Evaluation codes at singular points of algebraic differential equations

We use the special geometry of singular points of algebraic differential equations on the affine plane over finite fields to study the main features and parameters of error correcting codes giving by evaluating functions at sets of singular points. In particular, one gets new methods to construct codes with designed minimum distance. This work was partially supported by MCyT BFM2001-2251.     

A constructive approach to sequential Nash equilibria

We present a Coq-formalized proof that all non-cooperative, sequential games have a Nash equilibrium point. Our proof methodology follows the style advocated by LCF-style theorem provers, i.e., it is based on inductive definitions and is computational in nature. The proof (i) uses simple computational means, only, (ii) basically is by construction, and (iii) reaches a constructively stronger conclusion than informal efforts. We believe the development is a first as far as formalized game theory goes.     

Automated Theorem Proving in Temporal Logic:T-Resolution

This paper presentes a novel resolution method,T-resolution,based on the first order temporal logic.The primary claim of this method is its soundness and completeness.For this purpose,we construct the corresponding semantic trees and extend Herbrand‘s Theorem.     

On the algebraic formulation of certain geometry statements and mechanical geometry theorem proving

In this paper we analyze the algebraic formulations of certain geometry statements appearing in recent literature related to mechanical geometry theorem proving and give several examples to show that one of these formulations can cause serious problems. We clarify a formulation which is essentially due to W. T. Wu and, in our opinion, is the most satisfactory.This author was supported by NSF Grants DCR-8503498 and CCR-8702108.     

Elimination of fictitious penetrating rays from PO and hybridization with AFIM

Physical optics (PO) is an approximation method for high‐frequency scattering and diffraction problems. But PO fields are inaccurate in the shadow region where the source is screened by the scatter. Two key factors of the error for PO are (i) edge diffraction coefficients and (ii) existence of fictitious penetrating rays. The correction with respect to the former has been extensively investigated by many authors using various ray techniques such as GTD, UTD, and UAT. On the other hand, the latter was identified recently by the authors. This paper proposes novel PO‐based calculation procedures termed PO‐AF and PTD‐AF, where PO and Aperture Field Integration Method (AFIM) are merged with the help of special elementary diffraction coefficients. These can uniformly cover the whole angular region and only the error factor (ii) is removed in PO‐AF while both (i) and (ii) are removed in PTD‐AF. The theoretical backgrounds of PO currents are discussed in terms of field equivalence theorem and visualization of EM waves. Next, new methods are proposed and their validity is numerically demonstrated for 2D scattering problems of a strip, a corner reflector, and a cylinder of circular arc. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(2): 1–10, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20037     

随机过程的一个小波表示定理

得到一类随机过程 xt( E|xt|2 <+∞ )的一个小波表示定理     

Three-dimensional stability analysis of the dam foundation at Baise

It is usually difficult to determine the actual safety factors of rock masses in an ordinary two-dimensional stability analysis if the safety factors of the different cross sections in the rock mass vary significantly. In addition to the actual slope, arch dam abutment, and the actual foundation of a high building, another example is that the different cross sections of the foundation in the monolith of a gravity dam vary significantly, just like the condition at the overflow dam in the Baise project. A three-dimensional stability analysis method based on the upper-bound theorem was employed to solve this problem. The parameters used in the analysis were obtained from geomechanics tests, as well as continuity simulations of the randomly distributed joints. Two failure patterns against sliding are analyzed. One pattern is the foundation slide along deep-seated planes which were determined by calculations. The other pattern is the foundation slide along the planes across the bottom of the high steps in the foundation pit. The results indicate that a special overflow dam monolith can be considered to be safe in case of considering the three dimensional effect. However, a key wall with a depth of 5m must be constructed at the upper side of this monolith in order to ensure the safety of the foundation. Translated from Chinese Journal of Rock Mechanics and Engineering, 2006, 25(3): 533–538 [译自: 岩土力学与工程学报]     

Explosive Random‐Coefficient AR(1) Processes and Related Asymptotics for Least‐Squares Estimation

Abstract. Large sample properties of the least‐squares and weighted least‐squares estimates of the autoregressive parameter of the explosive random‐coefficient AR(1) process are discussed. It is shown that, contrary to the standard AR(1) case, the least‐squares estimator is inconsistent whereas the weighted least‐squares estimator is consistent and asymptotically normal even when the error process is not necessarily Gaussian. Conditional asymptotics on the event that a certain limiting random variable is non‐zero is also discussed.     

Stratified institutions and elementary homomorphisms

For conventional logic institutions, when one extends the sentences to contain open sentences, their satisfaction is then parameterized. For instance, in the first-order logic, the satisfaction is parameterized by the valuation of unbound variables, while in modal logics it is further by possible worlds. This paper proposes a uniform treatment of such parameterization of the satisfaction relation within the abstract setting of logics as institutions, by defining the new notion of stratified institutions. In this new framework, the notion of elementary model homomorphisms is defined independently of an internal stratification or elementary diagrams. At this level of abstraction, a general Tarski style study of connectives is developed. This is an abstract unified approach to the usual Boolean connectives, to quantifiers, and to modal connectives. A general theorem subsuming Tarski's elementary chain theorem is then proved for stratified institutions with this new notion of connectives.     

An actor-critic algorithm for constrained Markov decision processes

An actor-critic type reinforcement learning algorithm is proposed and analyzed for constrained controlled Markov decision processes. The analysis uses multiscale stochastic approximation theory and the envelope theorem' of mathematical economics.