Geometric singular perturbation analysis of oxidation heat pulses for two-phase flow in porous media

When air or oxygen is injected into a petroleum reservoir, and oxidation or combustion is induced, a combustion front forms if heat loss to the surrounding rock formation is negligible. Here, we employ a simple model for combustion, which takes into account oil viscosity reduction, but neglects gas density dependence on temperature and uses a simplified oxidation reaction. We show that for small heat loss, this combustion front is actually the lead part of a pulse, while the trailing part of the pulse is a slow cooling process. If the heat loss is too large, we show that such a pulse does not exist. The proofs use geometric singular perturbation theory and center manifold reduction.Dedicated to Constantine Dafermos on his 60^th birthdayThis work was supported in part by: CNPq under Grant 300204/83-3; CNPq/NSF under Grant 91.0011/99-0; MCT under Grant PCI 650009/97-5; FINEP under Grant 77.97.0315.00; FAPERJ under Grants E-26/150.936/99 and E-26/151.893/2000; NSF under Grant DMS-9973105.     

A finite-state,finite-memory minimum principle

A class of finite-state, finite-memory stochastic control problems is considered. A minimum principle is derived. Signaling strategies are defined and related to the necessary conditions of the minimum principle. Min-H algorithms for the problem are described.This research has been conducted in the MIT Electronic Systems Laboratory with support from AFOSR Grant No. 72-2273, NASA/AMES Grant No. NGL-22-009(124), and NSF Grant No. GK-25781.     

Remarks on lines and minimal rational curves

We determine all of lines in the moduli space M of stable bundles for arbitrary rank and degree. A further application of minimal rational curves is also given in last section. This work was supported by the Competitive Earmarked Research Grant (Grant No. HKU7025/03P) of the Research Grant Council, Hong Kong     

Dynamically Consistent Cooperative Solution in a Differential Game of Transboundary Industrial Pollution

This paper presents a cooperative differential game of transboundary industrial pollution. A noted feature of the game model is that the industrial sectors remain competitive among themselves while the governments cooperate in pollution abatement. It is the first time that time consistent solutions are derived in a cooperative differential game on pollution control with industries and governments being separate entities. A stochastic version of the model is presented and a subgame-consistent cooperative solution is provided. This is the first study of pollution management in a stochastic differential game framework. This research was supported by the Research Grant Council of Hong Kong Grant HKBU2103/04H and Hong Kong Baptist University Grant FRG/05-06/II22.     

An elementary and direct proof of the Painlevé property for the Painlevé equations I,II and IV

We present a direct and elementary proof that all the solutions of the Painlevé Equations I, II and IV are meromorphic functions on the whole complex plane. The proof uses some ideas from the existing proofs but applies the ideas in a different setting. Research was supported by Hong Kong Research Grant Council Earmark Grant HKUST6123/00P. Research was supported by Hong Kong Research Grant Council Earmark Grant HKUST6107/02P.     

Regularity Conditions in Differentiable Vector Optimization Revisited

This work is concerned with differentiable constrained vector optimization problems. It focus on the intrinsic connection between positive linearly dependent gradient sets and the distinct notions of regularity that come to play in this context. The main aspect of this contribution is the development of regularity conditions, based on the positive linear dependence or independence of gradient sets, for problems with general nonlinear constraints, without any convexity hypothesis. Being easy to verify, these conditions might be useful to define termination criteria in the development of algorithms. This work was supported by Fundación Antorchas, Grant 13900/4; by Southern National University, Grant UNS 24/L069; by Comahue National University, Grant E060/04; by CNPq-Brazil (Grants 302412/2004-2, 473586/2005-5 and 303465/2007-7) and by FAPESP-Brazil (06/53768-0).     

A class of “onto” multifunctions

A convex valued, upper continuous multifunction with pointed closed convex domain is proved to be onto, if there is a selection with certain coercive properties and if the selection for each point lies in the affine hull of the smallest face of the domain containing the point. The proof uses a piecewise affine homotopy construction. We apply the onto theorem to an approximation of a network of servers and show that arbitrary congestion levels can be realized with appropriate arrival levels.This research is based on work supported in part by the National Science Foundation Grant DMS 92-07409, by the Department of Energy Grant DE-FG03-87-ER-25028, by the United States—Israel Binational Science Foundation Grant 85-00295 and by ONR Grant N00014-92-J1142.     

Proximal Point Algorithms for General Variational Inequalities

This paper presents a unified framework of proximal point algorithms (PPAs) for solving general variational inequalities (GVIs). Some existing PPAs for classical variational inequalities, including both the exact and inexact versions, are extended to solving GVIs. Consequently, several new PPA-based algorithms are proposed. M. Li was supported by NSFC Grant 10571083 and SRFDP Grant 200802861031. L.Z. Liao was supported in part by grants from Hong Kong Baptist University and the Research Grant Council of Hong Kong. X.M. Yuan was supported in part by FRG/08-09/II-40 from Hong Kong Baptist University and NSFC Grant 10701055.     

On the eigenvalues of matrices with given upper triangular part

We give necessary and sufficient conditions for a set of numbers to be the eigenvalues of a completion of a matrix prescribed in its upper triangular part.Partially supported by the NSF Grant DMS-8701615-02Partially supported by the NSF Grant DMS-8802836 and United States-Israel Binational Science Foundation Grant 88-00304/I.     

On the rate of convergence in the entropic central limit theorem

We study the rate at which entropy is produced by linear combinations of independent random variables which satisfy a spectral gap condition.Mathematics Subjects Classification (2000):94A17; 60F05Supported in part by the EU Grant HPMT-CT-2000-00037, The Minkowski center for Geometry and the Israel Science Foundation.Supported in part by NSF Grant DMS-9796221.Supported in part by EPSRC Grant GR/R37210.Supported in part by the BSF, Clore Foundation and EU Grant HPMT-CT-2000-00037.     

Subgame Consistent Solutions of a Cooperative Stochastic Differential Game with Nontransferable Payoffs

Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that the extension of the solution policy to a later starting time and any possible state brought about by the prior optimal behavior of the players would remain optimal. Recently, mechanisms for the derivation of subgame consistent solutions in stochastic cooperative differential games with transferable payoffs have been found. In this paper, subgame consistent solutions are derived for a class of cooperative stochastic differential games with nontransferable payoffs. The previously intractable subgame consistent solution for games with nontransferable payoffs is rendered tractable.This research was supported by the Research Grant Council of Hong Kong, Grant HKBU2056/99H and by Hong Kong Baptist University, Grant FRG/02-03/II16.Communicated by G. Leitmann     

Packing λ-Fold Complete Multipartite Graphs with 4-Cycles

A maximum packing of any -fold complete multipartite graph (where there are edges between any two vertices in different parts) with edge-disjoint 4-cycles is obtained and the size of each minimum leave is given. Moreover, when =2, maximum 4-cycle packings are found for all possible leaves.This research was supported by Australian Research Council Grant A69701550This research was supported by NSC Grant 88-2115-M-009-013This research was supported by NSF Grant DMS-9531722 and ONR Grant N00014-97-1-1067     

QPCOMP: A quadratic programming based solver for mixed complementarity problems

QPCOMP is an extremely robust algorithm for solving mixed nonlinear complementarity problems that has fast local convergence behavior. Based in part on the NE/SQP method of Pang and Gabriel [14], this algorithm represents a significant advance in robustness at no cost in efficiency. In particular, the algorithm is shown to solve any solvable Lipschitz continuous, continuously differentiable, pseudo-monotone mixed nonlinear complementarity problem. QPCOMP also extends the NE/SQP method for the nonlinear complementarity problem to the more general mixed nonlinear complementarity problem. Computational results are provided, which demonstrate the effectiveness of the algorithm. This material is based on research supported by National Science Foundation Grant CCR-9157632, Department of Energy Grant DE-FG03-94ER61915, and the Air Force Office of Scientific Research Grant F49620-94-1-0036.     

Consistent parameter estimation for partially observed diffusions with small noise

In this paper we provide a consistency result for the MLE for partially observed diffusion processes with small noise intensities. We prove that if the underlying deterministic system enjoys an identifiability property, then any MLE is close to the true parameter if the noise intensities are small enough. The proof uses large deviations limits obtained by PDE vanishing viscosity methods. A deterministic method of parameter estimation is formulated. We also specialize our results to a binary detection problem, and compare deterministic and stochastic notions of identifiability.This research was supported: by Systems Research Center, University of Maryland through NSF Grant CDR-85-00108 and AFOSR-URI Grant 87-0073; by Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, under ARO/MIT Grant DAAL-03-86-K-0171; by INRIA Sophia Antipolis, under ERO/INRIA Grant DAJA45-90-C-0008, and by the CNRS-GRAutomatique.     

Algebraic theories, clones and their segments

Isomorphism and elementary equivalence of segments of clones of objects in concrete categories are investigated. A survey of results about the finitary case is presented and a new theorem about the infinitary case is proved.Financial support of the Grant Agency of the Czech Republic under the grant no. 201/93/0950 and of the Grant Agency of the Charles University under the grant GAUK 349 is gratefully acknowledged.     

Best Approximation and Perturbation Property in Hilbert Spaces

We study the perturbation property of best approximation to a set defined by an abstract nonlinear constraint system. We show that, at a normal point, the perturbation property of best approximation is equivalent to an equality expressed in terms of normal cones. This equality is related to the strong conical hull intersection property. Our results generalize many known results in the literature on perturbation property of best approximation established for a set defined by a finite system of linear/nonlinear inequalities. The connection to minimization problem is considered.The authors thank the referees for valuable suggestions.K.F. Ng - This author was partially supported by Grant A0324638 from the National Natural Science Foundation of China and Grants (2001) 01GY051-66 and SZD0406 from Sichuan Province. Y.R. He -This author was supported by a Direct Grant (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong.     

Chapter 6 On the construction of strong complementarity slackness solutions for DEA linear programming problems using a primal-dual interior-point method

A novel approach for solving the DEA linear programming problems using a primaldual interior-point method is presented. The solution found by this method satisfies the Strong Complementarity Slackness Condition (SCSC) and maximizes the product of the positive components among all SCSC solutions. The first property is critical in the use of DEA and the second one contributes significantly to the reliability of the solution.This research was partially supported by NSF Cooperative Agreement No. CCR-88-09615, ARO Grant 9DAAL03-90-G-0093, DOE Grant DEFG05-86-ER25017, and AFOSR Grant 89-0363.Partially supported by Fulbright/LASPAU.     

Scenario-based stochastic programs: Resistance with respect to sample

A contamination technique is presented as a numerically tractable tool to post-optimization and analysis of robustness of the optimal value of scenario-based stochastic programs and of the expected value problems. Detailed applications of the method concern the two-stage stochastic linear programs with random recourse and the corresponding robust optimization problems.This work was supported by the Grant Agency of the Czech Republic under Grant No. 402/93/0631.     

On the structure of stationary sets

We isolate several classes of stationary sets of [k]ωand investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets.     

Periodic Orbits for Some Systems of Delay Differential Equations

We provide sufficient conditions for the existence of periodic orbits of some systems of delay differential equations with a unique delay. We extend Kaplan-Yorke＇s method for finding periodic orbits from a delay differential equation with several delays to a system of delay differential equations with a unique delay.