A local–global principle for algebras with involution and hermitian forms

 Weakly hyperbolic involutions are introduced and a proof is given of the following local–global principle: a central simple algebra with involution of any kind is weakly hyperbolic if and only if its signature is zero for all orderings of the ground field. Also, the order of a weakly hyperbolic algebra with involution is a power of two, this being a direct consequence of a result of Scharlau. As a corollary an analogue of Pfister's local–global principle is obtained for the Witt group of hermitian forms over an algebra with involution. Received: 29 October 2001; in final form: 9 August 2002 / Published online: 16 May 2003 Mathematics Subject Classification (2000): 16K20, 11E39     

Evasion and prediction

 Say that a function π:n ^<ω →n (henceforth called a predictor) k-constantly predicts a real xn ^ω if for almost all intervals I of length k, there is iI such that x(i)=π(x↾i). We study the k-constant prediction number v _n ^const (k), that is, the size of the least family of predictors needed to k-constantly predict all reals, for different values of n and k, and investigate their relationship. Received: 27 June 2001 / Revised version: 10 September 2001 / Published online: 10 October 2002 RID="*" ID="*" Supported by Grant–in–Aid for Scientific Research (C)(2)12640124, Japan Society for the Promotion of Science RID="†" ID="†" Supported by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. Publication 762     

Primal separation for 0/1 polytopes

 The 0/1 primal separation problem is: Given an extreme point xˉ of a 0/1 polytope P and some point x ^*, find an inequality which is tight at xˉ, violated by x ^* and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalent. This implies that the problems 0/1 optimization, 0/1 standard separation, 0/1 augmentation, and 0/1 primal separation are polynomial time equivalent. Then we provide polynomial time primal separation procedures for matching, stable set, maximum cut, and maximum bipartite graph problems, giving evidence that these algorithms are conceptually simpler and easier to implement than their corresponding counterparts for standard separation. In particular, for perfect matching we present an algorithm for primal separation that rests only on simple max-flow computations. In contrast, the known standard separation method relies on an explicit minimum odd cut algorithm. Consequently, we obtain a very simple proof that a maximum weight perfect matching of a graph can be computed in polynomial time. Received: August 20, 2001 / Accepted: April 2002 Published online: December 9, 2002 RID="⋆" ID="⋆" This research was developed while the author was on leave at the Istituto di Analisi dei Sistemi ed Informatica, Viale Manzoni 30, 00185 Roma, supported by the project TMR-DONET nr. ERB FMRX-CT98-0202 of the European Union. Mathematics Subject Classification (2000): 90C10, 90C60, 90C57     

Minimising total average cycle stock subject to practical constraints

Silver and Moon (J Opl Res Soc 50(8) (1999) 789–796) address the problem of minimising total average cycle stock subject to two practical constraints. They provide a dynamic programming formulation for obtaining an optimal solution and propose a simple and efficient heuristic algorithm. Hsieh (J Opl Res Soc 52(4) (2001) 463–470) proposes a 0–1 linear programming approach to the problem and a simple heuristic based on the relaxed 0–1 programming formulation. We show in this paper that the formulation of Hsieh can be improved for solving very large size instances of this inventory problem. So the mathematical approach is interesting for several reasons: the definition of the model is simple, its implementation is immediate by using a mathematical programming language together with a mixed integer programming software and the performance of the approach is excellent. Computational experiments carried out on the set of realistic examples considered in the above references are reported. We also show that the general framework for modelling given by mixed integer programming allows the initial model to be extended in several interesting directions.     

Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, II

We construct the intertwining operator superalgebras and vertex tensor categories for the superconformal unitary minimal models and other related models.

     

Strong versus weak local minimizers for the perturbed Dirichlet functional

Let be a bounded domain and . In this paper we consider functionals of the form where the admissible function belongs to the Sobolev space of vector-valued functions and is such that the integral on the right is well defined. We state and prove a sufficiency theorem for local minimizers of where . The exponent is shown to depend on the dimension and the growth condition of and an exact expression is presented for this dependence. We discuss some examples and applications of this theorem. Received: 20 July 2000 / Accepted: 7 June 2001 / Published online: 19 October 2001     

Study on LiFe<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Sm<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>PO<Subscript>4</Subscript>/C used as cathode materials for lithium-ion batteries with low Sm component

LiFe_1???x Sm _x PO₄/C cathode materials were synthesized though a facile hydrothermal method. Compared with high-temperature solid-phase sintering, the method can allow for the fabrication of low Sm content (2 %), a scarce and expensive rare earth element, while the presence of an optimized carbon coating with large amount of sp²-type carbon sharply increases the material’s electrochemical performance. The high-rate dischargeability at 5 C, as well as the exchange current density, can be increased by 21 and 86 %, respectively, which were attributed to the fine size and the large cell parameter a/c as much. It should be pointed out that the a/c value will be increased for the LiFePO₄ Sm-doped papered by both of the two methods, while the mechanism is different: The value c is increased for the front and the value a is decreased for the latter, respectively.     

Plant location and procurement planning in knockdown production systems

We consider an integrated problem of plant location and capacity planning for components procurement in knockdown production systems. The problem is that of determining the schedule of opening components manufacturing plants, plans for acquisition of capacities in opened components manufacturing plants, and plans for components procurement in final assembly plants with the objective of minimizing the sum of fixed costs for opening plants, acquisition and operation costs of facilities, and delivery and subcontracting costs of components. The problem is formulated as a mixed integer linear program and solved by a two-stage solution procedure. In the solution procedure, the problem is decomposed into two tractable subproblems and these subproblems are solved sequentially. In the first stage, a dynamic plant location problem is solved using a cut and branch algorithm based on Gomory cuts, while a multiperiod capacity planning problem is solved in the second stage by a heuristic algorithm that uses a cut and branch algorithm and a variable reduction scheme. The solution procedure is tested on problems of a practical size and results show that the procedure gives reasonably good solutions.