Notes on Klee’s paper “Polyhedral sections of convex bodies”

In sections 2 and 3 two methods for proving the non existence of certain universal Banach spaces, are presented. In section 4 it is proved that every infinite-dimensional conjugate Banach space has a two-dimensional subspace whose unit cell is not a polygon. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18, through the European Office of Aerospace Research (OAR) United States Air Force.     

Integrated logistics planning for the air and space expeditionary force

The shift to a US Air Force structured for expeditionary operations has presented the Air Force with a number of challenges in planning, executing, and support operations involving resources such as munitions, fuel, engines, avionics, and war reserve material. In an expeditionary world, the logistics support processes must be capable of responding to rapidly deployed forces, either by deploying along with the fighting units or by connecting support processes in permanent locations to the remote forces. In this paper, we present a general approach for reshaping logistics processes to meet Air Force expeditionary operational goals. We develop capability-based logistics models consisting of rules and algorithms that compute process timelines and requirements for material, equipment, and personnel. We use both optimization and heuristic techniques to formulate a location–allocation solution that can further refine the process.     

Comparing the Spanish and the discriminatory auction formats: A discrete model with private information

The Spanish Treasury is the only Treasury in the world that uses a hybrid system of discriminatory and uniform price auctions to sell government debt: winning bidders pay their bid price for each unit if this is lower than the weighted average price of winning bids (WAP), and pay the WAP otherwise. Following Gordy [Gordy, M., 1996. Multiple bids in a multiple-unit common-value auction. Board of Governors of the Federal Reserve System], we model the Spanish auction as a common value auction of multiple units with private information, allowing for multiple bids. Numerical analysis shows that bidders spread their bids more in the Spanish than in the discriminatory auction and bid higher for the first unit, and that the expected seller’s revenue is higher in the Spanish than in the discriminatory auction within a reasonable set of parameter values.     

Strong dependence in the nominal exchange rates of the Polish zloty

We examine the nominal exchange rates of six currencies (Canadian, Australian and U.S. dollars, euro, Japanese yen and U.K. pound) against the Polish zloty by means of statistical techniques based on unit roots and other long memory processes. We use both parametric and semiparametric methods for estimating and testing integer and fractional orders of integration at the long run or zero frequency. The results show that unit roots are likely to occur in relation with the U.S. and the Canadian dollars, the Japanese yen and the U.K. pound. However, for the Australian dollar and the euro, this hypothesis is rejected in favour of smaller degrees of integration, implying mean reversion in their behaviour. Thus, for the former currencies, in the event of an exogenous shock affecting the exchange rates, strong policy actions must be required to bring the variables back to their original levels. On the other hand, for the Australian dollar and the euro, there exists less need of action since the series will return to their levels sometime in the future. Copyright © 2006 John Wiley & Sons, Ltd.     

Nonexistence of an a priori bound at the center in terms of anL 1 bound on the boundary for solutions of uniformly elliptic equations on a sphere

Summary Positive solutions on the unit sphere of second order uniformly elliptic nonvariational equations are found which exhibit behavior sharply differing from that of positive harmonic functions, despite the fact that the coefficients may be uniformly arbitrarily close (at least for n=2) to those of the Laplacian. A solution is found whose boundary integral on expanding concentric subspheres tends to zero and another is found for which this boundary iutegral tends to infinity. This work was supported by the Air Force Office of Scientific Research and the National Academy of Sciences through a Postdoctoral Research Fellowship for 1964–1965 at the University of Genova.     

Development of an Air Force Warehouse Logistics Index to continuously improve logistics capabilities

For the effective operation of air power in the modern war, the logistics systems of Air Force warehouses need to be well-maintained. The best logistics system can be established through continuous improvements in logistics capabilities. Although there have been some studies on key performance indicators for logistics capability, they have neither considered the structural relationship among various influential factors, nor the feedback mechanisms in warehouse logistics capabilities. In this study, we propose a structural equations model (SEM) to develop an Air Force Warehouse Logistics Index (WLI). The concept of a Customer Satisfaction Index is used to assess the WLI for strategic improvement plans for various warehouse groups. It is expected that our model can be used to evaluate the logistics support capability of ROKAF (Republic of Korea Air Force) warehouses and contribute to warehouse modernization plans.     

Decision support for the career field selection process at the US Air Force Academy

Each year, the US Air Force Academy graduates nearly 1000 young men and women. To support the decision of which cadets will be classified into which career fields, we describe a linear programming formulation with appealing computational properties that enable it as the core of a decision support tool. We explore methods for measuring and balancing cadets' class standing, Air Force career field requirements, and cadets' career field preferences in the context of this model. Our computational experiments demonstrate the improvement of this method over previous classification approaches, yielding more than 10% increase in the number of cadets assigned to their top career field choice and yielding nearly a 100% reduction in the number of cadets not receiving any of their career field choices. We also explore alternative methods for measuring cadets' career field preferences and demonstrate the positive effect of the new measurement scheme on the overall classification. Because of the short running time of this model, it will serve as a flexible, real-time component of the Academy's classification process.     

Assessing the efficiency of rapid transit configurations

Eight basic transit network configurations are analyzed with respect to two measures: passenger/network effectiveness and passenger/plane effectiveness. Assumptions are made with respect to trip distribution and competition with other transportation modes. This research was in part supported by Canadian Natural Sciences and Engineering Research Council under grant OGP0039682 and by the Junta de Andalucía. This support is gratefully acknowledged.     

A fundamental property of Markov processes with an application to equivalence under time changes

It is shown that Markov processes traverse their trajectories in just one way, and applications are given to the Blumenthal, Getoor and McKean theorem. This paper is dedicated to the memory of Shlomo Horowitz The second author received partial support from the Canadian Research Council and National Science Foundation (MCS-7606048).     

Positivity and strict contractivity of functions of operators

Carathéodory class functionsf(z) are described having the property that the self-adjoint part off(A) is positive definite for every contractionA whose spectral radius is less than 1. Analogous results are obtained for bounded analytic functions in the unit disc, and for the Nevanlinna class. Applications to Markov chains are indicated.Partially supported by the US Air Force Grant AFOSR-94-0293.Partially supported by the NSF Grant DMS-9500924.     

Evaluating the Efficiency of US Air Force Real-Property Maintenance Activities

The objective of this research is to evaluate a new methodology, data envelopment analysis (DEA), as a tool for measuring and evaluating the operational efficiency of US Air Force organizations. This study involves the application of DEA to locate possible inefficiencies in the performance of US Air Force real-property maintenance activities. Dynamic behaviour, as exhibited via window analyses, is reviewed along with static counterparts. The testing was done in close coordination with Air Force officials, who reviewed the results for accuracy, validity and relevance. We conclude that this type of efficiency analysis does have value for the Air Force, where it can serve as a guide to auditors, budget programmers, managers and others in measuring, evaluating and enhancing operational efficiency.     

A fixed-point representation of the generalized complementarity problem

Eaves and Kojima have separately provided fixed-point representations of the standard complementarity problem. Although the mappings used to describe their representations appear to be different, this paper shows they are essentially the same, a unification that is accomplished via a geometric programming argument in the context of a more general complementarity problem.The authors are indebted to Professor R. Saigal of Northwestern University for helpful discussions concerning this paper.This research was partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3134.     

Modeling and analysis of a Canadian Forces Geomatics division workflow

This paper addresses workflow issues of a Geomatics division in the Canadian Forces. This division is dedicated to the production of Geomatics Information under the US National Geospatial-Intelligence Agency’s Foundation Based Operations concept. This paper outlines a methodology for modeling and analyzing the workflow of the Canadian Forces Geomatics division. A discrete event simulation model is developed and applied to measure the performance of the workflow system for developing Geomatics products. A hybrid queueing network/optimization model is also developed to support the simulation model. The objective of the queueing network/optimization formulation is to provide the optimal configuration of the Geomatics division. The paper successfully addresses a complex workflow problem in the context of real world system and provides insights into the performance of the Canadian Forces Geomatics processing.     

Fast algorithms for the integral equations of the inverse scattering problem

The Gelfand-Levitan and Marchenko equations of inverse scattering theory are integral equations with Toeplitz and Hankel kernels respectively. It is shown that these facts can be used to reduce the integral equations to differential equations which can be solved with an order of magnitude less computation than generally envisaged.This work was supported by the Army Research Office under Contract DAAG29-77-C-0042, by the Air Force Office of Scientific Research, Air Force Systems Command, under Contract AF44-620-74-C-0068 and the Australian Research Grants Committee.     

Better management of blood supply-chain with GIS-based analytics

This paper presents a novel application of operations research, data mining and geographic information-systems-based analytics to support decision making in blood supply chain management. This, blood reserve availability assessment, tracking, and management system (BRAMS), research project has been funded by the Office of the Secretary of Defense. (This DoD funded SBIR project is performed by the researchers at Knowledge Based Systems, Inc. (KBSI).) The rapidly increasing demand, criticality of the product, strict storage and handling requirements, and the vastness of the theater of operations, make blood supply-chain management a complex, yet vital problem for the department of defense. In order to address this problem a variety of contemporary analytic techniques are used to analyze inventory and consumption patterns, evaluate supply chain status, monitor performance metrics at different levels of granularity, and detect potential problems and opportunities for improvement. The current implementation of the system is being actively used by 130 mangers at different levels in the supply chain including facilities at Osan Air Force Base in South Korea and Incirlik Air Force Base in Turkey.     

Generalized exterior boundary-value problems and optimization for the Helmholtz equation

A class of radiation problems is considered for the Helmholtz equation in exterior domains bounded by a smooth surface on which Dirichlet, Neumann, or Robin boundary conditions are imposed. The problem of finding the boundary data which maximizes far field power in a restricted subset of far field directions is formulated as a constrained maximization problem. Existence of an optimal solution in a variety of control domains is established. The particular case when the boundary is circular and the control domain is the unit ball inL ² is treated in detail. An algorithm for constructing the optimal solution is derived and used to obtain explicit numerical results.This work was supported by the US Air Force under Grant No. AFOSR 81-0156. The work was completed while the first author was on leave to the Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, BRD.     

On the global structure of crystalline surfaces

We bound the number of plane segments in a crystalline minimal surface S in terms of its Euler characteristic, the number of line segments in its boundary, and a factor determined by the Wulff shapeW of its surface energy function. A major technique in the proofs is to quantize the Gauss map ofS based on the Gauss map ofW. One thereby bounds the number of positive-curvature corners and the interior complexity ofS. The support of the National Science Foundation and the Air Force Office of Scientific Research and the hospitality of Stanford University, where this paper was extensively rewritten, are gratefully acknowledged.     

Real inversion and jump formulae for the Laplace transform. Part I

Generalizations of the Laplace asymptotic method are obtained and real inversion formulae of the Post-Widder type for the Laplace transform are generalized. This paper is to be a part of the first author’s Ph.D. thesis written under the direction of the second author at The Hebrew University of Jerusalem. The participation of the second author in this paper has been sponsored in part by the Air Force Office of Scientific Research OAR through the European Office, Aerospace Research, United States Air Force.     

Pseudo-minkowski differential geometry

Summary Minkowski geometry is studied by the method of moving frames. In memory of Guido Castelnuovo, in the recurrence of the first centenary of his birth. The support of the research presented in these lectures by the Air Force Office of Scientific Research is gratefully acknowledged.     

On the existence of equivalent finite invariant measures

Summary Necessary and sufficient conditions are given for the existence of a finite measure which is equivalent to a given measure and invariant with respect to each transformation in a given commutative semigroup of measurable null-invariant point transformations. This result was already known for denumerably generated semigroups. A complementary result is proved which states that if one such equivalent measure exists, then there exists a unique equivalent measure which agrees with the original measure on the invariant sets.Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under Grant No. AFOSR-68-1394.