A principal ideal theorem analogue for modules over commutative rings

The Principal Ideal Theorem states that if Re is a commutative Noetherian ring and ? is a prime ideal of Re which is minimal over a principal ideal then Pe has height at most 1. Also, if Re is a (not necessarily Noetherian) UFD and Pe is a prime ideal of Re minimal over a principal ideal then Pe has height at most 1. We shall show that there are analogues for modules over commutative rings, but they hold only in special cases.     

Uniqueness of the group topology of some homeomorphism groups

In this paper, we generalize a theorem of Kallman [2, Theorem 1.1] and we resolve the unsettled case there.     

Null controllability of von Kármán thermoelastic plates under the clamped or free mechanical boundary conditions

In this paper, we provide results of local and global null controllability for 2-D thermoelastic systems, in the absence of rotational inertia, and under the influence of the (nonLipschitz) von Kármán nonlinearity. The plate component may be taken to satisfy either the clamped or higher order (and physically relevant) free boundary conditions. In the accompanying analysis, critical use is made of sharp observability estimates which obtain for the linearization of the thermoelastic plate (these being derived in [G. Avalos, I. Lasiecka, The null controllability of thermoelastic plates and singularity of the associated minimal energy function, J. Math. Anal. Appl. 294 (2004) 34-61] and [G. Avalos, I. Lasiecka, Asymptotic rates of blowup for the minimal energy function for the null controllability of thermoelastic plates: The free case, in: Proc. of the Conference for the Control of Partial Differential Equations, Georgetown University, Dekker, in press]). Moreover, another key ingredient in our work to steer the given nonlinear dynamics is the recent result in [A. Favini, M.A. Horn, I. Lasiecka, D. Tataru, Addendum to the paper: Global existence, uniqueness and regularity of solution to a von Kármán system with nonlinear boundary dissipation, Differential Integral Equations 10 (1997) 197-200] concerning the sharp regularity of the von Kármán nonlinearity.     

Staffing decisions for heterogeneous workers with turnover

In this paper we consider a firm that employs heterogeneous workers to meet demand for its product or service. Workers differ in their skills, speed, and/or quality, and they randomly leave, or turn over. Each period the firm must decide how many workers of each type to hire or fire in order to meet randomly changing demand forecasts at minimal expense. When the number of workers of each type can by continuously varied, the operational cost is jointly convex in the number of workers of each type, hiring and firing costs are linear, and a random fraction of workers of each type leave in each period, the optimal policy has a simple hire- up-to/fire-down-to structure. However, under the more realistic assumption that the number of workers of each type is discrete, the optimal policy is much more difficult to characterize, and depends on the particular notion of discrete convexity used for the cost function. We explore several different notions of discrete convexity and their impact on structural results for the optimal policy.     

Factorization in finite-codimensional ideals of group algebras

Let G be a -compact, locally compact group and I be a closed2-sided ideal with finite codimension in L¹(G). It is shownthat there are a closed left ideal L having a right boundedapproximate identity and a closed right ideal R having a leftbounded approximate identity such that I = L + R. The proofuses ideas from the theory of boundaries of random walks ongroups. 2000 Mathematics Subject Classification: primary 43A20;secondary 42A85, 43A07, 46H10, 46H40, 60B11.     

A comprehensive approach of planning and scheduling based on petri nets

The main results available on the use of black-and-white Petri nets for modelling, planning and scheduling manufacturing systems are presented. In the first part of the paper, the basics of Petri nets necessary to understand the subsequent presentation are introduced. Particular attention is paid to event graphs, a particular type of Petri nets used for modelling and evaluating ratio-driven systems. The second part of the paper is devoted to ratio-driven systems, their modelling and their scheduling. Job-shops, assembly systems, and KANBAN systems are used to illustrate this section. Finally, the general case is investigated of manufacturing systems subject to changing demands. An approach based on conflict-free Petri nets with input and output transitions is proposed for planning and scheduling this type of system.     

Parity in partition identities

This paper considers a variety of parity questions connected with classical partition identities of Euler, Rogers, Ramanujan and Gordon. We begin by restricting the partitions in the Rogers-Ramanujan-Gordon identities to those wherein even parts appear an even number of times. We then take up questions involving sequences of alternating parity in the parts of partitions. This latter study leads to: (1) a bi-basic q-binomial theorem and q-binomial series, (2) a new interpretation of the Rogers-Ramanujan identities, and (3) a new natural interpretation of the fifth-order mock theta functions f ₀(q) along with a new proof of the Hecke-type series representation.     

Secant varieties and Hirschowitz bound on vector bundles over a curve

For a vector bundle V of rank n over a curve X and for each integer r in the range 1 ≤ r ≤ n ? 1, the Segre invariant s _r is defined by generalizing the minimal self-intersection number of the sections on a ruled surface. In this paper we generalize Lange and Narasimhan’s results on rank 2 bundles which related the invariant s ₁ to the secant varieties of the curve inside certain extension spaces. For any n and r, we find a way to get information on the invariant s _r from the secant varieties of certain subvariety of a scroll over X. Using this geometric picture, we obtain a new proof of the Hirschowitz bound on s _r .     

Stochastic matrices over cones

The notion of a stochastic operator in an ordered Banach space is specialized to a finite dimensional ordered real vector space. The classical limit theorems are obtained, and an application is made to non-homogeneous Markov chains. Finally, groups of nonnegative matrices are discussed.     

Generalized Bergman kernels on symplectic manifolds

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As a consequence, we calculate the density of states function of the Bochner-Laplacian and establish a symplectic version of the convergence of the induced Fubini-Study metric. We also discuss generalizations of the asymptotic expansion for non-compact or singular manifolds as well as their applications. Our approach is inspired by the analytic localization techniques of Bismut and Lebeau.