Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain

This paper addresses the theoretical analysis of a fully discrete scheme for the one-dimensional time-dependent Schrödinger equation on unbounded domain. We first reduce the original problem into an initial-boundary value problem in a bounded domain by introducing a transparent boundary condition, then fully discretize this reduced problem by applying Crank–Nicolson scheme in time and linear or quadratic finite element approximation in space. By a rigorous analysis, this scheme has been proved to be unconditionally stable and convergent, its convergence order has also be obtained. Finally, two numerical examples are performed to show the accuracy of the scheme.     

Natural and artificial weathering characteristics of stabilized acrylic–urethane paints

Depth-profiling by Fourier transform infrared (FTIR) spectroscopy, dynamic mechanical analysis (DMA), microhardness and scanning electron microscopy (SEM) observations have been used to monitor degradation chemistries in two-package acrylic–urethane coatings when exposed to different exposure conditions. Three artificial and three natural weathering protocols (QUV, ASTM D5894, ISO20340, Pipady (south of France), Bandol (south of France) and Kure Beach (USA)) were selected for this study. The same chemical events were found to occur under all conditions, particularly under natural and artificial exposures. Both loss of the amide II band at 1520 cm⁻¹ and carbonyl growth occurred but at relatively low rate owing to the presence of hindered-amine light stabilizers in the film. A less typical loss of urea biuret linkages also occurs during all exposures and results in a change in the balance between urethane and urea links across the depth of the film during weathering. The chemical degradation of the polymer matrix involves the formation of species that are readily ablated from the surface and results in loss of gloss, increase in hardness and a rougher topology. The dramatic loss of gloss observed after Pipady and Bandol exposures show that loss of gloss should not be systematically correlated to the advance in chemical degradation.     

Topological properties of stock market networks: The case of Brazil

This paper investigates the topological properties of the Brazilian stock market networks. We build the minimum spanning tree, which is based on the concept of ultrametricity, using the correlation matrix for a variety of stocks of different sectors. Our results suggest that stocks tend to cluster by sector. We employ a dynamic approach using complex network measures and find that the relative importance of different sectors within the network varies. The financial, energy and material sectors are the most important within the network.     

Strategic bidding in continuous electricity auctions: an application to the Spanish electricity market

In this paper we introduce an asymmetric model of continuous electricity auctions with limited production capacity and bounded supply functions. The strategic bidding is studied with this model by means of an electricity market game. We prove that for every electricity market game with continuous cost functions a mixed-strategy Nash equilibrium always exists. In particular, we focus on the behavior of producers in the Spanish electricity market. We consider a very simple form for the Spanish electricity market: an oligopoly consisting just of independent hydro-electric power production units in a single wet period. We show that a pure-strategy Nash equilibrium for the Spanish electricity market game always exists.     

Bilevel optimization applied to strategic pricing in competitive electricity markets

In this paper, we present a bilevel programming formulation for the problem of strategic bidding under uncertainty in a wholesale energy market (WEM), where the economic remuneration of each generator depends on the ability of its own management to submit price and quantity bids. The leader of the bilevel problem consists of one among a group of competing generators and the follower is the electric system operator. The capability of the agent represented by the leader to affect the market price is considered by the model. We propose two solution approaches for this non-convex problem. The first one is a heuristic procedure whose efficiency is confirmed through comparisons with the optimal solutions for some instances of the problem. These optimal solutions are obtained by the second approach proposed, which consists of a mixed integer reformulation of the bilevel model. The heuristic proposed is also compared to standard solvers for nonlinearly constrained optimization problems. The application of the procedures is illustrated in case studies with configurations derived from the Brazilian power system.     

技术市场聚类和预测

本依据1993～2000年全国及各省、市、自治区技术市场成交额，用聚类分析的方法分析了我国技术市场的发展状况，进而利用最小二乘法建立了我国技术市场的预测模型。实例计算表明模型是有效的。     

On a General Theorem of Set Theory Leading to the Gibbs, Bose-Einstein, and Pareto Distributions as well as to the Zipf-Mandelbrot Law for the Stock Market

The notion of density of a finite set is introduced. We prove a general theorem of set theory which refines the Gibbs, Bose-Einstein, and Pareto distributions as well as the Zipf law.     

The Böhm–Bawerk horse market: a cooperative analysis

Single–valued solutions for the case of two-sided market games without product differentiation, also known as Böhm–Bawerk horse market games, are analyzed. The nucleolus is proved to coincide with the τ value, and is thus the midpoint of the core. The Shapley value is in the core only if the game is a square glove market, and in this case also coincides with the two aforementioned solutions.Institutional support from research grants BEC 2002-00642, FEDER and SGR2001-0029 is gratefully acknowledged     

关于融资收缩现象成因的一个模型解释

本文通过构建一个关于企业融资与经济增长的理论模型对融资收缩形成的内在机理进行了揭示.     

Random marginal and random removal values

We propose two variations of the non-cooperative bargaining model for games in coalitional form, introduced by Hart and Mas-Colell (Econometrica 64:357–380, 1996a). These strategic games implement, in the limit, two new NTU-values: the random marginal and the random removal values. Their main characteristic is that they always select a unique payoff allocation in NTU-games. The random marginal value coincides with the Consistent NTU-value (Maschler and Owen in Int J Game Theory 18:389–407, 1989) for hyperplane games, and with the Shapley value for TU games (Shapley in In: Contributions to the theory of Games II. Princeton University Press, Princeton, pp 307–317, 1953). The random removal value coincides with the solidarity value (Nowak and Radzik in Int J Game Theory 23:43–48, 1994) in TU-games. In large games we show that, in the special class of market games, the random marginal value coincides with the Shapley NTU-value (Shapley in In: La Décision. Editions du CNRS, Paris, 1969), and that the random removal value coincides with the equal split value.