauer study of cation distribution in systems Co _x Mn_3?x?y Fe _y O₄ and Ni _x Mn_3?x?y Fe _y O₄ has been made. It has been found that in both systems all specimens withy<0.6 value exhibit quadrupole doublets corresponding to site symmetries Fe³⁺(I) and Fe³⁺(II) of octahedral site. As more and more cobalt or nickel is introduced into the matrix the intensity of the inner quadrupole doublet increases while on introducing iron that of the outer quadrupole doublet increases. After a certain concentration of iron the inner doublet starts becoming more intense. It is suggested that this arises possibly from the substitution of cations in the second co-ordination sphere of Fe³⁺(I) and Fe³⁺(II) sites. Fory>0.6 the Mössbauer spectra show relaxation effects.     

Single line queue with recurrent repeated demands

We analyze a model queueing system in which customers cannot be in continuous contact with the server, but must call in to request service. If the server is free, the customer enters service immediately, but if the server is occupied, the unsatisfied customer must break contact and reapply for service later. There are two types of customer present who may reapply. First transit customers who arrive from outside according to a Poisson process and if they find the server busy they join a source of unsatisfied customers, called the orbit, who according to an exponential distribution reapply for service till they find the server free and leave the system on completion of service. Secondly there are a number of recurrent customers present who reapply for service according to a different exponential distribution and immediately go back in to the orbit after each completion of service. We assume a general service time distribution and calculate several characterstic quantities of the system for both the constant rate of reapplying for service and for the case when customers are discouraged and reduce their rate of demand as more customers join the orbit.     

Myopia,amnesia, and consistent intertemporal choice

Social scientists often explain observed streams of behavior as the outcome of constrained choice at successive dates, with actors choosing among planned sequences of actions extending into the future. This paper presents four axioms for consistent intertemporal choice in such models. Within this framework, myopia and amnesia are defined to be choice processes in which future feasible actions and past decisions, respectively, play no role in current choice. Each of these modeling strategies is argued to have some plausibility on the basis of bounded rationality considerations. It is shown that an anticipatory process reduces to a behaviorally equivalent myopic process if and only if binary choices are lexically organized. Amnesia, or the absence of endogenous preference formation, is characterized by the condition that binary choices be ‘ahistorical’. The paper closes with some remarks on the methodological role of the consistency axioms, and the problems posed by inconsistent choice processes.     

A Mössbauer study of hyperfine interaction in the systems Co x Mn3−x−y Fe y O4 and Ni x Mn3−x−y Fe y O4

A Mössbauer study of systems Co _x Mn_3?x?y Fe _y O₄ and Ni _x Mn_3?x?y Fe _y O₄ for values ofx=0·1, 0·5, 1·0 andy ranging from 0·1 to 2·0 in steps of 0·2 have been made. At room temperature samples fory values ranging in between 0·1 to 0·5 exhibit paramagnetic behaviour while all spectra for values ofy between 0·6 to 0·8 show relaxation effects. Well-defined hyperfine Zeeman spectra are observed for all the samples withy>0·8 and resolved in two sextets corresponding to octahedral and tetrahedral site symmetries and a central doublet probably due to the presence of super-paramagnetic particles in the system. The hyperfine field at⁵⁷Fe nucleus reduces with decreasing iron cobalt and nickel concentration. These observations have been explained in terms of site preference of cations and exchange interactions.     

Weak axioms of choice for metric spaces

In the framework of ZF, i.e., Zermelo-Fraenkel set theory without the axiom of choice AC, we show that if the family of all non-empty, closed subsets of a metric space has a choice function, then so does the family of all non-empty, open subsets of . In addition, we establish that the converse is not provable in ZF.

We also show that the statement ``every subspace of the real line with the standard topology has a choice function for its family of all closed, non-empty subsets" is equivalent to the weak choice form ``every continuum sized family of non-empty subsets of reals has a choice function".

     

Symmetric social choices and collective rationality

A social choice function C defined on the m-element subsets of a set X for n voters assigns a non-empty subset C(A,R) of A to each pair (A,R) in which ¦A¦ = m,A X, and R is an n-tuple of voter preference orders on X. When n > 2, 3 m < ¦X¦, and C satisfies natural conditions of independence, symmetry among voters and alternatives, and collective rationality, it is proved that C is completely indecisive in the sense that C(A,R) = A for all (A,R). This non-binary result complements a binary (m = 2) result proved by Hanson. It suggests that there is a fundamental incompatibility between collective rationality and conditions designed to assure equitable treatment of voters and of alternatives.     

Lavrentiev's regularization method for nonlinear ill-posed equations in Banach spaces

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the implementation of Lavrentiev regularization method. Using general H¨older type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock(2005) for choosing the regularization parameter.