Showing papers on "Unitary state published in 1994"

Random unitary matrices

Abstract: Methods of constructing random matrices typical of circular unitary and circular orthogonal ensembles are presented. We generate numerically random unitary matrices and show that the statistical properties of their spectra (level-spacing distribution, number variance) and eigenvectors (entropy, participation ratio, eigenvector statistics) confer to the predictions of the random-matrix theory, for both CUE and COE.

Unitary integrators and applications to continuous orthonormalization techniques

Abstract: In this paper the issue of integrating matrix differential systems whose solutions are unitary matrices is addressed. Such systems have skew-Hermitian coefficient matrices in the linear case and a ...

Unitary versus Collective Models of the Household: Time to Shift the Burden of Proof?

Abstract: Until recently, most economists viewed the household as a collection of individuals who behave as if in agreement on how best to combine time and goods (purchased or produced at home) to produce commodities that maximize some common welfare index. This model has been extended far beyond standard demand analysis to include the determinants of health, fertility, education, child fostering, migration, labor supply, home production, land tenure, and crop adoption. The appeal of the unitary model is the simplicity of comparative statics generated and the diversity of issues it can address. But, argue the authors, its theoretical foundations are weak and restrictive; its underlying assumptions are of questionable validity; it has not stood up well to empirical testing; and it ignores or obscures important policy issues. They argue that economists should regard households as collective rather than unitary entities. They make a case for accepting the collective model (with cooperative and noncooperative versions) as the industry standard - with caveats. The unitary model should be regarded as a special subset of the collective approach, suitable under certain conditions. The burden of proof should shift to those who claim the unitary model as the rule and collective models as the exception. Implicit in the authors'argument is the view that household economics has not taken Becker seriously enough."A household is truly a'small factory,'"wrote Becker (1965)."It combines capital goods, raw materials, and labor to clean, feed, procreate, and otherwise produce useful commodities."The authors, too, perceive the household as a factory, which, like all factories, contains individuals who - motivated at times by altruism, at times by self-interest, and often by both - cajole, cooperate, threaten, help, argue, support, and, indeed, occasionally walk out on each other. Labor economists and industrial organization theorists have long exploited the value of going inside the black box of the factory. It is time to do the same for household economics, say the authors.

A Distinguished Family of Unitary Representations for the Exceptional Groups of Real Rank = 4

Abstract: In this note, we will construct three small unitary representations for each of the four simply-connected exceptional Lie groups G of real rank = 4. We will describe the restrictions of these representations to a maximal compact subgroup K of G, and will show they are multiplicity-free. The method of construction is by a continuation of the “quaternionic discrete series” for G. This works in more generality, and we will treat it fully in another paper, so we have only sketched the proofs here.

The President's Power to Execute the Laws

Abstract: Our thesis is that either the text or the relevant "legislative" history, considered separately, demonstrates that the founding generation fully embraced and wrote into the Constitution the "myth" of a chief administrator constitutionally empowered to administer all federal laws. We think the originalist textual and historical arguments for the unitary Executive, taken together, firmly establish the theory.

Classification and construction of unitary topological field theories in two dimensions

Abstract: It is proven that unitary two‐dimensional topological field theories are uniquely characterized by n positive real numbers λ1,,λn, which can be regarded as the eigenvalues of a Hermitian handle creation operator The number n is the dimension of the Hilbert space associated with the circle, and the partition functions for closed surfaces have the form Zg=∑ni=1λg−1i, where g is the genus The eigenvalues can be arbitrary positive numbers It is shown how such a theory can be constructed on triangulated surfaces

The President's Power To Execute the Laws

Abstract: Our thesis is that either the text or the relevant "legislative" history, considered separately, demonstrates that the founding generation fully embraced and wrote into the Constitution the "myth" of a chief administrator constitutionally empowered to administer all federal laws. We think the originalist textual and historical arguments for the unitary Executive, taken together, firmly establish the theory.

An analogue of the unitary displacement operator for the q-oscillator

Abstract: Using the concept of a non-standard Hilbert space over the quantum complex plane recently introduced by Kowalski et. al. (1993), we construct a unitary q-analogue of the Weyl-displacement operator. We investigate the q-displaced vacuum states and show that they exhibit properties analogous to coherent states in the undeformed theory. They are, however, distinct from any q-coherent states previously found in the literature.

Semantic memory and the granularity of semantic relations: Evidence from speed-accuracy decomposition

Abstract: In the present study we examined whether semantic relations are atomistic unitary associations, or are complex concepts consisting of a number of relational elements. The complexity of the ownership relation was assessed by combining a relation verification task (“Many people own [cars/ comets]”) with the speed-accuracy decomposition procedure (Meyer, Irwin, Osman, & Kounios, 1988). The latter permits one to determine whether subjects achieve their final state of response accuracy in a single, discrete all-or-none transition, or whether the relevant processes yield partial information representing intermediate states of knowledge. The rationale was that the retrieval of a unitary relational link from a classical associative network should be an all-or-none affair. In contrast, a set of relational elements need not be processed as a unitary bundle, thereby allowing partial response-information states. In two experiments, we found evidence of such partial information (i.e., sensitivity in units ofd′), lending support to the notion that relations are complex. Furthermore, the results suggest that the accumulation of guessing sensitivity was linear over time, weighing against alternate theoretical interpretations.

Variation of the Unitary Part of a Matrix

Abstract: The derivative of the map that takes an invertible matrix $A$ to the unitary factor $U$ in the polar decomposition $A = UP$ is evaluated. The same is done for the map that takes $A$ to the unitary factor $Q$ in the QR decomposition $A = QR$. These results lead to perturbation bounds for these maps. Other applications of the method developed are discussed.

The state of madison's vision of the state: a public choice perspective

Abstract: An enduring tradition in political theory depicts "the state" as the holder of a monopoly of legitimate force. Many of the most thoughtful early British writers sought to explain not only why there is (and ought to be) a government, but also why that government ought to be unitary and under the command of a single monarch. Hobbes named the state Leviathan.1 Locke likewise supported a unitary state.2 Although their reasons differed, Hobbes and Locke agreed on the model of "the state." Even modern thinkers in the liberal tradition, such as Rawls, conceive of government as a unitary institution, one that grows out of a social contract among all the people and that settles allocation of power for the long run.3 That current runs deep in contemporary society and among lawyers. To see how far this understanding extends one need not go beyond the papers presented at this conference, most of which treat "the state" as a single entity. Perhaps such a tendency is inevitable for scholars accustomed to the perspective of law, for the Supreme Court has often treated state and national governments alike when it has applied the Bill of Rights to state and local governments. Courts would thus treat as equally oppressive a national law that established a national religion (with an accompanying tax) and a state statute that permitted a congregation to object to the propinquity of a tavern4 -even though moving a short distance would take care of the latter problem, but only changing one's moral commitments or emigrating from the United States would overcome the former. When the portion of the Constitution to which contemporary scholars pay the greatest attention is understood to equate national and local measures, it is only natural for lawyers to assume that the government is unitary in fact. No surprise, then, that the monopoly-of-force idea is still in use, and that the concept of government-as-Colossus appears frequently in

Coherent states and coordinate-free quantization

Abstract: The usual quantization procedures interpret canonical transformations in an active way linking them with unitary transformations, while the quantization procedure offered by coherent states completely separates classical canonical transformations and unitary operator transformations. By exploiting this property, along with a physically motivated shadow metric, it is seen how to realize the quantization process in as coordinate-free a form as holds in classical mechanics.

Unitary molded single blade ski-sled

Abstract: A single runner ski-sled is provided wherein the main structure is adapted for one piece molding techniques with sufficient strength for effective use. The runner is designed to be rigid. The device of the invention also includes a seat attachment structure that allows for easy installation and removal yet can withstand strong pressures.

Normal Elements of a Simple C*-Algebra

Abstract: Evidence is assembled supporting the conjecture that a normal element of a simple C*-algebra is determined up to approximate unitary equivalence by the following elementary invariants: the spectrum of the element, the measure on its spectrum arising from each trace (or quasitrace) on the algebra, the K0-class of the spectral projection associated to each compact component of the spectrum together with the information whether the sum of these projections is the unit of the C*-algebra (if there is one), and, finally, the K1-class of the resolvent of the element over each bounded component of the complement of the spectrum. (In the case of a self-adjoint element the last invariant is trivial, and in the case of a unitary element it is the K1-class of the unitary itself.)

Unitary colligations and parametrization formulas

Abstract: The aim of this paper is to describe, in a rather concise but relatively self-contained manner, some relations between unitary colligations which are regarded as linear systems, and parametrization formulas for the solutions of some interpolation problems.

The Diagonal Torus of a Matrix Under Special Unitary Equivalence

Abstract: Given a matrix $A$, a sufficient condition is given for the vector of diagonal elements of $UAV$ to cover a torus with specified base circle radii as $U$ and $V$ run over the special unitary group.

Unitary state preparation, local position measurements, and spin in quantum mechanics

Abstract: The orthodox presentation of quantum theory often includes statements on state preparation and measurements without mentioning how these processes can be achieved. The often quoted projection postulate is regarded by many as problematical. This paper presents a systematic framework for state preparation and measurement. Within the existing Hilbert space formulation of quantum mechanics for spinless particles we show that it is possible (1)to prepare an arbitrary state and (2)to reduce all quantum measurements to local position measurements in an asymptotic way by unitary evolution processes without recourse to the projection postulate. A generalization to spin-1/2particles is also given. The theory presented provides a general mathematical and theoretical foundation for many practical schemes for state preparation and measurement.

Issues in the Design of Formulary Apportionment in the Context of NAFTA

Abstract: This article responds to Professor Paul McDaniel’s Formulary Taxation in the North American Free Trade Zone. In his article, Professor Paul McDaniel addresses whether the NAFTA countries should adopt a system of formulary apportionment taxation. My commentary serves to highlight, with an emphasis on the state tax experience, the unnecessary restrictions imposed on Professor McDaniel’s proposal, the issues inherent in any formulary system, and the NAFTA-specific problems that could arise.Professor McDaniel adopted two unnecessary constraints in his proposal. The first, the “water’s edge” constraint, which applies formulary apportionment only to income sourced within NAFTA countries and uses only NAFTA factors in the apportionment formula. He defends this water’s edge approach on the grounds that it may be both a requirement of existing tax treaties and a necessary concession to foreign countries that may resist worldwide unitary measures, though no case law exists to support the former; the latter is a political judgment call. A water’s edge approach would require source rules and arm’s length pricing rules to determine NAFTA sourced income. Sourcing in general is incompatible with a formulary system, and to do so negates one of the inherent benefits of formulary apportionment: eliminating the need to monitor transfer prices. Second, Professor McDaniel’s emphasis on the existence of a unitary business presumably borrows that concept from U.S. Supreme Court cases dealing with state taxation of multistate income. He does not define a unitary business or defend its use. In the state context, the Due Process and Commerce Clauses require the existence of a unitary business in the context of formulary apportionment. There is no similar concept in the federal system and no need to incorporate the concept should NAFTA adopt formulary apportionment. There are technical issues in any system of formulary apportionment, three of which are particularly relevant here. First, states are permitted to impose combined reporting requirements only on members of a unitary business. These combined reports require the in-state business to consolidate its income and factors with the income and factors of its unitary subsidiaries, regardless of whether or not those subsidiaries have any direct nexus with the taxing state. Combined reporting essentially treats out-of-state unitary subsidiaries as branches or divisions. Contrary to Professor McDaniel, a NAFTA approach should be free of the state condition that the members of the combined report be part of a unitary business. The only constraint on what entities should be included in the combined group is the threshold matter of a minimum ownership requirement.Combined reporting must resolve the level of stock ownership of entities that must be included in a combined report. There are two common thresholds: a minimum 50% ownership test, or a “more than 50%” ownership test. The latter is more subject to manipulation by taxpayers seeking to avoid a combined report. These taxpayers can reduce their level of ownership to 50% while still maintaining control over the subsidiary. Fifty-fifty joint ventures would not be subject to combined reporting under a “more than 50% test Designing an effective apportionment formula will likely be a complicated objective. The state experience suggests that the traditional three-factor formula composed of sales, property, and payroll is inefficient for activities that don’t constitute traditional manufacturing or merchandising. The state response has been the adoption of specific formulas particularly tailored to individual activities, though this solution necessitates the correct characterization of the taxed activity and an emphasis on arm’s length transactions between related businesses subject to different formulas. Any apportionment formula must be built on the principles of administrative simplicity, neutrality, economic nexus, inclination to tax, and sovereign control of tax. A final issue is that of nexus, that is, the application of jurisdictional threshold rules. Professor McDaniel supports the traditional permanent establishment approach, but under this approach the use of receipts in an apportionment formula could assign income to countries without the jurisdiction to tax it. A preferred approach might be a threshold based on a predetermined amount of gross receipts, regardless of a significant physical presence. As long as the NAFTA countries maintain their dissimilar tax codes, formulary apportionment applied in a NAFTA context has the unique effect of substituting treaty shopping for “rule shopping.” Mexico, for example, lacks provisions equivalent to the U.S. subpart F treatment of controlled foreign corporations. A U.S. parent could merge with its Mexican subsidiary to form a Mexican entity, avoiding subpart F. Ideally, the NAFTA countries would adopt uniform or equivalent provisions in their tax codes to avoid this kind of rule shopping, while also ensuring their revenue administrations are highly competent to avoid potential administration shopping.Finally, Professor McDaniel suggests that dividends paid between two NAFTA corporations that are not part of the same combined report should be excluded from taxation, treating the distribution as though it occurred between two entities in the same combined report. While I question the logic of a 100% exemption, it is clear that transitional and tracing rules would be required to decide the order in which profits from the pre- and post-formulary regimes are considered to be distributed.

Implosive consonants : Their representation and sound change effects

Abstract: . Oromo, a Cushitic language spoken in Ethiopia and Kenya, shows certain phonologically irregular phenomena with respect to the coronal implosive consonant that have never been explained satisfactorily. First, in some dialects, roots ending in a short /d/ behave like final-/?/ roots while in some others they behave like fmal-/t/ roots. Secondly, unlike the geminates of all other consonants, which behave like heterogeneous abutting consonants, the long implosive behaves, in some cases, like a single segment. Finally, it is sometimes assumed that in Proto-East-Cushitic, there is evidence for reconstructing two different implosive phonemes in the denti-alveolar region, i.e. *d and *d1, although no one has yet established the relevant difference between them. The aim of this paper is to provide a unitary account of all these facts by proposing an adequate underlying representation of single and long implosives within the model of Feature Geometry as well as suggesting a different diachronic origin for both types of reconstructed implosives.