A satellite system synthesis model for orbital arc allotment optimization

A mixed integer programming formulation of a satellite system synthesis problem if presented, which is referred to as the arc allotment problem (AAP). Each satellite administration is to be allotted a weighted-length segment of the geostationary orbital arc within which its satellites may be positioned at any longitudes. The objective function maximizes the length of the unweighted arc segment allotted to every administration, subject to single-entry co-channel interference restrictions and constraints imposed by the visible arc for each administration. Useful relationships between special cases of AAP and another satellite synthesis problem are established. Solutions to two example problems are presented

Pascal’s Wager: A Good Bet for Personal Evangelism

Blaise Pascal (1623-1662), a French scientist and mathematician, argued that it is advantageous to believe in or to “bet on” God because the rewards for doing so are at least as great as the rewards for not believing in God, regardless of whether or not God exists. His decision theoretic argument is commonly referred to as Pascal’s Wager. It is unlikely that everyone has the same estimates of the rewards for believing in God or for not believing in God that Pascal had. Consequently, a series of five questions, based on Pascal’s Wager, is suggested here for personalizing Pascal’s Wager. Results from an informal survey consisting of the five recommended questions are presented and analyzed. Finally, it is argued that a person’s responses to the five questions may be used to diagnose the person’s spiritual condition and to identify an appropriate evangelism strateg

Pascal’s Wager: A Good Bet for Personal Evangelism

Blaise Pascal (1623-1662), a French scientist and mathematician, argued that it is advantageous to believe in or to “bet on” God because the rewards for doing so are at least as great as the rewards for not believing in God, regardless of whether or not God exists. His decision theoretic argument is commonly referred to as Pascal’s Wager. It is unlikely that everyone has the same estimates of the rewards for believing in God or for not believing in God that Pascal had. Consequently, a series of five questions, based on Pascal’s Wager, is suggested here for personalizing Pascal’s Wager. Results from an informal survey consisting of the five recommended questions are presented and analyzed. Finally, it is argued that a person’s responses to the five questions may be used to diagnose the person’s spiritual condition and to identify an appropriate evangelism strateg

Using Markov Chain Simulation to Measure the Eternal Impact of Personal Evangelism,

All Christians have been commanded by Jesus Christ to share the Gospel message with unbelievers so that they too may be saved. However, few Christians regularly share the Gospel with non-Christians, and there are eternal consequences to this disobedience for everyone. A Markov chain model is proposed for estimating over time the proportions of persons who are saved and receive eternal life in heaven and who are condemned to hell. An evaluation and an analysis of the model are presented. Simulation results for the model indicate that a moderate increase in present personal evangelism efforts will result in only modestly more salvations over time. Therefore, substantially more intense evangelism efforts must be undertaken and sustained to make a significant difference in the number of souls that are ultimately saved. Sadly, some persons will choose never to be saved, regardless of how many and how often Christians share the Gospel

Using Markov Chain Simulation to Measure the Eternal Impact of Personal Evangelism,

All Christians have been commanded by Jesus Christ to share the Gospel message with unbelievers so that they too may be saved. However, few Christians regularly share the Gospel with non-Christians, and there are eternal consequences to this disobedience for everyone. A Markov chain model is proposed for estimating over time the proportions of persons who are saved and receive eternal life in heaven and who are condemned to hell. An evaluation and an analysis of the model are presented. Simulation results for the model indicate that a moderate increase in present personal evangelism efforts will result in only modestly more salvations over time. Therefore, substantially more intense evangelism efforts must be undertaken and sustained to make a significant difference in the number of souls that are ultimately saved. Sadly, some persons will choose never to be saved, regardless of how many and how often Christians share the Gospel

Engineering calculations for communications satellite systems planning

A procedure is described that was used to calculate minimum required satellite separations based on total link carrier to interference requirements. Also summarized are recent results with a switching algorithm for satellite synthesis problems. Analytic solution value bounds for two of the satellite synthesis models studied are described. Preliminary results from an empirical study of alternate mixed integer programming models for satellite synthesis are presented. Research plans for the near future are discussed

On orbital allotments for geostationary satellites

The following satellite synthesis problem is addressed: communication satellites are to be allotted positions on the geostationary arc so that interference does not exceed a given acceptable level by enforcing conservative pairwise satellite separation. A desired location is specified for each satellite, and the objective is to minimize the sum of the deviations between the satellites' prescribed and desired locations. Two mixed integer programming models for the satellite synthesis problem are presented. Four solution strategies, branch-and-bound, Benders' decomposition, linear programming with restricted basis entry, and a switching heuristic, are used to find solutions to example synthesis problems. Computational results indicate the switching algorithm yields solutions of good quality in reasonable execution times when compared to the other solution methods. It is demonstrated that the switching algorithm can be applied to synthesis problems with the objective of minimizing the largest deviation between a prescribed location and the corresponding desired location. Furthermore, it is shown that the switching heuristic can use no conservative, location-dependent satellite separations in order to satisfy interference criteria

Application of heuristic satellite plan synthesis algorithms to requirements of the WARC-88 allotment plan

Creation of an Allotment Plan for the Fixed Satellite Service at the 1988 Space World Administrative Radio Conference (WARC) represented a complex satellite plan synthesis problem, involving a large number of planned and existing systems. Solutions to this problem at WARC-88 required the use of both automated and manual procedures to develop an acceptable set of system positions. Development of an Allotment Plan may also be attempted through solution of an optimization problem, known as the Satellite Location Problem (SLP). Three automated heuristic procedures, developed specifically to solve SLP, are presented. The heuristics are then applied to two specific WARC-88 scenarios. Solutions resulting from the fully automated heuristics are then compared with solutions obtained at WARC-88 through a combination of both automated and manual planning efforts

ELECTRICAL CONDUCTIVITY OF POTASSIUM CHLORIDE

The electrical conductivity of potassium chloride is discussed within the framework of a four-defect model of the crystal. The four defects are mobile anion and cation vacancies and immobile divalent cation impurities and divalent cation impurity-cation vacancy complexes. The Teltow formulation of the four-defect mode1 fails to describe precisely the measured electrical conductivity of KCl over the entire intrinsic and extrinsic range

Ionic Transport in Potassium Chloride

The electrical conductivity and chlorine ion diffusion in KC1 and KCl:SrC12 single crystals have been analyzed by least-squares methods, using as a model a perfect crystal perturbed by five defects: isolated anion vacancies, isolated cation vacancies, divalent cation impurities, divalent cation-impurity-cation-vacancy complexes, and vacancy pairs. The transport equations were derived from this five-defect model using a simple theory for noninteracting particles, except for the nearest-neighbor binding to form complexes and vacancy pairs, and using the same theory including long-range Coulomb interactions between the isolated defects. This latter theory yielded the better description of the experimental results. However, the analyses showed that significant nonrandom deviations exist between theory and experiment. These deviations exist in both the intrinsic and extrinsic regions of conductivity. The failure of existing concepts for these transport properties is discussed in terms of possible additional mechanisms, i.e., electrons, cationic Frenkel defects, or trivacancies, and in terms of more complete theoretical treatment