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121.
Zhenbin Fan 《Optimization》2014,63(8):1205-1217
In this paper, we study the approximate controllability of a linear fractional differential equation by using the method of regularization of Tikhonov. New concepts and results about controllability are established. Then, under the condition of the positivity of the controllability operator, we obtain that the linear system can be steered to an arbitrary small neighbourhood of the fractional integral of the state at final time. 相似文献
122.
In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found. 相似文献
123.
124.
Ramin Vatankhah Ali Najafi Hassan Salarieh Aria Alasty 《Journal of Mathematical Analysis and Applications》2014
This study investigates the exact controllability problem for a vibrating non-classical Euler–Bernoulli micro-beam whose governing partial differential equation (PDE) of motion is derived based on the non-classical continuum mechanics. In this paper, it is proved that via boundary controls, it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time. This control objective is achieved based on the PDE model of the system which causes that spillover instabilities do not occur. 相似文献
125.
Roman Šimon Hilscher 《Mathematische Nachrichten》2014,287(5-6):704-716
In this work we derive new comparison results for (finite) eigenvalues of two self‐adjoint linear Hamiltonian eigenvalue problems. The coefficient matrices depend on the spectral parameter nonlinearly and the spectral parameter is present also in the boundary conditions. We do not impose any controllability or strict normality assumptions. Our method is based on a generalization of the Sturmian comparison theorem for such systems. The results are new even for the Dirichlet boundary conditions, for linear Hamiltonian systems depending linearly on the spectral parameter, and for Sturm–Liouville eigenvalue problems with nonlinear dependence on the spectral parameter. 相似文献
126.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(10):3492-3512
In this paper we develop, study, and test a Lie group multisymplectic integrator for geometrically exact beams based on the covariant Lagrangian formulation. We exploit the multisymplectic character of the integrator to analyze the energy and momentum map conservations associated to the temporal and spatial discrete evolutions. 相似文献
127.
In this note we define fibrations of topological stacks and establish their main properties. When restricted to topological spaces, our notion of fibration coincides with the classical one. We prove various standard results about fibrations (long exact sequence for homotopy groups, Leray–Serre and Eilenberg–Moore spectral sequences, etc.). We prove various criteria for a morphism of topological stacks to be a fibration, and use these to produce examples of fibrations. We prove that every morphism of topological stacks factors through a fibration and construct the homotopy fiber of a morphism of topological stacks. As an immediate consequence of the machinery we develop, we also prove van Kampen?s theorem for fundamental groups of topological stacks. 相似文献
128.
Kororbov V. I. Krabs W. Skylar G. M. 《Journal of Optimization Theory and Applications》2000,107(1):51-68
We consider the linear model of a slowly rotating Timoshenko beam in a horizontal plane whose moment is controlled by the angular acceleration of the disk of the driving motor into which the beam is clamped. This work complements our previous results on the controllability of the beam from a position of rest into another position of rest; we give a method of construction of a piecewise constant control solving the problem. 相似文献
129.
We investigate two different discretization approaches of a model optimal-control problem, chosen to be relevant for control
of instabilities in shear flows. In the first method, a fully discrete approach has been used, together with a finite-element
spatial discretization, to obtain the objective function gradient in terms of a discretely-derived adjoint equation. In the
second method, Chebyshev collocation is used for spatial discretization, and the gradient is approximated by discretizing
the continuously-derived adjoint equation. The discrete approach always results in a faster convergence of the conjugate-gradient
optimization algorithm. Due to the shear in the convective velocity, a low diffusivity in the problem complicates the structure
of the computed optimal control, resulting in particularly noticeable differences in convergence rate between the methods.
When the diffusivity is higher, the control becomes less complicated, and the difference in convergence rate reduces. The
use of approximate gradients results in a higher sensitivity to the degrees of freedom in time. When the system contains a
strong instability, it only takes a few iteration to obtain an effective control for both methods,even if there are differences
in the formal convergence rate. This indicates that it is possible to use the approximative gradients of the objective function
in cases where the control problem mainly consists of controlling strong instabilities.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
130.
This paper presents a family of High‐order finite volume schemes applicable on unstructured grids. The k‐exact reconstruction is performed on every control volume as the primary reconstruction. On a cell of interest, besides the primary reconstruction, additional candidate reconstruction polynomials are provided by means of very simple and efficient ‘secondary’ reconstructions. The weighted average procedure of the WENO scheme is then applied to the primary and secondary reconstructions to ensure the shock‐capturing capability of the scheme. This procedure combines the simplicity of the k‐exact reconstruction with the robustness of the WENO schemes and represents a systematic and unified way to construct High‐order accurate shock capturing schemes. To further improve the efficiency, an efficient problem‐independent shock detector is introduced. Several test cases are presented to demonstrate the accuracy and non‐oscillation property of the proposed schemes. The results show that the proposed schemes can predict the smooth solutions with uniformly High‐order accuracy and can capture the shock waves and contact discontinuities in high resolution. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献