On the monotonicity of (LDL) logic programs with set

LDL is one of the recently proposed logical query languages, which incorporate set, for data and knowledge base systems. Since LDL programs can simulate negation, they are not monotonic in general. On the other hand, there are monotonic LDL programs. This paper addresses the natural question of “When are the generally nonmonotonic LDL programs monotonic?” and investigates related topics such as useful applications for monotonicity. We discuss four kinds of monotonicity, and examine two of them in depth. The first of the two, called “ω-monotonicity”, is shown to be undecidable even when limited to single-stratum programs. The second, called “uniform monotonicity”, is shown to implyω-monotonicity. We characterize the uniform monotonicity of a program (i) by a relationship between its Bancilhon-Khoshafian semantics and its LDL semantics, and (ii) with a useful property called subset completion independence. Characterization (ii) implies that uniformly monotonie programs can be evaluated more efficiently by discarding dominated facts. Finally, we provide some necessary and/or sufficient, syntactic conditions for uniform monotonicity. The conditions pinpoint (a) enumerated set terms, (b) negations of membership and inclusion, and (c) sharing of set terms as the main source for nonuniform monotonicity.     

二型模糊集模糊推理方法的单调性

模糊推理是蓬勃发展中的模糊控制技术的数学核心,二型模糊集的模糊推理是研究二型模糊逻辑系统的基础。各种模糊推理方法都具有单调性,从而导致人们当使用这些模糊推理方法时,应首先判明所讨论问题领域的推理是否具有相应的性质,否则可能导致不恰当的推理结果。     

关于广义椭圆积分的几个性质

揭示了由广义椭圆积分定义的一些函数的单调性,从而获得若干不等式。这些结果有助于对广义Grtzsch环函数和Ramanujan模方程及其解φak(r)、φk(r)的研究,这些函数在拟共形理论、数论、几何学等领域中具有非常广泛的应用;同时,从这些结果中可以得到关于完全椭圆积分的一些新的性质。     

Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic

A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L₃-valued propositional logic, a multisequent is a triple Δ|Θ|Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. Correspondingly there is a sound and complete Gentzen deduction system G for multisequents which is monotonic. Dually, a comultisequent is a triple Δ : Θ : Γ, which is valid if there is an assignment v in which each formula in Δ has truth-value≠t, each formula in Θ has truth-value≠m, and each formula in Γ has truth-value≠f. Correspondingly there is a sound and complete Gentzen deduction system G⁻ for co-multisequents which is nonmonotonic.     

广义Agard偏差函数的不等式

通过对广义Agard偏差函数与一些初等函数组合形式的单调性和凹凸性的研究,获得了广义Agard偏差函数和广义线性偏差函数的最新上下界,从而推广了平面拟共形映射理论中Agard偏差函数与线性偏差函数的一些不等式。     

基于单调邻域粗糙集的特征基因提取

为了避免连续数据离散化处理时造成的信息损失,降低样本属性邻域求解的复杂度,提高特征基因提取的效率。该文在单调度量空间上,提出了一种基于单调邻域粗糙集的特征基因提取方法。并在两个标准的基因表达数据上进行了实验,结果证明该方法是有效可行的。     

Characterizing Strong Stability Preserving Additive Runge-Kutta Methods

Space discretization of some time dependent partial differential equations give rise to ordinary differential equations containing additive terms with different stiffness properties. In these situations, additive Runge-Kutta (additive RK) methods are used. For additive RK methods the curve of absolute monotonicity gives stepsize restrictions for monotonicity. Necessary conditions for nontrivial curves of absolute monotonicity are the nonnegativity of the additive RK coefficients and some inequalities on some incidence matrices. In this paper we characterize strong stability preserving additive Runge-Kutta methods giving some order barriers and structural properties. Research supported by the Ministerio de Educación y Ciencia, Project MTM2005-03894.     

On splitting-based numerical methods for nonlinear models of European options

We present a large class of nonlinear models of European options as parabolic equations with quasi-linear diffusion and fully nonlinear hyperbolic part. The main idea of the operator splitting method (OSM) is to couple known difference schemes for nonlinear hyperbolic equations with other ones for quasi-linear parabolic equations. We use flux limiter techniques, explicit–implicit difference schemes, Richardson extrapolation, etc. Theoretical analysis for illiquid market model is given. The numerical experiments show second-order accuracy for the numerical solution (the price) and Greeks Delta and Gamma, positivity and monotonicity preserving properties of the approximations.     

双并联神经网络在线梯度算法的收敛性

双并联前馈神经网络是一个单层前向网络和一个多层前向网络的并向联接,在实现线性映射的同时也能够反应非线性映射,尤其对于弱非线性问题效果更为明显。在线梯度算法是训练神经网络的一种常见、高效的训练算法。研究了双并联前馈神经网络在线梯度学习算法的确定性和收敛性,证明了误差函数单调性质,给出了双并联前馈神经网络弱（强）收敛性结果,即误差函数的梯度趋于零,权值序列收敛于固定点等结论。     

广义椭圆积分对参数的依赖性

给出了由广义椭圆积分κa(r)和εa(r)定义的某些函数依赖于参数a的分析性质.同时,揭示了广义椭圆积分与完全椭圆积分κ(r)和ε(r)的一些联系.