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991.
A. Yu. Kolesov E. F. Mishchenko N. Kh. Rozov 《Proceedings of the Steklov Institute of Mathematics》2007,256(1):206-222
The well-known sine-Gordon equation, supplemented with small damping and small quasiperiodic external force, is studied under the zero Dirichlet boundary conditions at the endpoints of a finite interval. The main assumption is that all frequencies of the external force are in 1:1 resonance with certain eigenfrequencies of the unperturbed equation; i.e., the socalled fundamental multifrequency resonance is observed. It is shown that in this case, by an appropriate choice of the parameters of the external force, one can make it so that the boundary value problem has a stable invariant torus of any finite dimension that bifurcates from zero on any preassigned finite set of spatial modes. It is also shown (by numerical analysis) that in a number of cases the above-mentioned torus coexists with a chaotic attractor. 相似文献
992.
993.
E. V. Karnaukh 《Ukrainian Mathematical Journal》2007,59(4):620-632
We consider almost upper-semicontinuous processes defined on a finite Markov chain. The distributions of functionals associated
with the exit of these processes from a finite interval are studied. We also consider some modifications of these processes.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 555–565, April, 2007. 相似文献
994.
A. G. Khovanskii 《Proceedings of the Steklov Institute of Mathematics》2007,259(1):82-100
We discuss the problem of representability and nonrepresentability of algebraic functions by radicals. We show that the Riemann
surfaces of functions that are the inverses of Chebyshev polynomials are determined by their local behavior near branch points.
We find lower bounds on the degrees of equations to which sufficiently general algebraic functions can be reduced by radicals.
We also begin to classify rational functions of prime degree whose inverses are representable by radicals. 相似文献
995.
Adam B. Levy 《Mathematical Programming》2007,110(3):615-639
Numerical methods for solving constrained optimization problems need to incorporate the constraints in a manner that satisfies
essentially competing interests; the incorporation needs to be simple enough that the solution method is tractable, yet complex
enough to ensure the validity of the ultimate solution. We introduce a framework for constraint incorporation that identifies
a minimal acceptable level of complexity and defines two basic types of constraint incorporation which (with combinations)
cover nearly all popular numerical methods for constrained optimization, including trust region methods, penalty methods,
barrier methods, penalty-multiplier methods, and sequential quadratic programming methods. The broad application of our framework
relies on addition and chain rules for constraint incorporation which we develop here. 相似文献
996.
M. V. Semenova 《Siberian Mathematical Journal》2007,48(4):718-732
We prove that the class of finite lattices embeddable into the subsemilattice lattices of semilattices which are (n-ary) trees can be axiomatized by identities within the class of finite lattices, whence it forms a pseudovariety. 相似文献
997.
G. I. Petrashen V. V. Reshetnikov Yu. A. Surkov 《Journal of Mathematical Sciences》2007,142(6):2645-2654
A nonstationary problem concerning the propagation of low-frequency waves for a model that consists of a packet of elastic
layers lying on an elastic half-space is considered, and exact mathematical solutions in the form of repeated integrals are
constructed in three basic forms. It is proved that these solutions satisfy initial conditions. The representation of solutions
as a superposition of multiple waves is treated. Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 220–239. 相似文献
998.
M. Abel 《Journal of Mathematical Sciences》2007,140(3):346-353
Bounded representations of bornological algebras are considered. The left and right bornological radicals in bornological
algebras are introduced. It is shown that the left (right) bornological radical of a bornological algebra A is equal to the
intersection of all bornologically closed maximal regular left (respectively, right) ideals of A, and both these radicals
of A and the Jacobson radical of A coincide if A is an advertive and simplicial bornological algebra (in particular, a bornological
Q-algebra). Bibliography: 16 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 9–22. 相似文献
999.
A theorem on the existence of a G-representation and a differential-geometric criterion of the kinematic integrability for nonlinear differential equations
from the Λ2-G-classes is proved. Examples of zero-curvature representations and metrics for some equations of mathematical physics are
presented.
__________
Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry,
2005. 相似文献
1000.
Ch. Tsitouras 《Numerical Algorithms》2007,44(3):291-307
Runge–Kutta (RK) pairs furnish approximations of the solution of an initial value problem at discrete points in the interval
of integration. Many techniques for enriching these methods with continuous approximations have been proposed. Here we construct
C
1 continuous, eighth and ninth order interpolation methods for a recently appeared RK pair of orders 9(8). These interpolants
share a very small leading truncation error making them suitable for use at quadruple precision, i.e. 32–33 decimal digits
of accuracy. Extended numerical results justify our effort. 相似文献