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61.
A computer search in the finite projective spaces PG(n, q) for the spectrum of possible sizes
k
of complete k-caps is done. Randomized greedy algorithms are applied. New upper bounds on the smallest size of a complete cap are given for many values of n
and q. Many new sizes of complete caps are obtained. 相似文献
62.
Alexander Koldobsky 《Advances in Applied Mathematics》2004,33(4):728-732
The Busemann–Petty problem asks whether origin-symmetric convex bodies in Rn with smaller areas of all central hyperplane sections necessarily have smaller n-dimensional volume. The solution was completed in the end of the 1990s, and the answer is affirmative if n4 and negative if n5. Since the answer is negative in most dimensions, it is natural to ask what information about the volumes of central sections of two bodies does allow to compare the n-dimensional volumes of these bodies in all dimensions. In this article we give an answer to this question in terms of certain powers of the Laplace operator applied to the section function of the body. 相似文献
63.
64.
Alexander Linkov Liliana Rybarska-Rusinek 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(10):821-831
The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation
of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable
when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power
expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion
of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge
axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first
terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots
to the third significant digit even for the wedge angle of 30°. 相似文献
65.
Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%... 相似文献
66.
A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity models used in electrotechnical practice. 相似文献
67.
The Heat Kernel on Hyperbolic Space 总被引:1,自引:0,他引:1
The purpose of this note is to provide a new proof for the explicitformulas of the heat kernel on hyperbolic space. By definition,the hyperbolic space Hn is a (unique) simply connected completen-dimensional Riemannian manifold with a constant negative sectionalcurvature 1. 1991 Mathematics Subject Classification58G32, 58G11. 相似文献
68.
A certain generalization of the algebra gl(N,
) of first-order differential operators acting on a space of inhomogeneous polynomials in
N−1 is constructed. The generators of this (non-) Lie algebra depend on permutation operators. It is shown that the Hamiltonian of the N-body Calogero model can be represented as a second-order polynomial in the generators of this algebra. The representation given implies that the Calogero Hamiltonian possesses infinitely-many finite-dimensional invariant subspaces with explicit bases, which are closely related to the finite-dimensional representations of the above algebra. This representation is an alternative to the standard representation of the Bargmann-Fock type in terms of creation and annihilation operators. 相似文献
69.
This study reports on the effect of input power to hexamethyldisiloxane (HMDSO) plasmas. The power dependence of the plasma-phase species and of the surface chemistry (of the deposits) has been investigated. Neutral and positive molecular species were detected within the plasma using mass spectrometry (MS). Secondary ion mass spectrometry (SIMS) was used to probe the molecular structure of the deposits. The elemental composition of the surface was determined by XPS and the deposition rate was monitored using a vibrating quartz crystal microbalance. Neutral and cationic molecules of mass greater than HMDSO were detected in the plasma. Their formation through ion-molecule reactions is proposed. Changes in the relative concentration of plasma-phase species follow those seen in molecular species detected at the deposit surface. Thus, we believe that the molecular structure of the deposits can be related to the species present in the plasma. While traditionally the dominant mechanism in deposit formation is assumed to be free radical combinations, we propose other possibilities involving cations with the aim of putting forward a new perspective on plasma polymerization mechanisms and thereby stimulating discussion. 相似文献
70.
Vladimir V. Bazhanov Sergei L. Lukyanov Alexander B. Zamolodchikov 《Communications in Mathematical Physics》1997,190(2):247-278
This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory.
We show here how to construct the operators ${\bf Q}_{\pm}(\lambda)$ which act in the highest weight Virasoro module and commute
for different values of the parameter λ. These operators appear to be the CFT analogs of the Q - matrix of Baxter [2], in particular they satisfy Baxter's famous T- Q equation. We also show that under natural assumptions about analytic properties of the operators as the functions of λ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV)
[3] for the eigenvalues of the Q-operators. We then use the DDV equation to obtain the asymptotic expansions of the Q - operators at large λ; it is remarkable that unlike the expansions
of the T operators of [1], the asymptotic series for Q(λ) contains the “dual” nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between
the vacuum eigenvalues of the Q - operators and the stationary transport properties in the boundary sine-Gordon model. On this basis we propose a number
of new exact results about finite voltage charge transport through the point contact in the quantum Hall system.
Received: 2 December 1996 / Accepted: 11 March 1997 相似文献