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991.
Alexander M. Krasnosel'skii Dmitrii I. Rachinskii 《Journal of Differential Equations》2006,226(1):30-53
We are concerned with a subharmonic bifurcation from infinity for scalar higher order ordinary differential equations. The equations contain principal linear parts depending on a scalar parameter, 2π-periodic forcing terms, and continuous nonlinearities with saturation. We suggest sufficient conditions for the existence of subharmonics (i.e., periodic solutions of multiple periods 2πn) with arbitrarily large amplitudes and periods. We prove that this type of the subharmonic bifurcation occurs whenever a pair of simple roots of the characteristic polynomial crosses the imaginary axis at the points ±αi with an irrational α. Under some further assumptions, we estimate asymptotically the parameter intervals, where large subharmonics of periods 2πn exist. These assumptions relate the quality of the Diophantine approximations of α, the rate of convergence of the nonlinearity to its limits at infinity, and the smoothness of the forcing term. 相似文献
992.
M. Sioen 《Journal of Pure and Applied Algebra》2006,207(3):675
In this work we investigate the natural algebraic structure that arises on dual spaces in the context of quantified functional analysis. We show that the category of absolutely convex modules is obtained as the category of Eilenberg-Moore algebras induced by the dualization functor [−,R] on locally convex approach spaces. We also establish a dual adjunction between the latter category and the category of seminormed spaces. 相似文献
993.
Masaki Hibino 《Journal of Differential Equations》2006,227(2):499-533
This article part I and the forthcoming part II are concerned with the study of the Borel summability of divergent power series solutions for singular first-order linear partial differential equations of nilpotent type. Under one restriction on equations, we can divide them into two classes. In this part I, we deal with the one class and obtain the conditions under which divergent solutions are Borel summable. (The other class will be studied in part II.) In order to assure the Borel summability of divergent solutions, global analytic continuation properties for coefficients are required despite of the fact that the domain of the Borel sum is local. 相似文献
994.
We investigate which boundary points in the closed unit ball of the Bergman space A1 are strongly exposed. This requires study of the Bergman projection and its kernel, the annihilator of Bergman space. We show that all polynomials in the boundary of the unit ball are strongly exposed. 相似文献
995.
James Camacho Jr. 《Periodica Mathematica Hungarica》1995,31(2):113-121
The subset of lattice regular zero-one valued measures on an algebra generated by a lattice (a Wallman-type space) which integrates all lattice continuous functions on an arbitrary setX is introduced and some properties of it are presented.Then repleteness of certain Wallman spaces is considered and used in finally establishing conditions whereby the space of lattice regular zero-one valued measures on the algebra generated by a lattice which are countably additive (a Wallman-type space) is realcompact. 相似文献
996.
R. Verfürth 《Numerische Mathematik》1998,80(4):641-663
Summary. We derive a posteriori error estimators for convection-diffusion equations with dominant convection. The estimators yield
global upper and local lower bounds on the error measured in the energy norm such that the ratio of the upper and lower bounds
only depends on the local mesh-Peclet number. The estimators are either based on the evaluation of local residuals or on the
solution of discrete local Dirichlet or Neumann problems.
Received February 10, 1997 / Revised version received November 4, 1997 相似文献
997.
Peter M. Gruber 《Monatshefte für Mathematik》2002,135(4):279-304
We estimate the error of asymptotic formulae for volume approximation of sufficiently differentiable convex bodies by circumscribed
convex polytopes as the number of facets tends to infinity. Similar estimates hold for approximation with inscribed and general
polytopes and for vertices instead of facets. Our result is then applied to estimate the minimum isoperimetric quotient of
convex polytopes as the number of facets tends to infinity.
Received 16 July 2001 相似文献
998.
In one space dimension we address the homogenization of the spectral problem for a singularly perturbed diffusion equation
in a periodic medium. Denoting by ε the period, the diffusion coefficient is scaled as ε2. The domain is made of two purely periodic media separated by an interface. Depending on the connection between the two cell
spectral equations, three different situations arise when ε goes to zero. First, there is a global homogenized problem as
in the case without an interface. Second, the limit is made of two homogenized problems with a Dirichlet boundary condition
on the interface. Third, there is an exponential localization near the interface of the first eigenfunction.
Received: January 10, 2001; in final form: July 9, 2001?Published online: June 11, 2002 相似文献
999.
In most practical cases, the convergence of the GMRES method applied to a linear algebraic systemAx=b is determined by the distribution of eigenvalues ofA. In theory, however, the information about the eigenvalues alone is not sufficient for determining the convergence. In this
paper the previous work of Greenbaum et al. is extended in the following direction. It is given a complete parametrization
of the set of all pairs {A, b} for which GMRES(A, b) generates the prescribed convergence curve while the matrixA has the prescribed eigenvalues. Moreover, a characterization of the right hand sidesb for which the GMRES(A, b) converges exactly inm steps, wherem is the degree of the minimal polynomial ofA, is given.
This work was supported by AS CR Grant A2030706. Part of the work was performed while the third author visited Instituto di
Analisi Numerica (IAN CNR). 相似文献
1000.
Niels Vigand Pedersen 《Aequationes Mathematicae》1994,48(2-3):228-253
Summary For a simply connected solvable Lie group we specify the structure of the product, the inverse and the exponential map expressed in suitable coordinates (canonical coordinates of the second kind), and point out that in these coordinates the product and inverse are expressed entirely in terms of polynomials, exponential functions and trigonometric functions. We devise algorithms for computing the product, the inverse and the exponential map. 相似文献