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941.
José F. Cariñena Manuel F. Rañada 《Journal of Mathematical Analysis and Applications》2007,332(2):975-988
Given a smooth vector field Γ and assuming the knowledge of an infinitesimal symmetry X, Hojman [S. Hojman, The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system, J. Phys. A Math. Gen. 29 (1996) 667-674] proposed a method for finding both a Poisson tensor and a function H such that Γ is the corresponding Hamiltonian system. In this paper, we approach the problem from geometrical point of view. The geometrization leads to the clarification of several concepts and methods used in Hojman's paper. In particular, the relationship between the nonstandard Hamiltonian structure proposed by Hojman and the degenerate quasi-Hamiltonian structures introduced by Crampin and Sarlet [M. Crampin, W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys. 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction. 相似文献
942.
Arman Melkumyan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):330-349
The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium
is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation”
[15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means
of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion
between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield
structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details.
The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly.
Numerical analysis is presented. 相似文献
943.
A. Yu. Kolesov E. F. Mishchenko N. Kh. Rozov 《Proceedings of the Steklov Institute of Mathematics》2007,259(2):101-127
We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate
from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by
a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit
RCL oscillator with delay in a feedback loop.
Original Russian Text ? A.Yu. Kolesov, E.F. Mishchenko, N.Kh. Rozov, 2007, published in Trudy Matematicheskogo Instituta imeni
V.A. Steklova, 2007, Vol. 259, pp. 106–133. 相似文献
944.
Infinite dimensional duality and applications 总被引:2,自引:0,他引:2
Patrizia Daniele Sofia Giuffrè Giovanna Idone Antonino Maugeri 《Mathematische Annalen》2007,339(1):221-239
The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has
an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality
theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete
problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite
dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example,
we find the Lagrange multiplier associated to a general elastic–plastic torsion problem. 相似文献
945.
We prove some extension theorems for analytic objects, in particular sections of a coherent sheaf, defined in semi q-coronae of a complex space. Semi q-coronae are domains whose boundary is the union of a Levi flat part, a q-pseudoconvex part and a q-pseudoconcave part. Such results are obtained mainly using cohomological techniques. 相似文献
946.
Optimal explicit Runge–Kutta methods consider more stages in order to include a particular spectrum in their stability domain
and thus reduce time-step restrictions. This idea, so far used mostly for real-line spectra, is generalized to more general
spectra in the form of a thin region. In thin regions the eigenvalues may extend away from the real axis into the imaginary
plane. We give a direct characterization of optimal stability polynomials containing a maximal thin region and calculate these
polynomials for various cases. Semi-discretizations of hyperbolic–parabolic equations are a relevant application which exhibit
a thin region spectrum. As a model, linear, scalar advection–diffusion is investigated. The second-order-stabilized explicit
Runge–Kutta methods derived from the stability polynomials are applied to advection–diffusion and compressible, viscous fluid
dynamics in numerical experiments. Due to the stabilization the time step can be controlled solely from the hyperbolic CFL
condition even in the presence of viscous fluxes. 相似文献
947.
F. Calogero 《Theoretical and Mathematical Physics》2007,152(1):882-893
We review recent results about classical isochronous systems characterized by the presence of an open (hence fully dimensional)
region in their phase space in which all their solutions are completely periodic (i.e., periodic in all degrees of freedom)
with the same fixed period (independent of the initial data provided they are inside the isochronicity region). We report
a technique for generating such systems, whose wide applicability justifies the statement that isochronous systems are not
rare. We also present an analogous technique applicable to a vast class of Hamiltonian systems and generating isochronous
Hamiltonian systems. We also report some results concerning the quantized versions of such systems. 相似文献
948.
Ding-kang WANG~ Yan ZHANG Key Laboratory of Mathematics Mechanization Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2007,50(10):1441-1450
We present an algorithm to decompose a polynomial system into a finite set of normal ascending sets such that the set of the zeros of the polynomial system is the union of the sets of the regular zeros of the normal ascending sets.If the polynomial system is zero dimensional,the set of the zeros of the polynomials is the union of the sets of the zeros of the normal ascending sets. 相似文献
949.
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on
manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of
the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and
extend the unpublished thesis of A. Karnaukh [Ka].
The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author
was supported by NSERC and FQRNT.
Received: April 2006 Revision: October 2006 Accepted: October 2006 相似文献
950.
N. N. Koval’ Yu. F. Ivanov I. M. Goncharenko O. V. Krysina Yu. A. Kolubaeva K. A. Koshkin 《Russian Physics Journal》2007,50(2):146-152
Phase composition, defect substructure, and mechanical properties of the Ti-Si-N coating deposited on metal and ceramic-metal substrates by electroarc sputtering of the Ti-Si composite cathode in an ionized
nitrogen atmosphere are investigated by the methods of modern materials science. It is established that coatings so formed
with a thickness of ∼1–3 μm are superhard (Hv ∼ 50 GPa), and have the nanocrystalline structure (with crystalline sizes D = 7 nm) based on titanium nitride δ-TiN.
__________
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 46–51, February, 2007. 相似文献