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The use of local coordinates in optimization problems 局部坐标在优化问题中的应用
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90013-I
D.V. Denisov

The necessary and sufficient conditions for an extremum are expressed in local coordinates. It is shown that in some cases irregularity of the constraints at the extremum points does not affect the form of the necessary conditions. A first-order numerical method with a linear rate of convergence is considered.

极值的充分必要条件用局部坐标表示。结果表明，在某些情况下，极值点约束的不规则性并不影响必要条件的形式。考虑了一种线性收敛的一阶数值方法。
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引用次数: 0
The properties of effective modulus of composition plates 复合材料板有效模量的性质
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90113-7
M.V. Reztsov

Some data are obtained which enable the results of previous papers on the averaging of composite plates to be generalized to the case of a composition layer whose structure is restricted by requirement of physical symmetry with respect to the middle plane.

本文所得到的一些数据，使以往关于复合板平均的研究结果可以推广到结构受中间平面物理对称要求限制的复合层的情况。
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引用次数: 0
A numerical method of control optimization in delay systems for immune response modelling 时滞系统免疫反应建模控制优化的数值方法
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90157-N
A.S. Buldayev
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引用次数: 4
A method for the numerical solution of integral equations in boundary value problems with finite-order Abelian symmetry groups 有限阶阿贝尔对称群边值问题积分方程数值解的一种方法
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90107-4
E.V. Zakharov, S.I. Safronov, R.P. Tarasov

It is shown that for boundary value problems with commutative finite-order symmetry groups it is possible to use the concepts of convolution and the Fourier transform for finite groups to reduce considerably the order of the matrix equations used to approximate the original integral equations, and thus to extend the range of problems amenable to numerical analysis. An implementation of this method is considered for boundary value problems with Abelian symmetry group of eighth order, describing a quadrupole-type system. Results of a numerical experiment are presented for this case, enabling the efficiency of the method to be estimated.

结果表明，对于可交换有限阶对称群的边值问题，可以使用有限群的卷积和傅里叶变换的概念，大大降低用于近似原始积分方程的矩阵方程的阶数，从而扩大了适用于数值分析的问题范围。研究了描述四极型系统的八阶阿贝尔对称群边值问题的一种实现方法。最后给出了该情况下的数值实验结果，从而对该方法的有效性进行了估计。
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引用次数: 0
Determination of the absorption coefficient in the spherically symmetric case 球对称情况下吸收系数的测定
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90160-T
V.I. Gryn
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引用次数: 0
Stability bounds for solutions of some conditionally well-posed problems on a set containing discontinuous functions 含不连续函数集上若干条件良定问题解的稳定性界
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90102-X
S.L. Logunov

Stability bounds for the solutions of conditionally well-posed problems for the case when the variation and the maximum absolute value of the solutions are bounded by known constants are derived. Differentiation problems, Volterra and Abel integral equations, and convolution equations are considered.

导出了当解的变分和最大绝对值以已知常数为界时，条件良定问题解的稳定性界。考虑了微分问题、Volterra和Abel积分方程以及卷积方程。
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引用次数: 0
The best single-layer brightening coating for a frequency band 最好的单层增亮涂层的频带
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90036-R
Yu.I. Khudak

The existence of a unique global minimum for the maximum of the power reflection coefficient of a single-layer coating in a specified frequency band is proved.

证明了在给定的频带内，单层涂层功率反射系数的最大值存在唯一的全局最小值。
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引用次数: 2
Quasioptimal control search algorithms using state-space partitioning 基于状态空间划分的准最优控制搜索算法
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90155-L
E.N. Orel
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引用次数: 0
The projection method for singularly perturbed boundary-value problems 奇异摄动边值问题的投影方法
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90043-R
I.A. Blatov

A finite element method for linear and non-linear singularly perturbed boundary-value problems is considered. It is proved that the approximate solutions converge to the exact solution in the norm of the space of continuous functions, uniformly in the small parameter. The proposed scheme is suitable for solving a wider class of problems than can be handled by the popular “hinged element method”, and also produces a higher order of approximation.

研究了求解线性和非线性奇摄动边值问题的有限元方法。证明了在连续函数空间范数上近似解收敛于精确解，在小参数下一致收敛于精确解。与常用的“铰链单元法”相比，该方法适用于解决更广泛的问题，并且具有更高的近似阶。
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引用次数: 8
The use of duality to determine the branching order of variables and to estimate the bounds in the solution of the knapsack problem 在背包问题的解中，利用对偶性来确定变量的分支阶和估计界
USSR Computational Mathematics and Mathematical Physics
Pub Date : 1990-01-01 DOI: 10.1016/0041-5553(90)90100-7
A.O. Alekseyev, O.G. Alekseyev, V.D. Kiselev
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引用次数: 0
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