Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

gl(2 vertical bar 2) current superalgebra and non-unitary conformal field theory

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate gl(2\2) current superalgebra at general level k. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented. (C) 2003 Elsevier B.V. All rights reserved.

More on exact bicoverings of 12 points

The minimum number of incomplete blocks required to cover, exactly lambda times, all t-element subsets from a set V of cardinality v (v > t) is denoted by y(lambda, t; v). The value of g(2, 2; v) is known for v = 3, 4,..., 11. It was previously known that 14 less than or equal to g(2, 2; 12) less than or equal to 16. We prove that g(2, 2; 12) greater than or equal to 15.

Factorizations of the complete graph into C-5-factors and 1-factors

In this paper, we show that K-10n can be factored into alpha C-5-factors and beta 1-factors for all non-negative integers alpha and beta satisfying 2alpha + beta = 10(n) - 1.

Skolem-type difference sets for cycle systems

Cyclic m-cycle systems of order v are constructed for all m greater than or equal to 3, and all v = 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic m-cycle system of K-v - F for all m greater than or equal to 3, and all v = 2(mod 2m).

Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces

In this paper we examine the effects of varying several experimental parameters in the Kane quantum computer architecture: A-gate voltage, the qubit depth below the silicon oxide barrier, and the back gate depth to explore how these variables affect the electron density of the donor electron. In particular, we calculate the resonance frequency of the donor nuclei as a function of these parameters. To do this we calculated the donor electron wave function variationally using an effective-mass Hamiltonian approach, using a basis of deformed hydrogenic orbitals. This approach was then extended to include the electric-field Hamiltonian and the silicon host geometry. We found that the phosphorous donor electron wave function was very sensitive to all the experimental variables studied in our work, and thus to optimize the operation of these devices it is necessary to control all parameters varied in this paper.

Climate of fear in organisational settings: Construct definition, measurement and a test of theory

This paper reports a study that explored a new construct: climate of fear. We hypothesised that climate of fear would vary across work sites within organisations, but not across organisations. This is in contrast a to measures of organisational culture, which were expected to vary both within and across organisations. To test our hypotheses, we developed a new 13-item measure of perceived fear in organisations and tested it in 20 sites across two organisations (N = 209). Culture variables measured were innovative leadership culture, and communication culture. Results were that climate of fear did vary across sites in both organisations, while differences across organisations were not significant, as we anticipated. Organisational culture, however, varied between the organisations, and within one of the organisations. The climate of fear scale exhibited acceptable psychometric properties.

Everyday incivility: towards a benchmark

Commonplace incivility is a topic of longstanding interest within social theory, perhaps best exemplified by Goffman's studies of the interaction order. Nevertheless we know very little about its distribution and expression in everyday life. Current empirical work is dominated by criminological agendas. These tend to focus on more serious and illegal activities rather than minor deviant acts that are simply inconsiderate or rude. The paper reports findings from a focus group study conducted in Melbourne, Australia that set out to benchmark everyday incivilities. The results suggest that perpetrators of incivility have a surprisingly broad social distribution as does the range of locales that might be characterised as 'high risk'. Turning to the work of Putnam and Wolfe, we call for a research focus on low-level incivilities as key symptoms of the state of civic virtue and the strength of moral ties within civil society. Drawing on Virilio, Bauman and Durkheim, it is suggested that the experience of incivility is underpinned by the growth of freedom and movement in contemporary urban settings, and has ambivalent implications that not only invoke boundary maintenance and retreatism, but also offer the possibility for boundary expansion and tolerance of difference.

Decompositions of complete graphs into theta graphs with fewer than ten edges

A theta graph is a graph consisting of three pairwise internally disjoint paths with common end points. Methods for decomposing the complete graph K-nu into theta graphs with fewer than ten edges are given.