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101.
Richard L. Liboff 《International Journal of Theoretical Physics》2002,41(10):1957-1970
Three problems related to the spherical quantum billiard in
are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in
. The second topic addresses the first-excited-state theorem for the spherical quantum billiard in
. Wavefunctions for this system are given by the product form, (
)Z
q+()Y
(n)
, where is dimensionless displacement,
is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written
. It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in
is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in
. In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in
by enumerating independent degenerate product eigenstates of the Laplacian. 相似文献
102.
A. V. Arhangel'skii R. Z. Buzyakova 《Proceedings of the American Mathematical Society》1999,127(8):2449-2458
We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed , and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.
103.
Kimberly K. J. Kinateder Patrick McDonald 《Proceedings of the American Mathematical Society》1999,127(9):2767-2772
Let be a smoothly bounded domain in Euclidean space and let be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from of a particle driven by where the average is taken over all starting points in
104.
S. Manoff 《Acta Appl Math》1999,55(1):51-125
The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and a metric
is considered. The functional, the Lie, the covariant, and the total variations of a Lagrangian density, depending on components of tensor fields (with finite rank) and their first and second covariant derivatives, are established. A variation operator is determined and the corollaries of its commutation relations with the covariant and the Lie differential operators are found. The canonical (common) method of Lagrangians with partial derivatives (MLPD) and the method of Lagrangians with covariant derivatives (MLCD) are outlined. They differ each other by the commutation relations the variation operator has to obey with the covariant and the Lie differential operator. The covariant Euler–Lagrange equations are found on the basis of the MLCD. The energy-momentum tensors are considered on the basis of the Lie variation and the covariant Noether identities.As an application of the investigated general scheme, (pseudo) Riemannian spaces with contravariant and covariant affine connections (whose components differ not only by sign)
are considered as a special case of
-spaces with Riemannian metric, symmetric covariant connection and a weaker definition of dual vector basis with conformal noncanonical contraction operator
. The geodesic and autoparallel equations in
-spaces are found as different equations in contrast to the case of V
4-spaces. The Euler–Lagrange equations as Einstein's field equations in
-spaces and the corresponding energy-momentum tensors (EMTs) are obtained and compared with the Einstein equations and the EMTs in V
4-spaces. The geodesic and the auto-parallel equations are discussed. 相似文献
105.
We want in this note to clarify some aspects of the Machian foundation of the concept of mass in classical mechanics; specifically, we show how the relations of transitivity for the mass-ratios, necessary for a well grounded definition of mass, can be derived from Machian postulates. 相似文献
106.
Tsugunori Nogura 《Topology and its Applications》1983,15(1):65-69
We study the question whether a topological space X with a property can be embedded in a countably compact space X? with the same property . 相似文献
107.
Sheldon M Ross 《Stochastic Processes and their Applications》1976,4(2):167-173
Consider an n-component reliability system having the property that at any time each of its components is either up (i.e., working) or down (i.e., being repaired). Each component acts independently and we suppose that each time the ith component goes up it remains up for an exponentially distributed time having mean μi, and each time it goes down it remains down for an exponentially distributed time having mean υi. We further suppose that whether or not the system itself is up at any time depends only on which components are up at that time. We are interested in the distribution of the time of first system failure when all components are initially up at time zero. In section 2 we show that this distribution has the NBU (i.e., new better than used) property, and in Section 3 we make use of this and other results to obtain a lower bound to the mean time until first system failure. 相似文献
108.
109.
Jan Grandell 《Stochastic Processes and their Applications》1979,8(3):243-255
We consider the classical model for an insurance business where the claims occur according to a Poisson process and where the distribution for the cost of each claim fulfills Cramér's tail-condition. Under these conditions Lundberg's constant R is of fundamental importance for ruin calculations.We derive estimates of R, based on an observation of the insurance business and investigate the statistical properties of those estimates. We further derive bounds and confidence intervals for ruin probabilities. 相似文献
110.
B K Godwal 《Pramana》1982,19(3):225-229
The method of first principle pseudopotential is used to simulate the volume variation of nuclear Grüneisen parameter. The
elements Al and Be, for which Neal’s experimental data exist are investigated. The nuclear Grüneisen obtained from the details
of phonon frequencies are in better agreement with the experimental data as compared to those obtained from approximate Slater
and Dugdale-MacDonald methods, often used in shock wave studies. 相似文献