Showing papers on "Unitary state published in 1981"

The Unitary group for the evaluation of electronic energy matrix elements

Abstract: 1. Unitary Group Approach to Many-Electron Correlation Problem.- 2. The Graphical Unitary Group Approach and its Application to Direct Configuration Interaction Calculations.- 3. A Harmonic Level Approach to Unitary Group Methods in CI and Perturbation Theory Calculations.- 4. Many-Body Correlations Using Unitary Groups l.- 5. Factorization of the Direct CI Coupling Coefficients into Internal and External Parts.- 6. Multiconfiguration Self-Consistent-Field Wavefuntion for Excited States.- 7. Minicomputer Implementation of the Vector Coupling Approach to the Calculation of Unitary Group Generator Matrix Elements.- 8. New Directions for the Loop-Driven Graphical Unitary Group Approach: Analytic Gradients and an MCSCF Procedure.- 9. The Occupation-Branching-Number Representation.- 10. Review of Vector Coupling Methods in the Unitary Group Approach to Many-Electron Problems.- 11. Symmetric Group Graphical Approach to the Configuration Interaction Method.- 12. Orbital Description of Unitary Group Basis.- 13. On the Relation Between the Unitary Group Approach and the Conventional Approaches to the Correlation Problem.- 14. Unitary Bases for X-Ray Photoelectron Spectroscopy.- 15. Broken Unitary Tableaus, Itinerant Nuclear Spins, and Spontaneous Molecular Symmetry Collapse.- 16. CI-Energy Expressions in Terms of the Reduced Density Matrix Elements of a General Reference.- 17. The Unitary Group Formulation of Quantum Chemistry: Generator States.- 18. The Unitary Group Approach to Bonded Functions.

Does Federalism Matter? Political Choice in a Federal Republic

Abstract: This paper builds upon some well-known facts about state government to generate new conclusions about social choice on the national level of a federal republic. Citizens vote against national laws that restrict their state's ability to export costs but support laws that reduce the costs imposed on them. Individuals may seek to extend the laws passed in some states to the entire nation or may oppose preemptive laws because they benefit from variety. Since these motivations are absent in a unitary system, national support for a law will depend upon whether a unitary or a federal structure prevails.

Reduced unitary k-theory. applications to algebraic groups

Abstract: In this paper a number of facts of reduced K-theory are proved, and some applications to algebraic groups are also considered. In § 2 a stability theorem is proved for reduced unitary Whitehead groups under certain imbeddings in the skew field of fractions of noncommutative polynomial rings. In §§ 3–4 the author considers reduced unitary Whitehead groups of skew fields over doubly henselian discretely valued fields; exact sequences are given for their computation. In particular, the nontriviality of the reduced unitary functor is proved for cyclic algebras. The fifth and sixth sections are devoted to applications to algebraic groups. In particular, general problems of weak approximation and rationality for special unitary groups are solved in the negative. Bibliography: 14 titles.

Unitary operators in the homogeneous wave field.

Abstract: The operations of diffraction, phase conjugation, and the rigid motions in the plane are shown to be unitary operators on the space of all the band-limited fields whose diffracted wave fields are homogeneous. Commutation relations are given for these operators that explain many of the symmetries of such wave fields. Some of these symmetries are known, and some have not been mentioned before.

The local ergodic theorem for groups of unitary operators and second order stationary processes

Abstract: Let , be a strongly continuous unitary group in , where is a -finite measure. The local ergodic theorem is the relation for . It is shown that this relation is not satisfied for all and . Necessary and sufficient conditions are obtained for the local ergodic theorem in terms of properties of the spectral measure , where is the resolution of the identity corresponding to the group . In particular, (1) is satisfied if the integral converges. Generalizations to multiparameter groups and homogeneous random fields are given. Bibliography: 10 titles.

Science of unitary man: a paradigm for nursing

Abstract: An organized conceptual system based on unitary man and environment as irreducible wholes. Postulates underlying the system include energy fields, open systems, pattern and organization, and four dimensionality. Descriptive, explanatory, and predictive principles derive from the system. Gives an optimistic view of man's innovative potentials. Implications for enhancing the quality of life.

Unitary hyperperfect numbers

Abstract: Unitary hyperperfect numbers are generalized unitary perfect numbers. In this paper a list of such numbers is given, and some results concerning them are proved.

Absolute continuity and hyponormal operators

Abstract: Let T be a completely hyponormal operator, with the rectangular representation T = A + i B , on a separable Hilbert space If 0 is not an eigenvalue of T * then T also has a polar factorization T = U P , with U unitary It is known that A , B and U are all absolutely continuous operators Conversely, given an arbitrary absolutely continuous selfadjoint A or unitary U , it is shown that there exists a corresponding completely hyponormal operator as above It is then shown that these ideas can be used to establish certain known absolute continuity properties of various unitary operators by an appeal to a lemma in which, in one interpretation, a given unitary operator is regarded as a polar factor of some completely hyponormal operator The unitary operators in question are chosen from a number of sources: the F and M Riesz theorem, dissipative and certain mixing transformations in ergodic theory, unitary dilation theory, and minimal normal extensions of subnormal contractions

Corrections and supplements to: "On the Schur indices of the finite unitary groups''

Abstract: Let Fq denote the finite group of characteristic p with q elements. We consider the finite unitary group U(n, (f) of rank n relative to the quadratic extension Ff\\Fq. For a complex irreducible character % of a finite group, the Schur index of % with respect to the field Q of rational numbers is defined to be the minimal degree among all the extensions K/Q()C) such that % is realizable in K. Here Q(%) is the extension of Q generated by the values of X. We denote this index by mQ(X). In this paper, we shall determine the Schur indices of all the complex irreducible characters of U(n, q) for sufficiently large p and q. Our main result is the following theorem.

Broken Unitary Tableaus, Itinerant Nuclear Spins, and Spontaneous Molecular Symmetry Collapse

Abstract: Applications of unitary group (Um) and permutation group (Sn) representations have been the subject of two conferences organized by Professor Jurgen Hinze. The proceedings of the present conference mostly emphasize applications of unitary groups, while the those of the preceeding conference (1) mostly emphasize the permutation groups. A number of papers notably those of Wormer and Sarma in this volume, have reminded us of the inescapable relations between Um and Sn groups. Many of the papers in these volumes have dealt with some number n of indistinguishable spin − 1/2 particles, for example, orbiting electrons, which may occupy some other number m of distinguishable states. The permutation group Sn of distinguishable particles serves as a symmetry group for the system Hamiltonian. The unitary group Um corresponds to the set of all superpositions of the m states which preserve quantum amplitudes. The group Um will be a symmetry group only if the m states remain degenerate in energy. Nevertheless, the Um operations always commute with the Sn permutations so in some sense the two groups are symmetries for each other.

A Unitary Approach to Social Work-Application and Practice Robin Currie and Brian Parrott BASW. £1.95 (£1.50 to members):

Abstract: 'criminal population' as a consequence of their dependence upon previously convicted offenders as suspects. Although the police do use 'known offenders' in this way, victim descriptions and the circumstances of the case (as in meter thefts), though not forensic work, play a far greater role in investigation than is commonly supposed by radical and interactionist sociologists. Those readers with no prior knowledge of the 'official statistics debate' may find some portions of this book particularly chapter 1 hard going (a task that is not made easier by typesetting whose visual effect is reminiscent of the op-art work of Bridget Riley), but it amply fulfils its aims of producing a fuller understanding of the contexts in which crime rates emerge. MIKE LEVI University College, Cardiff

Pais-uhlenbeck regularization of free quantum gravity: toward a unitary theory

Abstract: A method is sketched to make free quantum gravity finite and perhaps unitary, when one regards it as the formal four-dimensional limit of the renormalizable one in 2+ɛ dimensions at sufficiently small e. The method utilizes the higher-derivative regularization by a quadratic curvature term and is substantiated by some Symanzik’s conjectures on the nonrenormalizable theories.

Absolute continuityand hyponormal operators

Abstract: Let T be a completely hyponormal operator, with the rectangular representation T A + iB, on a separable Hilbert space. If 0 is not an eigenvalue of T* then T also has a polar factorization T UP, with U unitary. It is known that A, B and U are all absolutely continuous operators. Conversely, given an arbitrary absolutely continuous selfadjoint A or unitary U, it is shown that there exists a corresponding completely hyponormal operator as above. It is then shown that these ideas can be used to establish certain known absolute continuity properties of various unitary operators by an appeal to a lemma in which, in one interpretation, a given unitary operator is regarded as a polar factor of some completely hyponormal operator. The unitary operators in question are chosen from a number of sources: the F. and M. Riesz theorem, dissipative and certain mixing transformations in ergodic theory, unitary dilation theory, and minimal normal extensions of sub- normal contractions."

Unitary Structure of Orbital States

Abstract: In principle it is possible to analyse the permutational symmetry of orbital states entirely in terms of the symmetric group, and for the nuclear states this approach has been adopted in [KR 69, 69a, 72]. The use of the unitary and general linear groups for the same purpose can be justified both on physical and mathematical grounds.