CAS integration into learning environment

In order to successfully integrate computers into education, it is necessary to organize effectively the prerequisites of human-machine interaction. In the organization of competence-centred education computers could provide valuable assistance for both personal- and group- learning activities. In this paper, we will examine various applications of Computer Algebra Systems (CAS) in classroom settings. The elements of the learning environments are CAS. E-Learning-portal, and Tight VNC remote control system. CAS assisted teaching can become genuinely effective in a complex learning environment if students' instrumental-genesis evolve into instrumental-orchestration. We will demonstrate the evolution of thus process by using one of our developed applications. As an example, we developed, tested, and evaluated our model in the Department of Engineering at the University of Pecs. The study took place during the 2004–2005 academic year with computer science and computer engineering participants.     

Modelling Acid Deposition for Policy Analysis

The acid rain problem is just one amongst many complex environmental issues that are facing policy-makers today. Analytical advice normally takes the form of large and expensive studies, expressed in written reports. The availability of powerful dedicated and interactive computers opens the possibility for the analysis to be represented as an interactive computer program. The computer has considerable potential to improve the quality of the analysis available to a policy-maker.This paper will report on the construction of a decision aid on a powerful personal computer for the British Government, to study the acid deposition problem. As well as describing the technical issues involved in this model, the paper discusses the potential for this approach to policy analysis.     

Epistemological beliefs concerning the nature of mathematics among teacher educators and teacher education students in mathematics

Beliefs constitute a central part of a person’s professional competences as beliefs are crucial to the perception of situations and as they influence our choice of actions. The present article focuses on epistemological beliefs about the nature of mathematics among future teachers and their educators at university and post-university teacher-training institutions in Germany. The data reported are part of a larger sample originating from the MT21 study [supported by the National Science Foundation through a grant to W. S. Schmidt and M. T. Tatto (REC-0231886). MT21 started in 2003] which explores and compares mathematics teacher education in Bulgaria, Germany, Mexico, South Korea, Taiwan, and the United States. In this article, we examine the structure and level of beliefs concerning the nature of mathematics for teacher education students in Germany both at the beginning (n = 368) and the end of their education (n = 286) as well as their educators (n = 77) in three academic disciplines (mathematics, mathematics pedagogy and general pedagogy). In the first part of the article, the literature on epistemological beliefs and their structure will be reviewed. In the empirical part, analyses on the level and the structure of beliefs for our samples and subsamples will be presented. Relations between educators’ and students’ beliefs will be explored.     

On the optimality of list scheduling for online uniform machines scheduling

This paper considers classical online scheduling problems on uniform machines. We show the tight competitive ratio of LS for any combinations of speeds of three machines. We prove that LS is optimal when s ₃ ≥ s ₂ ≥ s ₁ = 1 and ${s_3^2\geq s_2^2+s_2s_3+s_2}$ , where s ₁, s ₂, s ₃ are the speeds of three machines. On the other hand, LS can not be optimal for all combinations of machine speeds, even restricted to the case of 1 = s ₁ = s ₂ < s ₃. For m ≥ 4 machines, LS remains optimal when one machine has very large speed, and the remaining machines have the same speed.     

Some mathematical limitations of the general-purpose analog computer

We prove that the Dirichlet problem on the disc cannot be solved by the general-purpose analog computer, by constructing, on the boundary, a function u₀ that does satisfy an algebraic differential equation, but whose Poisson integral u satisfies no algebraic differential equation on some line segment inside the disc.     

Statistical lacunary summability and a Korovkin type approximation theorem

In this paper, we introduce statistical lacunary summability and strongly ?? _q -convergence (0 < q < ??) and establish some relations between lacunary statistical convergence, statistical lacunary summability, and strongly ?? _q -convergence. We further apply our new notion of summability to prove a Korovkin type approximation theorem.     

An Efficient Algorithm to Identify DNA Motifs

We consider the problem of identifying motifs that abstracts the task of finding short conserved sites in genomic DNA. The planted (l, d)-motif problem, PMP, is the mathematical abstraction of this problem, which consists of finding a substring of length l that occurs in each s _i in a set of input sequences S = {s ₁, s ₂, . . . ,s _t } with at most d substitutions. Our propose algorithm combines the voting algorithm and pattern matching algorithm to find exact motifs. The combined algorithm is achieved by running the voting algorithm on t′ sequences, t′ < t. After that we use the pattern matching on the output of the voting algorithm and the reminder sequences, t ? t′. Two values of t′ are calculated. The first value of t′ makes the running time of our proposed algorithm less than the running time of voting algorithm. The second value of t′ makes the running time of our proposed algorithm is minimal. We show that our proposed algorithm is faster than the voting algorithm by testing both algorithms on simulated data from (9, d ≤ 2) to (19, d ≤ 7). Finally, we test the performance of the combined algorithm on realistic biological data.     

Effect of the CYBER 205 on the choice of method for solving the eigenvalue problem (A − λM)x = 0

We consider the generalized eigenvalue problem. (A − λM)x = 0, where A and M are large, sparse, symmetric matrices. For large problems finding only a few eigenpairs involves a major computational task. In a typical example from structural dynamic analysis with matrices of order 8000, O(10⁹) operations are required to compute 50 eigenpairs. It is therefore interesting to examine the advantage that vector computers such as CYBER 205 can offer.We adopted our best versions of the Subspace Iteration Method and the simple Lanczos Method in order to take advantage of the special vector processor of the CYBER 205. Both techniques lend themselves to vectorization. Our extensive comparisons support the following general statements. Both methods require the triangular factorization of the same large n by n matrix. This factorization dominates the total computation as n → ∞ provided that the number of wanted eigenpairs, p, remains fixed (independent of n). However, simple Lanczos is at least an order of magnitude more efficient (in CPU-time) for the remainder of the computation. For p = 40, n = 500 the factorization time is not important and the full order of magnitude difference is seen in the total CPU-time. When p = 40, n = 8000 simple Lanczos is only 4 times faster than Subspace Iteration on the CYBER 205. This confirms experience on serial computers.For problems that cannot fit into primary storage, input/output becomes increasingly important. We found that the cost of input/output dominated over the CPU-cost for a problem that required twice the available primary storage on our CYBER 205. However, this will depend on the billing algorithm of the computer center. We conclude that problems which have a substantial overhead in reading and writing the matrices, should not be solved by the simple Lanczos Method, but by a Block Lanczos Method.     

On the perturbation of the observability equation in linear control systems

The aim of this paper is to investigate stability and sensitivity of the observability variable in linear control systems, (LCS) for short. We first present two results of Hölder continuity in the abstract framework of the ordinary differential equation initial-value problem x′(t) = f(t,x(t)),x(t ₀) = x ₀. Afterwards, we apply our results to automatic systems, providing henceforth the sharpest bounds for the parametric input-output relation in LCS.     

Improved approximations for the Erlang loss model

Stochastic loss networks are often very effective models for studying the random dynamics of systems requiring simultaneous resource possession. Given a stochastic network and a multi-class customer workload, the classical Erlang model renders the stationary probability that a customer will be lost due to insufficient capacity for at least one required resource type. Recently a novel family of slice methods has been proposed by Jung et al. (Proceedings of ACM SIGMETRICS conference on measurement and modeling of computer systems, pp. 407–418, 2008) to approximate the stationary loss probabilities in the Erlang model, and has been shown to provide better performance than the classical Erlang fixed point approximation in many regimes of interest. In this paper, we propose some new methods for loss probability calculation. We propose a refinement of the 3-point slice method of Jung et al. (Proceedings of ACM SIGMETRICS conference on measurement and modeling of computer systems, pp. 407–418, 2008) which exhibits improved accuracy, especially when heavily loaded networks are considered, at comparable computational cost. Next we exploit the structure of the stationary distribution to propose randomized algorithms to approximate both the stationary distribution and the loss probabilities. Whereas our refined slice method is exact in a certain scaling regime and is therefore ideally suited to the asymptotic analysis of large networks, the latter algorithms borrow from volume computation methods for convex polytopes to provide approximations for the unscaled network with error bounds as a function of the computational costs.     

Non-relativistic global limits of entropy solutions to the extremely relativistic Euler equations

We are concerned in this paper with the non-relativistic global limits of the entropy solutions to the Cauchy problem of 3 × 3 system of relativistic Euler equations modeling the conservation of baryon numbers, momentum, and energy respectively. Based on the detailed geometric properties of nonlinear wave curves in the phase space and the Glimm’s method, we obtain, for the isothermal flow, the convergence of the entropy solutions to the solutions of the corresponding classical non-relativistic Euler equations as the speed of light c → +∞.     

Scheduling orders for multiple product types to minimize total weighted completion time

We consider the problem of scheduling orders for multiple different product types in an environment with m dedicated machines in parallel. The objective is to minimize the total weighted completion time. Each product type is produced by one and only one of the m dedicated machines; that is, each machine is dedicated to a specific product type. Each order has a weight and may also have a release date. Each order asks for certain amounts of various different product types. The different products for an order can be produced concurrently. Preemptions are not allowed. Even when all orders are available at time 0, the problem has been shown to be strongly NP-hard for any fixed number (?2) of machines. This paper focuses on the design and analysis of efficient heuristics for the case without release dates. Occasionally, however, we extend our results to the case with release dates. The heuristics considered include some that have already been proposed in the literature as well as several new ones. They include various static and dynamic priority rules as well as two more sophisticated LP-based algorithms. We analyze the performance bounds of the priority rules and of the algorithms and present also an in-depth comparative analysis of the various rules and algorithms. The conclusions from this empirical analysis provide insights into the trade-offs with regard to solution quality, speed, and memory space.     

The efficiency of application of dual-processor computers for the analysis of the three-dimensional second harmonic generation problem

The efficiency of application of dual-processor computers, various operating systems, and library functions adapted to the used processors for increasing the execution speed of a computer program used for solving a system of two 3D nonlinear Schrödinger equations is analyzed. The computation speeds obtained on computers with 32-bit and 64-bit processors are compared. It is shown that the use of all mentioned possibilities and the Intel Itanium 2 processor provides from to threefold to tenfold total saving of time, depending on the operating system and the computer type. Parallelization of the algorithm for different operating systems in combination with the use of a library adapted to the processor can increase the program’s execution speed by a factor of 1.5–3.     

The 3 × 3 × 3 Hyperdeterminant as a Polynomial in the Fundamental Invariants for {{SL_3(\mathbb{C}) \times SL_3(\mathbb{C}) \times SL_3(\mathbb{C})}}

We briefly review previous work on the invariant theory of 3 ×  3 ×  3 arrays. We then recall how to generate arrays of arbitrary size \({m_1 \times \cdots \times m_k}\) with hyperdeterminant 0. Our main result is an explicit formula for the 3 ×  3 ×  3 hyperdeterminant as a polynomial in the fundamental invariants I ₆, I ₉, I ₁₂ for the action of the Lie group \({SL_3(\mathbb{C}) \times SL_3(\mathbb{C}) \times SL_3(\mathbb{C})}\) . We apply our calculations to Nurmiev’s classification of normal forms for 3 ×  3 ×  3 arrays.     

Solving sparse linear least-squares problems on some supercomputers by using large dense blocks

Efficient subroutines for dense matrix computations have recently been developed and are available on many high-speed computers. On some computers the speed of many dense matrix operations is near to the peak-performance. For sparse matrices storage and operations can be saved by operating only and storing only nonzero elements. However, the price is a great degradation of the speed of computations on supercomputers (due to the use of indirect addresses, to the need to insert new nonzeros in the sparse storage scheme, to the lack of data locality, etc.). On many high-speed computers a dense matrix technique is preferable to sparse matrix technique when the matrices are not large, because the high computational speed compensates fully the disadvantages of using more arithmetic operations and more storage. For very large matrices the computations must be organized as a sequence of tasks in each of which a dense block is treated. The blocks must be large enough to achieve a high computational speed, but not too large, because this will lead to a large increase in both the computing time and the storage. A special “locally optimized reordering algorithm” (LORA) is described, which reorders the matrix so that dense blocks can be constructed and treated with some standard software, say LAPACK or NAG. These ideas are implemented for linear least-squares problems. The rectangular matrices (that appear in such problems) are decomposed by an orthogonal method. Results obtained on a CRAY C92A computer demonstrate the efficiency of using large dense blocks.     

Utilisation des modules de Drinfeld en cryptologie

We present in this Note a new and efficient public-key cryptosystem based on Drinfeld modules. The details will appear elsewhere. To cite this article: R. Gillard et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Time-dependent analysis of an <Emphasis Type="Italic">M</Emphasis> / <Emphasis Type="Italic">M</Emphasis> / <Emphasis Type="Italic">c</Emphasis> preemptive priority system with two priority classes

We analyze the time-dependent behavior of an M / M / c priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More particularly, we develop a method that determines the Laplace transforms of the transition functions when the system is initially empty. The Laplace transforms corresponding to states with at least c high-priority customers are expressed explicitly in terms of the Laplace transforms corresponding to states with at most \(c - 1\) high-priority customers. We then show how to compute the remaining Laplace transforms recursively, by making use of a variant of Ramaswami’s formula from the theory of M / G / 1-type Markov processes. While the primary focus of our work is on deriving Laplace transforms of transition functions, analogous results can be derived for the stationary distribution; these results seem to yield the most explicit expressions known to date.     

Lyapounov norms for random walks in low disorder and dimension greater than three

We consider a simple random walk on Z ^d , d > 3. We also consider a collection of i.i.d. positive and bounded random variables $\left(V_\omega(x)\right)_{x\in Z^d}$ , which will serve as a random potential. We study the annealed and quenched cost to perform long crossing in the random potential $-(\lambda+\beta V_\omega(x))$ , where λ is positive constant and β > 0 is small enough. These costs are measured by the Lyapounov norms. We prove the equality of the annealed and the quenched norm.     

Symmetric decompositions and the strong Sperner property for noncrossing partition lattices

We prove that the noncrossing partition lattices associated with the complex reflection groups G(d, d, n) for \(d,n\ge 2\) admit symmetric decompositions into Boolean subposets. As a result, these lattices have the strong Sperner property and their rank-generating polynomials are symmetric, unimodal, and \(\gamma \)-nonnegative. We use computer computations to complete the proof that every noncrossing partition lattice associated with a well-generated complex reflection group is strongly Sperner, thus answering affirmatively a question raised by D. Armstrong.     

A Mixed Heuristic for Circuit Partitioning

As general-purpose parallel computers are increasingly being used to speed up different VLSI applications, the development of parallel algorithms for circuit testing, logic minimization and simulation, HDL-based synthesis, etc. is currently a field of increasing research activity. This paper describes a circuit partitioning algorithm which mixes Simulated Annealing (SA) and Tabu Search (TS) heuristics. The goal of such an algorithm is to obtain a balanced distribution of the target circuit among the processors of the multicomputer allowing a parallel CAD application for Test Pattern Generation to provide good efficiency. The results obtained indicate that the proposed algorithm outperforms both a pure Simulated Annealing and a Tabu Search. Moreover, the usefulness of the algorithm in providing a balanced workload distribution is demonstrated by the efficiency results obtained by a topological partitioning parallel test-pattern generator in which the proposed algorithm has been included. An extented algorithm that works with general graphs to compare our approach with other state of the art algorithms has been also included.