One-dimensional optimal bounded-shape partitions for Schur convex sum objective functions

Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned n_i numbers with n_i lying in a given range. The goal is to maximize a Schur convex function F whose ith argument is the sum of numbers assigned to part i. The shape of a partition is the vector consisting of the sizes of its parts, further, a shape (without referring to a particular partition) is a vector of nonnegative integers (n₁,..., n_p) which sum to n. A partition is called size-consecutive if there is a ranking of the parts which is consistent with their sizes, and all elements in a higher-ranked part exceed all elements in the lower-ranked part. We demonstrate that one can restrict attention to size-consecutive partitions with shapes that are nonmajorized, we study these shapes, bound their numbers and develop algorithms to enumerate them. Our study extends the analysis of a previous paper by Hwang and Rothblum which discussed the above problem assuming the existence of a majorizing shape. This research is partially supported by ROC National Science grant NSC 92-2115-M-009-014.     

On the number of separable partitions

Consider partitions of a given set A of n distinct points in general position in ℝ ^d into parts where each pair of parts can be separated by a hyperplane that contains a given set of points E. We consider the problem of counting and generating all such partitions (correcting a classic 1967 result of Harding about the number of such partitions into two parts). Applications of the result to partition problems are presented.     

CAPITAL CONTROLS AND DEVIATIONS FROM PROPOSED INTEREST RATE PARITY; MEXICO 1982

An intervention analysis of the Mexican capital control policy of August 1982 shows the policy to have a negative, but temporary, impact on the Mexican deviation from interest rate parity. Previous studies concerning the impact of capital control inteventions have predicted positive effects of capital control policies. These stem from the effective tax capital controls place on foreign capital inflows. When capital controls are also designed to restrict domestic capital outflows, however, their net effect becomes an empirical, rather than theoretical, question.     

Love Poverty in Modern Culture and Sensitivity Training*

The social institutions of modern technological culture often fail to provide adequate opportunity for the exchange of emotions and personal feelings of affect and esteem. The widespread development of alternative institutions such as sensitivity training can be seen as an attempt to compensate for the scarcity of this type of interpersonal communication. Reasons for this scarcity are examined in terms of a structural model of individual and societal resource differentiation.     

Nonverbal communication: Toward syntax,by way of semantics

The identification of syntactical rules that govern nonverbal communication in humans and the determination of its semantic rules has often been viewed by researchers as two separate issues. In the present paper we depart from this traditional approach by studying the relationship among various nonverbal channels through their meaning. We propose that the functions which relate behavior to meaning are undulatory, and each is characterized by a different number of bending points. Supportive results of preliminary empirical testing are reported. Implications for cross-cultural research, development and psychopathology are discussed.The authors thank Sandra Tunis for her suggestions and Clara Mayo for her comments, as well as anonymous reviewers of this journal.