Exotic Galileian group in field theory

The exotic Galileian group is realized as a symmetry group of a family of nonrelativistic field theories on the noncommutative plane. This was obtained in a unique way consistent with the Seiberg—Witten mapping. The symmetry group of the free model is analyzed and a characterization of the class of the self-interacting theories is given. __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 1, Geometry of Integrable Models, 2004.     

Robust Optimal Stopping-Time Control for Nonlinear Systems

Abstract. We formulate a robust optimal stopping-time problem for a state-space system and give the connection between various notions of lower value function for the associated games (and storage function for the associated dissipative system) with solutions of the appropriate variational inequality (VI) (the analogue of the Hamilton—Jacobi—Bellman—Isaacs equation for this setting). We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense and a positive definite supersolution of the VI can be used for stability analysis.     

Robust Optimal Stopping-Time Control for Nonlinear Systems

   Abstract. We formulate a robust optimal stopping-time problem for a state-space system and give the connection between various notions of lower value function for the associated games (and storage function for the associated dissipative system) with solutions of the appropriate variational inequality (VI) (the analogue of the Hamilton—Jacobi—Bellman—Isaacs equation for this setting). We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense and a positive definite supersolution of the VI can be used for stability analysis.     

Reasons and passions

Jonathan Dancy has argued that agents’ reasons for their actions are facts or features of the situations rather than their psychological states. The purpose of the paper is to show that even if we grant that this is so in most of the cases, there is a class of mental states that can be reasons. Although beliefs and desires are not reasons for actions, some emotional states—like loving, liking or disliking someone—can generate reasons. The distinctive feature of these states is that their content is a particular, and not a proposition. Hence in certain situations their love or admiration can provide agents with reasons to do one particular thing rather than another.     

On the reversed sub-martingale property of empirical discrepancies in arbitrary sample spaces

The empirical discrepancy is defined as a supremum over a class of functions of a collection of centered sample averages. For uncountable classes the discrepancy need not be measurable, and distributional assertions can become dependent on the structure of the underlying probability space. This paper shows that one such assertion—the reversed sub-martingale property—is valid when interpreted in terms of measurable cover functions for the canonical model, but that it can fail in other constructions of the underlying model.     

Singular values of the Rogers-Ramanujan continued fraction

Let z∊ C be imaginary quadratic in the upper half plane. Then the Rogers-Ramanujan continued fraction evaluated at q = e ^{2π iz} is contained in a class field of Q(z). Ramanujan showed that for certain values of z, one can write these continued fractions as nested radicals. We use the Shimura reciprocity law to obtain such nested radicals whenever z is imaginary quadratic. 2000 Mathematics Subject Classification Primary—11Y65; Secondary—11Y40     

Extremal behavior of the heat random field

We study the exponential type inequalities for the distribution of the supremum of a random field that arises as the solution of the heat equation with a random initial condition that is a strictly sub-Gaussian random field. AMS 2000 Subject Classifications Primary—60G60; Secondary—60G17, 60F05     

A bootstrap-based aggregate classifier for model-based clustering

In model-based clustering, a situation in which true class labels are unknown and that is therefore also referred to as unsupervised learning, observations are typically classified by the Bayes modal rule. In this study, we assess whether alternative classifiers from the classification or supervised-learning literature—developed for situations in which class labels are known—can improve the Bayes rule. More specifically, we investigate the performance of bootstrap-based aggregate (bagging) rules after adapting these to the model-based clustering context. It is argued that specific issues, such as the label-switching problem, have to be carefully addressed when using bootstrap methods in model-based clustering. Our two Monte Carlo studies show that classification based on the Bayes rule is rather stable and difficult to improve by bootstrap-based aggregate rules, even for sparse data. An empirical example illustrates the various approaches described in this paper.     

Completely reducible Lie subalgebras

Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H ⊂ G. In this paper, we give a notion of G-complete reducibility—G-cr for short—for Lie subalgebras of Lie(G), and we show that if the closed subgroup H ⊂ G is G-cr, then Lie(H) is G-cr as well.     

Unitary integrals and related matrix models

We briefly review the basic properties of unitary matrix integrals, using three matrix models to analyze their properties: the ordinary unitary, the Brezin—Gross—Witten, and the Harish—Chandra—Itzykson—Zuber models. We especially emphasize the nontrivial aspects of the theory, from the De Witt’Hooft anomaly in unitary integrals to the problem of calculating correlators with the Itzykson-Zuber measure. We emphasize the method of character expansions as a technical tool. Unitary integrals are still insufficiently investigated, and many new results should be expected as this field attracts increased attention.     

Stochastic vendor selection problem: chance-constrained model and genetic algorithms

We study a vendor selection problem in which the buyer allocates an order quantity for an item among a set of suppliers such that the required aggregate quality, service, and lead time requirements are achieved at minimum cost. Some or all of these characteristics can be stochastic and hence, we treat the aggregate quality and service as uncertain. We develop a class of special chance-constrained programming models and a genetic algorithm is designed for the vendor selection problem. The solution procedure is tested on randomly generated problems and our computational experience is reported. The results demonstrate that the suggested approach could provide managers a promising way for studying the stochastic vendor selection problem. The authors would like to thank the referees for providing constructive comments that led to an improved version of the paper. Also, this research was partially supported by grants from National Natural Science Foundation (60776825)—China, 863 Programs (2007AA11Z208)—China, Doctorate Foundation (20040004012)—China, Villanova University Research Sabbatical Fall 2006, and the National Science Foundation (0332490)—USA.     

The Incoherence Objection in Moral Theory

J.J.C. Smart famously complained that rule utilitarianism is incoherent, and that rule utilitarians are guilty of “rule worship”. Much has been said about whether Smart’s complaint is justified, but I will assume for the sake of argument that Smart was on to something. Instead, I have three other goals. First, I want to show that Smart’s complaint is a specific instance of a more general objection to a moral theory—what I will call the Incoherence Objection. Second, I want to illustrate how the Incoherence Objection can apply both to consequentialist and, surprisingly, some nonconsequentialist theories. Finally, I want to demonstrate at least one way nonconsequentialist theories that make use of rules, principles, and the like can dodge the Incoherence Objection.     

Singular Functions with Applications to Fractal Dimensions and Generalized Takagi Functions

We study a class of singular functions via a generalized dyadic system and Hausdorff dimensions are calculated for several sets related with these functions. Furthermore, we introduce a class of monotonic type on no-interval and almost everywhere differentiable functions that includes—as an exceptional case—the continuous nowhere differentiable Takagi function (multiplied by 2) among them.     

The relation between intuitionistic and classical modal logics

Intuitionistic propositional logicInt and its extensions, known as intermediate or superintuitionistic logics, in many respects can be regarded as just fragments of classical modal logics containingS4. The main aim of this paper is to construct a similar correspondence between intermediate logics augmented with modal operators—we call them intuitionistic modal logics—and classical polymodal logics We study the class of intuitionistic polymodal logics in which modal operators satisfy only the congruence rules and so may be treated as various sorts of □ and ◇. Supported by the Alexander von Humboldt Foundation. Translated fromAlgebra i Logika, Vol. 36, No. 2, pp. 121–155, March–April, 1997.     

Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem

The purpose of the traffic assignment problem is to obtain a traffic flow pattern given a set of origin-destination travel demands and flow dependent link performance functions of a road network. In the general case, the traffic assignment problem can be formulated as a variational inequality, and several algorithms have been devised for its efficient solution. In this work we propose a new approach that combines two existing procedures: the master problem of a simplicial decomposition algorithm is solved through the analytic center cutting plane method. Four variants are considered for solving the master problem. The third and fourth ones, which heuristically compute an appropriate initial point, provided the best results. The computational experience reported in the solution of real large-scale diagonal and difficult asymmetric problems—including a subset of the transportation networks of Madrid and Barcelona—show the effectiveness of the approach.     

On riesz subsets of abelian discrete groups

We study the class of the Riesz subsets of abelian discrete groups, that is, the sets for which the F. and M. Riesz theorem extends. We show that the “classical” tools of the theory — Riesz projections, localization in the Bohr sense, products — are leading to Riesz sets which are satisfying nice additional properties, e.g., the Mooney-Havin result extends to this class. We give an alternative proof of a result of A. B. Alexandrov, and we improve a construction of H. P. Rosenthal. The connection is made between this class and theM-structure theory. We show a result of convergence at the boundary for holomorphic functions on the polydisc. The Bourgain-Davis result on convergence of analytic martingales is improved.     

Relaxation techniques for strictly convex network problems

Gauss—Seidel type relaxation techniques are applied in the context of strictly convex pure networks with separable cost functions. The algorithm is an extension of the Bertsekas—Tseng approach for solving the linear network problem and its dual as a pair of monotropic programming problems. The method is extended to cover the class of generalized network problems. Alternative internal tactics for the dual problem are examined. Computational experiments —aimed at the improved efficiency of the algorithm — are presented. This research was supported in part by National Science Foundation Grant No. DCR-8401098-A0l.     

Relations between variational derivatives of functions and scalar densities

In view of applications to relativistic field theories, we derive and discuss the appropriate “Leibnitz rule” for the first and second variation of a Lagrangian density (of the second order) explicitly expressed as the product of an invariant function and an invariant volume density, both depending dynamically on field variables.     

Measure and integration: the basic extension theorems

The present article returns to the new foundations of measure and integration due to the author. In this development the basic extension procedures lead from the so-called outer and inner premeasures to their unique maximal extensions. The initial version was for extended real valued set functions. In the sequel we want to achieve a major simplification, in that we develop the procedures—with no loss in the essentials—in the traditional frame of nonnegative set functions. The final section then will obtain an important extension theorem in the inner theories.