Optimum reliabilities and optimum design

The designer's task is to optimize. Designing for an intuitively fixed reliability is almost as arbitrary as designing for an intuitively fixed safety factor. Efforts to improve the calculation of reliabilities of proposed designs are commendable but sterile unless we take the additional step of optimizing the design reliabilities associated with the various potential limit states. Through examples it is shown how these reliabilities depend on the consequences of entrance into limit states and on the marginal initial cost of the reliability and how earthquake design spectra must differ radically from those for fixed return periods. It is further claimed that the optimum reliabilities depend on how a structure enters a limit state. A more realistic aim is not the establishing of design reliabilities but of optimum designs. This is illustrated in connection with progressive collapse.Mistakes (“human” or “gross” errors) are not considered in the present analysis.     

The Supporting Role of the Mangasarian-Fromovitz Constraint Qualification in Calculus of Variations

Journal of Dynamical and Control Systems - The Mangasarian-Fromovitz constraint qualification has played a fundamental role in mathematical programming problems involving inequality constraints. It...     

On computing normal reliabilities

No expression currently used for computing reliabilities given by the normal distribution is adequate over the entire range of interest in structural design. Although the expressions may involve small absolute errors, they introduce excessively large relative errors in the failure probabilities over some ranges. It is impractical to have two expressions depending on the reliability index β. Two equations are proposed here. The simpler one involves relative errors smaller than 1.7% when β 1. The other introduces relative errors smaller than 2 × 10⁻⁴ when B 0 and smaller than 4.5 × 10⁻⁵ when β 1.     

Maximum entropy and discretization of probability distributions

Using gaussian quadrature we can find m concentrations of probability that replace the density function of a random variable X and match 2m - 1 of its moments. This reduces a probabilistic analysis to m deterministic ones. Even small values of m provide excellent accuracy in many practical circumstances. When fewer than 2m - 1 moments are known there is arbitrariness in the choice of the concentrations, which is overcome by resorting to the maximum entropy formalism. Its use is here systematized for the case in which αXb and we know N moments of the density of X, so that calculation of N - 1 integrals suffices for finding the density function and any number of its moments. The approach is illustrated for m = 2 and 3, N = 2, 3, α = 0, B = ∞ and graphs are provided for finding the equivalent concentrations.     

Chart parsers as inference systems for fixed-mode logic programs

Logic programs resemble context-free grammars. Moreover, Prolog’s proof procedure can be viewed as a generalization of a simple top-down parser with backtracking. This simple parser has disadvantages that motivated the design of more sophisticated parsing methods. As similar disadvantages occur in Prolog’s proof procedure, it may be desirable to develop other proof procedures for logic programs than the one used by Prolog. The resemblance between definite clauses and productions suggests looking at parsing to develop such procedures. We obtain proof procedures for fixed-mode logic programs, based on “chart” parsers. Our approach concentrates on transforming (fixed-mode) logic programs rather than the parser. We first add unification to a chart parser obtaining a proof procedure for programs severely restricted in their syntax, in which the body of the clauses denotes the composition of binary relations: “chain” programs. We then show how to transform fixed-mode programs into chain form. We arrive at proof procedures that avoid some nonterminating loops as well as the recomputation of some partial results.     

Rhizobium tropici teu genes involved in specific uptake of Phaseolus vulgaris bean-exudate compounds

Rhizobium tropici nodulates and fixes nitrogen in bean. In the R. tropici strain CFN299 we identified and characterized teu genes (tropici exudate uptake) induced by bean root exudates, localized by insertion of a promoter-less Tn5-gusA1 transposon. teu genes are present on a plasmid of around 185 kb that is conserved in all R. tropici strains. Proteins encoded by teu genes show similarity to ABC transporters, specifically to ribose transport proteins. No induction of the teu genes was obtained by treatment with root exudates from any of several other plants tested, with the exception of Macroptilium atropurpureum, which is also a host plant for R. tropici. It appears that the inducing compound is characteristic of bean and closely related legumes. It is present in root exudates, but not in seeds. This compound is removed, presumably by metabolism, from the exudates by the majority of bean-nodulating rhizobia (such as R. etli, R. leguminosarum bv. phaseoli and R. giardinii). The principal inducing compound has not been identified, but some induction was obtained using trigonelline. The CFN299 strain seems to have an additional uptake system, as no phenotype is observed in two different mutants. R. tropici strain CIAT899, on the other hand, must have only one uptake system, since a mutant bearing an insertion in the teu genes could not remove the compound from the exudates as efficiently as the wild type, and it showed diminished nodulation competitiveness.     

Conditions for generic normality in optimal control

Optimal control problems in which the necessary conditions of Pontryagin's maximum principle do not involve the cost or performance index are called abnormal. In this paper we study normality through perturbations of the endpoint set. It is known that normality holds for all problems obtained by translating the original endpoint set in directions belonging to a dense set. When the equations of motion are linear in the state variable, we enlarge this set of directions to a full (Lebesgue) measure set, showing that its complement is contained in the relative boundary of a convex set. For nonlinear systems we show that by enlarging the endpoint set, instead of translating it, normality is also guaranteed almost everywhere.