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308

Jun 9, 2011
06/11

by
Ounaies, Z.; Young, J. A.; Simpson, J. O.; Farmer, B. L

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Molecular modeling and dielectric measurements are being used to identify mechanisms governing piezoelectric behavior in polyimides such as dipole orientation during poling, as well as degree of piezoelectricity achievable. Molecular modeling on polyimides containing pendant, polar nitrile (CN) groups has been completed to determine their remanent polarization. Experimental investigation of their dielectric properties evaluated as a function of temperature and frequency has substantiated...

Topics: FEEDBACK CONTROL, CONTROLLERS, DISSIPATION, CONTROL SYSTEMS DESIGN, EIGENVALUES, MINIMAX TECHNIQUE,...

The memorandum presents a method of fitting equally-spaced data by the use of Chebyshev polynomials. The method is explained and tables are given to facilitate its application. The tables provide for fitting with all ordinates adjusted, fitting with zero error at one end point, or fitting with zero error at both end points as the situation may demand.

Topics: DTIC Archive, Frick, C H, NAVAL WEAPONS LAB DAHLGREN VA, *POLYNOMIALS, *CURVE FITTING, MINIMAX...

The omega-value of a matrix is a function of a parameter sigma and is defined as a limit of a sequence of successive min and max operations applied to convex combinations of entries of the matrix. It arises naturally from a game- theoretical model. In the paper it is shown that the omega-value always exists and that it can be obtained from certain systems of nonlinear equations. Some of its properties are also investigated.

Topics: DTIC Archive, Shubert, Bruno O, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *GAME THEORY, INEQUALITIES,...

We consider the minimization of a function which is the maximum of a finite number of smooth but nonlinear functions. It is well-known that the minimax problem of this type connects naturally to a nonlinear program. Through this connection the effective quasi-Newton method becomes applicable. We show that this approach is valid and the resulting method has global convergence properties. (Author)

Topics: DTIC Archive, Han,Shih-Ping, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *NONLINEAR...

Topics: DTIC Archive, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM VARIABLES,...

199
199

Jun 9, 2011
06/11

by
Stokes, Eric H.; Shin, E. Eugene; Sutter, James K

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Carbon fiber thermoset polymer matrix composites (PMC) with high temperature polyimide based in-situ polymerized monomer reactant (PMR) resin has been used for some time in applications which can see temperatures up to 550 F. Currently, graphite fiber PMR based composites are used in several aircraft engine components including the outer bypass duct for the GE F-404, exit flaps for the P&W F-100-229, and the core cowl for the GE/Snecma CF6-80A3. Newer formulations, including PMR-II-50 are...

Topics: TRANSONIC FLUTTER, ACTIVE CONTROL, UNSTEADY AERODYNAMICS, LINEAR QUADRATIC GAUSSIAN CONTROL, WIND...

In this paper, we present a framework for a mixed estimation scheme for hidden Markov models (HMM). A robust estimation scheme is first presented using the minimax method that minimizes a worst case cost for HMMs with bounded uncertainties. Then we present a mixed estimation scheme that minimizes a risk-neutral cost with a constraint on the worst-case cost. Some simulation results are also presented to compare these different estimation schemes in cases of uncertainties in the noise model.

Topics: DTIC Archive, Dey, Subhrakanti, MARYLAND UNIV COLLEGE PARK INST FOR SYSTEMS RESEARCH, *MARKOV...

In this paper a new subset selection rule for selecting a subset containing the least probable multinomial cell is defined. The rule is shown to be minimax and admissible in the class of rules which have a preassigned probability of at least P* of selecting the least probable cell provided that P* is sufficiently large. The loss used is the number of non-best cells selected. (Author)

Topics: DTIC Archive, Berger,Roger L, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, *SET THEORY,...

This paper considers the minimax estimation of mu by delta relative to a certain quadratic loss function with unknown weights. To the best of our knowledge, this is the first time in the literature a loss function of this type is considered in estimating mu. The minimax estimation of mu relative to other types of quadratic loss functions has been extensively studied since Stein (1956) showed that the maximum likelihood estimator chi, is inadmissible, when p greater than or equal to 3, relative...

Topics: DTIC Archive, Lin,Pi-Erh, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, *MULTIVARIATE...

The multi-level programming problem is defined as an n-person nonzero-sum game with perfect information in which the players move sequentially. The bi-level linear case is addressed in detail. Solutions are obtained by recasting this problem as a standard mathematical program and appealing to its implicitly separable structure. The reformulated optimization problem is linear save for a complementarity constraint of the form u,g = 0. This constraint is decomposed in a manner that permits us to...

Topics: DTIC Archive, Bard,Jonathan F, GEORGE WASHINGTON UNIV WASHINGTON D C PROGRAM IN LOGISTICS,...

Most previous research on search for game playing has focused on improving search efficiency rather than on better utilizing available information. By developing models based on a notion we call playing strength, we acquire the insight needed to develop strategies which perform better than minimax against both perfect and imperfect opponents. In particular situations, our decision strategies yield improvements comparable to or exceeding those provided by an additional ply of search. (Author)

Topics: DTIC Archive, Reibman,Andrew L, DUKE UNIV DURHAM NC DEPT OF COMPUTER SCIENCE, *GAME THEORY,...

A differential correction technique for solving nonlinear minimax problems is presented. The basis of the technique is a linear programing algorithm which solves the linear minimax problem. By linearizing the original nonlinear equations about a nominal solution, both nonlinear approximation and estimation problems using the minimax norm may be solved iteratively. Some consideration is also given to improving convergence and to the treatment of problems with more than one measured quantity. A...

Topics: NASA Technical Reports Server (NTRS), LINEAR PROGRAMMING, MINIMAX TECHNIQUE, PROBLEM SOLVING,...

An implementation, using Gaussian LU decomposition with row interchanges, of Stiefel's exchange algorithm for determining a Chebyshev solution to an overdetermined system of linear equations is presented. The implementation is computationally more stable than those usually given in the literature. A generalization of Stiefel's algorithm is developed which permits the occasional exchange of two equations simultaneously. Finally, some experimental comparisons are offered.

Topics: DTIC Archive, Bartels, Richard H, STANFORD UNIV CA DEPT OF COMPUTER SCIENCE, *EQUATIONS,...

The effectiveness of Newton's method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified Newton methods for the nonconvex case. Linesearch modified Newton methods utilize a linear combination of a descent direction and a direction of negative curvature. If these directions are sufficient in a certain sense, and a suitable linesearch is used, the resulting method will generate limit points that...

Topics: DTIC Archive, Forsgren, Anders, STANFORD UNIV CA SYSTEMS OPTIMIZATION LAB, *FACTOR ANALYSIS,...

A number of attackers try to reach a goal guarded by several goalies. The goalies and attackers approach each other with fixed velocity but can maneuver transversely within a specified velocity range. The largest miss distance between an attacker and the nearest goalie at the termination of the game is determined for an arbitrary initial deployment of the goalies and the attackers. Optimal strategies and optimal initial placements for the defense and attack are determined. The problem may be...

Topics: DTIC Archive, Redmond, P J, GENERAL RESEARCH CORP SANTA BARBARA CA, *GAME THEORY, ALGORITHMS,...

This paper studies the existence of periodic solutions for a family of semilinear wave equations where the restoring force is independent of time, monotone, and grows at a more rapid rate than linear near infinity. With appropriate technical assumptions it is shown that there is an unbounded sequence of such free vibrations, i.e. there are solutions of arbitrarily large amplitude. If the restoring force is independent of x, the monotonicity assumption can be omitted.

Topics: DTIC Archive, Rabinowitz,Paul H, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *WAVE...

This paper considers the problem of finding locations of several new facilities in an imbedded tree network with respect to existing facilities at known locations so as to satisfy distance constraints, which impose upper bounds on distances between pairs of facilities. It is known that the existence of a feasible solution to the distance constraints is related to shortest paths through an auxiliary network, which has as arc lengths the upper bounds on pairwise facilities distances. This...

Topics: DTIC Archive, Francis,Richard L, FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS...

Uncertainty modeling is a critical element in the estimation of robust stability margins for stability boundary prediction and robust flight control system development. There has been a serious deficiency to date in aeroservoelastic data analysis with attention to uncertainty modeling. Uncertainty can be estimated from flight data using both parametric and nonparametric identification techniques. The model validation problem addressed in this paper is to identify aeroservoelastic models with...

Topics: NASA Technical Reports Server (NTRS), AEROSERVOELASTICITY, FLIGHT CONTROL, STABILITY TESTS,...

Appreciably larger domains of attraction were found for asymptotically stable equilibrium points of equations of the form x(double dot) + beta(x(dot)) + f(x) = 0; a generalization of a classical result for orthogonal polynomials was obtained; a new comparison theorem for conjugate points of equations (r(x)y) + p(x)y = 0 is given; the last yields a comparison theorem for the minimax function. (Author)

Topics: DTIC Archive, Leighton,Walter, MISSOURI UNIV-COLUMBIA DEPT OF MATHEMATICS, *LYAPUNOV FUNCTIONS,...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

The classical treatments of linear, homogeneous and quadratic programming given by Duffin, Eisenberg and Cottle are subsumed by a cone-augmented version of the Fenchel-Rockafellar duality model. Suboptimizations over auxiliary variables receive particular attention, and the entire model is seen to be the projection of another. (Author)

Topics: DTIC Archive, WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER, *MATHEMATICAL PROGRAMMING,...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

Topics: DTIC Archive, Moricz,F, JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICAL SCIENCES, *RANDOM...

The paper discusses duality for linear and nonlinear programs in which some of the variables are arbitrarily constrained. The most important class of such problems is that of mixed-integer (linear and nonlinear) programs. The paper introduces the duality constructions and discusses algorithms based on them.

Topics: DTIC Archive, Balas, Egon, CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP,...

A conditional lower bound on the minimand of an integer program is a number which would be a valid lower bound if the constraint set were amended by certain inequalities, also called conditional. If such a conditional lower bound exceeds some known upper bound, then every solution better than the one corresponding to the upper bound violates at least one of the conditional inequalities. This yields a valid disjunction, which can be used to partition the feasible set, or to derive a family of...

Topics: DTIC Archive, Balas,Egon, CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP,...

The fundamental theory and algorithms of quadratic programming and linear complementarity are presented in expository form. Computational experience is reviewed. (Author)

Topics: DTIC Archive, Cottle,Richard W, STANFORD UNIV CALIF SYSTEMS OPTIMIZATION LAB, *QUADRATIC...

Time delay estimation forms the base from which passive localization and tracking may function accurately. This report considers both the practical and theoretical aspects of time delay estimation when classical optimal estimation techniques break down. Of special concern are two adverse situations: the underlying statistics of the observations are incompletely specified; and the observations contain a narrowband component. Additional keywords: minimax technique; robust Wiener filter; center of...

Topics: DTIC Archive, Hero, A O, PRINCETON UNIV NJ DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE,...

Four classes of lifetimes which have been useful in describing situations where systems are assumed to have independent univariate component lifetimes are: the increasing failure rate (IFR) class; the increasing failure rate average (IFRA) class; the new better than used (NBU) class; and the new better than used in expectation (NBUE) class. These classes are reviewed and also multivariate analogs of the IFR and IFRA cases are discussed. New multivariate definitions of NBU and NBUE are...

Topics: DTIC Archive, Block,Henry W, PITTSBURGH UNIV PA DEPT OF MATHEMATICS AND STATISTICS, *MULTIVARIATE...

For estimating the mean of a p-variate normal distribution it is known that Stein's rule is minimax. It is shown for a subfamily of Stein's estimators that the vector consisting of any K or = 3 components of the estimator is also minimax for estimating corresponding components of the mean vector. (Author)

Topics: DTIC Archive, Alam,Khursheed, CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES, *NORMAL DISTRIBUTION,...

This document discusses probability density functions, lorally minimax tests, and matrices(mathematics).

Topics: DTIC Archive, Giri,N, PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS, *MULTIVARIATE ANALYSIS,...

Consider the following urn model, m urns and distribute n indistinguishable balls among the urns such that the distinguishable distributions of the balls all have the same probability. Let S sub K denote the number of balls in the Kth urn. Clearly S sub 1 + ... + S sub m = n. In this paper, random variables of the type Z = h(S sub 1,...,S sub m), especially h(S sub 1, ...,S sub m) = h sub 1 (S sub 1) + ... + h sub m (S sub m), are studied when m,n approaches the limit of infinity m/n approaches...

Topics: DTIC Archive, Holst,Lars, WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER, *COMBINATORIAL...

The thesis discusses the solution of concave-convex games. An algorithm is developed, a computer program written and applied to an anti- submarine warfare force allocation problem as an illustration. Techniques for handling concave-convex problems in high dimensions are included.

Topics: DTIC Archive, Gunn, Lee F, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *GAME THEORY, COMPUTER PROGRAMS,...

The newsboy problem solutions under the conditions of risk and of uncertainty about demand are well known. The former is the case where the distribution of demand is known or estimated, and the latter is the case where it is not known but the range of demand is given. Minimizing the expected cost under risk and the minimax approach under uncertainty are well-known methods to solve the problem. The situation is considered where demand frequency data is acquired, one observation per decision...

Topics: DTIC Archive, Sok, Yong-u, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *MINIMAX TECHNIQUE, COMPUTATIONS,...

A variational principle of a minimax nature is developed and used to prove the existence of critical points of certain variational problems which are indefinite. The proofs are carried out directly in an infinite dimensional Hilbert space. Special cases of these problems previously had been tractable only by an elaborate finite dimensional approximation procedure. The main applications given here are to Hamiltonian systems of ordinary differential equations where the existence of time periodic...

Topics: DTIC Archive, Benci,Vieri, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *HILBERT SPACE,...

The subject matter of this work is minimax parameter estimation. In the present chapter the author intorduces some basic concepts and definitions from the theory of parameter estimation and through these arrives at the results and techniques which are used to search for minimax solutions to parameter estimation problems.

Topics: DTIC Archive, Antonio, Rafael, Lovera, Padilla, ILLINOIS UNIV AT URBANA COORDINATED SCIENCE LAB,...

This paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of Hamiltonian systems when a singular potential is present. The singularity satisfies the strong force condition of Gordon. When milder singularities are permitted a notion of generalized T-periodic solution is introduced and we get existence and multiplicity results for such solutions. Keywords: Minimax method; Calculus of variations; Hamiltonian systems; Singular...

Topics: DTIC Archive, Bahri, Abbas, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *MINIMAX...

The minimax problem is an unconstrained optimization problem whose objective functions is not differentiable everywhere, and hence cannot be solved efficiently by standard techniques for unconstrained optimization. It is well known that the problem can be transformed into a nonlinearly constrained optimization problem with one extra variable, where the objective and constraint functions are continuously differentiable. This equivalent problem has special properties which are ignored if solved...

Topics: DTIC Archive, Murray,Walter, STANFORD UNIV CALIF SYSTEMS OPTIMIZATION LAB, *QUADRATIC PROGRAMMING,...

This document considers a statistical decision problem in which nature has a finite number of states. The elementary theorems of decision theory, namely the Minimax theorem, the Complete class room theorem, and theorems on the structure of admissible rules, are proved in most texts under the assumptions that the risk set is closed from below and bounded from below. The condition that the risk set is bounded from below is sufficient for the existence of the lower boundary points; however, that...

Topics: DTIC Archive, Chaganty,Narassinga R, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, *DECISION...

The representation min t s.t. F(I)(x). - t less than or equal to 0 for all i is examined. An active set strategy is designed of functions: active, semi-active, and non-active. This technique will help in preventing zigzagging which often occurs when an active set strategy is used. Some of the inequality constraints are handled with slack variables. Also a trust region strategy is used in which at each iteration there is a sphere around the current point in which the local approximation of the...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, APPROXIMATION, COMPUTER PROGRAMS, ITERATION,...

This paper proves the existence of infinitely many distinct T-periodic solutions of a certain perturbed Hamiltonian system under the conditions that H is of C sub 1, superquadratic, and possesses exponential or polynomial growth at infinity and that f is of sub 1, 2 and T-periodic, via minimax methods. Keywords: Monotone truncations, A priori estimates, Multiple periodic solutions.

Topics: DTIC Archive, Long, Yiming, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, EXPONENTIAL...

For a subset A of Euclidean n-space, the location problem of finding the point x which minimizes the maximum distance d(x, a) for a in A may be interpreted as finding the smallest sphere which encloses A. Algorithms have previously been developed for the situations when A is finite or a polytope. Here we concentrate on interpretations and properties of the problem, particularly its relation to other problems: cases where the sphere problem is dual to that of finding a shortest vector in A,...

Topics: DTIC Archive, Hearn,Donald, FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING,...

The distributions with lower truncation parameters are important models in statistics and have been studied in recent years. In this paper, we consider the one-sided testing problem for lower truncation parameters through the empirical Bayes approach. The optimal rate of the monotone empirical Bayes tests is obtained and a monotone empirical Bayes test delta sub n in achieving the optimal rate is constructed. It is shown that delta sub n has good performance for both small samples and large...

Topics: DTIC Archive, Gupta, Shanti S, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *BAYES THEOREM,...

The properties were studied of the direction formed by taking the difference of two successive dual iterates of generalized linear programming (GLP), and pointed out that this direction is also solution to an associated direction finding problem. This study shows that this direction finding problem belongs to a new class of direction finding problems and propose a modification of GLP in which its original direction finding problems is replaced by another in this new class. This new direction...

Topics: DTIC Archive, Lawphongpanich, Siriphong, FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS...