Hillel Kumin

A random walk approximation for a solar energy storage system

Abstract A solar energy storage system is modelled as a reservoir model with input and output conversion efficiency factors. Using Walds Identity, an approximation is obtained for the steady-state distribution of the energy storage level and the steady-state expected value of the energy storage level.

An analysis of solar heating systems that use vapor-compression cycles

Abstract This paper analyzes the technical and economic performance of solar heating systems that use vapor-compression cycles, circulating a compressible fluid as the working fluid. With conventional solar heating systems that use water or as their working fluid, the collector inlet temperature is equal to that of the storage outlet temperature. Operating the system on a cold day can result in large thermal losses to the surroundings and, thus, low useful heat gains. A vapor-compression cycle may be attractive because it allows the collector inlet temperature to be lowered so that the heat gain of the collector can be increased. Such a system is simulated and a preliminary economic analysis performed. The results indicate that the vapor-compression system can collect almost 50% more solar energy than a conventional system if the collector area of the two systems are the same.

A time-sharing interactive program for class scheduling

Abstract The purpose of this paper is to describe a time-shared class scheduling program that has been implemented and used for the past three years by the Oklahoma City Public Schools. The program uses heuristic procedures in an attempt to minimize student conflicts in a “modified modular scheduling” environment. In addition, the program is interactive so that the scheduler takes an active role in the scheduling decisions.

Convexity and optimization of condense discrete functions

A function with one integer variable is defined to be integer convex by Fox [3] and Denardo [1] if its second forward differences are positive. In this paper, condense discrete convexity of nonlinear discrete multivariable functions with their corresponding Hessian matrices is introduced which is a generalization of the integer convexity definition of Fox [3] and Denardo [1] to higher dimensional space Zn. In addition, optimization results are proven for C1 condense discrete convex functions assuming that the given condense discrete convex function is C1. Yuceer [17] proves convexity results for a certain class of discrete convex functions and shows that the restriction of the adaptation of Rosenbrooks function from real variables to discrete variables does not yield a discretely convex function. Here it is shown that the adaptation of Rosenbrooks function considered in [17] is a condense discrete convex function where the set of local minimums is also the the set of global minimums.

A Dynamic Programming Approach to a Bidder Selection Problem

Abstract This paper deals with a set of combinatorial decision problems that arise in large-scale governmental or military procurement operations. After stating the problems, they are then mathematically formulated as linear integer programming problems. However, because a specified sensitivity analysis is required, a dynamic programming approach is shown to give all solutions needed after one pass through the DP tableaus. A model has been implemented and is currently being used by a large buying activity of the Department of the Army.

Condense Mixed Convexity and Optimization with an Application in Data Service Optimization

Elements of matrix theory are useful in exploring solutions for optimization, data mining, and big data problems. In particular, mixed integer programming is widely used in data based optimization research that uses matrix theory see for example [13]. Important elements of matrix theory, such as Hessian matrices, are well studied for continuous see for example [11] and discrete [9] functions, however matrix theory for functions with mixed i.e. continuous and discrete variables has not been extensively developed from a theoretical perspective. There are many mixed variable functions to be optimized that can make use of a Hessian matrix in various fields of research such as queueing theory, inventory systems, and telecommunication systems. In this work we introduce a mixed Hessian matrix, named condense mixed Hessian matrix, for mixed variable closed form functions

Thermodynamic analysis of the aluminum silicate triple point

g: \mathbb {Z}^{n}\times \mathbb {R}^{m}\rightarrow \mathbb {R}

On Characterizing the Extrema of a Function of Two Variables, One of Which is Discrete

g:Zn×Rmi¾?R, and the use of this matrix for determining convexity and optimization results for mixed variable functions. These tasks are accomplished by building on the definition of a multivariable condense discrete convex function and the corresponding Hessian matrix that are introduced in [14]. In addition, theoretical condense mixed convexity and optimization results are obtained. The theoretical results are implemented on an M/M/s queueing function that is widely used in optimization, data mining, and big data problems.