Optimal Discrete Approximations for Continuous Outcomes with Applications in Decision and Risk Analysis

In decision and risk analysis, it is common to use discrete probability distributions to approximate uncertain events with continuous outcomes. This paper discusses how these approximations may be selected. A class of approximations based on a modification to Taguchi's work on tolerance analysis is shown to be optimal under assumptions of independent uncertainties with normally distributed outcomes. The approximation procedure is shown to be robust in many other situations and is extremely easy to use in practice. We also show how the approximation may be integrated into the process of subjective probability estimation by a ‘subject-matter expert’.     

Optimal Inventory Policies with Service-Level Constraints

In a practical situation it is often difficult to determine the value of the shortage costs for use in in ventory-control systems. However, in cost-minimization problems including service-level constraints, shortage costs are implicitly prevailing. With the purpose of exploring these relations, a continuous review (Q, r) stock-control system is considered, where the order points and lot sizes are computed simultaneously. Instead of explicitly expressing the shortage cost in the objective function, it is taken into consideration through a service-level constraint. The shadow price of this constraint can in some sense be interpreted as the shortage cost corresponding to the requested service level. By changing the value of the service level, interesting relations between shortage costs and service levels can be viewed for different sets of other inventory parameters. In order to investigate the sensitivity for probabilistic variations in the input data, two different probability distributions are used to describe the lead-time demand.     

Hereditary optimal control problems: Numerical method based upon a padé approximation

In this paper, we consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argumentx(t – ). In our approximation scheme, we first replace the variable with an augmented statey(t) x(t - ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four problems are solved to illustrate the validity and usefulness of this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant NCC-2-106.     

Differential form methods in the theory of variational systems and Lagrangian field theories

This paper will attempt to unify diverse material from physics and engineering in terms of differential forms on manifolds. A variational system will be defined by means of a scalar-valued differential form on a manifold and an ideal in the Grassmann algebra of differential forms on that manifold to serve as constraints. Two types of extremal submanifolds will be defined. The first-called the Euler-Lagrange extremals-will be defined by a method that is the generalization of the classical methods in the calculus of variations. The second—a generalization of a method used by Cartan in his treatise Leçons sur les invariants intégraux-will define extremals as integral submanifolds of an exterior differential system invariently attached to the variational system. As examples, the variational systems attached to string theories in Riemannian manifolds and Yang-Mills fields will be discussed from this differential form point of view. Finally, as application, the differential geometric properties and definition of energy will be presented from the differential form point of view.This work was supported by a grant from the Applied Mathematics program of the National Science Foundation.     

Asymptotic expansions for renewal measures in the plane

Summary Let P be a distribution in the plane and define the renewal measure R=P ^*nwhere * denotes convolution. The main results of this paper are three term asymptotic expansions for R far from the origin. As an application, expansions are obtained for distributions in linear boundary crossing problems.Research supported by NSF grants MCS-8102080 and DMS-8504708     

Γ andX bandgap hydrostatic deformation potentials for epitaxial In0.52Al0.48As on InP(001)

The pressure dependence of the direct and indirect bandgap of epitaxial In_0.52Al_0.48As on InP(001) substrate has been measured using photoluminescence up to 92 kbar hydrostatic pressure. The bandgap changes from Γ toX at an applied pressure of ∼ 43 kbar. Hydrostatic deformation potentials for both the Γ andX bandgaps are deduced, after correcting for the elastic constant (bulk modulus) mismatch between the epilayer and the substrate. For the epilayer we obtain and+(2.81±0.15)eV for the Γ andX bandgaps respectively. From the pressure dependence of the normalized Γ-bandgap photoluminescence intensity a Γ-X lifetime ratio, (τ_Γ/τ _X ), of 4.1×10⁻³ is deduced.     

Phase space dependence of the multiplicity distribution in π+ andpp collisions at 250 GeV/c

The charged particle multiplicity distribution has been studied for non-single-diffractive π⁺ p andpp collisions at \(\sqrt s = 22\) GeV, for full phase space as well as for intervals in rapidity, azimuthal angle and transverse momentum. In general, the multiplicity distribution is well described by a negative binomial. From comparison of the distribution for negative or positive particles to that of all charged particles, cascading is favoured as an interpretation over stimulated emission. Interesting consequences follow from a comparison of our results to those at collider energies and toe ⁺ e ^? data at comparable energy. Furthermore, evidence is given that the multiplicity distribution is not exactly of negative binomial type in every (connected or disconnected) phase space region.     

Optical humidity and ammonia gas sensors using Reichardt's dye-polymer composites

Optical intensity reflected at 750 nm by Reichardt's betain dye-polymer (PMMA or PEO) composite increased with an increase in humidity and was not affected by ammonia vapor. For the composites treated with hydrochloric acid, the intensity at around 590 nm decreased with an increase in ammonia concentration, and the sensitivity was enhanced by the presence of water vapor. The treatment with hydrochloric acid induced the formation of phenolic group, O⁻---H⁺ and N⁺---Cl⁻ in the dye. The sorption of NH₃ decreases the ionic interactions.     

Improved spectrophotometric determination of osmium(VIII) with 4-(2-pyridylazo) resorcinol in mixed surfactants

The colour development between 4-(2-pyridylazo)-resorcinol(PAR) and osmium(VIII) in the presence of cationic and nonionic surfactants in a weakly acidic medium was more stable and reproducible than in the absence of surfactant (PAR-alone method). An improved spectrophotometric determination of osmium(VIII) with PAR was investigated in the presence of mixed surfactants of N-hexadecyltrimethylammonium chloride (HTAC) and Brij 58 [poly(oxyethylene)lauryl ether] as cationic and nonionic surfactants at pH 6.0-7.2. The calibration graph was linear in the range 0-110 microg/10 ml osmium(VIII), and the apparent molar absorptivity was 2.4 x 10(4) l.mole(-1).cm(-1) with a Sandell sensitivity of 0.0079 microg/cm(2) osmium(VIII).