The Depot Siting Problem with Discontinuous Delivery Cost<Superscript>†</Superscript>

Discontinuities may occur in the distribution cost function for a variety of reasons. Some of these, notably discontinuous trunking costs and depot costs dependent on location, have been examined in the literature. In this paper the problem which arises when discontinuities occur in the local delivery cost function is examined and a method of solution incorporating heuristics is described. An illustrative example is given.     

Modelling of flow pattern in a shallow aquifer affected by reservoirs

A compartmental model is developed to estimate flow parameters of a shallow aquifer affected by water loads in surface reservoirs and to evaluate its nonsteady flow distribution. The method incorporates temporal piezometric head measurements and sampling of water for dissolved chemicals and isotopes analyses. Each compartment is governed by a set of equations describing the conservation of linear momentum and mass balance expressions for water, isotopes, and dissolved chemicals. The number of compartmental balance expressions always must be greater than that of the unknown flow parameters associated with each compartment. An optimization method is described to yield spatial distribution of aquifer storativity, transmissivity, porosity, leakage, and compliance coefficients and fluxes leaking into an aquifer's lower boundary. Future predictions of an aquifer's piezometric head distribution in a compartmental system is formulated on the basis of the estimated flow parameters and the leakage components.Compartmental modelling which incorporates concentrations of environmental tracers, may yield efficiency in computing resources and accuracy enhancement for predicting an aquifer's flow regime.     

Sampling Procedures for Risk Simulation

Risk simulation has become a standard alternative to the utilization of single estimates for input data to investment appraisal models. Under the risk simulation approach managers define probability distributions for relevant input factors. During this process management may consciously or subconsciously assume certain relationships between the input variables. These interdependencies are often omitted from the models, however, under the justification that they are accounted for implicitly in the values attributed to the variables by management. It is demonstrated in this paper that such omissions may lead to significant errors in the observed distributions of the selected appraisal criteria. Various forms of discriminate sampling are introduced and an example is cited for which certain discriminate schemes are shown to be more accurate than traditional independent sampling.     

Economic Batch-Size Determination for Multi-Product Scheduling

In the determination of batch-sizes in batch production, different criteria can be used as guiding principles, depending on the specified objectives. In a production schedule consisting of several products, an optimum solution for the whole production schedule is sought. At the same time it is necessary to ensure that the total production costs of each individual product will not exceed a certain pre-determined value. Solutions for overall optimization of the schedule with respect to maximum profit per batch, or with respect to maximum return on the total cost of production of the batch, have already been published. This paper suggests a method for determining the economic batch-sizes when it is desirable to maximize the rate of return per unit time for a multi-product schedule.     

The modified stochastic game

We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a vector that assigns a real number to each element of the partition. We study properties of the modified game, like its equilibria, min–max value, and max–min value. We then show how this tool can be used to prove the existence of a uniform equilibrium in a certain class of multiplayer stochastic games.     

Restoration of images degraded by extreme mechanical vibrations

A method of numerically calculating the optical transfer function appropriate to any type of image motion and vibration, including random, has been recently developed. This method has been verified experimentally with real vibrations, and the close agreement justifies implementation in image restoration from blur deriving from any type of image motion, including random displacement. Here, image restorations of actual physically degraded images are presented, based on a constrained least squares improvement of the original Wiener filter. Even for extreme vibrations where the blur extent is much larger than the blurred detail, restoration is quite complete. The key to restoration is the determination of the optical transfer function unique to the particular image motion and vibration causing the blur. Results are also presented for low vibration frequency motion of random blur extent, as well as for high vibration frequencies.     

Stochastic games with two non-absorbing states

In the present paper we consider recursive games that satisfy an absorbing property defined by Vieille. We give two sufficient conditions for existence of an equilibrium payoff in such games, and prove that if the game has at most two non-absorbing states, then at least one of the conditions is satisfied. Using a reduction of Vieille, we conclude that every stochastic game which has at most two non-absorbing states admits an equilibrium payoff. This paper is part of the Ph.D. thesis of the author completed under the supervision of Prof. Abraham Neyman at the Hebrew University of Jerusalem. I would like to thank Prof. Neyman for many discussions and ideas and for the continuous help he offered. I also thank Nicolas Vieille for his comments on earlier versions of the paper.     

Computational studies on the electrocyclizations of 1-amino-1,3,5-hexatrienes

Electrocyclizations of 1,3,5-hexatrienes containing up to four electron-donating and/or electron withdrawing substituents have been studied computationally using the hybrid density functional, B3LYP. Electron donating substituents at positions C-1 and C-5 decrease activation barriers by 0.3 to 2.3 kcal/mol. Introducing of an electron-withdrawing group, CO(2)Me, at C-4 further decreases the activation energy by 7 kcal/mol. Electron-withdrawing groups (NO(2), SO(2)Ph and C=N(+)Me(2)) at C-2 have a profound effect of 17-25 kcal/mol on the activation energy.