Minute displacement and strain analysis using lensless Fourier transformed holographic interferometry

An optical system for lensless Fourier transformed holographic interferometry is constructed to enable the measurement of minute displacements from nanometers to micrometers scale and to obtain corresponding strain distributions using a CCD camera with poor spatial resolution. Since a Fourier spectrum of an object beam is recorded on a hologram in this technique, the image reconstruction is easily performed with a single pass of 2-D fast Fourier transformation. Then, the map of the phase difference over the whole field is obtained by comparing two images before and after deformation. A suitable and effective unwrapping process is, however, inevitably required since the phase difference distribution is wrapped from −π to π in this technique. For phase unwrapping, the maximum spanning tree method is adopted here, which seeks a spanning tree that maximizes overall edge weights given by the cross amplitude. In-plane and out-of-plane displacements are obtained separately from the phase difference distributions at one's request. Moreover, in-plain strain is easily calculated from the in-plane displacement distribution.     

Denumerable state semi-Markov decision processes with unbounded costs,average cost criterion

This paper establishes a rather complete optimality theory for the average cost semi-Markov decision model with a denumerable state space, compact metric action sets and unbounded one-step costs for the case where the underlying Markov chains have a single ergotic set. Under a condition which, roughly speaking, requires the existence of a finite set such that the supremum over all stationary policies of the expected time and the total expected absolute cost incurred until the first return to this set are finite for any starting state, we shall verify the existence of a finite solution to the average costs optimality equation and the existence of an average cost optimal stationary policy.     

Multiple criteria decision problems with fuzzy domination structures

The concepts of domination structures and nondominated solutions in multiple criteria decision problems, which were introduced by Yu, enable us to tackle general situations in which there exists information concerning the decision maker's preferences.In many of the multiple criteria decision problems the underlying domination structures are not known precisely but only fuzzily determined. Yu primarily works with the case where the domination structure at each point is a convex cone. As a result, there exists a sharp borderline dividing all solutions into nondominated solutions and the others.This paper fuzzifies the concepts of domination structures and nondominated solutions to allow them to be applied to a larger class of the multiple criteria decision problems mentioned above. Introducing the concepts of fuzzy convex cones and fuzzy polar cones, it is shown how some of the main results obtained by Yu are extended.     

Nonstationary Markov decision problems with converging parameters

This paper considers the solution of Markov decision problems whose parameters can be obtained only via approximating schemes, or where it is computationally preferable to approximate the parameters, rather than employing exact algorithms for their computation.Various models are presented in which this situation occurs. Furthermore, it is shown that a modified value-iteration method may be employed, both for the discounted version and for the undiscounted version of the model, in order to solve the optimality equation and to find optimal policies. In both cases, the convergence rate is determined.As a side result, we characterize the asymptotic behavior of backward products of a geometrically convergent sequence of Markov matrices.     

Duality for nonlinear multiple-criteria optimization problems

In this paper, we develop a duality theory for nonlinear multiple-criteria optimization problems. The theory associates to efficient points a matrix, rather than a vector, of dual variables. We introduce a saddle-point dual problem, study stability concepts and Kuhn-Tucker conditions, and provide an economic interpretation of the dual matrix. The results are compared to the classical approach of deriving duality, by applying nonlinear programming duality theory to a problem obtained by conveniently weighting the criteria. Possible directions for future research are discussed.This work was performed under Grant No. MCS-77-24654, National Science Foundation.The author is grateful to Professors S. C. Graves and T. L. Magnanti, and two anonymous referees for helpful comments on an earlier version of this paper.     

Control of ruin probabilities by discrete-time investments

The control problem of controlling ruin probabilities by investments in a financial market is studied. The insurance business is described by the usual Cramer-Lundberg-type model and the risk driver of the financial market is a compound Poisson process. Conditions for investments to be profitable are derived by means of discrete-time dynamic programming. Moreover Lundberg bounds are established for the controlled model.     

Random suffix search trees

A random suffix search tree is a binary search tree constructed for the suffixes X_i = 0 · B_iB_i+1B_i+2… of a sequence B₁, B₂, B₃, … of independent identically distributed random b‐ary digits B_j. Let D_n denote the depth of the node for X_n in this tree when B₁ is uniform on ?_b. We show that for any value of b > 1, ??D_n = 2 log n + O(log²log n), just as for the random binary search tree. We also show that D_n/??D_n → 1 in probability. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003     

Generalization of domination structures and nondominated solutions in multicriteria decision making

The concepts of domination structures and nondominated solutions are important in tackling multicriteria decision problems. We relax Yu's requirement that the domination structure at each point of the criteria space be a convex cone (Ref. 1) and give results concerning the set of nondominated solutions for the case where the domination structure at each point is a convex set. A practical necessity for such a generalization is discussed. We also present conditions under which a locally nondominated solution is also a globally nondominated solution.     

Second-order game problem: Decision dynamics in gaming phenomena

The paradigm of decision dynamics (Ref. 1) is used to describe the decision dynamics involving more than one decision-maker. The framework supplied in this paper is different from traditional game theory or differential games. Traditional simplicity assumptions are replaced by a more complicated, but more realistic, setting. Although many mathematically beautiful results in traditional game theory or differential games have disappeared in second-order games, the more realistic setting of the latter does make it easier for the decision-makers to find agood decision. Concepts of time optimality and time stability, and their necessary and/or sufficient conditions are described. Unconventional concepts of strategies and uncertainty involved in gaming phenomena are discussed. A highlight of the paper is a systematic discussion on reframing tactics of gaming situations, which do not exist in the context of traditional game theory or differential games. Various research topics are discussed at the end of the paper.     

Confidence structures in decision making

Decision making is defined in terms of four elements: the set of decisions, the set of outcomes for each decision, a set-valued criterion function, and the decision maker's value judgment for each outcome. Various confidence structures are defined, which give the decision maker's confidence of a given decision leading to a particular outcome. The relation of certain confidence structures to Bayesian decision making and to membership functions in fuzzy set theory is established. A number of schemes are discussed for arriving atbest decisions, and some new types of domination structures are introduced.This research was partly supported by Project No. NR-047-021, ONR Contract No. N-00014-75-C-0569 with the Center for Cybernetic Studies, The University of Texas, Austin, Texas, and by ONR Contract No. N-00014-69-A-0200-1012 with the University of California, Berkeley, California.