Converting triangulations to quadrangulations

We study the problem of converting triangulated domains to quadrangulations, under a variety of constraints. We obtain a variety of characterizations for when a triangulation (of some structure such as a polygon, set of points, line segments or planar subdivision) admits a quadrangulation without the use of Steiner points, or with a bounded number of Steiner points. We also investigate the effect of demanding that the Steiner points be added in the interior or exterior of a triangulated simple polygon and propose efficient algorithms for accomplishing these tasks. For example, we give a linear-time method that quadrangulates a triangulated simple polygon with the minimum number of outer Steiner points required for that triangulation. We show that this minimum can be at most n/3, and that there exist polygons that require this many such Steiner points. We also show that a triangulated simple n-gon may be quadrangulated with at most n/4 Steiner points inside the polygon and at most one outside. This algorithm also allows us to obtain, in linear time, quadrangulations from general triangulated domains (such as triangulations of polygons with holes, a set of points or line segments) with a bounded number of Steiner points.     

Different ways to represent weighted majority games

It is well known that every simple game is the intersection of weighted majority games. the aim of this paper is to gather together various ways of expressing weighted majority games and, for each game of this type, to give the simplest way to define it. Normalized representations, the parameters of a simple game and the characteristic invariants of a complete game merit special attention. Research partially supported by projects PR9509 of the Polytechnic University of Catalonia and PB96-0493 of DGES     

Simple Emission Model of Supersonic Molecular Beam

Recently some modes of supersonic molecular beam injection （SMBI）have been put forward. Among them there are electrostatic “double layer”-shielding, simple collective and optimized numerical models to explain the experiment phenomenon. The penetrated depth A and particle deposition were calculated theoretically. About 1/7 in- cident thermal electron flux was amputated and, A increased seven times. The previous simulation is not enough for the SMBI fueling mechanism research. Hence, further investigations, both in experiment and in theory should be developed. The phenomena of line emission due to supersonic molecular beam （SMB） are of particular importance.     

Quantale的若干新的性质

讨论Quantale的若干性质，给出Prequantale构成Quantale的两个充要条件，论证在严格双侧Quantale上逆序对合对应的惟一性并给出了Quantale是分配格的一个条件。     

The hierarchical and social decision making procedure for bi-objective optimization problems by using the simple majority decision rule

Multi-objective optimization has been successfully applied to problems of industrial design, problems of quality control and production management, and problems of finance. The theme of these applications is how to choose the best solution for the decision makers out of a set of non-inferior solutions to a multi-objective optimization problem. For this purpose, an optimization model with hierarchical structure, whose lower problem is a multi-objective optimization problem and the upper problem is a preference optimization problem on a set of non-inferior solutions, must be constructed. This kind of hierarchical problems have been previously analyzed only with regard to linear programming problems by Benson[6]. In this paper, an algorithm is derived that provides a solution as a social choice, obtained by aggregating plural decision-makers' preferences. In the case of the simple majority rule, the bi-objective problem is transformed into an -parameter choice problem, and the golden section method is applied. The availability of the approach is demonstrated with the means of an illustrative example.Technische Universität BerlinFaculty of Science and Technology, Keio University     

Influence of the ratio copper(II) to ligand concentrations and the nature of entering and leaving ligands on the lability of copper(II) complexes

The influence of the ratio Cu : L on the lability of copper(II) complexes with simple ligands of different thermodynamic stabilities (L=EDTA, NTA, cysteine, proline or glycine) was investigated in the range 4:1–1:3. Chelex-100 and chitin were used parallel and batch wise, to cause the dissociation of the complexes, and the results were compared. A few experiments were also performed with the yeast, Saccharomyces cerevisiae. The effect of the exposure time, between 5 and 30 min, and mass (or number of sites) of the particulate matter (PM), always in large excess, were also studied. For all systems, but Cucysteine with chitin, the lability of CuL showed no marked dependence on the mass of PM: when the mass of PM was duplicated, an increase in lability by ≤ 10% was found. For cysteine and proline with Chelex-100, and cysteine and glycine with chitin, the lability of Cu---L complexes markedly increased with the time of exposure, which indicated that the kinetics of the substitution reactions were relatively slow. These results indicate the role of both the leaving and entering ligands in the kinetics of the ligand substitution reactions. The effect of Cu : L on the complex dissociation was more marked with chitin than with Chelex-100. When the leaving ligand is in excess (Cu : L < 1) the magnitude of that excess did not affect markedly the lability. But, when Cu : L> 1, the lability decreased with the increase of the excess of metal for cysteine or glycine with Chelex-100, and for all ligands in presence of chitin. The heterogenous behaviour of the PM may be partially responsible for these results. A maximum lability was observed for 1:1 ratio, particularly for the complexes that are thermodynamically more stable. In the presence of yeast cells, the tendencies mentioned above were confirmed. The present results reinforce the operational character of the speciation studies based on lability data, and that relationship between lability and bioavailability must be analysed for each individual case and should not be extrapolated to different PM or experimental conditions.     

二次微分简易示波伏安法用于葛根素测定

根据在 0 .1 mol/ L Na OH溶液中 ,葛根素在二次微分简易示波伏安图阴极支-0 .95V ( vs.SCE)产生一灵敏峰的示波特性 ,建立了二次微分简易示波伏安法测定药品中葛根素含量的新方法。线性范围为 2 .5× 1 0 - 6～ 3 .5× 1 0 - 5mol/ L,相关系数为 0 .9985,检出限为 1× 1 0 - 6mol/ L,对 9.0× 1 0 - 6mol/ L葛根素进行 5次测定的RSD为 1 .5%。利用该法测定中药葛根及心可舒片剂中葛根素的回收率分别为 1 0 0 .2 %和 96.9%。     

Molecular iodine-catalyzed one-pot synthesis of 4-substituted-1,4-dihydropyridine derivatives via Hantzsch reaction

A simple, inexpensive and efficient one-pot synthesis of 1,4-dihydropyridine derivatives at room temperature using catalytic amount of iodine were reported with excellent product yields. An easy access to various substituted 1,4-dihydropyridine derivatives quantitatively using commercially available iodine as a catalyst.     

OD-characterization of all simple groups whose orders are less than 108

Let M be a simple group whose order is less than 10⁸. In this paper, we prove that if G is a finite group with the same order and degree pattern as M, then the following statements hold: (a) If M ≠ A ₁₀, U ₄(2), then G ≅ M; (b) If M = A ₁₀, then G ≅ A ₁₀ or J ₂ × ℤ₃; (c) If M = U ₄(2), then G is isomorphic to a 2-Frobenius group or U ₄(2). In particular, all simple groups whose orders are less than 10⁸ but A ₁₀ and U ₄(2) are OD-characterizable. As a consequence of this result, we can give a positive answer to a conjecture put forward by W. J. Shi and J. X. Bi in 1990 [Lecture Notes in Mathematics, Vol. 1456, 171–180].