Application of the recursion method in the numerical solution of multidiagonal nonlinear systems

The recursion method of solving banded matrix equations is presented. End conditions are shown to be automatically incorporated in the recursion formulae thus simplifying computer programming. Application of the method to the numerical solution of the nonlinear liquid jet equations by finite differences is given as an example.     

A symbolic algorithm for computing recursion operators of nonlinear partial differential equations

A recursion operator is an integro-differential operator which maps a generalized symmetry of a nonlinear partial differential equation (PDE) to a new symmetry. Therefore, the existence of a recursion operator guarantees that the PDE has infinitely many higher-order symmetries, which is a key feature of complete integrability. Completely integrable nonlinear PDEs have a bi-Hamiltonian structure and a Lax pair; they can also be solved with the inverse scattering transform and admit soliton solutions of any order.

A straightforward method for the symbolic computation of polynomial recursion operators of nonlinear PDEs in (1+1) dimensions is presented. Based on conserved densities and generalized symmetries, a candidate recursion operator is built from a linear combination of scaling invariant terms with undetermined coefficients. The candidate recursion operator is substituted into its defining equation and the resulting linear system for the undetermined coefficients is solved.

The method is algorithmic and is implemented in Mathematica. The resulting symbolic package PDERecursionOperator.m can be used to test the complete integrability of polynomial PDEs that can be written as nonlinear evolution equations. With PDERecursionOperator.m, recursion operators were obtained for several well-known nonlinear PDEs from mathematical physics and soliton theory.     

Formalizing non-termination of recursive programs

In applicative theories the recursion theorem provides a term which solves recursive equations. However, it is not provable that a solution obtained by is minimal. In the present paper we introduce an applicative theory in which it is possible to define a least fixed point operator. Still, our theory has a standard recursion theoretic interpretation.     

An exercise in program synthesis: algorithms for computing the transitive closure of a relation

This paper contains the synthesis of several transitive closure algorithms (including Warshall's) from one common high level definition.For deriving recursion equations Burstall's and Darlington's unfolding-and folding-technique is used. A special effort is made to treat the first step of the syntheses (i.e. finding appropriate recursion arguments) systematically.     

Markov-modulated stochastic recursive equations with applications to delay-tolerant networks

We investigate a class of Markov-modulated stochastic recursive equations. This class includes multi-type branching processes with immigration as well as linear stochastic equations. Conditions are established for the existence of a stationary solution and expressions for the first two moments of this solution are found. Furthermore, the transient characteristics of the stochastic recursion are investigated: we obtain the first two moments of the transient solution as well. Finally, to illustrate our approach, the results are applied to the performance evaluation of packet forwarding in delay-tolerant mobile ad-hoc networks.     

Four domains for concurrency

We give four domains for concurrency in a uniform way by means of domain equations. The domains are intended for modelling the four possible combinations of linear time versus branching time, and of interleaving versus noninterleaving concurrency. We use the linear time, noninterleaved domain to give operational and denotational semantics for a simple concurrent language with recursion, and prove that .     

A system which automatically improves programs

Summary Here we give methods of mechanically converting programs that are easy to understand into more efficient ones, converting recursion equations using high level operations into lower level flowchart programs.The main transformations involved are (i) recursion removal (ii) eliminating common subexpressions and combining loops (iii) replacing procedure calls by their bodies (iv) introducing assignments which overwrite list cells no longer in use (compiletime garbage collection).The operations we use are based on the POP-2 language, Burstall, Collins and Popplestone [1]. The main features to note are that hd is the LISP car, tl the LISP cdr and concat joins two lists (the LISP append).     

LU分解递归算法的实现

§1.引言 以LU分解, Cholesky分解等为代表的线性代数问题的数值计算在现代科学研究和工程技术中得到广泛应用.随着计算机技术的发展,实现这些线性代数数值计算的计算机算法和软件也在不断发展.目前,具有多级存储结构的高性能RISC计算机已占据了数值计算领域的主导地位. RSIC处理器的运算速度非常快,它们与存储器之间的速度差距很大.计算机的性能能不能充分发挥,多级存储结构与高缓能否得到有效利用成为关键.为此,现行的     

Notes and annotations as information resources in a social networking platform

Taking notes and annotations contributes in the learning process. Many platforms are developed as Computer Supported Collaborative Learning (CSCL) thanks to advancements in new technologies. A common limitation of these platforms is the restricted ability to share/retrieve notes and annotations (Su, Yang, Hwang, & Zhang, 2010a). This is because the annotations in these platforms are disconnected from the information system and they are only accessible in the annotation system. As a result, the annotations could not be indexed as any other information resources (e.g., a document). This means that the annotations are not accessible/visible like other resources. In this paper, we present an original semantic model in which notes and annotations are modeled as information resources. The semantic model is used within the MEMORAe web platform. Then we detail an experiment of collaborative learning made within a university course using the MEMORAe web platform. The feedback of this experiment shows us that students are satisfied with the use of the MEMORAe web platform for helping them to index and retrieve notes and annotations as any information resources.     

UnQL: a query language and algebra for semistructured data based on structural recursion

Abstract. This paper presents structural recursion as the basis of the syntax and semantics of query languages for semistructured data and XML. We describe a simple and powerful query language based on pattern matching and show that it can be expressed using structural recursion, which is introduced as a top-down, recursive function, similar to the way XSL is defined on XML trees. On cyclic data, structural recursion can be defined in two equivalent ways: as a recursive function which evaluates the data top-down and remembers all its calls to avoid infinite loops, or as a bulk evaluation which processes the entire data in parallel using only traditional relational algebra operators. The latter makes it possible for optimization techniques in relational queries to be applied to structural recursion. We show that the composition of two structural recursion queries can be expressed as a single such query, and this is used as the basis of an optimization method for mediator systems. Several other formal properties are established: structural recursion can be expressed in first-order logic extended with transitive closure; its data complexity is PTIME; and over relational data it is a conservative extension of the relational calculus. The underlying data model is based on value equality, formally defined with bisimulation. Structural recursion is shown to be invariant with respect to value equality. Received: July 9, 1999 / Accepted: December 24, 1999     

HYPERINCURSIVE METHODS FOR GENERATING FRACTALS IN AUTOMATA RELATED TO DIFFUSION AND WAVE EQUATIONS

This paper provides modelling tools for automata design in the field of information and formal systems. The concept and methods of incursion and hyperincursion are firstly applied to the Fractal Machine, a hyperiacursive cellular automaton with sequential computations with exclusive OR, where time plays a central role. Simulations will show the generation of fractal patterns. The computation is incursive, for inclusive recursion, in the sense that an automaton is computed at the future time l+1 as a function of its neighbour automata at the present and/or past time steps but also at the future time l+1. The hyperincursion is an incursion when several values can be generated at each time step. External incursive inputs cannot be transformed to recursion. (This is really an example of the Final Cause of Aristotle.) But internal incursive inputs defined at the future time can be transformed to recursive inputs by self-reference. A particular case of self-reference with the Fractal Machine shows a non deterministic hyper-incursive field. Interference of particles in the Fractal Machine gives rise to fractal patterns which follow Huygens Principle of Secondary Sources. The superimposition of states is similar to Deutsch's quantum computing principle. This is also related to digital cellular automata obtained from diffusion and wave finite difference equations. Zuse proposed to represent physical systems by a computing space based on such a digitalisation of differential equations. I show that the digital wave equation exhibits waves by digital particles with interference effects and uncertainty.     

A historical and contemporary study on annotations to derive key features for systems design

This paper provides a comprehensive study on annotations by defining their contours and complexity. This work adds a new complementary approach to the usual case and user studies, and also investigates history in order to benefit from previous knowledge and our cultural heritage. This study emphasizes an aspect which has never previously been taken into account: the temporal dimension involved in annotations. Moreover, it discusses both the notion of hypertext between documents and annotations and the idea of annotations as context for documents. The study gives the necessary historical and cultural background to derive a set of key features of annotations that must be taken into account when designing systems that have to support the management of digital annotations on digital contents.     

广义重心坐标的递推关系

从线性方程组解空间的角度理解广义重心坐标(GBCs),给出平面重心坐标从n 边形 到n 1边形的递推关系式。将构造重心坐标的问题转化为构造函数的问题,不需考虑坐标函数的 几何意义,选取满足约束条件的函数即可构造重心坐标。在推导过程中,n 1边形(n≥3)可看 作n边形与一顶点的组合,将该顶点用n边形的顶点线性表出,可将n 1边形上的重心坐标化为 n边形上的齐次坐标(homogeneous coordinates)。为第n 1个坐标函数施加一定限制条件,即得到 n 边形上一组重心坐标。     

基于腕力传感器的机器人操作臂惯性参数辨识方法

针对工业机器人结构设计及动力控制中，在比现有方法少用了基座力传感器的基础上，充分挖掘了腕力传感器的信息，利用机械臂运动学及动力学递推关系，由Newton-Euler方程导出了各连杆惯性参数逆向的辨识模型．以一个算例说明了方法的运用，为机器人操作臂动力学建模提供了理论基础．     

Proving Resource Consumption of Low-level Programs Using Automated Theorem Provers

In this paper we use a program logic and automatic theorem provers to certify resource usage of low-level bytecode programs equipped with annotations describing resource consumption for methods. We have adapted an existing resource counting logic [Aspinall, D., L. Beringer, M. Hofmann, H.-W. Loidl and A. Momigliano, A program logic for resource verification, in: Proceedings of 17th International Conference on Theorem Proving in Higher Order Logics (TPHOLs2004), Lecture Notes in Computer Science 3223 (2004), pp. 34–49] to fit the first-order setting, implemented a verification condition generator, and tested our approach on programs that contain recursion and deal with recursive data structures. We have successfully applied our framework to programs that did not involve any updates to recursive data structures. But mutation is more tricky because of aliasing of heap. We discuss problems related to this and suggest techniques to solve them.     

Numerical solution of recirculating flow by a simple finite element recursion relation

A time-split finite element recursion relation, based on linear basis function, is used to solve the two-dimensional equations of motion. Recirculating flow in a rectangular cavity and free convective flow in an enclosed container are analyzed. The relation has the advantage of finite element accuracy and finite difference speed and simplicity. Incorporating dissipation parameters in the functionals decreases numerical dispersion and improves phase lag.     

Recording concerns in source code using annotations

A concern can be characterized as a developer׳s intent behind a piece of code, often not explicitly captured in it. We discuss a technique of recording concerns using source code annotations (concern annotations). Using two studies and two controlled experiments, we seek to answer the following 3 research questions: (1) Do programmers׳ mental models overlap? (2) How do developers use shared concern annotations when they are available? (3) Does using annotations created by others improve program comprehension and maintenance correctness, time and confidence? The first study shows that developers׳ mental models, recorded using concern annotations, overlap and thus can be shared. The second study shows that shared concern annotations can be used during program comprehension for the following purposes: hypotheses confirmation, feature location, obtaining new knowledge, finding relationships and maintenance notes. The first controlled experiment with students showed that the presence of annotations significantly reduced program comprehension and maintenance time by 34%. The second controlled experiment was a differentiated replication of the first one, focused on industrial developers. It showed a 33% significant improvement in correctness. We conclude that concern annotations are a viable way to share developers׳ thoughts.