Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

The number of 4-cycles in 2-factorizations of K2n minus a 1-factor

In this paper we give a complete solution to problem of determining the number of 4-cycles in a 2-factorization of K-2n\ 1-factor. (C) 2000 Elsevier Science B.V. All rights reserved.

A family of perfect factorisations of complete bipartite graphs

A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n = p(2) for an odd prime p. We construct a family of (p-1)/2 non-isomorphic perfect 1-factorisations of K-n,K-n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltoilian if the permutation defined by any row relative to any other row is a single Cycle. (C) 2002 Elsevier Science (USA).

C4-saturated bipartite graphs

Let H be a graph. A graph G is said to be H-free if it contains no subgraph isomorphic to H. A graph G is said to be an H-saturated subgraph of a graph K if G is an H-free subgraph of K with the property that for any edge e is an element of E(K)\E(G), G boolean OR {e} is not H-free. We present some general results on K-s,K-t-saturated subgraphs of the complete bipartite graph K-m,K-n and study the problem of finding, for all possible values of q, a C-4-saturated subgraph of K., having precisely q edges. (C) 2002 Elsevier Science B.V. All rights reserved.

Quantum Lie algebras, their existence, uniqueness and q-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules L-h(g) of the quantized enveloping algebras U-h(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g(h) independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras L-h(g) are isomorphic to an abstract quantum Lie algebra g(h). In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras L-h(g) associated to the same g are isomorphic, 2) the quantum Lie product of any Ch(B) is q-antisymmetric. We also describe a construction of L-h(g) which establishes their existence.

Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential

We consider the quantum dynamics of a neutral atom Bose-Einstein condensate in a double-well potential, including many-body hard-sphere interactions. Using a mean-field factorization we show that the coherent oscillations due to tunneling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence.

Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. (C) 1997 by John Wiley & Sons, Ltd.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

Factorizations of and by powers of complete graphs

Let K-k(d) denote the Cartesian product of d copies of the complete graph K-k. We prove necessary and sufficient conditions for the existence of a K-k(r)-factorization of K-pn(s), where p is prime and k > 1, n, r and s are positive integers. (C) 2002 Elsevier Science B.V. All rights reserved.

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9).

Time will tell: Ambiguous non-responses on internet relay chat

The design of Internet Relay Chat (IRC) affords for, and itself produces, non-response situations that are not possible in FTF or telephone interaction. These system-occasioned nonresponses produce almost isomorphic stimuli to participant non-responses. Situations thus arise in which non-responses are interpersonally accountable despite agentive ambiguity. This study explores four intersections of participant-action and system-occasioned non-responses. An extension to Pomerantz's (1984b) 'pursuing a response' problems/solutions is proposed. The impact of IRC's design on its popularity is discussed in contrast to more recent chat systems. Suggestions are made for active and passive presence and non-response accounting features in future chat systems.

Institucionalização de estruturas e processos de TI : uma análise das pressões isomórficas que podem influenciar o processo de institucionalização da TI de um órgão do judiciário brasileiro

Orlikowski e Barley (2001) apontam a importância da pesquisa em TI sob a ótica dos Estudos Organizacionais, principalmente quando é utilizada a análise neoinstitucional, porque dessa forma há uma compreensão mais sistêmica sobre como a tecnologia está entrelaçada nas complexas redes interdependentes, sociais, econômicas e políticas. O estudo de caso ocorreu em um órgão do judiciário, onde foram obtidos dados por meio de entrevistas, que foram triangulados com uma pesquisa documental. A dissertação busca elucidar como pressões isomórficas podem influenciar estruturas e processos de TI recomendados pela legislação em vigor, de forma a contribuir para gestores de organizações públicas durante a definição de prioridades para a TI. Para analisar o estágio institucional utilizou-se a classificação proposta por Tolbert e Zucker (1996) e como resultado, apesar das pressões isomórficas coercitivas, obteve-se que poucas estruturas e processos se institucionalizaram totalmente e, aparentemente, só aquelas que traziam com si outros tipos de pressões isomórficas é que parecem ter maior chance de chegar ao último estágio institucional. Foi constatada que a organização, durante o processo de institucionalização, pode incorrer em novas falhas, gerando mitos burocráticos e ritos cerimoniais que por exemplo, podem causar maior descolamento da preocupação por efetividade em seus resultados. Para determinados problemas, apontados durante as entrevistas, não foi possível encontrar influência de nenhuma pressão isomórfica. Tal fato sugere que a teoria neoinstitucional não conseguiu explicar todo o cenário da organização.

O discurso e a ação : análise do processo de mudança no sistema de controle gerencial em uma organização industrial brasileira sob a ótica da teoria institucional

O objetivo desse estudo foi investigar o processo de mudança no sistema de controle gerencial (SCG), analisando a alteração das práticas de controle gerencial na estrutura desse sistema, sob a ótica da teoria institucional. A questão de pesquisa é: como ocorre o processo de mudança no SCG em uma organização industrial brasileira? Para tanto, optou-se por uma abordagem qualitativa do tipo descritiva, num estudo de caso único, utilizando como métodos de coleta de dados entrevistas individuais não estruturadas e semiestruturadas com 11 gestores e usuários do SCG, observação não participante e levantamento documental. A coleta dos dados ocorreu entre agosto/2014 e março/2015. Como método de análise e interpretação de dados foram utilizados elementos da análise do discurso (AD). Os principais referenciais teóricos foram os trabalhos de Meyer e Rowan (1977), Dimaggio e Powel (1983, 1991, 2007), Scott (1995, 2008a, 2008b) e Machado-da- Silva e Vizeu (2007) sobre a teoria institucional; Huy (2001), Beekman, Chenhall e Euske (2007) e Machado-da-Silva, Fonseca e Crubellate (2010) referente ao processo de mudança; e Malmi e Brown (2008) e Simons (1995) referente ao SCG; destacando a aplicação empírica dos modelos teóricos de Malmi e Brown (2008), Simons (1995) e Huy (2001). Na análise dos dados, foi identificado o desenho e o uso do SCG, relatando como está transcorrendo a alteração de suas práticas de controle gerencial, identificando os fatores de estímulo e resistência à institucionalização dessas práticas e quais os atores organizacionais que estão atuando como agentes da mudança. Por fim, foram identificados os aspectos discursivos recorrentes que permeiam o discurso da empresa pesquisada, alinhados ao processo de mudança no SCG. Como contribuições, foi demonstrada a influência dos fatores isomórficos na escolha das práticas de controle gerencial, a evidência de que o SCG é socialmente construído, as implicações da centralização do poder e da ausência de estratégias para o SCG, evidências de que o processo de mudança no SCG não é meramente mecânico ou automatizado e ainda, que o discurso da mudança pode permear a organização sem que a ação seja concretizada, revelando um descompasso entre o discurso e a ação

On semigroups of endomorphisms of a chain with restricted range

Let X be a finite or infinite chain and let be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of and Green's relations on. In fact, more generally, if Y is a nonempty subset of X and is the subsemigroup of of all elements with range contained in Y, we characterize the largest regular subsemigroup of and Green's relations on. Moreover for finite chains, we determine when two semigroups of the type are isomorphic and calculate their ranks.

Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.