A set of axioms for a value for partition function games

Myerson (1977) derived an efficient value for games in partition function form. In this paper, we present a set of axioms which characterize a different efficient value for such games. This latter value assigns value 0 to dummies and assigns nonnegative values to players in monotone simple games.     

When Ramification points meet

Summary This paper contains three applications of the technique of limit series (our [1986]) to the theory of ramification of linear series on smooth curves, and curves of compact type, overC.Let {L _t t|<}, be a family of linear series on a smooth family of smooth curves {C _t }, and letp ₁(t),p ₂(t)C _t be sections of the family which coincide (only) att=0. Setp=p ₁())=p ₂(0)C ₀.We first give a condition related to the Schubert calculus which must be satisfied by the ramification series and the . We then take up the converse problem: In what ways can a given ramification point arise as a limit? We show that if the ramification point isdimensionally proper in the sense of our [1986], then families of every kind allowed by the Schubert calculus condition can actually be constructed. Finally, we prove that dimensional propriety is in a strong sense an open condition, so that ramification points constructed as above are again dimensionally proper.In the body of the paper we work not with pairs of points, as above, but with arbitrary finite collections of points approaching (possibly) several points of the limit curve. Further, by their nature, the results are valid for families of curves of compact type.     

Template-directed self-assembly of 10-microm-sized hexagonal plates

This article presents a strategy for the fabrication of ordered microstructures using concepts of design inspired by molecular self-assembly and template-directed synthesis. The self-assembling components are 4-microm-thick hexagonal metal plates having sides 10 microm in length ("hexagons"), and each template consists of a 4-microm-thick circular metal plate surrounding a central cavity, the perimeter of which is complementary in shape to the external edges of a two-dimensional, close-packed array of hexagons. The hexagons and templates (collectively, "pieces") were fabricated via standard procedures and patterned into hydrophobic and hydrophilic regions using self-assembled monolayers (SAMs). Templated self-assembly occurs in water through capillary interactions between thin films of a nonpolar liquid adhesive coating the hydrophobic faces of the pieces. The hexagons tile the cavities enclosed by the templates, and the boundaries of the cavities determine the sizes and shapes of the assemblies. Curing the adhesive with ultraviolet light furnishes mechanically stable arrays having well-defined morphologies. By allowing control over the structures of the resulting aggregates, this work represents a step toward the development of practical methods for microfabrication based on self-assembly.     

Prediction and realisation of high mobility and degenerate p-type conductivity in CaCuP thin films

Phosphides are interesting candidates for hole transport materials and p-type transparent conducting applications, capable of achieving greater valence band dispersion than their oxide counterparts due to the higher lying energy and increased size of the P 3p orbital. After computational identification of the indirect-gap semiconductor CaCuP as a promising candidate, we now report reactive sputter deposition of phase-pure p-type CaCuP thin films. Their intrinsic hole concentration and hole mobility exceed 1 × 10²⁰ cm⁻³ and 35 cm² V⁻¹ s⁻¹ at room temperature, respectively. Transport calculations indicate potential for even higher mobilities. Copper vacancies are identified as the main source of conductivity, displaying markedly different behaviour compared to typical p-type transparent conductors, leading to improved electronic properties. The optical transparency of CaCuP films is lower than expected from first principles calculations of phonon-mediated indirect transitions. This discrepancy could be partly attributed to crystalline imperfections within the films, increasing the strength of indirect transitions. We determine the transparent conductor figure of merit of CaCuP films as a function of composition, revealing links between stoichiometry, crystalline quality, and opto-electronic properties. These findings provide a promising initial assessment of the viability of CaCuP as a p-type transparent contact.

We synthesize air-stable, p-type CaCuP thin films with high hole concentration and high hole mobility as potential p-type transparent conductors. We study their optoelectronic properties in detail by advanced experimental and computational methods.     

Elements of the Lagrangian Whitney trick

We investigate the possibility of a Lagrangian Whitney trick, a process to remove a pair of intersection points of a self-transverse Lagrangian immersion by a homotopy through Lagrangian immersions. There is a model for which a Lagrangian Whitney trick with compact support works assuming the model satisfies an area-capacity condition. Reduction of more general cases to the model, not necessarily fulfilling the area-capacity requirement, is possible if the given pair of double points admits a suitable symplectic disc and a certain Maslov-Viterbo index is 1. We look into an example to see the actualities of the Maslov-Viterbo index and the area-capacity conditions. The authors would like to thank the anonymous referee whose suggestions improved remarkably the exposition of the paper. This work was supported by the grant no.R01-2000-000-00004-0 from Korea Science & Engineering Foundation.     

Relationship between tetrahedron shape measures

Tetrahedron shape measures are used for evaluating the quality of tetrahedra in finite element meshes. Three shape measures, theminimum solid angle _min theradius ratio , and themean ratio , are discussed in this paper. A new formula for the computation of a solid angle of tetrahedron is derived. For different shape measures andv (with values 1), we establish a relationship between andv of the form wherec ₀,c ₁,e ₀, ande ₁ are positive constants. This means that if one measure approaches zero for a poorly-shaped tetrahedron, so does the other. Combined with the property that each measure attains a maximum value only for the regular tetrahedron, this means that the shape measures are equivalent.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Corrections to Lee's visibility polygon algorithm

We present a modification and extension of the (linear time) visibility polygon algorithm of Lee. The algorithm computes the visibility polygon of a simple polygon from a viewpoint that is either interior to the polygon, or in its blocked exterior (the cases of viewpoints on the boundary or in the free exterior being simple extensions of the interior case). We show by example that the original algorithm by Lee, and a more complex algorithm by El Gindy and Avis, can fail for polygons that wind sufficiently. We present a second version of the algorithm, which does not extend to the blocked exterior case.This work was partially supported by grants from the Central Research Fund of the University of Alberta and the Natural Sciences and Engineering Research Council of Canada.     

Vibrational spectra and ab initio computations of sarcosinium oxalate monohydrate

Single crystals of sarcosinium oxalate monohydrate (SOM) are grown by the slow-evaporation technique at ambient temperature, and vibrational spectroscopic analysis is carried out using NIR-FT Raman, FT-IR, and SERS spectra. The normal mode frequencies and corresponding vibrational analysis of SOM are examined theoretically using the Gaussian’98 set of quantum chemical codes. The two bands present in the SOM ν C=O region, clearly observed in the Raman spectrum, are assigned to “free” and “bonded” carbonyl groups with the hydrogen atom. Vibrational analysis indicates the presence of C-H—O hydrogen bonding interaction producing a blueshift of the C-H stretching frequency.