The Limits of Horn Logic Programs

Given a sequence $\{\Pi_n\}$ of Horn logic programs, the limit $\Pi$ of $\{\Pi_n\}$ is the set of the clauses such that every clause in $\Pi$ belongs to almost every $\Pi_n$ and every clause in infinitely many $\Pi_n$'s belongs to $\Pi$ also. The limit program $\Pi$ is still Horn but may be infinite. In this paper, we consider if the least Herbrand model of the limit of a given Horn logic program sequence $\{\Pi_n\}$ equals the limit of the least Herbrand models of each logic program $\Pi_n$. It is proved that this property is not true in general but holds if Horn logic programs satisfy an assumption which can be syntactically checked and be satisfied by a class of Horn logic programs. Thus, under this assumption we can approach the least Herbrand model of the limit $\Pi$ by the sequence of the least Herbrand models of each finite program $\Pi_n$. We also prove that if a finite Horn logic program satisfies this assumption, then the least Herbrand model of this program is recursive. Finally, by use of the concept of stability from dynamical systems, we prove that this assumption is exactly a sufficient condition to guarantee the stability of fixed points for Horn logic programs.Comment: 11 pages, added new results. Welcome any comments to [email protected]

The chinese financial system at the Dawn of the 21st century: An Overview

Based on a systematic review and summarization of China’s 30 years of financial reform and development, this paper comprehensively analyzes the past, present and future development of China’s financial system and also presents the mechanism for China’s financial development from the view of political economics. Generally, the Chinese financial system is bank-oriented. The property rights structure, led by state-owned banks, is the prominent feature of the Chinese banking system. Equity, bond, money, currency and real estate markets have been developing rapidly; however, the development rate of these markets varies, and institutional construction generally falls behind the market development. China’s financial decision-making authority belongs to the State Council, and the financial supervision system adopts the mode of “separate regulation.” China’s state-driven, progressive financial reforms have promoted the formation of the government-led financial structure, which is composed of three parts: first, monetary policy, balancing both inflation control and economic growth; second, bank credit expansion under the implicit guarantee of the state; and third, the adjustable pegged exchange rate system based on capital controls. The next phase of financial reform in China will mainly focus on the following four key goals: first, to further improve the corporate governance and the mixed operation of financial institutions; second, to construct the institution of a financial market system and improve the effectiveness of the financial markets; third, to re-integrate regulatory resources, combine macro- and micro-prudent views, and establish a comprehensive framework for financial stability; fourth, to promote the liberalization of interest rates, marketization of the exchange rate and the opening of capital accounts based on a progressive approach and to improve the openness of the financial system based on macroeconomic stability.China, Financial System, Bank-oriented, Political Economics

O(αsv2)O(\alpha_s v^2) Corrections to Hadronic and Electromagnetic Decays of 1S0^1S_0 Heavy Quarkonium

We study $O(\alpha_sv^2)$ corrections to decays of $^1S_0$ heavy quarkonium into light hadrons and two photons within the framework of nonrelativistic QCD, and find these $O(\alpha_sv^2)$ corrections to have significant contributions especially for the decay into light hadrons. With these new results, experimental measurements of the hadronic width and the $\gamma\gamma$ width of $\eta_c$ can be described more consistently. By fitting experimental data, we find the long-distance matrix elements of $\eta_c$ to be $|\mathcal{R}_{\eta_c}(0)|^2=0.834^{+0.281}_{-0.197}\ \textrm{GeV}^3$ and $< \bm{v}^2 >_{\eta_c}=0.232^{+0.121}_{-0.098}$. Moreover, $\eta_c(2S)$ is also discussed and the $\gamma\gamma$ decay width is predicted to be $3.34^{+2.06}_{-2.10}\ \textrm{KeV}$.Comment: Version published in PRD, 22 pages, 7 figures, references adde

Dynamic Pricing Problems Arising in the Adoption of Renewable Energy

There are two problems at the interface of electrical power and economics that are examined in this thesis. The first problem addresses the issue of optimally operating electric vehicle (EV) charging stations, where price as well as scheduling of purchasing, storing, and charging play key roles. The second problem addresses the challenge faced by electric power system operators who have to balance power generation and demand at all times, and are faced with the task of maximizing the social welfare of all affected entities comprised of producers, consumers and prosumers (e.g., homes with solar panels who may be producers at some times and consumers at other times). For the first problem, we have developed a layered decomposition approach that permits a holistic solution to solving the scheduling, storage and pricing problems of charging stations. The key idea is to decompose problems by time-scale. For the second problem, we have shown that for the special case of LQG agents, by careful construction of a sequence of layered VCG payments over time, the intertemporal effect of current bids on future payoffs can be decoupled, and truth-telling of dynamic states is guaranteed if system parameters are known and agents are rational. We have also shown that a modification of the VCG payments, called scaled-VCG payments, achieves Budget Balance and Individual Rationality for a range of scaling, under a certain identified Market Power Balance condition