Showing papers on "Unitary state published in 1993"

Sequential versus Unitary Trials: An Economic Analysis

Abstract: WHEN Polaroid successfully sued Kodak for infringing its patents on instant photography, the question of damages was litigated in a separate trial before a different judge than the one who found Kodak liable for patent infringement.' A bifurcated or \"sequential\" trial on liability and damages, as opposed to a \"unitary\" trial on both issues, is the exception rather than the norm. A sequential trial is not limited to separating liability and damages. Indeed, the entire structure of the Federal Rules of Civil Procedure calls for sequential decision making. The parties first may litigate whether the court has jurisdiction over the matter (Rule 12(b)(1)) or over the defendant (Rule 12(b)(2)) and, if it does, whether each element of the complaint states a claim under which relief can be granted (Rule 12(b)(6)). Next, the parties may litigate summary-judgment motions (Rule 56). Rule 42(b) gives courts wide discretion to separate substantive issues. These include bifurcating liability and damages, separating claims asserted by the plaintiff, separating counterclaims raised by the defendant, deciding whether a contract exists before considering claims based on its existence, and deciding whether a product-liability defendant manufactured the allegedly defective product before considering liability and

Processing Integral Dimensions: The Whole View

Abstract: In the traditional view, integral dimensions are said to be processed as unitary whole and only occasionally analyzed. Converging operations establish that (a) pitch and loudness and (b) hue, saturation, and brightness are true psychological dimensions and yet constitute integral dimensions in just this sense. Recent challenges provided by R. D. Melara, L. E. Marks, and their colleagues are shown to be based on narrow and faulty interpretations of evidence for privileged axes. They are also undermined by strong evidence of the holistic processing of pitch and loudness and of the dimensions of color that emerge within both their own data and the larger literature. The traditional view--including the strong claim that integrality entails mandatory holistic processing--continues to fare very well as an account of a substantial and varied set of findings. Language: en

On the Matrices Which Reduce the Kronecker Products of Representations of S. R. Groups

Abstract: The present article deals with simply reducible groups which are finite or compact and with their unitary representations (more precisely: with their representations which are in unitary form) in general. A simply reducible group satisfies two criteria. First, all classes are ambivalent, i.e., contain with an element X also its reciprocal, X −1. Since the characters of all elements of a class are equal to each other in every representation, it follows that the characters of X and X −1 are equal. If the representation is in unitary form, it is at once evident that the characters of reciprocals are conjugate complex. It therefore follows from the ambivalent nature of all classes that all characters are real in every representation of a simply reducible group. As a result, every representation is equivalent to the conjugate complex representation.

Irreducible unitary representations of quantum Lorentz group

Abstract: A complete classification of irreducible unitary representations of a one parameter deformationSqL(2,C) (0

Convergence of unitary and complex decompositions of exponential operators

Abstract: The convergence of the fractal unitary and complex decompositions of exponential operators is proved for Hermitian operators in a Banach space

An external approach to unitary representations

Abstract: The main aim of this paper is to present the ideas which lead first to the solution of the unitarizability problem for $\GL(n)$ over nonarchimedean local fields and to the recognition that the same result holds over archimedean local fields, a result which was proved by Vogan using an internal approach. Let us say that the approach that we are going to present may be characterized as external. At no point do we go into the internal structure of representations.

Unitary Knowing in Nursing Practice

Abstract: The purpose of this article is to elaborate the unitary knowing perspective which was derived from using the science of unitary human beings in practice and considering phenomena within a unitary picture of reality. The systems perspective and the unitary perspective are contrasted as structures for understanding human phenomena in the realm of practice. A model of practice is offered which encompasses the use of experience, perceptions, and expressions as the source of pattern information. The features of unitary knowing involving construction and derivation are presented within the context of unitary pattern nursing.

2-weights for unitary groups

Abstract: This paper gives a description of the local structures of 2-radical subgroups in a finite unitary group and proves Alperin's weight conjecture for finite unitary groups when the characteristic of modular representation is even

Unitary representations of the hyperfinite Heisenberg group and the logical extension methods in physics

Abstract: In order to provide a general framework for applications of nonstandard analysis to quantum physics, the hyperfinite Heisenberg group, which is a finite Heisenberg group in the nonstandard universe, is formulated and its unitary representations are examined. The ordinary Schrodinger representation of the Heisenberg group is obtained by a suitable standardization of its internal representation. As an application, a nonstandard-analytical proof of noncommutative Parseval's identity based on the orthogonality relations for unitary representations of finite groups is shown. This attempt is placed in a general framework, called the logical extension methods in physics, which aims at the systematic applications of methods of foundations of mathematics to extending physical theories. The program and the achievement of the logical extension methods are explained in some detail.

Policy Uncertainty in Two-Level Games: Examples of Correlated Equilibria

Abstract: Recent research on two-level game models emphasizes the close interaction between the domestic and foreign policies of states, but these states are usually interpreted as unitary rational actors and these two policy arenas are generally kept separate. We develop integrated models of multi-level policy games in which the locus of strategic action remains at the individual (or group) level. Social choice theory identifies fundamental dilemmas associated with assuming that states have consistent preferences, yet empirical observation reveals that domestic political competition results in regularized patterns of behavior at the state and international levels. In our models the expectations of individual Bayesian policy actors converge to a “correlated equilibrium” that defines a probability distribution over domestic and foreign policy outcomes. We compare examples of correlated equilibria in a Chicken game between two unitary rational states, a voting game among three domestic groups, and a two-level game in which each state's foreign policy is determined by this voting game. By focusing on the collective consequences of the strategic interactions of Bayesian rational individuals, this synthesis of game, social choice, and Bayesian decision theories highlights fundamental linkages among the regularities observed in domestic politics, foreign policy, and international relations.

"How to make a market: reflections on the attempt to create a single unitary market in the European Community"

Abstract: [From the Introduction]. The European Community is in the midst of attempting to create a "Single Unitary Market" across western Europe (European Community, 1985; Moravcsik, 1991; Garrett, 1992). This project is fascinating for two reasons. First, some think we are witnessing one of the most important peaceful assaults upon national sovereignty in history. The construction of the single unitary market will require nation states to give up power to control their economic and geographic boundaries. Analyzing the negotiations towards a single unitary market - and taking particular notice of which aspects of the market are more difficult to change than others - gives us insights into the multiple dimensions of sovereignty. Second, it provides scholars interested in economic sociology, the sociology of markets, and political economy an opportunity to see if their theories can give them any leverage on what the causes and outcomes of this process are likely to be.

Unitary equivalence of the metric and holonomy formulations of (2+1)-dimensional quantum gravity on the torus.

Abstract: Recent work on canonical transformations in quantum mechanics is applied to transform between the Moncrief metric formulation and the Witten-Carlip holonomy formulation of (2+1)-dimensional quantum gravity on the torus. A nonpolynomial factor ordering of the classical canonical transformation between the metric and holonomy variables is constructed which preserves their classical modular transformation properties. An extension of the definition of a unitary transformation is briefly discussed and is used to find the inner product in the holonomy variables which makes the canonical transformation unitary. This defines the Hilbert space in the Witten-Carlip formulation which is unitarily equivalent to the natural Hilbert space in the Moncrief formulation. In addition, gravitational $\ensuremath{\theta}$ states arising from "large" diffeomorphisms are found in the theory.

Non-vanishing of L-functions of 2 × 2 unitary groups

Abstract: Let π be a cuspidal automorphic representation of GL(2, E), E a totally real field, and let Jf be a CM quadratic extension of E', let π^ denote the base change of π to JT. We show, using the quaternionic theta correspondence, that there exist algebraic Hecke characters ω of Jf, satisfying precise local and global conditions, such that the L-function of π^ ® ω does not vanish at s = /2. 1991 Mathematics Subject Classification: 11F67 Introduction Let E be a totally real field of degree d over Q, Σ = {σ1?..., σά] the set of real embeddings of E, G = RE/Q GL(2, E). Fix a maximal compact subgroup K^ c= G(fR), and denote by , s) at the center s = V2 of symmetry of its functional equation, for certain Hecke characters ω of Jf * Partially supported by NSF Grant DMS-8901101 and by the NAS exchange program with the USSR.

Preemption in the U.S. Federal System

Abstract: The sharp increase in the number of congressional partial and total preemption statutes and innovative use ofpreemptionpowers since 1965 haveproducedmajor changes infederal-state relations. The Congress has become a unitary government in several regulatoryfields and alsofinances itspolicies in otherfields inpart by imposing burdensome mandates and restraints on state and local governments. Current federalism theories fail to account for the changes produced by preemption or to address alternatives to preemption other than conditional grants-in-aid.

Tensor operators and Clebsch–Gordan coefficients of the quantum algebra suq(1,1)

Abstract: Two kinds of suq(1,1) tensor operators are considered. One of them carries a nonunitary finite dimensional representation of suq(1,1), and the other carries a unitary infinite dimensional representation. Explicit formulas of the former tensor operators are constructed and a useful formula to calculate the matrix elements of rank 1 tensors is derived. By making use of the q analog of the Wigner–Eckart’s theorem, the Clebsch–Gordan coefficient can be extracted from the matrix element of a tensor operator. Explicit formulas of three kinds of the suq(1,1) Clebsch–Gordan coefficients are given, that is, the Clebsch–Gordan coefficient which couples two (non) unitary representations to get the third (non) unitary representation, and the one which couples a nonunitary and a unitary representations to get a new unitary representation. It is shown that these Clebsch–Gordan coefficients and the one of suq(2) can transmute one another by the appropriate replacement of their variables. It is further shown that, by usi...

Unitary highest weight representation of Uq(su(1,1)) when q is a root of unity

Abstract: Unitary representation of Uq(su(1,1)) with q being roots of unity are studied. The authors construct unitary irreducible highest weight modules and find that the representations are discrete series owing to the unitarity. Moreover, it is revealed that each unitary irreducible highest weight module is equivalent to the tensor product of two modules. They show that one of them is just the unitary irreducible highest weight module of su(1,1) and the other is the same as that of Uq(su(2)). It is also shown that the number of the latter modules is finite in their representation.

Computability in Unitary Representations of Compact Groups

Abstract: This paper deals with the computability of unitary representations of compact groups. An algorithm is given to effectively decompose a unitary representation into its irreducible parts. Difficulties in finding the effective procedure are caused by the absolute lack of a priori information about the irreducible representations and the obligation of making decisions from inexact data. Several lemmas on group representations (classical, i.e. computability not mentioned) have been proved in order to design the algorithm which overcomes these difficulties.

Accountability and a Unitary Transfer Definition

Abstract: Increasing reliance on state funding coupled with diminishing dollars in the public coffers has led to calls for community college \"accountability\" models in several states. Recently, California joined a growing number of other states (including Florida, Tennessee, New Jersey, and Texas) that have recently enacted (or are considering enacting) accountability systems for community colleges. The increased interest in community college accountability comes from five major sources: