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991.
Generalized billiards describe nonequilibrium gas, consisting of finitely many particles, that move in a container, whose
walls heat up or cool down. Generalized billiards can be considered both in the framework of the Newtonian mechanics and of
the relativity theory. In the Newtonian case, a generalized billiard may possess an invariant measure; the Gibbs entropy with
respect to this measure is constant. On the contrary, generalized relativistic billiards are always dissipative,and the Gibbs
entropy with respect to the same measure grows under some natural conditions.
In this article, we find the necessary and sufficient conditions for a generalized Newtonian billiard to possess a smooth
invariant measure, which is independent of the boundary action: the corresponding classical billiard should have an additional
first integral of special type. In particular,the generalized Sinai billiards do not possess a smooth invariant measure. We
then consider generalized billiards inside a ball, which is one of the main examples of the Newtonian generalized billiards
which does have an invariant measure. We construct explicitly the invariant measure, and find the conditions for the Gibbs
entropy growth for the corresponding relativistic billiard both formonotone and periodic action of the boundary. 相似文献
992.
Based on the concept of adiabatic invariant, this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained. 相似文献
993.
In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results. 相似文献
994.
The transmission properties of one-dimensional photonic crystals containing double-negative and singlenegative materials are studied theoretically.A special kind of photonic band gap is found in this structure.This gap is invariant with scaling and insensitive to thickness fluctuation.But when changing the ratio of the thickness of two media.the width of the gap could be enlarged.The defect modes are analyzed by inducing a linear defect layer in the structure.It is found that the number of defect modes will increase when the thickness of the defect layer becomes larger. 相似文献
995.
We consider the energy bounds of inhomogeneous current states in doped antiferromagnetic insulators in the framework of the two-component Ginzburg-Landau model. Using the formulation of this model in terms of the gauge-invariant order parameters (the unit vector n, spin stiffness field ρ2, and particle momentum c), we show that this strongly correlated electron system involves a geometric small parameter that determines the degree of packing in the knots of filament manifolds of the order parameter distributions for the spin and charge degrees of freedom. We find that as the doping degree decreases, the filament density increases, resulting in a transition to an inhomogeneous current state with a free energy gain.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 182–189, July, 2005. 相似文献
996.
J. R. Choi 《International Journal of Theoretical Physics》2003,42(4):853-861
We use the dynamical invariant method to derive quantum-mechanical solution of time-dependent Hamiltonian system consisting quadratic potential, inverse quadratic potential, and
. The term in Hamiltonian containing
gives the expression such as
in coordinate space, which we can often meet in radial equation of quantum many body problem. The wave functions differed only a time-dependent phase factor from the eigenstates of the invariant operator Î and expressed in terms of an associated Laguerre function. 相似文献
997.
New relativity groups for spacetime admitting invariant velocities are considered. It is shown that most of them restrict the maximal allowed velocities of reference frames. 相似文献
998.
Some Results on the <Emphasis Type="BoldItalic">m</Emphasis>-Laplace Equations with Two Growth Terms
We prove the existence of positive radial solutions of the following equation:
and give sufficient conditions on the positive functions K1(r) and K2 (r) for the existence and nonexistence of ground states (G.S.) and Singular ground states (S.G.S.), when
or
. We also give sufficient conditions for the existence of radial S.G.S. and G.S. of equation
when
and
, respectively. We are also able to classify all the S.G.S. of this equation. The proofs use a new Emden–Fowler transform which allow us to use techniques taken from dynamical system theory, in particular the ones developed in Johnson et al. (Nonlinear Anal, T.M.A. 20, 1279–1302 (1993)) for the problems obtained by substituting the ordinary Laplacian Δ for the m-Laplacian Δm in the preceding equations.MSC: 37B55, 35H30, 35J70 相似文献
999.
In this paper, we introduce the star-shape models, where the precision matrix Ω (the inverse of the covariance matrix) is
structured by the special conditional independence. We want to estimate the precision matrix under entropy loss and symmetric
loss. We show that the maximal likelihood estimator (MLE) of the precision matrix is biased. Based on the MLE, an unbiased
estimate is obtained. We consider a type of Cholesky decomposition of Ω, in the sense that Ω=Ψ′Ψ, where Ψ is a lower triangular
matrix with positive diagonal elements. A special group
, which is a subgroup of the group consisting all lower triangular matrices, is introduced. General forms of equivariant estimates
of the covariance matrix and precision matrix are obtained. The invariant Haar measures on
, the reference prior, and the Jeffreys prior of Ψ are also discussed. We also introduce a class of priors of Ψ, which includes
all the priors described above. The posterior properties are discussed and the closed forms of Bayesian estimators are derived
under either the entropy loss or the symmetric loss. We also show that the best equivariant estimators with respect to
is the special case of Bayesian estimators. Consequently, the MLE of the precision matrix is inadmissible under either entropy
or symmetric loss. The closed form of risks of equivariant estimators are obtained. Some numerical results are given for illustration.
The project is supported by the National Science Foundation grants DMS-9972598, SES-0095919, and SES-0351523, and a grant
from Federal Aid in Wildlife Restoration Project W-13-R through Missouri Department of Conservation. 相似文献
1000.
Let be a polynomial semigroup containing an element with degree at least 2 with the semigroup operation being functional composition. We prove that is nearly abelian if and only if the smallest completely invariant closed subset of the Riemann sphere is not equal to the Riemann sphere. We also give a positive answer to Conjecture 7.1 in Hinkkanen and Martin's paper on the dynamics of semigroups of rational functions.