The Two-Dimensional Finite Bin Packing Problem. Part II: New lower and upper bounds

This paper is the second of a two part series and describes new lower and upper bounds for a more general version of the Two-Dimensional Finite Bin Packing Problem (2BP) than the one considered in Part I (see Boschetti and Mingozzi 2002). With each item is associated an input parameter specifying if it has a fixed orientation or it can be rotated by . This problem contains as special cases the oriented and non-oriented 2BP. The new lower bound is based on the one described in Part I for the oriented 2BP. The computational results on the test problems derived from the literature show the effectiveness of the new proposed lower and upper bounds.     

Positive value of information in games

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments à la Blackwell. AMS 2000 Subject Classification:Primary 91A35.The work of Bruno Bassan and Marco Scarsini was partially supported by MIUR-COFIN. The authors express their thanks to Sylvain Sorin for enlightening comments.     

Characterization theorems for the projective space and vector bundle adjunction

 We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction. We use methods and techniques of the so called Mori theory, in particular the study of rational curves on projective manifolds. Received: 16 May 2002 / Revised version: 18 November 2002 Published online: 3 March 2003 Mathematics Subject Classification (2000): 14E30, 14J40, 14J45     

Homotopical algebra in homotopical categories

We develop here a version of abstract homotopical algebra based onhomotopy kernels andcokernels, which are particular homotopy limits and colimits. These notions are introduced in anh-category, a sort of two-dimensional context more general than a 2-category, abstracting thenearly 2-categorical properties of topological spaces, continuous maps and homotopies. A setting which applies also, at different extents, to cubical or simplicial sets, chain complexes, chain algebras, ... and in which homotopical algebra can be established as a two-dimensional enrichment of homological algebra.Actually, a hierarchy of notions ofh-,h1-, ...h4-categories is introduced, through progressive enrichment of thevertical structure of homotopies, so that the strongest notion,h4-category, is a sort of relaxed 2-category. After investigating homotopy pullbacks and homotopical diagrammatical lemmas in these settings, we introduceright semihomotopical categories, ash-categories provided with terminal object and homotopy cokernels (mapping cones), andright homotopical categories, provided also with anh4-structure and verifying second-order regularity properties forh-cokernels.In these frames we study the Puppe sequence of a map, its comparison with the sequence of iterated homotopy cokernels and theh-cogroup structure of the suspension endofunctor. Left (semi-) homotopical categories, based on homotopy kernels, give the fibration sequence of a map and theh-group of loops. Finally, the self-dual notion of homotopical categories is considered, together with their stability properties.Lavoro esequito nell'ambito dei progetti di ricerca del MURST.     

Reactivity of β-aluminas with water

The reactivity with air moisture of finely divided crystals of Na β and Li⁺-containing β-aluminas is analyzed with thermogravimetric and X-ray techniques. For Na β-alumina two distinct water intake processes are evident: 1) a fast one, controlled by the elastic interactions among water molecules near the crystal boundaries; 2) a slow one, driven by water diffusion away from the boundaries. For finely divided crystals of Li β-alumina the two processes cannot be distinguished but the slow one is observable in crystals of macroscopic dimensions. The water intake is generally accompanied by an expansion of the c-axis. However, the relationship between water content and c-parameter is highly non-linear and the c-axis length at room temperature depends upon the thermal history of the sample. Our results confirm previous reports suggesting that β-aluminas absorb about one water molecule per cation of the conducting plane.     

Numerical solution of eigenvalue problems for Hamiltonian systems

This paper discusses the numerical solution of eigenvalue problems for Hamiltonian systems of ordinary differential equations. Two new codes are presented which incorporate the algorithms described here; to the best of the author’s knowledge, these are the first codes capable of solving numerically such general eigenvalue problems. One of these implements a new new method of solving a differential equation whose solution is a unitary matrix. Both codes are fully documented and are written inPfort-verifiedFortran 77, and will be available in netlib/aicm/sl11f and netlib/aicm/sl12f.     

Characterization of a Marshall-Olkin type class of distributions

Summary A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function. Work performed while the authors were members of CNR-GNAFA.     

The conformal Gauss map of submanifolds of the Möbius space

In this paper we study the conformal geometry of immersed submanifolds of the Möbius spaceS ⁿ introducing the conformal Gauss map. In particular we relate its harmonicity to an extended notion of Willmore surface which originated from the work of Bryant. For a more detailed account the reader is referred to the Introduction.(on leave)