This paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition, such as, for example, the von Mises condition. After discretization with the finite element method, using divergence-free elements for the plastic flow, the kinematic formulation reduces to the problem of minimizing a sum of Euclidean vector norms, subject to a single li...

Control systems design by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with mixed bounding conditions on the twoand/or the infinity-norms of the inputs and their derivatives. The original...

Given an arbitrary standardized (zero mean and unit variance) probability density, we measure its departure from the standard normal density by the L distance between the two density functions. In particular, we consider three different L norms, each distinguished by their weight functions. We investigate the reciprocal Gaussian, uniform, and Gaussian weight functions, and present respective He...

Let X1, . . . , XN ∈ R be independent centered random vectors with log-concave distribution and with the identity as covariance matrix. We show that with overwhelming probability one has sup x∈Sn−1 ∣∣∣∣ 1 N N ∑ i=1 ( |〈Xi, x〉| − E|〈Xi, x〉| ) ∣∣∣∣ ≤ C√ n N , where C is an absolute positive constant. This result is valid in a more general framework when the linear forms (〈Xi, x〉)i≤N,x∈Sn−1 and th...

Consider the N -person non-cooperative game in which each player’s cost function and the opponents’ strategies are uncertain. For such an incomplete information game, the new solution concept called a robust Nash equilibrium has attracted much attention over the past several years. The robust Nash equilibrium results from each player’s decision-making based on the robust optimization policy. In...

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In this talk we propose explicit a priori error bounds for approaching f(A)b by help of the Arnoldi method. Here A is a large real not necessarily symmetric matrix, and f some function analytic on the field of values or numerical range W (A) = {y∗Ay : ‖y‖ = 1}. An essential tool in our work is the inequality ‖Fn(A)‖ ≤ 2 derived in [1] where Fn is the nth Faber polynomial corresponding to W (A),...

This paper proposes nonparametric deconvolution density estimation over S 2. Here we would think of the S 2 elements of interest being corrupted by random SO(3) elements (rotations). The resulting density on the observations would be a convolution of the SO(3) density with the true S 2 density. Consequently, the methodology, as in the Euclidean case, would be to use Fourier analysis on SO(3) an...

There has been considerable work on matrix approximation problems in the space of matrices with Euclidean and unitarily invariant norms. We initiate the study of approximation problems in the space P of all n×n positive definite matrices with the Riemannian metric δ2. Our main theorem reduces the approximation problem in P to an approximation problem in the space of Hermitian matrices and then ...

A dual neural network is presented for the bi-criteria kinematic control of redundant manipulators. To diminish the discontinuity of minimum infinity-norm solutions, the kinematiccontrol problem is formulated in the bi-criteria of the infinity and Euclidean norms. Physical constraints such as joint limits and joint velocity limits are also incorporated simultaneously into the proposed kinematic...