The discrete moment problem DMP has been formulated as a methodology to nd the minimum and or maximum of a linear functional acting on an unknown probability distribution the support of which is a known discrete usually nite set where some of the moments are known The moments may be binomial power or of more general type The multivariate discrete moment problem MDMP has been initiated by the se...

Estimation theory has been developed over centuries. There are several approaches to utilizing this theory; in this chapter, these approaches are classified into three types. Type I includes the oldest two methods, the least squares (LS) and moment methods; both of these methods are non-optimal estimators. The least squares method was introduced by Carl Friedrich Gauss. Least squares problems f...

Progressive collapse is a chain reaction of failures propagating throughout a portion of the structure disproportionate to the original local failure occurring when a sudden loss of a critical load‐bearing element initiates a structural element failure, eventually resulting in partial or full collapse of the structure. Both General Services Administration (GSA) and United States Department of D...

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...

We produce a new proof of the reciprocity law for the twisted second moment of Dirichlet L-functions that was recently proved by Conrey. Our method is to analyze certain two-variable sums where the variables satisfy a linear congruence. We show that these sums satisfy an elegant reciprocity formula. In the case that the modulus is prime, these sums are closely related to the twisted second mome...

Let μ be a given Borel measure on K ⊆ R and let y = (yα), α ∈ N, be a given sequence. We provide several conditions linking y and the moment sequence z = (zα) of μ, for y to be the moment sequence of a Borel measure ν on K which is absolutely continuous with respect to μ and such that its density is in L∞(K, μ). The conditions are necessary and sufficient if K is a compact basic semi-algebraic ...