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71.
A family of subspaces of a complex separable Hilbert space is transitive if every bounded operator which leaves each of its
members invariant is scalar. This article surveys some results concerning transitive families of small cardinality, and adds
some new ones. The minimum cardinality of a transitive family in finite dimensions (greater than 2) is 4. In infinite dimensions
a transitive pair of linear manifolds exists but the minimum cardinality of a transitive family of dense operator ranges or
norm-closed subspaces is not known. However, a transitive family of dense operator ranges with 5 elements can be found, and
so can a transitive family of norm-closed subspaces with 4 elements. In finite dimensions (> 1) three nest algebras (corresponding
to maximal nests) can intersect in the scalar operators, but two cannot. It is not known if this is the case in infinite dimensions
for maximal nests of type ω + 1. Four such nest algebras can intersect in the scalar operators.
Received June 15, 2002, Accepted November 27, 2002 相似文献
72.
Global Optimality Conditions in Maximizing a Convex Quadratic Function under Convex Quadratic Constraints 总被引:2,自引:0,他引:2
Jean-Baptiste Hiriart-Urruty 《Journal of Global Optimization》2001,21(4):443-453
For the problem of maximizing a convex quadratic function under convex quadratic constraints, we derive conditions characterizing a globally optimal solution. The method consists in exploiting the global optimality conditions, expressed in terms of -subdifferentials of convex functions and -normal directions, to convex sets. By specializing the problem of maximizing a convex function over a convex set, we find explicit conditions for optimality. 相似文献
73.
74.
Shu-min Li 《Reports on Mathematical Physics》2007,60(1):107-116
By analyzing the virtual work of reaction forces, we prove the failure of the vakonomic model in obtaining the correct equations of motion for nonholonomic mechanical systems. Only when the constraint is integrable can the actual equation of motion be obtained. We show that the null virtual work condition of reaction forces is a robust criterion on the validity of various models of analytical mechanics. For an illustration, classical examples are discussed. 相似文献
75.
为提高移动机器人的位置估计精度和跟踪效果,提出一种基于道路约束条件下的移动机器人鲁棒约束H∞滤波(CHF)跟踪算法.首先,将机器人移动的道路网络作为跟踪的约束条件,并利用当前统计模型对机器人的运动进行建模.其次,将道路约束条件作为机器人跟踪的非线性状态约束,利用最小协方差估计推导了鲁棒CHF递推方程.通过拉格朗日乘子法对非线性约束优化估计问题进行求解,并利用约束信息对CHF算法的状态更新过程进行了改进.最后,通过对CHF算法和无约束的H∞滤波算法的跟踪性能进行了对比分析和验证.仿真结果表明,该算法可以实现机器人的跟踪,且跟踪精度优于HF算法. 相似文献
76.
We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first examples, to our knowledge, of a simply connected smooth variety whose sets of integral points are never Zariski-dense. Some of our results are connected with divisibility problems, i.e. the problem of describing the integral points in the plane where the values of some given polynomials in two variables divide the values of other given polynomials. 相似文献
77.
A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty
function, nor a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different
trust-regions to cope with the nonlinearities of the objective function and the constraints, and allows inexact SQP steps
that do not lie exactly in the nullspace of the local Jacobian. Preliminary numerical experiments on CUTEr problems indicate that the method performs well.
相似文献
78.
Firdaus E. Udwadia 《Applied mathematics and computation》2010,217(3):1253-1265
This paper deals with an explanation of a paradox posed by Hamel in his 1949 book on Theoretical Mechanics. The explanation deals with the foundations of mechanics and points to new insights into analytical dynamics. 相似文献
79.
Wies?awa T. Obuchowska 《European Journal of Operational Research》2012,218(1):58-67
In this paper we address the problem of the infeasibility of systems defined by reverse convex inequality constraints, where some or all of the variables are integer. In particular, we provide a polynomial algorithm that identifies a set of all constraints critical to feasibility (CF), that is constraints that may affect a feasibility status of the system after some perturbation of the right-hand sides. Furthermore, we will investigate properties of the irreducible infeasible sets and infeasibility sets, showing in particular that every irreducible infeasible set as well as infeasibility sets in the considered system, are subsets of the set CF of constraints critical to feasibility. 相似文献
80.
For stochastic control problems with mixed state-control constraints, we develop a dynamics aggregation method which replaces the stochastic differential or difference equation with a simpler constraint. Solutions of such simplified problems are used to construct a sequence of approximations to the original problem. Convergence properties of the method for both discrete-time and continuous-time models are analyzed in detail. 相似文献