基于三角范数的模糊逻辑中的三Ⅰ方法

三I推理方法是一种新的模糊推理方法,通过已有的研究成果表明,在许多方面它优于传统的CRI推理方法,它将成为模糊系统和人工智能的理论和应用研究中一个比较理想的推理机制。最近,国外学者提出了一个新的模糊逻辑形式系统,叫做Monoidal t-norm based logics(简记为MTL),已经证明这个形式系统是所有基于左连续三角范数的模糊逻辑的共同形式化。本文基于这类逻辑将三I推理方法形式化,从而在这些逻辑系统中为三推理方法找到了可靠的逻辑依据。     

Non-commutative Hopf algebra of formal diffeomorphisms

This paper deals with two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the group law being multiplication of series, while the second is the set of formal diffeomorphisms with the group law being a composition of series. The motivation to introduce these Hopf algebras comes from the study of formal series with non-commutative coefficients. Invertible series with non-commutative coefficients still form a group, and we interpret the corresponding new non-commutative Hopf algebra as an alternative to the natural Hopf algebra given by the co-ordinate ring of the group, which has the advantage of being functorial in the algebra of coefficients. For the formal diffeomorphisms with non-commutative coefficients, this interpretation fails, because in this case the composition is not associative anymore. However, we show that for the dual non-commutative algebra there exists a natural co-associative co-product defining a non-commutative Hopf algebra. Moreover, we give an explicit formula for the antipode, which represents a non-commutative version of the Lagrange inversion formula, and we show that its coefficients are related to planar binary trees. Then we extend these results to the semi-direct co-product of the previous Hopf algebras, and to series in several variables. Finally, we show how the non-commutative Hopf algebras of formal series are related to some renormalization Hopf algebras, which are combinatorial Hopf algebras motivated by the renormalization procedure in quantum field theory, and to the renormalization functor given by the double-tensor algebra on a bi-algebra.     

Specification on the interval

We study the consequences of discontinuities on the specification property for interval maps. After giving a necessary and sufficient condition for a piecewise monotonic, piecewise continuous map to have this property, we show that for a large and natural class of families of such maps (including the -transformations), the set of parameters for which the specification property holds, though dense, has zero Lebesgue measure. Thus, regarding the specification property, the general case is at the opposite of the continuous case solved by A.M. Blokh (Russian Math. Surveys 38 (1983), 133-134) (for which we give a proof).

     

Infinitesimal Lifting and Jacobi Criterion for Smoothness on Formal Schemes

This a first step to develop a theory of smooth, étale, and unramified morphisms between Noetherian formal schemes. Our main tool is the complete module of differentials, which is, a coherent sheaf whenever the map of formal schemes is of pseudofinite type. Among our results, we show that these infinitesimal properties of a map of usual schemes carry over into the completion with respect to suitable closed subsets. We characterize unramifiedness by the vanishing of the module of differentials. Also we see that a smooth morphism of Noetherian formal schemes is flat and its module of differentials is locally free. The article closes with a version of Zariski's Jacobian criterion.     

一类具有1:-4共振奇点的复三次Lotka-Volterra系统的可积性条件

对于一类具有1:-4共振奇点的复三次Lotka-Volterra系统,通过前12阶广义奇点量的计算,给出系统可积的充分条件.这些条件通过构造积分因子或形式积分得以证明.     

对比分析两种规范确定的桩基竖向承载力

分析了《建筑地基基础规范》《建筑桩基技术规范》所确定的桩基承载力计算公式和参数影响。通过工程实例的对比分析，得到了两个承载力的差异程度，并对桩基规范的基础设计提出了建议的简化设计方法。     

Sequentially Estimating the Approximate Conditional Mean Using Extreme Learning Machines

This study examined the extreme learning machine (ELM) applied to the Wald test statistic for the model specification of the conditional mean, which we call the WELM testing procedure. The omnibus test statistics available in the literature weakly converge to a Gaussian stochastic process under the null that the model is correct, and this makes their application inconvenient. By contrast, the WELM testing procedure is straightforwardly applicable when detecting model misspecification. We applied the WELM testing procedure to the sequential testing procedure formed by a set of polynomial models and estimate an approximate conditional expectation. We then conducted extensive Monte Carlo experiments to evaluate the performance of the sequential WELM testing procedure and verify that it consistently estimates the most parsimonious conditional mean when the set of polynomial models contains a correctly specified model. Otherwise, it consistently rejects all the models in the set.     

两线阵CCD相机几何指标差异对立体测绘的影响

为了准确、全面地揭示相机几何指标在立体测绘中的误差传播规律,研究了两线阵CCD相机几何指标差异与定位准确度之间的关系.针对两线阵立体测绘特点,分析了影响测绘定位的几何指标差异参量.在前方空间交会地面点计算公式的基础上,推导并建立了两线阵相机定位准确度模型,据此研究了内方位元素标定误差间的几何指标差异对定位准确度的影响规律.结果表明:主点位置x方向误差间的差异对定位准确度影响显著,当其值从1 μm增至2.5 μm时,定位准确度明显下降了60%,焦距f误差间的差异对定位准确度的影响几乎可忽略.本文所建立的模型与相关研究结论对两线阵CCD相机指标的量化与优化设计具有重要指导意义.     

Uniqueness of Gibbs State for Nonideal Gas in ℝ d : The Case of Pair Potentials

We consider a classical gas of particles in ^d interacting via a pair potential. We prove that in a given region of the (, ) plane, where is the inverse temperature, and is the chemical potential, either the Gibbs state is unique or it does not exist. Our method uses a version of the well-known Dobrushin uniqueness theorem adapted for lattice systems with a noncompact spin space and proved by Dobrushin and Pechersky. The advantage of this version is that using it one needs to check Dobrushin's contraction condition not for all boundary configurations, but only for those that have spin values in some compact subset of the spin space.     

Applications of Category Theory to the Area of Algebraic Specification in Computer Science

The theory of algebraic specifications – one of the most important mathematical approaches to the specification of abstract data types and software systems – is reviewed from a mathematical and a computer science point of view. The important role of category theory in this area is discussed and it is shown how the following selected problems are treated using category theory: First, a unified framework for specification logics, second compositional semantics, third partial algebras and their specification, and fourth specifications and models for concurrent systems. For the solution of two of the problems classifying categories are used. They allow to present categories of algebras as functor categories and to derive a number of important properties from well known results for functor categories.