Higher-dimensional twistor transforms using pure spinors

Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (euclidean) dimension d = 2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on ℝ2n. For d = 4 and d = 6, these spaces are ℂℙ1 and ℂℙ3 and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d > 6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations. © SISSA/ISAS 2005.

EXPLICIT SOLUTIONS FOR TRUNCATED COULOMB POTENTIAL OBTAINED FROM SUPERSYMMETRY

The Schrodinger equation with the truncated Coulomb potential is solved using the supersymmetric quantum mechanics formalism, with and without the cutoff in the angular momentum potential. We obtain some analytical eigenfunctions and eigenvalues for particular values of the cutoff parameter.

Simple analytical expression for vector hypernuclear asymmetry in nonmesonic decay ofΛ 5He andΛ 12C

We present general explicit expressions for a shell-model calculation of the vector hypernuclear parameter in nonmesonic weak decay. We use a widely accepted effective coupling Hamiltonian involving the exchange of the complete pseudoscalar and vector meson octets (π, η, K, ρ, ω, K*). In contrast to the approximated formula widely used in the literature, we correctly treat the contribution of transitions originated from single-proton states beyond the s-shell. Exact and simple analytical expressions are obtained for the particular cases of Λ 5He and Λ 12C, within the one-pion-exchange model. Numerical computations of the asymmetry parameter, aΛ, are presented. Our results show a qualitative agreement with other theoretical estimates but also a contradiction with recent experimental determinations. Our simple analytical formulas provide a guide in searching the origin of such discrepancies, and they will be useful for helping to solve the hypernuclear weak decay puzzle.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Predictive formulas for food base excess and urine pH estimations of cats

Food base excess (BE, mEq/kg) can be calculated from the diet macroelements, together with either the sulfur amino acids methionine and cysteine (BEaa) or total sulfur (BEs) concentrations. The present study compared the use of sulfur or methionine and cysteine for calculating the food BE (experiment 1) and investigated the influence of food BE on blood gas analysis and the urine pH of cats, and proposes a prediction equation to estimate the urine pH of cats fed kibble diets based on the calculated food BE (experiments 2 and 3). In experiment 1, nine healthy, adult cats were used in a change-over design and fed with nine commercial dry cat foods. The cats were housed in metabolism cages over seven days for adaptation and three days for total urine collection. All of the urine produced over 24h was pooled by cat and diet. The cats' acid-base status was assessed through blood gas analysis after 10 days of diet consumption. A mean difference of -115mEq/kg between BEs and BEaa was observed, which could be explained by a greater concentration of sulfur in the whole diet than in methionine and cysteine. Urine pH presented a stronger correlation with food BEs (R2=0.95; P<0.001) than with food BEaa (R2=0.86; P<0.001). Experiment 2 included 30 kibble diets, and each diet was tested in six cats. The food BEs varied between -180 and +307mEq/kg, and the urine pH of the cats varied between 5.60 and 7.74. A significant correlation was found between the measured urine pH and the food BEs (urinary pH=6.269+[0.0036×BEs]+[0.000003×BEs2]; R2=0.91; P<0.001). In experiment 3, eight kibble diets were tested (food BEs between -187mEq/kg and +381mEq/kg) to validate the equation proposed in experiment 2 and to compare the obtained results with previously published formulae. The results of the proposed formula presented a high concordance correlation coefficient (0.942) and high accuracy (0.979) with the measured values, and the estimates of urine pH did not differ from the values obtained in cats (P>0.05). The cats' venous blood pH, bicarbonate, and blood BE were correlated with food BEs (P<0.001); the consumption of diets with low food BEs induced a reduction in these parameters. In conclusion, food macroelement composition has a strong influence on cats' acid-base equilibrium and food BEs calculation is a useful tool to formulate and balance kibble diets for felines. © 2013 Elsevier B.V.

Massless scattering at special kinematics as Jacobi polynomials

We study the scattering equations recently proposed by Cachazo, He and Yuan in the special kinematics where their solutions can be identified with the zeros of the Jacobi polynomials. This allows for a non-trivial two-parameter family of kinematics. We present explicit and compact formulas for the n-gluon and n-graviton partial scattering amplitudes for our special kinematics in terms of Jacobi polynomials. We also provide alternative expressions in terms of gamma functions. We give an interpretation of the common reduced determinant appearing in the amplitudes as the product of the squares of the eigenfrequencies of small oscillations of a system whose equilibrium is the solutions of the scattering equations.

Explicit and implicit knowledge of environment states induce adaptation in postural control

The aim of this study was to investigate the effects of explicit and implicit knowledge about visual surrounding manipulation on postural responses. Twenty participants divided into two groups, implicit and explicit, remained in upright stance inside a moving room. In the fourth trial participants in the explicit group were informed about the movement of the room while participants in the implicit group performed the trial with the room moving at a larger amplitude and higher velocity. Results showed that postural responses to visual manipulation decreased after participants were told that the room was moving as well as after increasing amplitude and velocity of the room, indicating decreased coupling (down-weighting) of the visual influences. Moreover, this decrease was even greater for the implicit group compared to the explicit group. The results demonstrated that conscious knowledge about environmental state changes the coupling to visual information, suggesting a cognitive component related to sensory re-weighting. Re-weighting processes were also triggered without awareness of subjects and were even more pronounced compared to the first case. Adaptive re-weighting was shown when knowledge about environmental state was gathered explicitly and implicitly, but through different adaptive processes. (C) 2014 Elsevier Ireland Ltd. All rights reserved.

Orthogonality relations and supercharacter formulas of U(m vertical bar n) representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented. © 1997 American Institute of Physics.

Mistura de sabor e violação de CP

Pós-graduação em Física - IFT