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21.
Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szegő's bounds on the zeros of Jacobi polynomials for , are completed with results for the rest of parameter values, Grosjean's inequality (J. Approx. Theory 50 (1987) 84) on the zeros of Legendre polynomials is shown to be valid for Jacobi polynomials with |β|1, bounds on ratios of consecutive zeros of Gauss and confluent hypergeometric functions are derived as well as an inequality involving the geometric mean of zeros of Bessel functions. 相似文献
22.
23.
The standard model on non-commutative space-time 总被引:1,自引:0,他引:1
X. Calmet B. Jurčo P. Schupp J. Wess M. Wohlgenannt 《The European Physical Journal C - Particles and Fields》2002,23(2):363-376
We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter . No new particles are introduced; the structure group is . We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order
in we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings
between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity
is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the
NCSM to the order considered.
Received: 29 November 2001 / Published online: 25 January 2002 相似文献
24.
Sajewicz Mieczysław Hauck Heinz-E. Drabik Gabriela Namysło Ewa Głód Bronisław Kowalska Teresa 《平面色谱法杂志一现代薄层色谱法》2006,19(4):278-281
JPC – Journal of Planar Chromatography – Modern TLC - We have previously described unexpected two-dimensionality in the thin-layer chromatographic separation of pairs of enantiomers of... 相似文献
25.
Rafael R. del Río Castillo 《Communications in Mathematical Physics》1991,142(2):421-431
In this work we study the behavior of embedded eigenvalues of Sturm-Liouville problems in the half axis under local perturbations. When the derivative of the spectral function is strictly positive, we prove that the embedded eigenvalues either disappear or remain fixed. In this case we show that local perturbations cannot add eigenvalues in the continuous spectrum. If the condition on the spectral function is removed then a local perturbation can add infinitely many eigenvalues. 相似文献
26.
Maria Conceição A. Silva Portela Emmanuel Thanassoulis 《Annals of Operations Research》2006,145(1):129-147
This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero
slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights
restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding
zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output
constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to
well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights
in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also
in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending
existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing
facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed
integer programming models, which are computationally demanding. 相似文献
27.
We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions. 相似文献
28.
The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n 1ef and n 2ef, can be applied. Analytical dependences of n 1ef and n 2ef on the modulation amplitudes of the refractive index n 1 and n 2 at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material. 相似文献
29.
René Meziat Diego Patiño Pablo Pedregal 《Computational Optimization and Applications》2007,38(1):147-171
We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control
problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control
variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex
optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on
global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking
of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also
present the numerical schemes to solve several examples arising in science and technology. 相似文献
30.
The equilibrium statistical volume distribution in foams, which has been previously demonstrated to be the so-called log-normal, is accounted on probability grounds by a scaling law on the bubble's volume time-evolution. This law states that the conditional probability for a given bubble to have the volume v(t + Δt), he assumption that it was v(t), to depend solely on the relationship v(t + Δt)/v(t), and in particular, to be independent of the time t. The theoretical results, however, allow to go further. Indeed, since the time dependece of its parameters (expectation and variance) are given functions of time, only two parameters are necessary to describe completely the foam. 相似文献