Eigenvalues of Casimir invariants for unitary irreps of Uq(gl(m vertical bar n))

A fully explicit formula for the eigenvalues of Casimir invariants for U-q(gl(m/n)) is given which applies to all unitary irreps. This is achieved by making some interesting observations on atypicality indices for irreps occurring in the tensor product of unitary irreps of the same type. These results have applications in the determination of link polynomials arising from unitary irreps of U-q(gl(m/n)).

Isotopically resolved (B)over-tilde<-(X)over-tilde electronic spectrum of Ag-3 and calculation of its Jahn-Teller effects

Ag-3 was produced by pulsed-nozzle laser vaporisation and jet-cooled in a Ne supersonic expansion. One-color resonant two-photon ionisation (R2PI) spectra of the (B) over tilde(2) E '' <-- (X) over tilde(2) E' transition of Ag-3 were separately measured for all four isotopic combinations. Long vibrational progressions are observed, involving clearly resolved bands at low energy, merging into a dense but resolvable spectrum up to 1000 cm(-1) above the origin. Both the ground (X) over tilde(2) E' and excited (B) over tilde(2) E '' states of Ag-3 are susceptible to Jahn-Teller distortion along the degenerate e' bending coordinate. The Jahn-Teller analysis includes both linear and quadratic terms, simultaneously with the spin-orbit coupling. Following extensive parameter fitting, the absorption spectrum is calculated, and bands assigned. The spin-orbit splitting is quenched below the localization energy, but becomes observable approximate to 300 cm(-1) above the origin.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

A novel target-field method for finite-length magnetic resonance shim coils: I. Zonal shims

This paper presents a new approach for the design of genuinely finite-length shim and gradient coils, intended for use in magnetic resonance imaging equipment. A cylindrical target region is located asymmetrically, at an arbitrary position within a coil of finite length. A desired target field is specified on the surface of that region, and a method is given that enables winding patterns on the surface of the coil to be designed, to produce the desired field at the inner target region. The method uses a minimization technique combined with regularization, to find the current density on the surface of the coil. The method is illustrated for linear, quadratic and cubic magnetic target fields located asymmetrically within a finite-length coil.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.

Exploring complex fitness surfaces: Multiple ornamentation and polymorphism in male guppies

The sexual ornamentation used by male guppies to attract females comprises many components, each of which varies considerably among males. Although natural and sexual selection have been shown to contribute to divergence among populations in male sexual ornaments, the role of sexual selection in maintaining polymorphism within populations is less clear. We used both parametric quadratic regression and nonparametric projection pursuit regression techniques to reveal the major axes of non-linear sexual selection on male ornaments. We visualized the fitness surfaces defined by these axes using thin-plate splines to allow a direct comparison of the two methodologies. Identification of the major axes of selection and their visualization was critical in determining the form and strength of nonlinear selection. Both types of analysis revealed fitness surfaces comprising three peaks, suggesting that there is more than one way to make an attractive guppy. Disruptive selection may be an important process underlying the presence of multiple sexual ornaments and may contribute to the maintenance of the high levels of polymorphism in male sexual ornaments found in guppy populations.

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.

Effects of levels of potassium and nitrogen on yields and post-harvest conservation of onions in winter

Potassium and nitrogen are the elements present in the highest percentage in the onion dry matter. The objective of this experiment was to evaluate yield and post-harvest conservation of Vale Ouro IPA-11 onion cultivar regarding to nitrogen and potassium levels. The experiment was carried out in Petrolina-PE, Brazil, from June to September 2009. The experimental design was a completely randomized block in a 4 x 3 factorial design, composed of four nitrogen levels (0, 60, 120 and 180 kg ha-1) and three potassium levels (0, 90 and 180 kg ha-1) with three replications. The highest yield of commercial bulbs was achieved at an estimated N level of 172.6 kg ha-1. The lowest yield of noncommercial bulbs was estimated at N level of 147.0 kg ha-1. Lower percentage of smaller bulbs (class 2) were obtained by increasing levels of N x K, with a quadratic effect at the dose of 90 kg ha-1 K2O and minimum production point with 127.6 kg N ha-1 (20.3%). Regarding larger caliber bulbs (class 4), linear effects were found both in the absence and for the level of 90 kg ha-1 of K2O as levels of N were increased. When the highest level of 180 kg ha-1 K2O was applied, the level of 92.8 kg ha-1 of N was estimated as the one that would promote the highest bulb yield of this class (35.4%), and 5.3% was found in the lack of potassium fertilization.

Application of GA3 and girdling of branches on the production of extemporaneous fruits of 'Tahiti' acid lime

The objective of this study was to evaluate the effect of girdling of branches and the application of GA3, still in the main crop flowering on the formation of reproductive structures, the fruit set of the following extemporaneous flowering of 'Tahiti' acid lime. This work used a randomized block design with five replications in a 4x3 factorial design. The first factor was the foliar application of GA3, 88 days before extemporaneous flowering at five concentrations (0, 7, 14 and 21 mg.L-1). The second factor was the girdling times, 108 days before flowering onset (A108AF), 78 days before flowering (A78AF) plus no-girdling control (NG). In extemporaneous flowering, the proportion of buds, flowers and fruits that abscised was 38.75, 31.25 and 18.64% respectively and 11.34% of all reproductive structures formed were collected. GA3 did not affect fruit set. Girdling increased fruit set by 229 and 256% at A108DAF and A78DAF respectively, in relation to NG plants. The GA3 reduced the formation of floral structures, which resulted in a quadratic increase in field production by reducing the competition for photoassimilates among fruits. The concentration of 21 mg.L-1 was the most productive, with 15.97 fruit.plant-1.

O ensino e aprendizagem do gráfico da função quadrática com e sem auxílio do Software Winplot

RESUMO: A utilização adequada das TIC no ensino da Matemática, nos dias de hoje é considerada por alguns como justificada e inevitável, esperando que a sua utilização melhore o ensino e a aprendizagem da Matemática. Nesta investigação, pretende-se testar o Software Winplot), no ensino e aprendizagem do gráfico da função quadrática com alunos do 10ºano, da Escola do segundo ciclo do Ensino Secundário nº9099, de modo a verificar se melhora o ensino e na aprendizagem desta temática.Para a nossa investigação Seleccionámos dois grupos de alunos do 10º ano que funcionaram como grupo de controlo e grupo experimental; depois de ambos os grupos terem realizado dois pré-testes, o grupo experimental realizou as aprendizagens no laboratório de informática com auxílio do Software Winplot, ao longo de 8 semanas, durante o 2º trimestre do ano lectivo de 2009/2010. O grupo de controlo realizou as aprendizagens, ao mesmo tempo que o grupo experimental, na sala normal de aulas sem auxílio do Software Winplot.Ao compararmos os dois grupos, o teste T de pares para amostras independentes, mostra-nos que estatisticamente não há diferenças significativas entre os dois grupos, porque os níveis de significância são maiores que p=0,05, desta feita podemos dizer que o grupo experimental, não obteve melhores resultados que o grupo de controlo, logo o Software Winplot não resultou o efeito desejado nas aprendizagens com alunos da 10ºano da Escola do segundo ciclo do ensino Secundário nº9099, sita no município de Viana (Luanda/Angola). ABSTRACT:The appropriate use of ICTs in teaching mathematics, today is considered by somo to be justified and inevitable, hoping that their use will improve the teaching and learning of mathematics.In this investigation, we intend to test the Software Winplot, teaching and learning of the graph of quadratic functions with students of grade 10, attending the second cycle of secondary School nº9099 in order to verify that improves teaching and learning of this subject.For our research selected two groups of students in 10th grade who acted as the controlo group and experimental group, after both group had undergone two pre-test, the experimental group performed the learning in the computer lab with the aid of Software Winplot, over 8 weeks during the second quarter of the academic year 2009/2010. Thr control gropu performed the learning, while the experimental group, in rregular class room without help of the Software Winplot.Comparing the two groups, the t test for independent samples pairs, shows us that there is no statistically significant differences between the two groups, because the significance levels are greater than p=0,05, this time we can say that experimental group, not yielded better results than the control group, so the Software did not result the desired effect on the learning with students from 10th grade of the School of the second cycle of Secondary nº9099, located in Viana (Luanda/Angola).