A New Thermodynamic Calculation Method for Binary Alloys: Part I: Statistical Calculation of Excess Functions

The improved form of calculation formula for the activities of the components in binary liquids and solid alloys has been derived based on the free volume theory considering excess entropy and Miedema's model for calculating the formation heat of binary alloys. A calculation method of excess thermodynamic functions for binary alloys, the formulas of integral molar excess properties and partial molar excess properties for solid ordered or disordered binary alloys have been developed. The calculated results are in good agreement with the experimental values.

EXCESS FUNCTIONS OF RAYS ON COMPLETE NONCOMPACT MANIFOLDS

This paper gives an estimate of excess functions of rays on complete non-compact manifolds. By using this estimation, the authors can get the results in [3] as corollaries, which asserts that a complete manifold is diffeomorphic to Rn under some curvature and pinching conditions. At last, they obtain a refinement of them with extra Ricci condition.

Small Excess and the Topology of Open Manifolds with Ricci Curvature Negatively Lower Bounded

In this paper, we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry. We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius, which improves some results in [4].

Complete Open Manifolds with Nonnegative Ricci Curvature

In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain distance functions satisfy a reasonable condition.

Open Manifolds with Nonnegative Ricci Curvature and Large Volume Growth

in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1）/k＋1（1-α/2）}≤for some COllstant ε〉0 We also prove that a conlplete Riemannian manifold with nonnegative kth-Ricci curvature and undler some pinching conditions is diffeomorphic to R^n.

ON THE FUNDAMENTAL GROUP OF OPEN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE

The authors establish some uniform estimates for the distance to halfway points of minimalgeodesics in terms of the distantce to end points on some types of Riemannian manifolds, andthen prove some theorems about the finite generation of fundamental group of Riemannianmanifold with nonnegative Ricci curvature, which support the famous Milnor conjecture.

Characterizations and dynamic results for consistent indexes under weighted consideration

In real-world management systems,agents might represent constituencies of different sizes;agents might have different bargaining abilities.It is reasonable that weights are assigned to agents and any utility should be divided according to these weights.On the other hand,agents might take different activity levels to participate;agents might represent administrative areas of different scales.Therefore,we introduce two indexes to investigate the distribution mechanism by applying the maximal-utilities among activity level vectors and the weights simultaneously.In order to present the rationality for these weighted indexes,we adopt extended reductions to provide several characterisations.Based on these extended reductions,we also introduce two dynamic processes to illustrate that these weighted indexes could be reached by agents who start from an arbitrary efficient payoff vector and make successive adjustments.By focusing on a different viewpoint,we apply excess functions to propose alternative formulations and related dynamic results for these weighted indexes.

The normalizations and related dynamic processes for two power indexes

Here,we introduce the normalisations for the marginal index and the Banzhaf–Owen index,respectively.We show that there exists reduced games that could be adopted to characterise these two normalisations.Further,alternative formulations are also proposed by applying excess functions.Based on reduced games and excess functions,we provide different dynamic processes for these two normalisations.

Axiomatisations, alternative formulation anddynamic processes for the maximal self-consistentvalue under multicriteria decision situations

By considering multicriteria decision situations, we adopt excess functions to introduce alternativeformulation and related dynamic processes for the maximal self-consistent value. In orderto present the rationality, we provide several equivalent relations to characterise the maximalself-consistent value.