Given a sequence of n arbitrary events in a probability space we as sume that the individual probabilities as well as some or all joint probabilities of up to m events are known where m n Using this information we give lower and upper bounds for the probability of the union The bounds are obtained as optimum values of linear programming problems or objective function values corre sponding to fe...

A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite. Motivated by the fact that diagonal LMIs define polyhedra, the solution set of an LMI is called a spectrahedron. Linear images of spectrahedra are called semidefinite representable sets. Part of the interest in spectrahedra and semid...

This paper shows how to use semi-definite programming to find lower bounds on (and sometimes solve globally) a large class of nonlinear optimal control problems. This is done by relaxing an optimal control problem into a linear programming problem on measures, also known as a generalized moment problem. The handling of measures by their moments reduces the problem to a convergent series of stan...

The problem of moment matching with preservation of port Hamiltonian and gradient structure is studied. Based on the time-domain approach to linear moment matching, we characterize the (subset of) port Hamiltonian/gradient models from the set of parameterized models that match the moments of a given port Hamiltonian/gradient system, at a set of finite points.

This paper investigates finite sample properties of localized version of moment estimator including Local Generalized Method of Moments(LGMM) and conditional Euclidean Empirical Likelihood(CEEL) estimator. By comparing the performance of LGMM estimator and C-EEL estimator with various nonparametric techniques including the choice of bandwidth, choice of kernel and trimming strategies, this pape...

In this paper, we mainly introduced a definition of moment exponential stability for multifactor uncertain differential equation. For illustrating of stability concept, several examples and counterexamples are given. Furthermore, a necessary and sufficient condition of stability in pth moment exponential of linear multifactor uncertain differential equation is obtained. Also, the necessary and ...

Fragility curves represent the probabilities that structural damages, under various levels of seismic excitation, will exceed the specified damage states by means of earthquake intensity damage relations. Conceptual aspects related to seismic vulnerability, damage and risk evaluation are discussed first, together with a short review of the most widely used possibilities for the seismic evaluati...

Patellar tendon moment arm length (PTma) changes at different knee flexion angles have not been determined in invivo studies. We aimed to determine PTma in four different knee angles using Magnetic Resonance Imaging (MRI) topredict in vivo changes in the moment arm length from different knee angles during running.PTma was measured as the perpendicular distance from muscle–tend...

This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties and the moment map. In particular, we explain the relation between linear precision and the moment map.

We investigate and discuss when the inverse of a multivariate truncated moment matrix has zeros in some prescribed entries. We find that the key factor behind that property is a certain conditional triangularity property of orthonormal polynomials associated with the linear functional underlying the moment matrix.