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Abstract: The aim of this note is to show that the optimization algorithm proposed in may not lead to the optimal solution in some cases. In fact, the optimization problem remains open if we do not apply the branch-and-bound method to solve it or compute all the objective values of minimal solutions of the feasible domain. [Copyright &y& Elsevier]

Abstract: In abstract of the paper [A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Comput. 195 (2008) 819–821] we can find the following sentences. We cite: Ujević et al. introduced a family of methods for solving nonlinear equations. However the main Algorithm 1 put forward by Ujević et al. (p. 7) is wrong. This is the main aim of this note. We also point out some major bugs in the results of Ujević et al. – the end of the citation. Here it is shown that all of the mentioned assertions are not true. In other words, the Algorithm 1 is correct (up to an obvious misprint, which is not mentioned in the above paper) and there are no major bugs in the paper by Ujević et al. In fact, these observations, which will be given in this note, show that the main aim of the paper by Rafiq is wrong. [Copyright &y& Elsevier]

The solution of discrete ill-posed problems has been a subject of research for many years. Among the many methods described in the literature, the Bregman algorithm has attracted a great deal attention and been widely investigated. Recently, a nonstationary preconditioned version of this algorithm, referred to as the nonstationary modified linearized Bregman algorithm, was proposed. The aim of this paper is to discuss numerical aspects of this algorithm and to compare computed results with known theoretical properties. We also discuss the effect of several parameters required by the algorithm on the computed solution. [ABSTRACT FROM AUTHOR]

The concept of mono-component is widely used in non-stationary signal processing and time-frequency analysis. A special class of mono-components, called ϵ-mono-components, were proposed in our recent publication. It was illustrated that this model coincides with the intuition of human beings on the physical mono-components very well provided that the parameter ϵ is sufficiently small. It is then very meaningful to construct desired ϵ-mono-components and design algorithms to decompose and represent non-stationary signals adaptively. This paper studies the constructions of ϵ-mono-components and makes mathematical analysis on an adaptive signal decomposition algorithm based on ϵ-mono-components. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes an algorithm designed for the automatic coarsening of three-dimensional unstructured simplicial meshes. This algorithm can handle very anisotropic meshes like the ones typically used to capture the boundary layers in CFD with Low Reynolds turbulence modeling that can have aspect ratio as high as 104. It is based on the concept of mesh generation governed by metrics and on the use of a natural metric mapping the initial (fine) mesh into an equilateral one. The paper discusses and compares several ways to define node based metric from element based metric. Then the semi-coarsening algorithm is described. Several application examples are presented, including a full three-dimensional complex model of an aircraft with extremely high anisotropy. [Copyright &y& Elsevier]

Abstract: The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, two anticontrol algorithms for synthesis of discrete chaos are introduced. In these algorithms, the control parameter of a discrete dynamical system is switched, either randomly or in a deterministic way, between two or more values corresponding to periodic motions, the result being chaotic behavior. These algorithms require no knowledge of specific mathematical properties of the underlying map modeling the system. The existence of chaos is demonstrated using various tools including graphical iteration, histogram, Lyapunov exponent and surrogate tests. In this paper, these very simple and implementable chaotifiers are applied to the logistic map. [Copyright &y& Elsevier]

Abstract: Shape detection is a fundamental problem in image processing field. In shape detection, lines, circles, and ellipses are the three most important features. In the past four decades, the robustness and the time speedup are two main concerned issues in most developed algorithms. Previously, many randomized algorithms were developed to speed up the computation of the relevant detection successfully. This paper does focus on the time speedup issue. Based on Bresenham’s drawing paradigm, this paper first presents a novel lookup table (LUT)-based voting platform. According to the proposed LUT-based voting platform, we next present a novel computational scheme to significantly speed up the computation of some existing randomized algorithms for detecting lines, circles, and ellipses. Moreover, the detailed time complexity analyses are provided for the three concerned features under our proposed computational scheme and these derived nontrivial analyses also show the relevant computational advantage. Under some real images, experimental results illustrate that our proposed computational scheme can significantly speed up the computation of some existing randomized algorithms. In average, the execution-time improvement ratios are about 28%, 56%, and 48% for detecting lines, circles, and ellipses, respectively, and these improvement ratios are vary close to the theoretic analyses. [Copyright &y& Elsevier]

Abstract: “Transshipment” is a very popular and important issue in the present international trade container transportation market. In order to reduce the international trade container transportation operation cost, it is very important for shipping companies to choose the best transshipment container port. The aim of this paper is to present a new Fuzzy Multiple Criteria Decision Making Method (FMCDM) for solving the transshipment container port selection problem under fuzzy environment. In this paper we present first the canonical representation of multiplication operation on three fuzzy numbers, and then this canonical representation is applied to the selection of transshipment container port. Based on the canonical representation, the decision maker of shipping company can determine quickly the ranking order of all candidate transshipment container ports and select easily the best one. [Copyright &y& Elsevier]

Abstract: The job-shop scheduling problem (JSSP) is a branch of production scheduling, and it is well known that this problem is NP-hard. Many different approaches have been applied to JSSP and a rich harvest has been obtained. However, some JSSP, even with moderate size, cannot be solved to guarantee optimality. The standard particle optimization algorithm generally is used to solve continuous optimization problems, and is used rarely to solve discrete problems such as JSSP. This paper presents a similar PSO algorithm to solve JSSP. At the same time, some new valid algorithm operators are proposed in this paper, and through simulation we find out the effectiveness of them. Three representative (Taillard) instances were made by computational experiments, through comparing the SPSO algorithm with standard GA, and we obtained that the SPSOA is more clearly efficacious than standard GA for JSSP to minimize makespan. [Copyright &y& Elsevier]

Abstract: In this paper, a new definition of the filled function is given, it is different from the primary definition which was given by Ge in paper [R.P. Ge, A filled function method for finding a global minimzer of a function of several variables, Math. Program. 46 (1990) 191–204]. Based on the definition, a new filled function is proposed, and it has better properties. An algorithm for unconstrained global optimization is developed from the new filled function. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories of mathematical analysis, the authors systematically studied the problem of integrating of trigonometric functions utilizing omnipotence expressions tan . A new integral algorithm for the integral of trigonometric functions was established. And a new Maple program trigint for the calculation mechanizing for the integral of trigonometric functions was established, trigint could evaluate not only the integral of trigonometric functions utilizing omnipotence expresssions correctly but also all the other kinds of functions. The results indicated that the algorithm established in this paper had advantages of simple idea, excellent property for operation and powerful competence. This would be useful for some calculating problems of engineering mathematics. [Copyright &y& Elsevier]

In this paper, by using the theories and methods of mathematical analysis and computer algebra, a new algorithm of symbolic integral was established, a new Maple procedure myint for it was established, too. And it was applied to the automatic proving the mean-value theorems for derivatives. The results indicated that the algorithm of symbolic integral had been established in this paper had advantage of simple idea, excellent property for operation and powerful competence. This would be useful for the problem of solving differential equations, automatic proving some mathematical theorems, and so on. [Copyright &y& Elsevier]

In this paper, we propose a new filled function, and give an efficient criterion to choose its two parameters appropriately. An algorithm for unconstrained global optimization is developed from this new filled function. numerical results with a comparison on many test problems show that this algorithm is efficient and reliable. [ABSTRACT FROM AUTHOR]

In this paper, a novel algorithm based on reproducing kernel theory for neutral functional–differential equation with proportional delays is proposed. The advantages of the presented method are the establishment of complete ɛ-approximate solution theory and high precision of absolute error. Some examples are given to demonstrate the validity and applicability of the new method and some comparisons are made with the existing results. [ABSTRACT FROM AUTHOR]

An efficient diagnosis is very important for a multiprocessor system. The ability of identifying all the faulty devices in a multiprocessor system is known as diagnosability. The PMC model is the tested-based diagnosis with a processor performing the diagnosis by testing on the neighboring processors via the links between them. Recently, some researches such as the conditional diagnosability and the local diagnosability, are concerned with the measure which is able to better reflect fault patterns in real systems. In this paper, we propose a specific structure for local diagnosis. Under the PMC model, we design a test round controllable local diagnosis algorithm for a t ∗ -diagnosable network. For some conditional constraint, we give a conditional local diagnosis algorithm for a ( 2 t - 1 ) ∗ -diagnosable network. With our algorithm, a diagnosis is completed in k test rounds. [ABSTRACT FROM AUTHOR]

Abstract: In this paper scheduling communications in data gathering networks is analyzed. We study collecting information by a set of sensors, each of which stores the data in its memory buffer and then passes them to a base station. The network lifetime ends as soon as the first node is out of memory. We use a divisible load model to propose a communication scheduling algorithm that maximizes the system lifetime, and hence, the total amount of gathered information. The influence of the sensor communication rates on the obtained schedules is exposed in a series of computational experiments. [Copyright &y& Elsevier]

In this paper, two explicit conversion formulae between triangular and rectangular Bézier patches are derived. Using the formulae, one triangular Bézier patch of degree n can be converted into one rectangular Bézier patch of degree n × n. And one rectangular Bézier patch of degree m × n can be converted into two triangular Bézier patches of degree m + n. Besides, two stable recursive algorithms corresponding to the two conversion formulae are given. Using the algorithms, when converting triangular Bézier patches to rectangular Bézier patches, we can computer the relations between the control points of the two types of patches for any based on the relationships for When converting rectangular Bézier patches to triangular Bézier patches, we can computer the relations between the control points of the two types of patches for any , and , based on the relationships for . [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this article is first to introduce the concept of total quasi-ϕ-asymptotically nonexpansive semigroups which contains many kinds of semi-groups as its special cases, and then to modify the Halpern–Mann-type iteration algorithm for this kind of semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results announced by many authors. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the convergence of the double-shift and multi-shift QR algorithms for symmetric tridiagonal matrices. We analyze how to choose multi-shifts by comparing the relationships between the number of iterations, CPU time and the number of multi-shifts. Numerical tests and figures are performed. [Copyright &y& Elsevier]

Abstract: The paper deals with the calculation of higher order derivatives of the inverse function. A simple and fast recursive procedure is presented and compared with other methods known in literature both with respect to the computation time and memory usage. [Copyright &y& Elsevier]

Abstract: The 0-1 knapsack problem is an open issue in discrete optimization problems, which plays an important role in real applications. In this paper, a new bio-inspired model is proposed to solve this problem. The proposed method has three main steps. First, the 0-1 knapsack problem is converted into a directed graph by the network converting algorithm. Then, for the purpose of using the amoeboid organism model, the longest path problem is transformed into the shortest path problem. Finally, the shortest path problem can be well handled by the amoeboid organism algorithm. Numerical examples are given to illustrate the efficiency of the proposed model. [Copyright &y& Elsevier]

Abstract: In this paper we provide three benchmark problems with known exact solutions that can be used to assess the ability of adaptive finite element algorithms to handle anisotropically-behaved solutions. The first one is a Poisson equation with a smooth solution that only changes in one spatial direction. The second one is a singularly-perturbed linear elliptic equation whose solution exhibits a boundary layer, and the last one is a two-equation system that contains a boundary layer in one solution component only. In an appendix we show sample results obtained with the open source library Hermes. (http://hpfem.org/hermes.) [Copyright &y& Elsevier]

Abstract: Particle swarm optimization (PSO) has undergone many changes since its introduction in 1995. Being a stochastic algorithm, PSO and its randomness present formidable challenge for the theoretical analysis of it, and few of the existing PSO improvements have make an effort to eliminate the random coefficients in the PSO updating formula. This paper analyzes the importance of the randomness in the PSO, and then gives a PSO variant without randomness to show that traditional PSO cannot work without randomness. Based on our analysis of the randomness, another way of using randomness is proposed in PSO with random dimension selection (PSORDS) algorithm, which utilizes random dimension selection instead of stochastic coefficients. Finally, deterministic methods to do the dimension selection are proposed, and the resultant PSO with distance based dimension selection (PSODDS) algorithm is greatly superior to the traditional PSO and PSO with heuristic dimension selection (PSOHDS) algorithm is comparable to traditional PSO algorithm. In addition, using our dimension selection method to a newly proposed modified particle swarm optimization (MPSO) algorithm also gets improved results. The experiment results demonstrate that our analysis about the randomness is correct and the usage of deterministic dimension selection method is very helpful. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and analyze the new generalized mixed equilibrium problems (NGMEP) and the bilevel new generalized mixed equilibrium problems (BNGMEP) in Banach spaces. First, by using a minimax inequality, some new existence theorems of the solution and the behavior of solution set for the NGMEP and the BNGMEP are obtained in both arbitrary Banach spaces with the coercive conditions and a reflexive Banach space without the coercive conditions. Next, by using auxiliary principle technique, some new iterative algorithms for solving the NGMEP and the BNGMEP are suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithms are also proved in both arbitrary Banach spaces with the coercive conditions and a reflexive Banach space without the coercive conditions. These results are new and generalize some recent results in this field. [Copyright &y& Elsevier]

Abstract: This paper deals with the theory of mixtures which have as constituents two micropolar incompressible fluids. First, using a specific algorithm, a Galerkin type representation of solution is given for the linearized two-dimensional dynamical problem. Then, the steady-state vibration problem is considered and uniqueness theorems are established for both bounded and unbounded domains. Finally, the Galerkin type representation is used to construct the fundamental solution for two-dimensional steady-state vibration problem. [Copyright &y& Elsevier]

Abstract: Block upper triangular matrices with elements in have very interesting properties for many applications. Some of them involve powers of this type of matrices with very large exponents requiring specific exponentiation algorithms to compute them efficiently. In this paper, we analyze quick exponentiation in block upper triangular matrices of size blocks as an extension of the quick exponentiation in block upper triangular matrices of blocks. [Copyright &y& Elsevier]

Abstract: This paper is devoted to construct an algorithm that allows us to calculate the explicit expression of the Green’s function related to a th-order linear ordinary differential equation, with constant coefficients, coupled with two-point linear boundary conditions. We develop this algorithm by making a Mathematica package. [Copyright &y& Elsevier]

Abstract: In this paper some numerical algorithms generating the full invertible matrices and full matrices with a given spectrum are presented. [Copyright &y& Elsevier]

Abstract: In this paper, we consider numerical simulation to a class of constrained dynamic problems where the overall dynamics are determined by the interactions between two sub-systems. We present an iterative algorithm that naturally decouples the computation of the two sub-systems and that ensures an accurate and efficient solution procedure. We conduct rigorous error analysis for the convergence of the iterative algorithm, and verify the analytical results through careful numerical tests. [Copyright &y& Elsevier]

Abstract: In this paper, a new technique of homotopy analysis method (nHAM) is proposed for solving second order nonlinear differential equations. This method improves the convergence of the series solution, eliminates the unneeded terms and reduces time consuming in the standard homotopy analysis method (HAM). The proposed provides an approximate solution by rewriting the second order nonlinear differential equation in the form of two first order differential equations. The solution of these two differential equations is obtained as a power series solution. This scheme is tested on four non-linear exactly solvable differential equations. Three of the examples are initial value problems and the fourth is boundary value problem. The results demonstrate reliability and efficiency of the algorithm developed. [Copyright &y& Elsevier]

Abstract: Discriminant common vectors (DCV), which can effectively extract the features of face images, is a recently proposed algorithm to overcome the small sample size (SSS) problem encountered by linear discriminant analysis (LDA). Its numerical accuracy is high and computational complexity is low, however, the DCV algorithm is not suitable for online training problems. In order to address this problem, an incremental DCV (IDCV) method is developed in this paper. The IDCV algorithm can incrementally learn the optimal projection matrix instead of recomputing the DCV again when new sample is added into the training set. Theoretical analysis denotes that IDCV is much more efficient that DCV. Experiments on ORL, PIE and AR face databases demonstrate the efficiency of our proposed IDCV algorithm over the original batch DCV algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new penalty-free-type method for nonlinear equality constrained problems. The new algorithm uses trust region framework and feasibility safeguarding technique. Moreover, it has no choice of penalty parameter and penalty function as a merit function, and it does not use the filter technique to avoid the penalty function either. We analyze the global convergence of the main algorithm under the standard assumptions. The preliminary numerical tests are reported. [Copyright &y& Elsevier]

Abstract: The Knapsack Problems (KPs) are classical NP-hard problems in Operations Research having a number of engineering applications. Several traditional as well as population based search algorithms are available in literature for the solution of these problems. In this paper, a new Modified Binary Particle Swarm Optimization (MBPSO) algorithm is proposed for solving KPs, particularly 0–1 Knapsack Problem (KP) and Multidimensional Knapsack Problem (MKP). Compared to the basic Binary Particle Swarm Optimization (BPSO), this improved algorithm introduces a new probability function which maintains the diversity in the swarm and makes it more explorative, effective and efficient in solving KPs. MBPSO is tested through computational experiments over benchmark problems and the results are compared with those of BPSO and a relatively recent modified version of BPSO namely Genotype–Phenotype Modified Binary Particle Swarm Optimization (GPMBPSO). To validate our idea and demonstrate the efficiency of the proposed algorithm for KPs, experiments are carried out with various data instances of KP and MKP and the results are compared with those of BPSO and GPMBPSO. [Copyright &y& Elsevier]

Abstract: Synthetic pattern generation procedures have various applications, and a number of approaches (fractals, L-systems, etc.) have been devised. A fundamental underlying question is: will new pattern generation algorithms continue to be invented, or is there some “universal” algorithm that can generate all (and only) the perceptually distinguishable images, or even all members of a restricted class of patterns such as logos or letterforms? In fact there are many complete algorithms that can generate all possible images, but most images are random and not perceptually distinguishable. Counting arguments show that the percentage of distinguishable images that will be generated by such complete algorithms is vanishingly small. In this paper we observe that perceptually distinguishable images are compressible. Using this observation it is evident that algorithmic complexity provides an appropriate framework for discussing the question of a universal image generator. We propose a natural thesis for describing perceptually distinguishable images and argue its validity. Based on it, we show that there is no program that generates all (and only) these images. Although this is an abstract result, it may have importance for graphics and other fields that deal with compressible signals. In essence, new representations and pattern generation algorithms will continue to be developed; there is no feasible “super algorithm” that is capable of all things. [Copyright &y& Elsevier]

Abstract: The inverse of a Schur complement is a very useful tool in many algorithms for the computation of the matrix inversion. In this paper we study the inverse of a special Schur complement CD −1 B. We proved that always exist some X and Y such that XDY is a inverse of CD −1 B. Furthermore, using minimal rank properties, we give some explicit expressions for X, Y and the inverse of CD −1 B. Numerical examples also given. [Copyright &y& Elsevier]

Abstract: The discounted {0–1} knapsack problem (DKP) is an extension of the classical {0–1} knapsack problem (KP) that consists of selecting a set of item groups where each group includes three items and at most one of the three items can be selected. The DKP is more challenging than the KP because four choices of items in an item group diversify the selection of the items. Consequently, it is not possible to solve the DKP based on a classical definition of a core consisting of a small number of relevant variables. This paper partitions the DKP into several easier sub-problems to achieve problem reductions by imitating the core concept of the KP to derive an alternative core for the DKP. Numerical experiments with DP-based algorithms are conducted to evaluate the effectiveness of the problem partition by solving the partitioned problem and the original problem based on different types of DKP instances. [Copyright &y& Elsevier]

Abstract: This paper considers the design problem of parameter dependent H ∞ filters for linear parameter varying (LPV) systems whose parameters are measurable. Conditions for existence of parameter-dependent Lyapunov function are proposed via parametrical linear matrix inequality (LMI) constraints. Based on the solutions to the LMIs, an algorithm for the gain matrices of LPV filter is presented. The design method is applied to a missile system to demonstrate the effectiveness. [Copyright &y& Elsevier]

Abstract: The recent application of the diagonal dominance in the development of the optimization algorithms in the wireless sensor networks design, has been done by Yuan and Yu (2006) , extended in Yu et al. (2006) , and surveyed in Machado and Tekinay . In this paper, we will use the concept of generalized diagonal dominance, to improve the obtained results regarding the power control game, in three directions. We also discuss the applicability of such improvements. [Copyright &y& Elsevier]

Abstract: This paper studies a single machine scheduling problem simultaneously with deteriorating jobs and learning effects. The objectives are to minimize the makespan and the number of tardy jobs, respectively. Two polynomial time algorithms are proposed to solve these problems optimally. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of optimal control problem involving an impulsive systems in which some of its coefficients are subject to variation. We formulate this optimal control problem as a two-stage optimal control problem. We first formulate the optimal impulsive control problem with all its coefficients assigned to their nominal values. This becomes a standard optimal impulsive control problem and it can be solved by many existing optimal control computational techniques, such as the control parameterizations technique used in conjunction with the time scaling transform. The optimal control software package, MISER 3.3, is applicable. Then, we formulate the second optimal impulsive control problem, where the sensitivity of the variation of coefficients is minimized subject to an additional constraint indicating the allowable reduction in the optimal cost. The gradient formulae of the cost functional for the second optimal control problem are obtained. On this basis, a gradient-based computational method is established, and the optimal control software, MISER 3.3, can be applied. For illustration, two numerical examples are solved by using the proposed method. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel hybrid immune algorithm (HIA) that can overcome the typical drawback of the artificial immune algorithm (AIA), which runs slowly and experiences slow convergence. The HIA combines the adaptive AIA based on the steepest descent algorithm. The HIA fully displays global search ability and the global convergence of the immune algorithm. At the same time, it inserts a quasi-descent operator to strengthen its local search ability. A good convergence of the HIA with the quasi-descent idea is shown as well. Numerical experiment results show that the HIA successfully improves running speed and convergence performance. [Copyright &y& Elsevier]

Abstract: By a quasi-permutation matrix we mean a square matrix over the complex field with non-negative integral trace. For a given finite group G, let p(G) denote the minimal degree of a faithful representation of G by permutation matrices, and let c(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices. See . It is easy to see that c(G) is a lower bound for p(G). Behravesh [H. Behravesh, The minimal degree of a faithful quasi-permutation representation of an abelian group, Glasg. Math. J. 39 (1) (1997) 51–57] determined c(G) for every finite abelian group G and also [H. Behravesh, Quasi-permutation representations of p-groups of class 2, J. Lond. Math. Soc. (2) 55 (2) (1997) 251–260] gave the algorithm of c(G) for each finite group G. In this paper, we first improve this algorithm and then determine c(G) and p(G) for an arbitrary minimal non-abelian p-group G. [Copyright &y& Elsevier]

Abstract: In this paper, the notion of two-direction vector-valued multiresolution analysis and the two-direction orthogonal vector-valued wavelets are introduced. The definition for two-direction orthogonal vector-valued wavelet packets is proposed. An algorithm for constructing a class of two-direction orthogonal vector-valued compactly supported wavelets corresponding to the two-direction orthogonal vector-valued compactly supported scaling functions is proposed by virtue of matrix theory and time–frequency analysis method. The properties of the two-direction vector-valued wavelet packets are investigated. At last, the direct decomposition relation for space L 2(R) r is presented. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a double projection algorithm for a generalized variational inequality with a multi-valued mapping. Under standard conditions, our method is proved to be globally convergent to a solution of the variational inequality problem. Moreover, we present a unified framework of projection-type methods for multi-valued variational inequalities. Preliminary computational experience is also reported. [Copyright &y& Elsevier]

Abstract: We present in this paper a wavelet packet based QRS complex detection algorithm. Our proposed algorithm consists of a particular combination of two vectors obtained by applying a designed routine of QRS detection process using ‘haar’ and ‘db10’ wavelet functions respectively. The QRS complex detection routine is based on the histogram approach where our key idea was to search for the node with highest number of histogram coefficients, at center, which we assume that they are related to the iso-electric baseline whereas the remaining least number coefficients reflect the R waves peaks. Following a classical approach based of a calculated fixed threshold, the possible QRS complexes will be determined. The QRS detection complex algorithm has been applied to the whole MIT-BIH arrhythmia Database to assess its robustness. The algorithm reported a global sensitivity of 98.68%, positive predictive value of 97.24% and a percentage error of 04.12%. Eventhough, the obtained global results are not as excellent as expected, we have demonstrate that our designed QRS detection algorithm performs good on a partial selected high percentage of the whole database, e.g., the partial results, obtained when applying the algorithm on 85.01% of the whole MIT-BIH arrhythmia Database, are 99.14% of sensitivity, 98.94% of positive predictive value and 01.92% of percentage error. [Copyright &y& Elsevier]

Abstract: In this paper we consider identical parallel machines scheduling problems with a deteriorating maintenance activity. In this model, each machine has a deteriorating maintenance activity, that is, delaying the maintenance increases the time required to perform it. We need to make a decision on when to schedule the rate-modifying activities and the sequence of jobs to minimize some objective function. We concentrate on two goals separately, namely, minimizing the total absolute differences in completion times (TADC) and the total absolute differences in waiting times (TADW). We show that the problems remain polynomially solvable under the proposed model. [Copyright &y& Elsevier]

Abstract: In this paper, the issue of multi-degree reduction of Bézier curves with C 1 and G 2-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method. [Copyright &y& Elsevier]

Abstract: In the first part of this paper, we investigate the reduced forms of circulant matrices and quasi-skew circulant matrices. By using their properties we present two efficient algorithms to compute the square roots of circulant matrices and quasi-skew circulant matrices, respectively. Those methods are faster than the traditional algorithm which is based on the Schur decomposition. In the second part, we further consider circulant H-matrices with positive diagonal entries and develop two algorithms for computing their principal square roots. Those two algorithms have the common advantage that is they only need matrix–matrix multiplications in their iterative sequences, an operation which can be done very efficiently on modern high performance computers. [Copyright &y& Elsevier]

Abstract: Let γ(P m □ C n ) denote the domination number of the cylindrical grid graph formed by the Cartesian product of the graphs P m , the path of length m, m ⩾2 and the graph C n , the cycle of length n, n ⩾3. In this paper, methods to find the domination numbers of graphs of the form P m □ C n with n ⩾3 and m =2, 3 and 4 are proposed. Moreover, bounds on domination numbers of the graphs P 5 □ C n , n ⩾3 are found. The methods that are used to prove that results readily lead to algorithms for finding minimum dominating sets of the above mentioned graphs. [ABSTRACT FROM AUTHOR]