ON THE SUSTAINABLE GROWTH IN AN ECONOMY WITH PERFECTLY SUBSTITUTABLE EXHAUSTIBLE RESOURCES

Abstract A model of sustainable economic growth in an economy with two types of exhaustible resources is analyzed. The resources are assumed to be perfect substitutes with marginal rate of substitution varying over time. The optimal control framework is used to characterize the optimal paths under the maximin criterion. It is shown that the resource with increasing productivity is not used before the constant productivity resource is depleted. Afterwards the resource with an increasing productivity is asymptotically depleted as well. The results are based on an assumption that transversality conditions hold. A new sufficient condition for the transversality conditions is derived. Finally, an analogue of Hartwick’s rule for this non‐autonomous case is established.     

Modulation of curved graphene nanoribbon optical absorption spectra by an electric field

The optical absorption spectra of curved graphene nanoribbons exhibit rich dependence on the magnitude and direction of the electric field. The wave functions have spatial symmetry originating from the equivalence of the two sublattices. There exists an optical selection rule caused by the special structure of the Hamiltonian matrix and the wave function spatial symmetry. An electric field may or may not disrupt such spatial symmetry depending on its direction and magnitude. Therefore, the optical selection rule can be controlled. In addition, the two-fold degeneracy of the optical absorption peaks is lifted by the electric field, and the variations of the absorption peak energies with the field are explored.     

The role of problem representation and feature knowledge in algebraic equation-solving

Domain experts have two major advantages over novices with regard to problem solving: experts more accurately encode deep problem features (feature encoding) and demonstrate better conceptual understanding of critical problem features (feature knowledge). In the current study, we explore the relative contributions of encoding and knowledge of problem features (e.g., negative signs, the equals sign, variables) when beginning algebra students solve simple algebraic equations. Thirty-two students completed problems designed to measure feature encoding, feature knowledge and equation solving. Results indicate that though both feature encoding and feature knowledge were correlated with equation-solving success, only feature knowledge independently predicted success. These results have implications for the design of instruction in algebra, and suggest that helping students to develop feature knowledge within a meaningful conceptual context may improve both encoding and problem-solving performance.     

Computation of the random arrival rule for bankruptcy problems

Bankruptcy problems are a fundamental class of fair division problems in microeconomics. Among the various solution concepts proposed for the problem, the random arrival rule is one of the most prominent. In this paper, we conduct a computational analysis of the rule. It is shown that the allocation returned by the rule is #P-complete to compute. The general complexity result is complemented by a pseudo-polynomial-time dynamic programming algorithm for the random arrival rule.     

Regularized Versions of Continuous Newton's Method and Continuous Modified Newton's Method Under General Source Conditions

Regularized versions of continuous analogues of Newton's method and modified Newton's method for obtaining approximate solutions to a nonlinear ill-posed operator equation of the form F(u) = f, where F is a monotone operator defined from a Hilbert space H into itself, have been studied in the literature. For such methods, error estimates are available only under Hölder-type source conditions on the solution. In this paper, presenting the background materials systematically, we derive error estimates under a general source condition. For the special case of the regularized modified Newton's method under a Hölder-type source condition, we also carry out error analysis by replacing the monotonicity of F by a weaker assumption. This analysis facilitates inclusion of certain examples of parameter identification problems, which was not possible otherwise. Moreover, an a priori stopping rule is considered when we have a noisy data f _δ instead of f. This rule yields not only convergence of the regularized approximations to the exact solution as the noise level δ tends to zero but also provides convergence rates that are optimal under the source conditions considered.     

网络用法挖掘及其应用

介绍了数据挖掘、网络挖掘和网络用法挖掘技术的理论发展及其它们在实际中的应用情况,并在挖掘算法的改善提高过程中进行了探索性的研究.为了有效地帮助Web站点管理员管理Web站点,帮助商家调整整个市场策略,提出了一种在给定的Web日志中利用事务数据库中的挖掘序列模式的方法来发现所有的大访问路径的算法.结果证明该算法是行之有效的.