Numerical radius of positive matrices

We study some properties of the numerical radius of matrices with non-negative entries, and explicit ways to compute it. We also characterize positive matrices with equal spectral and numerical radii, i.e., positive spectral matrices.     

An Analysis of a Dynamic Project Cost Problem

This paper presents a stochastic allocation model for a sequential financial problem involving the allocation of funds to uncertain future payments. It is shown that under certain conditions the optimal allocation policies are piece-wise linear with the budget available, and that there exists an intimate relationship between these policies and the myopic policies obtained from the solution of a sequence of single-payment problems. A numerical example is provided and, finally, certain technical and methodological issues associated with a chance constraint version of the problem are discussed.     

Cash flow optimization in delivery scheduling

The paper examines the inventory routing problem from the perspective of the present value of the cash flow associated with the distribution of a commodity such as propane. We analyze this problem for both deterministic and stochastic customer demands and validate our results on data from a real life distribution operation of propane. The analysis based on the present value of the cash flow indicates that optimization of propane deliveries based on efficiency/cost criteria alone will generate inferior solutions and it would be more advantageous for the company to set deliveries for a large percentage of the customers based on the present value of cash flow. In addition, in the case of stochastic demands, deliveries based on the cash flow consideration will tend to reduce the number of stockouts (i.e. improve both profit and service).     

Interaction of kerogen and mineral matrix of an oil shale in an oxidative atmosphere

The effects of the inorganic matrix of the oil shale on the oxidation of the kerogen at temperatures up to 1000°C in an air atmosphere were investigated Kerogen was isolated by successive HCl, HF and LiAlH₄ treatments. The initial shale and each product of every demineralization process were oxidized in a thermogravimetric system in an air atmosphere. The oxidation products were analyzed by Fourier transform infrared spectroscopy. Changes in the chemical structure of the organic material of the shale were correlated with the separated constituents of the inorganic matrix. Oxidation of the kerogen occurred in two stages. The first stage was complete at about 400°C. The oxidized product after the first stage contained a char of an aromatic ring system substituted with some aliphatic material and carbonyl groups. Calcium minerals increased the reactivity of the aromatic part of the organic material towards the oxidation reactions. Where calcium minerals were absent, mainly the aliphatic and the carbonyl groups decomposed. Silicates and pyrites did not affect the reactivity of the organic material in oxidation reactions.     

Some comments on preference order dynamic programming models

A simple deterministic dynamic programming model is used as a general framework for the analysis of stochastic versions of three classical optimization problems: knapsack, traveling salesperson, and assembly line balancing problems. It is shown that this model can provide an alternative to the preference order models proposed for these problems. Counterexample to the optimality of the preference order models are presented.     

Diamagnetic susceptibility effects in NMR measurements of the properties of water in polymeric membranes

The NMR spectra of water adsorbed at various relative humidities on various cellulose ester membranes have been studied. Membranes of cellulose acetate (CA), cellulose triacetate (CTA), and cellulose acetate butyrate (CAB) were investigated. It was found that the resonance peak of a liquid imbibed in or adsorbed on membranes from high relative humidity is very sensitive to the angle between the membrane plane and the direction of the magnetic field, shifting 5–7 ppm to higher fields as the membrane plane is rotated from a perpendicular to a parallel position with respect to the direction of the external magnetic field. This phenomenon was found to be independent of the nature of the polymeric material (namely CA, CTA, or CAB), porosity of the membrane (varying from an “all bulk” dense sheet to an 80% porosity and 0.2 μm average pore size membrane), nature of the magnetic nuclei (H₂O or D₂O), intensity of the external magnetic field (60 Mcps or 100 Mcps), and nature of the liquid in the membrane (water, methanol, or n-hexane). It is therefore concluded that the dependence of the position of the resonance peak on the position of the membrane plane with respect to the external magnetic field, is a geometrical phenomenon due to the magnetic “bulk susceptibility” of the medium. Quantitative estimations of the magnitude of the diamagnetic susceptibility effect in a cylindrically rolled sheet are given. These estimates agree well with the experimentally observed “splittings.”     

Ion survival probabilities for 3 keV Ar+ scattering from La,Yb, and chemisorbed H2, O2, and H2O on La surfaces

TOF spectra of scattered primary and surface recoiled neutrals and ions for 3 keV Ar⁺ bombardment of clean La and Yb and H₂, O₂, and H₂O saturated La surfaces are presented. The spectra are analyzed in terms of single (SS) and multiple (MS) scattering of the primary ions and surface recoiling (SR) of adsorbate atoms. Measurement of spectra of neutrals + ions and neutrals alone allows determination of scattered ion fractions Y. The Y values for the SS event are high for clean La (37%) and lower for adsorbate covered La (32% for H₂, 13% for O₂, and 8% for H₂O); Yb exhibits a similar behavior, i.e. 16% for clean Yb and 5% for O₂ + H₂O covered Yb. Photon emission accompanying the scattering collision has been observed from clean La and Yb and adsorbate covered La. A preferential inelastic energy loss of 15 ± 3 eV for the SS event has been observed for scattered neutrals as opposed to ions for La and H₂ saturated La at 135°. These results are interpreted within the models for Auger and resonant electronic charge exchange transitions during approach or departure of an ion with a surface and the electron promotions occuring during close atomic encounters where the electron shells are interpenetrating.     

Differentiation formulas for stochastic integrals in the plane

For a one-parameter process of the form X_t=X₀+∫^t₀φ_sdW_s+∫^t₀ψ_sds, where W is a Wiener process and ∫φdW is a stochastic integral, a twice continuously differentiable function f(X_t) is again expressible as the sum of a stochastic integral and an ordinary integral via the Ito differentiation formula. In this paper we present a generalization for the stochastic integrals associated with a two-parameter Wiener process.Let {W₂, z∈R²₊} be a Wiener process with a two-dimensional parameter. Ertwhile, we have defined stochastic integrals ∫ φdWand ∫ψdWdW, as well as mixed integrals ∫h dz dW and ∫gdW dz. Now let X_z be a two-parameter process defined by the sum of these four integrals and an ordinary Lebesgue integral. The objective of this paper is to represent a suitably differentiable function f(X_z) as such a sum once again. In the process we will also derive the (basically one-dimensional) differentiation formulas of f(X_z) on increasing paths in $\text{R}{}^2{}_{\mathrm{+}}$.