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991.
Asymptotic Stability for a Class of Neutral Systems with Discrete and Distributed Time Delays 总被引:4,自引:0,他引:4
In this note, the asymptotic stability for a class of neutral systems with discrete time and distributed time delays is considered. Delay-dependent criteria are proposed to guarantee the stability for such systems. Some numerical examples are given to illustrate that our results are less conservative than previous results. 相似文献
992.
通过建立高阶椭圆算子Picone型恒等式,建立了比文献中更一般的Rellich不等式。 相似文献
993.
994.
J. F. RODRIGUES 《数学年刊B辑(英文版)》2002,23(2):253-266
InroductlonThe classical obstacle problem canbe formulated as the 相似文献
995.
Yiorgos-Sokratis Smyrlis 《BIT Numerical Mathematics》2006,46(1):163-194
We investigate the Method of Fundamental Solutions (MFS) for the solution of certain elliptic boundary value problems. In
particular, we study the case in which the number of collocation points exceeds the number of singularities, which leads to
an over-determined linear system. In such a case, the resulting linear system is over-determined and the proposed algorithm
chooses the approximate solution for which the error, when restricted to the boundary, minimizes a suitably defined discrete
Sobolev norm. This is equivalent to a weighted least-squares treatment of the resulting over-determined system. We prove convergence
of the method in the case of the Laplace’s equation with Dirichlet boundary data in the disk. We develop an alternative way
of implementing the numerical algorithm, which avoids the inherent ill-conditioning of the MFS matrices. Finally, we present
numerical experiments suggesting that introduction of Sobolev weights improves the approximation.
AMS subject classification (2000) 35E05, 35J25, 65N12, 65N15, 65N35, 65T50 相似文献
996.
The generalized Roper-Suffridge extension operator Ф(f) on the bounded complete Reinhardt domain Ω in Cn with n ≥ 2 is defined by Φrn,β2,γ2,…,βn,γn(f)(z)=(rf(z1/r),(rf(z1/r)/z1)β2(f'(z1/r))γ2z2,…,(rf(z1/r)/z1)βn(f'(z1/r)γnzn) for (z1,z2,…,zn) ∈Ω, where r = r(Ω) = sup{|z1| (z1,z2,…,zn) ∈ Ω},0 ≤ γj ≤ 1 -βj,0 ≤ βj ≤ 1,and we choose the branch of the power functions such that (f(z1)/z1)βj |z1=0 = 1 and (f′(z1))γj |z1=0 =1,j = 2,…,n. In this paper, we prove that the operator Фrn,β2,γ2,…,βn,γn(f) is from the subset of S*α(U) to S*α(Ω)(0 ≤ α < 1) on Ω and the operator Фrn,β2,γ2,…, βn,γn(f) preserves the starlikeness of order α or the spirallikeness of type β on Dp for some suitable constantsβj,γj,pj, where Dp ={(z1,z2,…,zn) ∈ Cn ∑nj=1|zj|pj < 1} (pj > 0, j = 1,2,…,n), U is the unit disc in the complex plane C, and Sα* (Ω) is the class of all normalized starlike mappings of order α on Ω. We also obtain that Φrn,β2,γ2,…,γn(f) ∈ S*α(Dp) if and only if f ∈ S*a(U) for 0 ≤ α < 1 and some suitable constants βj,γj,pj. 相似文献
997.
In modern short-pulse fiber lasers, there is significant pulse breathing over each round trip of the laser loop. Consequently, averaged models cannot be used for quantitative modeling and design. Instead, lumped models, which are obtained by concatenating models for the various components of the laser, are required. As the pulses in lumped models are periodic rather than stationary, their linear stability is evaluated with the aid of the monodromy operator obtained by linearizing the round-trip operator about the periodic pulse. Conditions are given on the smoothness and decay of the periodic pulse that ensure that the monodromy operator exists on an appropriate Lebesgue function space. A formula for the essential spectrum of the monodromy operator is given, which can be used to quantify the growth rate of continuous wave perturbations. This formula is established by showing that the essential spectrum of the monodromy operator equals that of an associated asymptotic operator. Since the asymptotic monodromy operator acts as a multiplication operator in the Fourier domain, it is possible to derive a formula for its spectrum. Although the main results are stated for a particular experimental stretched pulse laser, the analysis shows that they can be readily adapted to a wide range of lumped laser models. 相似文献
998.
Sonia Mazzucchi Valter Moretti Ivan Remizov Oleg Smolyanov 《Mathematische Nachrichten》2023,296(3):1244-1284
Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks. 相似文献
999.
Turhan Koprubasi Ram N. Mohapatra 《Mathematical Methods in the Applied Sciences》2023,46(2):1466-1478
In this paper, an inverse scattering problem for discrete Sturm–Liouville equation with eigenparameter-dependent boundary condition is investigated. In quest of finding scattering function and the main equation of this problem, the uniqueness of the kernel is proven. Also, an appropriate Levinson-type formula based on the continuity of scattering function is given. 相似文献
1000.
In this paper, the authors extend the Roper-Suffridge operator on the generalized Hartogs domains. They mainly research the properties of the extended operator.By the characteristics of Hartogs domains and the geometric properties of subclasses of spirallike mappings, they obtain the extended Roper-Suffridge operator preserving almost starlikeness of complex order λ, almost spirallikeness of type β and order α, parabolic spirallikeness of type β and order ρ on the Hartogs domains in different co... 相似文献