How to Make the Generality Problem Work for You

Reliabilist theories of knowledge face the “generality problem”; any token of a belief-forming processes instantiates types of different levels of generality, which can vary in reliability. I argue that we exploit this situation in epistemic evaluation; we appraise beliefs in different ways by adverting to reliability at different levels of generality. We can detect at least two distinct uses of reliability, which underlie different sorts of appraisals of beliefs and believers.     

Young Children Do Not Hold the Classic Earth's Shadow Misconception to Explain Lunar Phases

This research explored young children's early thoughts about natural phenomena and investigated sources of influence toward their knowledge construction. Two Piagetian interviews were conducted with four children. Each child was questioned about two phenomena in particular: (a) the moon and its changing appearance (moon phases) and (b) the formation of shadows. The first Piagetian interview involved a lunar protocol, and the second (given a week later) was a shadow protocol. The external interest of this research study concerns when and why do children develop the commonly held Earth's shadow misconception as the cause of the moon's phases. Findings showed that none of the young children believed that various lunar phases were due to an Earthly shadow cast upon the moon. The shadow interview results revealed that young children had primitive understandings of the shadow concept. In fact, two of the four children indicated that no light source was needed to produce a shadow.     

How and Why to Solve the Operator Equation AX-XB = Y

The entities A, B, X, Y in the title are operators, by whichwe mean either linear transformations on a finite-dimensionalvector space (matrices) or bounded (= continuous) linear transformationson a Banach space. (All scalars will be complex numbers.) Thedefinitions and statements below are valid in both the finite-dimensionaland the infinite-dimensional cases, unless the contrary is stated.1991 Mathematics Subject Classification 15A24, 47A10, 47A62,47B47, 47B49, 65F15, 65F30.     

Concepts and Perceptual Belief: How (Not) to Defend Recognitional Concepts

Recognitional concepts have the following characteristic property: thinkers are disposed to apply them to objects merely on the basis of undergoing certain perceptual experiences. I argue that a prominent strategy for defending the existence of constitutive connections among concepts, which appeals to thinkers’ semantic-cum-conceptual intuitions, cannot be used to defend the existence of recognitional concepts. I then outline and defend an alternative argument for the existence of recognitional concepts, which appeals to certain psychological laws.     

如何不用复数讲解常系数线性微分方程

在高等数学课程中,复指数函数及其导数知识的严格讲解,通常要比微分方程知识的讲解晚很多.这使得微分方程的教学在逻辑上有些不足.用复值函数解的复系数线性组合推导出实值函数解,在教学实践中,学生经常感到迷惑.不以复数的任何知识作为前提,给出了常系数微分方程的一种自然的讲解方法.     

Extremality with respect to the estimates of Dubreil-Campanella: Splitting theorems

Campanella's refinements of Dubreil's theorem are sharp upper and lower bounds, formulated in postulational terms, for the number of forms of any given degree in the standard bases of 2-codimensional perfect homogeneous polynomial ideals. This note considers the implications of upper-bound-extremality. Its principal discovery is that such extremality implies a splitting of the syzygy module of any standard basis of such an ideal into syzygy modules of the standard bases of ‘component’ ideals explicitly describable in terms of the standard basis in question.     

基于PCA-VAR模型的房地产信贷政策调控效应分析

有效的房地产调控,既要实现稳定房价、控制房地产开发投资过快增长等调控目标,同时也不会对宏观经济带来过大的负面影响.在分析各类房地产调控政策传导机制的基础上,通过构建PCA-VAR模型,并综合运用了协整分析、Granger因果检验、方差分解和脉冲效应分析等方法,细致测算了房地产信贷政策对房地产市场和宏观经济的影响,据此为我国实施房地产调控提供政策建议.     

用辗转相除法求循环矩阵的逆矩阵

利用两个多项式的最大公因式的求法,给出了用辗转相除法求循环矩阵的逆矩阵的算法,该方法不需要计算循环矩阵的特征值。     

On Stochastic Mirror-prox Algorithms for Stochastic Cartesian Variational Inequalities: Randomized Block Coordinate and Optimal Averaging Schemes

Motivated by multi-user optimization problems and non-cooperative Nash games in uncertain regimes, we consider stochastic Cartesian variational inequality problems where the set is given as the Cartesian product of a collection of component sets. First, we consider the case where the number of the component sets is large and develop a randomized block stochastic mirror-prox algorithm, where at each iteration only a randomly selected block coordinate of the solution vector is updated through implementing two consecutive projection steps. We show that when the mapping is strictly pseudo-monotone, the algorithm generates a sequence of iterates that converges to the solution of the problem almost surely. When the maps are strongly pseudo-monotone, we prove that the mean-squared error diminishes at the optimal rate. Second, we consider large-scale stochastic optimization problems with convex objectives and develop a new averaging scheme for the randomized block stochastic mirror-prox algorithm. We show that by using a different set of weights than those employed in the classical stochastic mirror-prox methods, the objective values of the averaged sequence converges to the optimal value in the mean sense at an optimal rate. Third, we consider stochastic Cartesian variational inequality problems and develop a stochastic mirror-prox algorithm that employs the new weighted averaging scheme. We show that the expected value of a suitably defined gap function converges to zero at an optimal rate.     

Randomized Algorithms for Robust Stability and Guaranteed Cost Control of Stochastic Jump Parameter Systems with Uncertain Switching Policies

It has been suggested recently that the uncertainty randomization approach may offer numerical advantages when applied to robust control problems. This paper investigates new possibilities which this approach may offer in relation to the robust stability and control of stochastic systems governed by uncertain discrete-state Markov processes.This work was supported by the Australian Research Council.The author thanks Professors R. Tempo and B. Polyak for discussions concerning possible applications of the results of Refs. 9--10. Also, technical discussions with Professor R. Tempo and Dr. Y. Fujisaki during the author visit to IRITI-CNR, Torino, Italy are gratefully acknowledged.     

How to deal with the unbounded in optimization: Theory and algorithms

The aim of this survey is to show how the unbounded arises in optimization problems and how it leads to fundamental notions which are not only useful for proving theoretical results such as convergence of algorithms and the existence of optimal solutions, but also for constructing new methods.     

Adaptive multi-element polynomial chaos with discrete measure: Algorithms and application to SPDEs

We develop a multi-element probabilistic collocation method (ME-PCM) for arbitrary discrete probability measures with finite moments and apply it to solve partial differential equations with random parameters. The method is based on numerical construction of orthogonal polynomial bases in terms of a discrete probability measure. To this end, we compare the accuracy and efficiency of five different constructions. We develop an adaptive procedure for decomposition of the parametric space using the local variance criterion. We then couple the ME-PCM with sparse grids to study the Korteweg–de Vries (KdV) equation subject to random excitation, where the random parameters are associated with either a discrete or a continuous probability measure. Numerical experiments demonstrate that the proposed algorithms lead to high accuracy and efficiency for hybrid (discrete–continuous) random inputs.