Linear Problems and Linear Algorithms

Using predicate logic, the concept of a linear problem is formalized. The class of linear problems is huge, diverse, complex, and important. Linear and randomized linear algorithms are formalized. For each linear problem, a linear algorithm is constructed that solves the problem and a randomized linear algorithm is constructed that completely solves it, that is, for any data of the problem, the output set of the randomized linear algorithm is identical to the solution set of the problem. We obtain a single machine, referred to as the Universal (Randomized) Linear Machine, which (completely) solves every instance of every linear problem. Conversely, for each randomized linear algorithm, a linear problem is constructed that the algorithm completely solves. These constructions establish a one-to-one and onto correspondence from equivalence classes of linear problems to equivalence classes of randomized linear algorithms.Our construction of (randomized) linear algorithms to (completely) solve linear problems as well as the algorithms themselves are based on Fourier Elimination and have superexponential complexity. However, there is no evidence that the inefficiency of our methods is unavoidable relative to the difficulty of the problem.     

数据与技术驱动下的人类活动对生态系统的影响及评价研究——“人类活动的数量化表征与生态效应”专刊序言

本期《科研信息化技术与应用》的“人类活动的数量化表征与生态效应”专刊刊登了 11 篇文章,涉及了不同的主题,其中综述性论文 2 篇,研究性论文 9 篇。综述文章分别对城市研究中多源地理大数据的应用和大数据在生态环境监测评价中的应用进行了总结和热点论述。研究性论文方向之一是针对人类活动的数量化表达开展分析,主要是利用灯光数据刻画建设用地的扩展、卫星数据提取干扰特征、无人机刻画公路建设与灾害监测方面的应用和通过构建人类活动强度指数分析对自然遗产地的影响。其二是生态评价和管理信息化方面的研究,主要包括自然保护区与湿地公园的信息化数据库的构建,可以体现人类活动与景观服务的数据化框架;河岸带缓冲区的地理信息图谱方法,可以较好地反应生态空间格局与土壤侵蚀之间的关系,基于 MODIS 影像和模型分析的方法能够揭示生物多样性的空间分布,用于生态保护红线的划定;城市遥感地表能量的反演与定量分级,也能很好地揭示城市开敞空间的特征与影响,为城市规划提供科学依据。     

A Tale of Two More Metaphors: Storylines About Mathematics Education in Canadian National Media

In this companion piece to the article “A Tale of Two Metaphors: Storylines About Mathematics Education in Canadian National Media” (this issue), we further explore constructed meanings through the use of positioning theory. In our examination of 71 articles in the two Canadian national newspapers (The Globe and Mail and The National Post), we focus primarily on communication acts and further our investigation into storylines and positionings concerned with mathematics education. Elaborating on aspects of two more metaphors, those of war and competition, we highlight the production of dichotomies and the shared aspect of taking sides. An investigation of the ramifications and effects that are brought to the fore in the articles we examined involves two general themes: the purpose of education and the point of mathematics education itself. We draw on David Labaree's framework identifying social efficiency and social mobility as different patterns of educational goals and highlight its parallels with the storylines in the articles we examined. The messages of the storylines feed the continued production of culturally shared narratives surrounding the purposes of mathematics education and education in general.     

Introduction: New approaches to linear programming

This issue ofAlgorithmica present papers on various aspects of nonlinear methods for solving linear programming problems, inspired by the work of Karmarkar. This introduction describes some of these aspects and briefly mentions other recent developments in the field. A bibliography of recent articles is included.     

Introduction: New approaches to linear programming

This issue ofAlgorithmica present papers on various aspects of nonlinear methods for solving linear programming problems, inspired by the work of Karmarkar. This introduction describes some of these aspects and briefly mentions other recent developments in the field. A bibliography of recent articles is included.     

布尔函数线性结构分析及构造

通过对部分Bent函数中线性空间进行研究, 定量地刻画出线性空间对相关免疫阶、扩散次数和代数次数的影响; 利用Maiorana-McFarland方法构造出一类高非线性度的平衡相关免疫函数, 证明了构造出的函数不含线性结构。     

Understanding and facilitating the browsing of electronic text

Browsing tends to be used in two distinctive ways, alternatively associated with the goal of the activity and with the method by which the goal is achieved. In this study, the definition of browsing combines aspects of both concepts to define browsing as an activity in which one gathers information while scanning an information space without an explicit purpose. The objective of this research was to examine how browsers interact with their browsing environment while manipulating two types of interface tools constructed from the content.Forty-seven adults (24 males) performed the two types of tasks (one with no purpose and the second, a control, purposeful) in four sessions over a period of four weeks. Participants scanned and/or searched the textual content of current issue plus three months of back issues of the Halifax Chronicle Herald/Mail Star using a system designed specifically for this research. At any one time only one of each type of tool was available.Those with no assigned goal examined significantly more articles and explored more menu options. They made quick decisions about which articles to examine, spending twice as much time reading the content. They tended not to explore the newspaper to a great extent, examining only 24% of the articles in a single issue. About three-quarters of what they examined was new information on topics that they had not known about before being exposed to the paper. The type of menu had no impact on performance, but differences were discovered between the two items-to-browse tools. Those with no goal selected more articles from the Suggestions and found more interesting articles when the Suggestions were available.     

The method of piecewise constant control of the solidification temperature field

In this paper, a boundary control problem for the solidification temperature field is discussed. The problem is modified into one consisting of the minimization of a linear form over a set of positive measures satisfying linear constraints; the minimization in the new problem is global and can be approximated by a finite-dimensional linear programming problem. A nearly optimal control is constructed. An example is given to illustrate the procedure.     

Discrete gradient methods and linear projection methods for preserving a conserved quantity of stochastic differential equations

Numerical methods preserving a conserved quantity for stochastic differential equations are considered. A class of discrete gradient methods based on the skew-gradient form is constructed, and the sufficient condition of convergence order 1 in the mean-square sense is given. Then a class of linear projection methods is constructed. The relationship of the two classes of methods for preserving a conserved quantity is proved, which is, the constructed linear projection methods can be considered as a subset of the constructed discrete gradient methods. Numerical experiments verify our theory and show the efficiency of proposed numerical methods.     

Interval observers for discrete‐time systems

Interval observers are constructed for discrete‐time systems. First, time‐invariant interval observers are proposed for a family of nonlinear systems. Second, it is shown that, for any time‐invariant exponentially stable discrete‐time linear system with additive disturbances, time‐varying exponentially stable discrete‐time interval observers can be constructed. The latter result relies on the design of time‐varying changes of coordinates, which transform a linear system into a nonnegative one. Copyright © 2013 John Wiley & Sons, Ltd.     

TREATISE ON BASIC PHILOSOPHY,VOLUME 4, ONTOLOGY II: A WORLD OF SYSTEMS,Mario Bunge,D. Reidel Publishing Company,Boston, 1979. 291 pp.

Abstract

This is the third and last part of a series of articles concerned with the study of fractal relaxation systems in the linear range. The article focuses on the discussion of the self-similar and affine features of fractal relaxation systems in the linear range. The singularity structure is shown to be scale invariant, hence it can be reconstructed by applying a given generator, which consists of a simple recursive rule, to an initiator. The related concepts of view scale and structure scale are introduced to investigate the invariants of the singularity structure both in the frequency and relaxation domains.     

Two classes of passive time-varying well-posed linear systems

We investigate two classes of time-varying well-posed linear systems. Starting from a time-invariant scattering-passive system, each of the time-varying systems is constructed by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of linear systems are motivated by physical examples such as the electromagnetic field around a moving object. To prove the well-posedness of these systems, we use the Lax–Phillips semigroup induced by a well-posed linear system, as in scattering theory.     

New Minimum Distance Bounds for Linear Codes over GF(9)

Thirty-one new linear codes over GF(9) are constructed, and the nonexistence of thirty codes is proved.     

一类完全非线性S-盒的构造

完全非线性S-盒在对称密码中有着重要的运用。给出有限域上完全非线性S-盒的一种构造方法。与在向量空间上构造的方法比,有限域上置换多项式的代数次数等性质更容易研究。该方法可以构造多类完全非线性S-盒,例如,通过选择幂函数形式的置换α^x,得到Satoh等人构造的S-盒;通过选取指数形式的置换x^d,所得完全非线性S-盒的分量函数的任意非零线性组合的代数次数达到最高。     

Extended Gram-type determinant solutions to the Kadomtsev–Petviashvili equation

In this paper, we would give a broad set of sufficient conditions of systems of linear partial differential equations which guarantee that the Grammian determinant solves the KP (Kadomtsev–Petviashvili) equation in the bilinear form. A systematic analysis of linear partial differential equations is made for solving the resultant linear systems. A special method is constructed to solve the representative systems.     

Linear estimator stabilization of nonlinear sampled-data systems

It has been shown that the state of a linear system can be constructed from observations of its inputs and outputs. The observer which performs the construction is itself a linear system with time constants which may be chosen by the designer. This linear asymptotic estimator has been used previously to stabilize certain types of contimuous nonlinear systems. In this paper, a linear sampled-data estimator is developed. This estimator is used first to stabilize a linear sampled-data system and then it is used to stabilize a class of nonlinear sampled-data systems by the choice of the estimator's time constants and the feedback gain. Typical example applications are analyzed to illustrate the theoretical investigations.     

Meaning of state-space representation and its relation to canonical form Part 2. Controllability and constructibility

State space is one of the key concepts of systems theory. In the previous paper (Nakano et al. 1987) a system-theoretic framework about the choice of a state space was developed and the canonical forms of linear control theory were interpreted. Four realizations of a single-input and single-output discrete basic linear system were constructed. The isomorphism between the realizations and the universal state space representation shows systemic meanings of the state space. In this paper, using the same approach, two other realizations—a controllability realization and a constructibility realization—are constructed. By the matrix representations of these realizations the meanings of the controllability and constructibility canonical forms are shown in relation to the universal state-space representation.     

On the Stability of Switched Positive Linear Systems

It was recently conjectured that the Hurwitz stability of the convex hull of a set of Metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching. In this note, we show that (1) this conjecture is true for systems constructed from a pair of second-order Metzler matrices; (2) the conjecture is true for systems constructed from an arbitrary finite number of second-order Metzler matrices; and (3) the conjecture is in general false for higher order systems. The implications of our results, both for the design of switched positive linear systems, and for research directions that arise as a result of our work, are discussed toward the end of the note.     

连铸方坯的二冷水控制问题

对连铸过程的二冷水控制问题进行了讨论;将二维凝固温度场的边界控制问题,用线性化方法将原问题等价地转化为在几个Ｒａｎｄｏｎ测试空间求最优测度的有限维线性优化问题,从而得到全局最优控制律。数值试验显示此方法是有效的。     

Optimal distributed Kalman filtering fusion for a linear dynamic system with cross-correlated noises

In this article, we study the distributed Kalman filtering fusion problem for a linear dynamic system with multiple sensors and cross-correlated noises. For the assumed linear dynamic system, based on the newly constructed measurements whose measurement noises are uncorrelated, we derive a distributed Kalman filtering fusion algorithm without feedback, and prove that it is an optimal distributed Kalman filtering fusion algorithm. Then, for the same linear dynamic system, also based on the newly constructed measurements, a distributed Kalman filtering fusion algorithm with feedback is proposed. A rigorous performance analysis is dedicated to the distributed fusion algorithm with feedback, which shows that the distributed fusion algorithm with feedback is also an optimal distributed Kalman filtering fusion algorithm; the P matrices are still the estimate error covariance matrices for local filters; the feedback does reduce the estimate error covariance of each local filter. Simulation results are provided to demonstrate the validity of the newly proposed fusion algorithms and the performance analysis.