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In this paper, a Galerkin method based on the second kind Chebyshev wavelets (SKCWs) is established for solving the multi-term time fractional diffusion-wave equation. To do this, a new operational matrix of fractional integration for the SKCWs must be derived and in order to improve the computational efficiency, the hat functions are proposed to create a general procedure for constructing this matrix. Implementation of these wavelet basis functions and their operational matrix of fractional integration simplifies the problem under consideration to a system of linear algebraic equations, which greatly decreases the computational cost for finding an approximate solution. The main privilege of the proposed method is adjusting the initial and boundary conditions in the final system automatically. Theoretical error and convergence analysis of the SKCWs expansion approve the reliability of the approach. Also, numerical investigation reveals the applicability and accuracy of the presented method. [ABSTRACT FROM AUTHOR]

Quantum effects can enhance information-processing capabilities and speed up the solution of certain computational problems. Whether a quantum advantage can be rigorously proven in some setting or demonstrated experimentally using near-term devices is the subject of active debate. We show that parallel quantum algorithms running in a constant time period are strictly more powerful than their classical counterparts; they are provably better at solving certain linear algebra problems associated with binary quadratic forms. Our work gives an unconditional proof of a computational quantum advantage and simultaneously pinpoints its origin: It is a consequence of quantum nonlocality. The proposed quantum algorithm is a suitable candidate for near-future experimental realizations, as it requires only constant-depth quantum circuits with nearest-neighbor gates on a two-dimensional grid of qubits (quantum bits). [ABSTRACT FROM AUTHOR]

In this paper, new approach to parameterized homotopy perturbation method is presented to solve non-oscillatory problems. In contrast to the classical version of the homotopy method, optimal value of α is identified and used to obtain approximate solutions. The new approach is powerful as it effectively handled nonoscillatory problems and gives results with the smallest known errors. [ABSTRACT FROM AUTHOR]

Let G be a connected graph with vertex set V ( G ) and edge set E ( G ). Let T ( G ) be the diagonal matrix of vertex transmissions of G and D ( G ) be the distance matrix of G . The distance Laplacian matrix of G is defined as L ( G ) = T ( G ) − D ( G ) . The distance signless Laplacian matrix of G is defined as Q ( G ) = T ( G ) + D ( G ) . In this paper, we show that the complements of path and cycle are determined by their distance (signless) Laplacian spectra. [ABSTRACT FROM AUTHOR]

Optimal control problems involving non-separated multipoint and integral conditions are investigated. For numerical solution to the problem, we propose to use first order optimization methods with application of the formulas for the gradient of the functional obtained in the work. To solve the adjoint boundary problems, we propose an approach. This approach makes it possible to reduce solving initial boundary problems to solving supplementary Cauchy problems and a linear algebraic system of equations. Results of numerical experiments are given. [ABSTRACT FROM AUTHOR]

For a square-free bivariate polynomial p of degree n we introduce a simple and fast numerical algorithm for the construction of n × n matrices A , B , and C such that det ⁡ ( A + x B + y C ) = p ( x , y ) . This is the minimal size needed to represent a bivariate polynomial of degree n . Combined with a square-free factorization one can now compute n × n matrices for any bivariate polynomial of degree n . The existence of such symmetric matrices was established by Dixon in 1902, but, up to now, no simple numerical construction has been found, even if the matrices can be nonsymmetric. Such representations may be used to efficiently numerically solve a system of two bivariate polynomials of small degree via the eigenvalues of a two-parameter eigenvalue problem. The new representation speeds up the computation considerably. [ABSTRACT FROM AUTHOR]

The most important factor of High performance computing (HPC) systems nowadays is to limit or decrease the power consumption while preserving a high utilization. And with the availability of alternative energy, which powers such systems, there is a need to maximize the usage of alternative energy over brown power. For now, the usage of alternative energy is varying in time due to different factors such as sunny days, the wind, etc. and it is crucial to have an energy-aware algorithm to maximize the usage of this energy. In this paper a SaaS service is presented to optimize a usage of alternative energy, to reduce the power consumption and to preserve a best possible percentage of resource utilization. [ABSTRACT FROM AUTHOR]

Linear algebra is a basic mathematical subject taught in mathematics and science departments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing student-generated examples regarding the concepts. With the help of these examples, we have analysed students’ understanding of linear dependence/independence and determined the effect of the example-generation process on student understanding of linear algebra. In addition, we identified some difficulties that were experienced by students learning the concepts of linear dependence/independence. In this study, APOS (action-process-object-schema) theory is the main tool utilized to explain students’ written responses. It was also used with regard to the interview questions that were posed to students with the purpose of identifying possible difficulties with linear dependence/independence and observing the adequacy of the relations that students might form between different elements of the genetic decomposition of linear dependence/independence concepts. The findings of this study confirmed that many students do not have appropriate mental structures at object and schema levels. Moreover, in order to ensure the success of such exercises, students must be encouraged to review and validate their responses to the example requests. [ABSTRACT FROM PUBLISHER]

In this work we consider parallel variational algorithms for solution of linear systems. Theoretical analysis explains the superlinear convergence rate for two step gradient descent method. A new modification of the algorithm is proposed. Results of computational experiments are given for a linear system of equations approximating 3D elliptic boundary value problem. All algorithms are implemented using parallel array object tool ParSol, then a parallel algorithm follows semi‐automatically from the serial one. Results of the scalability analysis are presented and the efficiency of the presented parallel algorithm is investigated experimentally. First Published Online: 14 Oct 2010

The article presents information on a student research project that was performed to enable students to investigate an abstract algebra class through modular arithmetic. It further depicts the mathematical palette by topping idempotents off with modular arithmetic and a series of exercises determining for which n there are more than two idempotents. Several numerical calculations are also presented to elaborate this.

Mathematical tools have long held an important place in classrooms. With the innovation of information and communication technologies, many tools have appeared and been adapted for educational purposes. Sage-Math is a popular mathematical software which was released in 2005. This software has efficient features which utilize the internet and can handle most mathematical problems, including linear algebra, algebra, combinatorics, numerical mathematics and calculus. In this paper, we will introduce this powerful software and discuss how it can be used in classes. We also demonstrate the mobile infrastructure of Sage-Math and its mobile-learning environment. [ABSTRACT FROM AUTHOR]

Let [image omitted] be a unital ring. An element [image omitted] is said to be a Jordan full-derivable point of [image omitted] if every additive map δ from [image omitted] into itself Jordan derivable at Z (i.e. δ(A)B + Aδ(B) + δ(B)A + Bδ(A) = δ(Z) for every A, B ∈ [image omitted] with AB + BA = Z) is a Jordan derivation. In this article, under some mild conditions on unital prime ring or triangular ring [image omitted], it is shown that the unit I is a Jordan full-derivable point of [image omitted]. Particularly, the unit I is a Jordan full-derivable point of prime Banach algebras containing a non-trivial idempotent, factor von Neumann algebras, and nest algebras. [ABSTRACT FROM AUTHOR]

In this article, we study the reverse order laws for {1, 2, 3}- and {1, 2, 4}-inverses of multiple matrix products by using the maximal and minimal ranks of the generalized Schur complements. The necessary and sufficient conditions for the inclusions [image omitted] and [image omitted] are presented. [ABSTRACT FROM AUTHOR]

Local projection based stabilized finite element methods for the solution of Darcy flow offer several advantages as compared to mixed Galerkin methods. In particular, the avoidance of stability conditions between finite element spaces, the efficiency in solving the reduced linear algebraic system, and the convenience of using equal order continuous approximations for all variables. In this paper we analyze the pressure gradient method for Darcy flow and investigate its stability and convergence properties. [ABSTRACT FROM AUTHOR]

The article discusses the solution for the Lights Out puzzle, considering the use of matrix algebra and graph-theory approaches. It states that base from the linear algebra theory, the Lights Out puzzle's final state is set through the parity of the number of times a button is pressed. It says that in the graph-theory, the puzzle which has initial state of all buttons on bears the answer that turns off all buttons. Meanwhile, a solution for Lights Out puzzle is possible when all lights start on.

In this work we consider parallel variational algorithms for solution of linear systems. Theoretical analysis explains the superlinear convergence rate for two step gradient descent method. A new modification of the algorithm is proposed. Results of computational experiments are given for a linear system of equations approximating 3D elliptic boundary value problem. All algorithms are implemented using parallel array object tool ParSol, then a parallel algorithm follows semi- automatically from the serial one. Results of the scalability analysis are presented and the efficiency of the presented parallel algorithm is investigated experimentally. [ABSTRACT FROM AUTHOR]

Bounds for joint spectral radii of a set of nonnegative matrices are established by using the apparatus of idempotent algebra. [ABSTRACT FROM AUTHOR]