Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems

We provide two approaches to the numerical analysis of stochastic control problems. The analyses rely on linear programming formulations of the control problem and allow numerical comparison between controls and numerical verification of optimality. The formulations characterize the processes through the moments of the induced occupation measures. We deal directly with the processes rather than with some approximation to the processes. Excellent software is readily available, since the computations involve finite-dimensional linear programs.     

Noncooperative stochastic games under a n-stage local contraction assumption

We consider a class of noncooperative stochastic games with general state and action spaces and with a state dependent discount factor. The expected time duration between any two stages of the game is not bounded away from zero, so that the usual N-stage contraction assumption, uniform over all admissible strategies, does not hold. We propose milder sufficient regularity conditions, allowing strategies that give rise with probability one to any number of simultaneous stages. We give sufficient conditions for the existence of equilibrium and ∈-equilibrium stationary strategies in the sense of Nash. In the two-player zero-sum case, when an equilibrium strategy exists, the value of the game is the unique fixed point of a specific functional operator and can be computed by dynamic programming.     

On oracle factoring of integers

We present an oracle factorisation algorithm, which in polynomial deterministic time, finds a nontrivial factor of almost all positive integers n based on the knowledge of the number of points on certain elliptic curves in residue rings modulo n.     

Benzene Induced 1H NMR Shifts of Chromeno-Compounds: An Aid to Differentiate Linear and Angular Chromenoflavones

Benzene-induced shifts (BIS) in the ¹H NMR spectra of nine chromeno-compounds have been studied. It provides a simple non-destructive technique for distinguishing linear isomers of chromenoflavones from their angular counterparts. BIS also assists in the assignment of chromene proton signals in chromeno-compounds.     

Available-To-Promise modeling for multi-plant manufacturing characterized by lack of homogeneity in the product: An illustration of a ceramic case

Lack of homogeneity in the product (LHP) appears in some production processes which incorporate raw materials that originate directly from nature and/or production processes with operations that confer heterogeneity to the characteristics of the outputs obtained, even when the inputs used are homogeneous. Poor LHP management may have a very negative impact on the customer service level and on the supply chains’ operation costs, especially when the customer needs to be served with homogeneous units of one same product. One of the key processes for suitable LHP management is the order-promising process. This work presents a mathematical programming order-promising model for make-to-stock environments with LHP. The model considers two objectives placed within a single objective by the weighted sum method. For the purpose of testing the validity of the proposed model and to evaluate the characteristics of the solutions obtained in different scenarios, numerical experiments based on realistic data from a ceramic tile company have been conducted. The results show that better results are obtained for the defined performance measures if multiple objectives are considered when promising orders than the single objective of maximizing profits. Furthermore, the superiority of the results obtained from the proposed model, if compared with current company practice, proves the model’s utility.     

Exploiting special structure in semidefinite programming: A survey of theory and applications

Semidefinite programming (SDP) may be seen as a generalization of linear programming (LP). In particular, one may extend interior point algorithms for LP to SDP, but it has proven much more difficult to exploit structure in the SDP data during computation.     

Searching for Flavor-Changing Neutral-Current Signals via e＋e-（γγ） →tcht0 in Topcolor-Assisted Technicolor Model

In the context of the top-color-assisted technicolor （TC2） model, the flavor-changing neutral-current （FCNC） interaction induced by the top-higgs （hOt） are predicted at tree level. We study the relevant processes of e＋e-（γγ）→tcht0 at the International Linear Collider （ILC）. It is found that these rare processes production rates can be enhanced significantly in the TC2 model. Especially for the process γγ→tcht0, the total cross section will reach a few fb in the reasonable parameter space. We also calculate the distributions of transverse momenta, pseudo-rapid and invariant mass of the top-higgs. In view of the main decay modes of top-higgs for mho 〈 2mr, we find that there will be several hundreds FCNC events produced at the ILC with annually integral luminosity of 500 fb-1. Due to the clean background, such FCNC signals can possibly be detected at the ILC.     

Exact Equilibrium Solutions for Linearly Elastic Plate-Like Bodies

A three-dimensional, explicit and exact, equilibrium solution is derived for transversely isotropic, linearly elastic bodies in the form of a right cylinder simply supported over its lateral boundary and loaded over its end faces. This solution, which generalizes an earlier proposal of Levinson in various respects, is to serve as a benchmark for the corresponding plate theories. This revised version was published online in August 2006 with corrections to the Cover Date.     

A single supplier–single retailer system with an order-up-to level inventory policy

We consider a two-level vendor-managed system in which external demand occurs only at a retailer and a supplier replenishes the retailer employing an order-up-to S policy over T periods. We present an O(T³) algorithm to coordinate the system when S is known. We also show that S can be optimized in O(aT³) time for an input parameter a.     

Orbits of rational n-sets of projective spaces under the action of the linear group

Let k=Fq be a finite field. We enumerate k-rational n-sets of (unordered) points in a projective space PN over k, and we compute the generating function for the numbers of PGLN+1(k)-orbits of these n-sets. For N=1,2 we obtain a formula for these numbers of orbits as a polynomial in q with integer coefficients.