共查询到20条相似文献,搜索用时 31 毫秒
1.
给出并证明了函数在一点处广义二阶可导的一个充分条件,分析了二元函数在一点的广义二阶导数和二阶混合偏导数之间的关系. 相似文献
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H. Kawasaki 《Mathematical Programming》1990,49(1-3):213-229
The second derivative of an envelope cannot be expressed only by second derivatives of the constituent functions. By taking account of this fact, we derive new second order necessary optimality conditions for minimization of a sup-type function. The conditions involve an extra term besides the second derivative of the Lagrange function. Furthermore, we will comment on the relationship between the extra term and a kind of second order directional derivative of the sup-type function. 相似文献
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Rui Ling Meirong WuYan Dong Yi Chai 《Communications in Nonlinear Science & Numerical Simulation》2012,17(8):3406-3416
A novel high order sliding-mode control is proposed based on finite state machine by combination of relay algorithm and an improved second order algorithm to solve uncertain nonlinear system stabilization with relative degree three in finite time. This approach drives finite state machines to switch according to sliding variable and first order derivative of it, forces sliding variable, first order derivative and second order derivative of it to zero, without the knowledge of second order derivative of sliding variable, and stabilizes the system in finite time. 相似文献
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Two recent methods (Shanno, 1978; Toint, 1980) for revisingestimates of sparse second derivative matrices in quasi-Newtonoptimization algorithms reduce to variable metric formulae whenthere are no sparsity conditions. It is proved that these methodsare equivalent. Further, some examples are given to show thatthe procedure may make the second derivative approximationsworse when the objective function is quadratic. Therefore theconvergence properties of the procedure are sometimes less goodthan the convergence properties of other published methods forrevising sparse second derivative approximations. 相似文献
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We study the positivity of the second shape derivative around an equilibrium for a 2-dimensional functional involving the perimeter of the shape and its the Dirichlet energy under volume constraint. We prove that, generally, convex equilibria lead to strictly positive second derivatives. We also exhibit some examples where strict positivity of the second order derivative holds at an equilibrium while existence of a minimum does not. 相似文献
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M. J. D. Powell 《Mathematical Programming》1981,20(1):144-151
In order to apply quasi-Newton methods to solve unconstrained minimization calculations when the number of variables is very large, it is usually necessary to make use of any sparsity in the second derivative matrix of the objective function. Therefore, it is important to extend to the sparse case the updating formulae that occur in variable metric algorithms to revise the estimate of the second derivative matrix. Suitable extensions suggest themselves when the updating formulae are derived by variational methods [1, 3]. The purpose of the present paper is to give a new proof of a theorem of Dennis and Schnabel [1], that shows the effect of sparsity on updating formulae for second derivative estimates. 相似文献
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Roger Moser 《偏微分方程通讯》2013,38(9):1654-1689
The second derivative of a map into a Riemannian manifold is given by a nonlinear differential operator. We study minimizers and critical points of the L 2-norm of this second derivative. We show existence of minimizers with the direct method and we prove a partial regularity result. 相似文献
10.
Shape derivative of the volume integral operator in electromagnetic scattering by homogeneous bodies
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Hamdi Sakly 《Mathematical Methods in the Applied Sciences》2017,40(18):7125-7138
We study the shape derivative of the strongly singular volume integral operator that describes time‐harmonic electromagnetic scattering from homogeneous medium. We show the existence and a representation of the derivative, and we deduce a characterization of the shape derivative of the solution to the diffraction problem as a solution to a volume integral equation of the second kind. 相似文献
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M. J. D. Powell 《Mathematical Programming》1984,29(3):297-303
Many trust region algorithms for unconstrained minimization have excellent global convergence properties if their second derivative
approximations are not too large [2]. We consider how large these approximations have to be, if they prevent convergence when
the objective function is bounded below and continuously differentiable. Thus we obtain a useful convergence result in the
case when there is a bound on the second derivative approximations that depends linearly on the iteration number. 相似文献
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In this paper, we present a class of A(α)-stable hybrid linear multistep methods for numerical solving stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The method considered uses a second derivative like the Enright’s second derivative linear multistep methods for stiff IVPs in ODEs. 相似文献
13.
Chongsheng Cao 《Journal of Differential Equations》2010,248(9):2263-2274
This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one direction while the second one requires suitable boundedness of the derivative of the pressure in one direction. 相似文献
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A class of second derivative Runge Kutta methods (SD-RKM) which has a simple transformation to the general linear methods (GLM) are employed for the numerical integration of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The new GLM which incorporates second derivative (SD) terms have the advantage of higher order L-stable methods for a given number of stages compared with the classical GLM. 相似文献
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《数学物理学报(B辑英文版)》2020,(3)
In this article, we focus on the short time strong solution to a compressible quantum hydrodynamic model. We establish a blow-up criterion about the solutions of the compressible quantum hydrodynamic model in terms of the gradient of the velocity, the second spacial derivative of the square root of the density, and the first order time derivative and first order spacial derivative of the square root of the density. 相似文献
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J.S.C. Prentice 《Applied mathematics and computation》2011,217(9):4576-4581
We use linear combinations of Taylor expansions to develop three-point finite difference expressions for the first and second derivative of a function at a given node. We derive analytical expressions for the truncation and roundoff errors associated with these finite difference formulae. Using these error expressions, we find optimal values for the stepsize and the distribution of the three points, relative to the given node. The latter are obtained assuming that the three points are equispaced. For the first derivative approximation, the distribution of the points relative to the given node is not symmetrical, while it is so for the second derivative approximation. We illustrate these results with a numerical example in which we compute upper bounds on the roundoff error. 相似文献
17.
We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative and satisfies the equation classically. We show here that the second derivative is continuous if and only if the flow has a single singular time where it becomes extinct and the singular set consists of a closed C1 manifold with cylindrical singularities. © 2017 Wiley Periodicals, Inc. 相似文献
18.
考虑由未知二元函数的近似值计算其Laplace算子与二阶混合偏导数的问题,给出稳定逼近Laplace算子与二阶混合偏导数的两类Lanczos方法,其逼近精度分别为O(δ~(1/2))和O(δ~(2/3)),其中δ是近似函数的误差水平. 相似文献
19.
Fabio Paronetto 《Journal of Differential Equations》2006,226(2):525-540
We give an existence and uniqueness result for a linear abstract evolution equation of second order with some coefficient in front of the second temporal derivative which may degenerate to zero and change sign. 相似文献
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We obtain some new inequalities of Hermite–Hadamard type. We consider functions that have convex or generalized convex derivative. Additional inequalities are proven for functions whose second derivative in absolute values are convex. Applications of the main results are presented.
相似文献