Compromise solutions for bankruptcy situations with references

This paper deals with bankruptcy situations in which in addition to the claims, an exogenously given reference point for the allocation of the estate is present. We introduce and analyse two types of compromise solutions and show that they coincide with the τ value of two corresponding TU games. We apply our solutions to a real-life case of allocating university money to degree courses. Research supported by Generalitat Valenciana, through ACOMP06/040, ACOMP07/136 and GV05/189, and by the Government of Spain and FEDER fund under project MTM2005-09184-C02-02. M. Pulido’s research is partially supported by Fundación Séneca of Comunidad Autónoma de la Región de Murcia, through 02911/PI/05. Ruud Hendrickx author acknowledges financial support from the Netherlands Organisation for Scientific Research (NWO).     

A note on coalitional manipulation and centralized inventory management

In this note we deal with inventory games as defined in Meca et al. (Math. Methods Oper. Res. 57:483–491, 2003). In that context we introduce the property of immunity to coalitional manipulation, and demonstrate that the SOC-rule (Share the Ordering Cost) is the unique allocation rule for inventory games which satisfies this property. The authors acknowledge the financial support of Ministerio de Educación y Ciencia, FEDER and Xunta de Galicia through projects SEJ2005-07637-C02-02 and PGIDIT06PXIC207038PN.     

<Emphasis Type="Italic">p</Emphasis>-additive games: a class of totally balanced games arising from inventory situations with temporary discounts

We introduce a new class of totally balanced cooperative TU games, namely p-additive games. It is inspired by the class of inventory games that arises from inventory situations with temporary discounts (Toledo Ph.D. thesis, Universidad Miguel Hernández de Elche, 2002) and contains the class of inventory cost games (Meca et al. Math. Methods Oper. Res. 57:481–493, 2003). It is shown that every p-additive game and its corresponding subgames have a nonempty core. We also focus on studying the character of concave or convex and monotone p-additive games. In addition, the modified SOC-rule is proposed as a solution for p-additive games. This solution is suitable for p-additive games, since it is a core-allocation which can be reached through a population monotonic allocation scheme. Moreover, two characterizations of the modified SOC-rule are provided. This work was partially supported by the Spanish Ministry of Education and Science and Generalitat Valenciana (grants MTM2005-09184-C02-02, ACOMP06/040, CSD2006-00032). Authors acknowledge valuable comments made by the Editor and the referee.     

Semigroups of Composition Operators in BMOA and the Extension of a Theorem of Sarason

In this paper we deal with the maximal subspace in BMOA where a general semigroup of analytic functions on the unit disk generates a strongly continuous semigroup of composition operators. Particular cases of this question are related to a well-known theorem of Sarason about VMOA. Our results describe analytically that maximal subspace and provide a condition which is sufficient for the maximal subspace to be exactly VMOA. A related necessary condition is also proved in the case when the semigroup has an inner Denjoy-Wolff point. As a byproduct we provide a generalization of the theorem of Sarason. This research has been partially supported by the Ministerio de Educación y Ciencia projects n. MTM2006-14449-C02-01 and MTM2005-08350-C03-03 and by La Consejería de Educación y Ciencia de la Junta de Andalucía.     

Local embeddings of some families of subgroups of finite groups

In this paper we study the influence of the partial cover and avoidance property on the subgroups of some relevant families of subgroups in a finite group.     

Wall Rational Functions and Khrushchev’s Formula for Orthogonal Rational Functions

The Nevalinna–Pick algorithm yields a continued fraction expansion of every Schur function, whose approximants are identified. These approximants are quotients of rational functions which can be understood as the rational analogs of the Wall polynomials. The properties of these Wall rational functions and the corresponding approximants permit us to obtain a Khrushchev’s formula for orthogonal rational functions. An introduction to the convergence of the Wall approximants in the indeterminate case is presented. This work was partially realized during two stays of the second author at the Norwegian University of Science and Technology (NTNU) financed respectively by Secretaría de Estado de Universidades e Investigación from the Ministry of Education and Science of Spain and by the Department of Mathematical Sciences of NTNU. The work of the second author was also partially supported by the Spanish grants from the Ministry of Education and Science, project code MTM2005-08648-C02-01, and the Ministry of Science and Innovation, project code MTM2008-06689-C02-01, and by Project E-64 of Diputación General de Aragón (Spain).     

Evolution families and the Loewner equation II: complex hyperbolic manifolds

We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, providing the solution to a very general Loewner type differential equation on manifolds. M. D. Contreras and S. Díaz-Madrigal were partially supported by the Ministerio de Ciencia e Innovación and the European Union (FEDER), project MTM2006-14449-C02-01, by La Consejería de Educación y Ciencia de la Junta de Andalucía, and by the European Science Foundation Research Networking Programme HCAA.     

Rational quadrature formulae on the unit circle with arbitrary poles

Interpolatory quadrature rules exactly integrating rational functions on the unit circle are considered. The poles are prescribed under the only restriction of not lying on the unit circle. A computable upper bound of the error is obtained which is valid for any choice of poles, arbitrary weight functions and any degree of exactness provided that the integrand is analytic on a neighborhood of the unit circle. A number of numerical examples are given which show the advantages of using such rules as well as the sharpness of the error bound. Also, a comparison is made with other error bounds appearing in the literature. The work of the first author was supported by the Dirección General de Investigación, Ministerio de Educación y Ciencia, under grants MTM2006-13000-C03-02 and MTM2006-07186 and by UPM and Comunidad de Madrid under grant CCG06-UPM/MTM-539. The work of the second author was partially supported by the Dirección General de Investigación, Ministerio de Educación y Ciencia, under grant MTM2005-08571.     

Local Rings of Rings of Quotients

The aim of this paper is to characterize those elements in a semiprime ring R for which taking local rings at elements and rings of quotients are commuting operations. If Q denotes the maximal ring of left quotients of R, then this happens precisely for those elements if R which are von Neumann regular in Q. An intrinsic characterization of such elements is given. We derive as a consequence that the maximal left quotient ring of a prime ring with a nonzero PI-element is primitive and has nonzero socle. If we change Q to the Martindale symmetric ring of quotients, or to the maximal symmetric ring of quotients of R, we obtain similar results: an element a in R is von Neumann regular if and only if the ring of quotients of the local ring of R at a is isomorphic to the local ring of Q at a. Partially supported by the Ministerio de Educación y Ciencia and Fondos Feder, jointly, trough projects MTM2004-03845, MTM2007-61978 and MTM2004-06580-C02-02, MTM2007-60333, by the Junta de Andalucía, FQM-264, FQM336 and FQM02467 and by the Plan de Investigación del Principado de Asturias FICYT-IB05-017.     

Holomorphic Operators Generating Dense Images

The existence of infinite dimensional closed linear spaces of holomorphic functions f on a domain G in the complex plane such that Tf has dense images on certain subsets of G, where T is a continuous linear operator, is analyzed. Necessary and sufficient conditions for T to have the latter property are provided and applied to obtain a number of concrete examples: infinite order differential operators, composition operators and multiplication operators, among others. This work was supported in part by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 and by MEC DGES Grants MTM2006-13997-C02-01 and MTM2004-21420-E.     

A maschke type theorem for weak Hopf algebras

In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke＇s Theorem for （H, B）-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.     

Rational Brauer characters

It is known that every finite group of even order has a non-trivial complex irreducible character which is rational valued. We prove the modular version of this result: If p is an odd prime and G is any finite group of even order, then G has a non-trivial irreducible p-Brauer character which is rational valued. The first author is partially supported by the Ministerio de Educación y Ciencia proyecto MTM2004-06067-C02-01, while the second gratefully acknowledges the support of the NSA (grant H98230-04-0066).     

Groups with three real valued irreducible characters

We obtain strong restrictions on the structure of a Sylow 2-subgroup of a group with at most three real valued irreducible characters. This extends results of Iwasaki, who studied groups with at most two real valued irreducible characters. This research was partially supported by the Spanish Ministerio de Educación y Ciencia, MTM2004-06067-C02-01 and MTM2004-04665, and the FEDER. The first author was also supported by the Programa Ramón y Cajal and the Generalitat Valenciana.     

A new numerical quadrature formula on the unit circle

In this paper we study a quadrature formula for Bernstein–Szegő measures on the unit circle with a fixed number of nodes and unlimited exactness. Taking into account that the Bernstein–Szegő measures are very suitable for approximating an important class of measures we also present a quadrature formula for this type of measures such that the error can be controlled with a well-bounded formula. This work was supported by Ministerio de Educación y Ciencia under grants number MTM2005-01320 (E. B. and A. C.) and MTM2006-13000-C03-02 (F. M.).     

Numerical Properties of Shifted Tridiagonal LU Factorizations

In this paper, we consider shifted tridiagonal matrices. We prove that the standard algorithm to compute the LU factorization in this situation is mixed forward-backward stable and, therefore, componentwise forward stable. Moreover, we give a formula to compute the corresponding condition number in O(n) flops. This research has been partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain through grants BFM2003-06335-C03-02 and MTM2006-06671 as well as by the Postdoctoral Fellowship EX2004-0658 provided by Ministerio de Educación y Ciencia of Spain.     

On Birkhoff integrability for scalar functions and vector measures

The Bartle–Dunford–Schwartz integral for scalar functions with respect to vector measures is characterized by means of Riemann-type sums based on partitions of the domain into countably many measurable sets. In this setting, two natural notions of integrability (Birkhoff integrability and Kolmogoroff integrability) turn out to be equivalent to Bartle–Dunford–Schwartz integrability. A. Fernández, F. Mayoral and F. Naranjo were supported by MEC and FEDER (project MTM2006–11690–C02–02) and La Junta de Andalucía. J. Rodríguez was supported by MEC and FEDER (project MTM2005-08379), Fundación Séneca (project 00690/PI/04) and the Juan de la Cierva Programme (MEC and FSE).     

A core-allocation family for generalized holding cost games

Inventory situations, introduced in Meca et al. (Eur J Oper Res 156: 127–139, 2004), study how a collective of firms can minimize its joint inventory cost by means of co-operation. Depending on the information revealed by the individual firms, they analyze two related cooperative TU games: inventory cost games and holding cost games, and focus on proportional division mechanisms to share the joint cost. In this paper we introduce a new class of inventory games: generalized holding cost games, which extends the class of holding cost games. It turns out that generalized holding cost games are totally balanced.We then focus on the study of a core-allocation family which is called N-rational solution family.It is proved that a particular relation of inclusion exists between the former and the core. In addition, an N-rational solution called minimum square proportional ruleis studied. This work was partially supported by the Spanish Ministry of Education and Science, and the Generalitat Valenciana (grants MTM2005-09184-C02-02, CSD2006-00032, ACOMP06/040). The author thanks Javier Toledo, Josefa Cá novas, and two anonymous referees for helpful comments.     

The extended Freudenthal Magic Square and Jordan algebras

The Lie superalgebras in the extended Freudenthal Magic Square in characteristic 3 are shown to be related to some known simple Lie superalgebras, specific to this characteristic, constructed in terms of orthogonal and symplectic triple systems, which are defined in terms of central simple degree three Jordan algebras. I. Cunha was supported by CMUC, Department of Mathematics, University of Coimbra. A. Elduque was supported by the Spanish Ministerio de Educación y Ciencia and FEDER (MTM 2004-081159-C04-02) and by the Diputación General de Aragón (Grupo de Investigación de álgebra).     

Asymptotics and Zeros of Sobolev Orthogonal Polynomials on Unbounded Supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we focus on the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some directions for future research are formulated.Research of Juan José Moreno Balcázar was partially supported by Ministerio de Educación y Ciencia of Spain under grant MTM2005-08648-C02-01 and Junta de Andalucía (FQM 229 and FQM 481).     

The isodiametric problem for lattice-point-free convex sets

The isodiametric problem in the Euclidean plane is solved for lattice-point-free convex sets: we characterize the planar convex sets containing no points of the rectangular lattice in their interior, which have maximum area, for each given value of the diameter. Then we use this result for giving also an answer to the isodiametric problem in the case of an arbitrary lattice. The first author is supported by Dirección General de Investigación (MEC) MTM2004-04934-C04-02 and by Fundación Séneca (C.A.R.M.) 00625/PI/04.