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991.
992.
We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) (No. 15340005) from the Ministry of Education, Culture, Sports, Science and Technology.Mathematics Subject classifications (2000). primary, 34M35, secondary, 33E20.This revised version was published online in March 2005 with corrections to the cover date. 相似文献
993.
We report for the first time to our knowledge on the preparation of colloidal solution of chalcogenide semiconductor As2S3 by laser ablation and the measurements of its nonlinear-optical characteristics using Z-scan method at the wavelength of Nd:YAG laser radiation ( = 1064 nm, = 25 ns). The nonlinear refractive index was measured to be –7.5 × 10–18 m2 W–1. Nonlinear absorption coefficient of chalcogenide solution was measured to be 1 cm GW–1. 相似文献
994.
We show that with the help of a suitable coupling between dark energy and cold dark matter it is possible to reproduce any scaling solution
X
M
a
, where
X
and
M
are the densities of dark energy and dark matter, respectively. We demonstrate how the case = 1 alleviates the coincidence problem. Future observations of supernovae at high redshift as well as quasar pairs which are planned to discriminate between different cosmological models will also provide direct constraints on the coupling between dark matter and dark energy. 相似文献
995.
András Kornai 《International Journal of Theoretical Physics》2003,42(2):301-307
This paper takes the first steps in developing a theory of explicit finitism which puts explicit limits on the size of finite objects. We provide motivation in the physics of computation sense, survey some of the difficulties and describe the appropriate computing machinery. We introduce the subset J of the real numbers that is the central mathematical object emerging from considerations of explicit finitism, and take the first steps in studying its properties. 相似文献
996.
J. Socorro 《International Journal of Theoretical Physics》2003,42(9):2087-2096
The quantization of gravity coupled to barotropic perfect fluid matter field with a cosmological constant is carried out. The wave function can be determined for any curvature index in the FRW minisuperspace model. The meaning of the existence of the classical solution is discussed in the WKB semiclassical approximation. 相似文献
997.
Akio?OhtaEmail author Satoru?Nakashima Hiroki?Matsuyanagi Tsuyoshi?Asakawa Shigeyoshi?Miyagishi 《Colloid and polymer science》2003,282(2):162-169
The Krafft temperatures and enthalpies of solution of N-hexadecanoyl alaninate and valinate, and N-tetradecanoyl phenylalaninate were obtained from differential scanning calorimetry. The Krafft temperature of N-acyl amino acid surfactant increased with decreasing size of the counter ion, with some exceptions. The enthalpy of solution was endothermic and increased with decreasing size of the counter ion except for the cases of lithium salt. The results showed that the L-L interaction in the solid state of N-hexadecanoyl amino acid surfactant salt was superior to the D-L interaction for both the alanine and valine systems when the counter ion size increased. However, the D-L interaction was still advantageous for the phenylalanine system with Cs+ as a counter ion. Both Fourier transform infrared spectroscopy studies and theoretical calculations suggested that the difference in magnitudes of the interactions between peptide and counter ion was a dominant factor for the chiral effect. 相似文献
998.
In this paper strongly nonlinear oscillator equations will be studied.It will be shown that the recently developed perturbation method based onintegrating factors can be used to approximate first integrals. Not onlyapproximations of first integrals will be given, butit will also be shown how in a rather efficient way the existence and stability oftime-periodic solutions can be obtained from these approximations. In particularthe generalized Rayleigh oscillator equation
will be studied in detail, and it will beshown that at least five limit cycles can occur. 相似文献
999.
U. Schröter 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(3):297-310
Green's dyadic technique represents a powerful tool for calculations in electrodynamics, especially in modelling optical properties
of nanoscopic objects. The method does not only provide field distributions, but also maps of susceptibilities and densities
of states. Whereas the formalism is well established for dielectrics and electric fields, I present here a straight forward
extension to tensors of both electric and magnetic type as well as mixed ones and furthermore to the situation where objects
with dielectric and magnetic permeabilities are present together. As examples, characteristic field patterns are compared
for elementary dielectric and magnetic perturbations. Green's tensors calculated for a coral structure reveal that mixed susceptibilities
can exhibit other symmetries than pure electric or magnetic ones. Maps of all tensor components can thus give essential clues
to the interpretation of near-field images.
Received 15 December 2002 Published online 20 June 2003
RID="a"
ID="a"Files “maths.ps” and “tensors.ps” are only available in electronic form at http://www.edpsciences.org
RID="b"
ID="b"e-mail: Ursula.Schroeter@uni-konstanz.de 相似文献
1000.
§ 1 IntroductionRecently,certain three-point boundary value problems for nonlinear ordinarydifferential equations have been studied by many authors[1— 6] .However,few papers havebeen published on the same problems for nonlinear functional differential equations.In thispaper,we are concerned with the following second order differential equation with anadvanced argumentu″(t) +λa(t) f(u(h(t) ) ) =0 ,t∈ (0 ,1 ) (1 .1 )with the three-point boundary conditionsu(0 ) =0 ,αu(η) =u(1 ) ,(1 .2 )… 相似文献