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Many real-life problems using mathematical modeling can be reduced to scalar and system of nonlinear equations. In this paper, we develop a family of three-step sixth-order method for solving nonlinear equations by employing weight functions in the second and third step of the scheme. Furthermore, we extend this family to the multidimensional case preserving the same order of convergence. Moreover, we have made numerical comparisons with the efficient methods of this domain to verify the suitability of our method. [ABSTRACT FROM AUTHOR]

This paper suggests a data envelopment analysis (DEA) model for selecting the most efficient alternative in advanced manufacturing technology in the presence of both cardinal and ordinal data. The paper explains the problem of using an iterative method for finding the most efficient alternative and proposes a new DEA model without the need of solving a series of LPs. A numerical example illustrates the model, and an application in technology selection with multi-inputs/multi-outputs shows the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a variational Bayesian (VB)-based iterative algorithm for ARX models with random missing outputs is proposed. The distributions of missing outputs can be estimated in the VB-E step, and the distributions of unknown parameters can be estimated in the VB-M step by the estimated missing outputs and the available outputs. Compared with the expectation-maximization-based iterative algorithm, this algorithm computes the latent variable and the parameter distributions at each iteration. Therefore, it is more accurate. The simulation results demonstrate the advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we establish an iterative algorithm and estimation of solutions for a fractional turbulent flow model in a porous medium under a suitable growth condition. Our main tool is the monotone iterative technique. [ABSTRACT FROM AUTHOR]

The paper deals with a steady state version of a nonlocal nonlinear parabolic problem defined on a bounded polygonal domain. The nonlocal term involved in the strong formulation essentially increases the complexity of the problem and the necessary total computational work. The nonlinear weak formulation of the problem is reduced to a linear one suitable for applications of Newtonian type iterative methods. A discrete problem is obtained by the FEM. A fast and stable iterative method with ninth-order of convergence is applied for solving the discrete problem. The iterative algorithm is described by a pseudo-code. The method is computer implemented and the approximate solutions are presented graphically. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and consider a new hybrid shrinking projection method for finding a common element of the set EP of solutions of a generalized equilibrium problem, the common fixed point set F of finite uniformly closed families of countable Bregman quasi-Lipschitz mappings in reflexive Banach spaces. It is proved that under appropriate conditions, the sequence generated by the hybrid shrinking projection method converges strongly to some point in $\mathit{EP} \cap F$. Relative examples are given. Strong convergence theorems are proved. The application for Bregman asymptotically quasi-nonexpansive mappings is also given. The main innovative points in this paper are as follows: (1) the notion of the uniformly closed family of countable Bregman quasi-Lipschitz mappings is presented and the useful conclusions are given; (2) the relative examples of the uniformly closed family of countable Bregman quasi-Lipschitz mappings are given in classical Banach spaces $l^{2}$ and $L^{2}$; (3) the application for Bregman asymptotically quasi-nonexpansive mappings is also given; (4) because the main theorems do not need the boundedness of the domain of mappings, so a corresponding technique for the proof is given. This new results improve and extend the previously known ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we present a family of optimal, in the sense of Kung-Traub's conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chun's fourth-order method. We use the Ostrowski's efficiency index and several numerical tests in order to compare the new methods with other known eighth-order ones. We also extend this comparison to the dynamical study of the different methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence, uniqueness and asymptotic behavior of solutions for the quasilinear parabolic systems with mixed quasimonotone reaction functions endowed with Dirichlet boundary condition, in which the elliptic operators are allowed to be degenerate. By the method of the coupled upper and lower solutions and its monotone iterations, it is shown that a pair of coupled upper and lower solutions ensures that the unique positive solution exists and is globally stable if the quasisolutions are equal. Moreover, we study the asymptotic behavior of solutions to the Lotka-Volterra predator-prey model with the density-dependent diffusion. [ABSTRACT FROM AUTHOR]

In this paper we re-examine the commonly accepted meaning of the two kinetic constants characterizing any enzymatic reaction, according to Michaelis-Menten kinetics. Expanding in terms of exponentials the solutions of the ODEs governing the reaction, we determine a new constant, which corrects some misinterpretations of current biochemical literature. [ABSTRACT FROM AUTHOR]

Abstract  This paper is concerned with a diffusive vector disease model with distributed delay. The existence of travelling wave front solutions connecting the zero equilibrium and the positive equilibrium is established by using an iterative technique and a nonstandard ordering for the set of profiles of the corresponding wave system recently developed by Wang, Li and Ruan (Travelling wave fronts in reactiondiffusion systems with spatio-temporal delays. J. Differential Equations 222 (2006), 185–232). The existence of travelling front solutions shows that there is a moving zone of transition from the disease free state to the infective state. [ABSTRACT FROM AUTHOR]

In this paper, we study a kind of 2–dimensional axi–symmetrical piston problem in compressible flow. The corresponding mathematical model is the well–known Euler system. With the Newton iteration procedure and energy estimate, we give the local existence of the shock front solution to this problem. [ABSTRACT FROM AUTHOR]

We consider iterative propositional calculi that are finite sets of propositional formulas together with modus ponens and an operation of superposition defined by a set of Mal'tsev operations. For such formulas, the question is studied whether the derivability problem for formulas is decidable. In the paper, we construct an undecidable iterative propositional calculus whose axioms depend on three variables. A derivation of formulas in the given calculus models the solution process for Post's correspondence problem. In particular, we prove that the general problem of expressibility for iterative propositional calculi is algorithmically undecidable. [ABSTRACT FROM AUTHOR]

A stage-structured predator-prey model (stage structure for both predator and prey) with modified Leslie-Gower and Holling-II schemes is studied in this paper. Using the iterative technique method and the fluctuation lemma, sufficient conditions which guarantee the global stability of the positive equilibrium and boundary equilibrium are obtained. Our results indicate that for a stage-structured predator-prey community, both the stage structure and the death rate of the mature species are the important factors that lead to the permanence or extinction of the system. [ABSTRACT FROM AUTHOR]

Iterative localization algorithms are critical part in the control of mobile autonomous robots because they feed fundamental position information to the robots. In a harsh unknown environment, the estimation of environmental noise is hardly obtained during the movement of the robots. It means that the state-of-the-art methods, which increase localization accuracy using error management, are unsuitable. In this paper, we deduced an upper bound of the localization error without knowing the precise model of environment noise when the anchor nodes have position errors. Utilizing the minimum upper bound, we can construct an optimal localization linear system of iterative localization algorithms based on least square. An algorithm of generating localization linear system is proposed by using the minimum upper bound. The algorithm reduces the impact of the shortage of environmental information on localization error propagation. Our simulation results show that the algorithm is insensitive to noise and can improve the localization accuracy by constructing a proper localization linear system with a high probability. [ABSTRACT FROM AUTHOR]

The methodologies for the construction of a knowledge structure mainly refer to the query to experts, the skill maps, and the data-driven approaches. This last method is of growing interest in recent literature. In this paper, an iterative procedure for building a skill map from a set of data is introduced. This procedure is based on the minimization of the distance between the knowledge structure delineated by a given skill map and the data. The accuracy of the proposed method is tested through a number of simulation studies where the amount of noise in the data is manipulated as well as the kind of structure to be reconstructed. Results show that the procedure is accurate and that its performance tends to be sufficiently stable even with high error rates. The procedure is compared to two already-existing methodologies to derive knowledge structures from a set of data. The use of the corrected Akaike Information Criterion (AICc) as a stopping criterion of the iterative reconstruction procedure is tested against the app criterion introduced by Schrepp. Moreover, two empirical applications on clinical data are reported, and their results show the applicability of the procedure. [ABSTRACT FROM AUTHOR]

In this paper we revisit coronoids, in particular multiple coronoids. We consider a mathematical formalisation of the theory of coronoid hydrocarbons that is solely based on incidence between hexagons of the infinite hexagonal grid in the plane. In parallel, we consider perforated patches, which generalise coronoids: in addition to hexagons, other polygons may also be present. Just as coronoids may be considered as benzenoids with holes, perforated patches are patches with holes. Both cases, coronoids and perforated patches, admit a generalisation of the altan operation that can be performed at several holes simultaneously. A formula for the number of Kekulé structures of a generalised altan can be derived easily if the number of Kekulé structures is known for the original graph. Pauling Bond Orders for generalised altans are also easy to derive from those of the original graph. [ABSTRACT FROM AUTHOR]

In this paper, a new algorithm for the numerical solution of the Bratu-type and the Lane-Emden problems with boundary conditions is presented. The proposed algorithm is based on the variational iteration method (VIM), where all the boundary conditions are used before designing the recursive scheme for the approximate solutions of considered boundary value problems. Unlike the VIM, the proposed algorithm avoids solving a sequence of nonlinear algebraic or (transcendental) equations for the undetermined coefficients. Convergence and error analysis of the proposed method is also given. Illustrative examples, of two different models, are examined to demonstrate the accuracy, applicability, and generality of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditions. More precisely, it is demonstrated that the preconditioned Mixed-Type Splitting (MTS) iterative methods can surpass the preconditioned AOR iterative methods for an entirely general class of preconditioners handled by Wang and Song [J. Comput. Appl. Math. 226 (2009), no. 1, 114-124]. Finally some numerical results are elaborated which confirm the validity of the established results. [ABSTRACT FROM AUTHOR]

This paper provides a new exact iterative method for the following problem. Two decision makers, a leader and a follower, compete to attract customers from a given market. The leader opens $$p$$ facilities, anticipating that the follower will react to the decision by opening $$r$$ facilities. Each customer patronizes the closest opened facility. The goal is to find $$p$$ facilities for the leader to maximize his market share. It is known that this problem is $$\Sigma ^P_2$$ -hard and can be presented as an integer linear program with a large number of constraints. Based on this representation, we design the new iterative exact method. A local search algorithm is used at each iteration to find a feasible solution for a system of constraints. Computational results and comparison with other exact methods show that the new method can be considered as one of the alternative approaches among the most advanced exact methods for the problem. [ABSTRACT FROM AUTHOR]

In this paper, a piecewise linear classifier based on polyhedral conic separation is developed. This classifier builds nonlinear boundaries between classes using polyhedral conic functions. Since the number of polyhedral conic functions separating classes is not known a priori, an incremental approach is proposed to build separating functions. These functions are found by minimizing an error function which is nonsmooth and nonconvex. A special procedure is proposed to generate starting points to minimize the error function and this procedure is based on the incremental approach. The discrete gradient method, which is a derivative-free method for nonsmooth optimization, is applied to minimize the error function starting from those points. The proposed classifier is applied to solve classification problems on 12 publicly available data sets and compared with some mainstream and piecewise linear classifiers. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a viscosity iterative algorithm for finding a common element of the set of solutions of a general variational inequality problem for two inverse strongly accretive operators and the set of fixed points of a δ-strict pseudocontraction in a real q-uniformly smooth Banach space. Some strong convergence theorems are obtained under appropriate conditions. As an application, we prove some strong convergence theorems for fixed point problems and variational inequality problems or equilibrium problems in Hilbert spaces. These results improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, based on the Noda iteration, we present inexact Noda iterations (INI), to find the smallest eigenvalue and the associated positive eigenvector of a large irreducible nonsingular $$M$$ -matrix. The positivity of approximations is critical in applications, and if the approximations lose the positivity then they may be meaningless and could not be interpreted. We propose two different inner tolerance strategies for solving the inner linear systems involved, and prove that the convergence of resulting INI algorithms is globally linear and superlinear with the convergence order $$\frac{1+\sqrt{5}}{2}$$ , respectively. The proposed INI algorithms are structure preserving and maintains the positivity of approximate eigenvectors. We also revisit the exact Noda iteration and establish a new quadratic convergence result. All the above is first done for the problem of computing the Perron root and the positive Perron vector of an irreducible nonnegative matrix and is then adapted to computing the smallest eigenpair of the irreducible nonsingular $$M$$ -matrix. Numerical examples illustrate that the proposed INI algorithms are practical, and they always preserve the positivity of approximate eigenvectors. We compare them with the Jacobi-Davidson method, the implicitly restarted Arnoldi method and the explicitly restarted Krylov-Schur method, all of which cannot guarantee the positivity of approximate eigenvectors, and illustrate that the overall efficiency of the INI algorithms is competitive with and can be considerably higher than the latter three methods. [ABSTRACT FROM AUTHOR]

The present paper aims to deal with a new iterative method to find a common solution of a generalized equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a sequence of nearly nonexpansive mappings. It is proved that the proposed method converges strongly to a common solution of above problems under some assumptions. The results here improve and extend some recent corresponding results by many other authors. [ABSTRACT FROM AUTHOR]

The computation of a defective eigenpair of nonlinear algebraic eigenproblems of the form $$T(\lambda )v=0$$ is challenging due to its ill-posedness and the linear convergence of classical single-vector Newton-like methods. In this paper, we propose and study new accelerated Newton-like methods for defective eigenvalues which exhibit quadratic local convergence at the cost of solving two linear systems per iteration. To the best of our knowledge, the accelerated algorithms are the most efficient methods for solving defective eigenpairs. The analyses are illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

Hesitant fuzzy linguistic term set (HFLTS) provides a new and useful tool for expressing decision makers (DMs)'s qualitative views and ideas since it allows DMs to hesitate about several possible linguistic terms. Consistency is the fundamental research in decision-making process under hesitant fuzzy linguistic preference relations (HFLPRs) decision-making environment and the distance measure is utilized as a technology to measure the consistency level of HFLPRs. However, traditional distance measures were developed based on an assumption that the number of linguistic terms in the corresponding HFLTSs is the same. Some optimization models to improve consistency level of HFLPRs did not give DMs strong sense of participation and a sense of respect for their preferences. To solve the above issues, in this paper, a new distance measure of HFLTSs is defined, and some desirable properties are discussed. After that, in line with the distance measure, we propose a consistency index of HFLPRs by computing the deviation between the normalized hesitant fuzzy linguistic preference relation (N-HFLPR) and its expected hesitant fuzzy linguistic preference relation (E-HFLPR). Furthermore, for unacceptable consistent HFLPRs, some local revised strategies provided by an automatic iterative algorithm are used to modify original HFLPRs until it satisfies acceptable consistency. Finally, some comparisons between the existing methods and our proposed approaches are to demonstrate the feasibility of the proposed approaches by utilizing several illustrative examples. [ABSTRACT FROM AUTHOR]

The inconsistency issue of pairwise comparison matrices has been an important subject in the study of the analytical network process. Most inconsistent elements can efficiently be identified by inducing a bias matrix only based on the original matrix. This paper further discusses the induced bias matrix and integrates all related theorems and corollaries into the induced bias matrix model. The theorem of inconsistency identification is proved mathematically using the maximum eigenvalue method and the contradiction method. In addition, a fast inconsistency identification method for one pair of inconsistent elements is proposed and proved mathematically. Two examples are used to illustrate the proposed fast identification method. The results show that the proposed new method is easier and faster than the existing method for the special case with only one pair of inconsistent elements in the original comparison matrix. [ABSTRACT FROM AUTHOR]

For $${b \in {^{\omega}}{\omega}}$$ , let $${\mathfrak{c}^{\exists}_{b, 1}}$$ be the minimal number of functions (or slaloms with width 1) to catch every functions below b in infinitely many positions. In this paper, by using the technique of forcing, we construct a generic model in which there are many coefficients $${\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}$$ with pairwise different values. In particular, under the assumption that a weakly inaccessible cardinal exists, we can construct a generic model in which there are continuum many coefficients $${\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}$$ with pairwise different values. In conjunction with these results, we give a generic model in which there are many Yorioka's ideals $${\mathcal{I}_{f_\alpha}}$$ with pairwise different covering numbers. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new parallel sparse iterative method (PPSIA) for computing the stationary distribution of large-scale Markov chains. The PPSIA method is based on Markov chain state isolation and aggregation techniques. The parallel method conserves as much as possible the benefits of aggregation, and Gauss-Seidel effects contained in the sequential algorithm (SIA) using a pipelined technique. Both SIA and PPSIA exploit sparse matrix representation in order to solve large-scale Markov chains. Some Markov chains have been tested to compare the performance of SIA, PPSIA algorithms with other techniques such as the power method, and the generalized minimal residual GMRES method. In all the tested models, PPSIA outperforms the other methods and shows a super-linear speed-up. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new hybrid iterative scheme for finding a common element of the set of zeroes of a maximal monotone operator, the set of fixed points of a relatively quasi-nonexpansive mapping, the sets of solutions of an equilibrium problem and the variational inequality problem in Banach spaces. As applications, we apply our results to obtain strong convergence theorems for a maximal monotone operator and quasi-nonexpansive mappings in Hilbert spaces and we consider a problem of finding a minimizer of a convex function. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlinear multigrid method for solving a general image denoising model with two L-regularization terms. Different from the previous studies, we give a simpler derivation of the dual formulation of the general model by augmented Lagrangian method. In order to improve the convergence rate of the proposed multigrid method, an improved dual iteration is proposed as its smoother. Furthermore, we apply the proposed method to the anisotropic ROF model and the anisotropic LLT model. We also give the local Fourier analysis (LFAs) of the Chambolle's dual iterations and a modified smoother for solving these two models, respectively. Numerical results illustrate the efficiency of the proposed method and indicate that such a multigrid method is more suitable to deal with large-sized images. [ABSTRACT FROM AUTHOR]

In this paper, we give an example of a complete computable infinitary theory T with countable models $${\mathcal{M}}$$ and $${\mathcal{N}}$$ , where $${\mathcal{N}}$$ is a proper computable infinitary extension of $${\mathcal{M}}$$ and T has no uncountable model. In fact, $${\mathcal{M}}$$ and $${\mathcal{N}}$$ are (up to isomorphism) the only models of T. Moreover, for all computable ordinals α, the computable $${\Sigma_\alpha}$$ part of T is hyperarithmetical. It follows from a theorem of Gregory (JSL 38:460-470, ; Not Am Math Soc 17:967-968, ) that if T is a Π set of computable infinitary sentences and T has a pair of models $${\mathcal{M}}$$ and $${\mathcal{N}}$$ , where $${\mathcal{N}}$$ is a proper computable infinitary extension of $${\mathcal{M}}$$ , then T would have an uncountable model. [ABSTRACT FROM AUTHOR]

In this paper a model reduction approach for elastic-viscoplastic evolution problems is considered. Enhancement of the PGD reduced model by a new iterative technique involving only elastic problems is investigated and allows to reduce CPU cost. The accuracy of the solution and convergence properties are tested on an academic example and a calculation time comparison with the commercial finite element code Abaqus is presented in the case of an industrial structure. [ABSTRACT FROM AUTHOR]

In this paper, we consider a modified disease model with distributed delay. The existence of traveling wave fronts connecting the zero equilibrium and the positive equilibrium is established by using an iterative technique and a nonstandard ordering for the set of profiles of the corresponding wave system. We also study the critical wave speed and give a detailed analysis on its location and asymptotic behavior with respect to the time delay. Our work extends some previous results. [ABSTRACT FROM AUTHOR]

The option pricing problem when the asset is driven by a stochastic volatility process and in the presence of transaction costs leads to solving a nonlinear partial differential equation. The nonlinear term in the PDE reflects the presence of transaction costs. Under a particular market completion assumption we derive the nonlinear PDE whose solution may be used to find the price of options. In this paper under suitable conditions, we give an algorithmic scheme to obtain the solution of the problem by an iterative method and provide numerical solutions using the finite difference method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide a general procedure to extract the constitutive parameters of a plasticity model starting from displacement measurements and using the Virtual Fields Method. This is a classical inverse problem which has been already investigated in the literature, however several new features are developed here. First of all the procedure applies to a general three-dimensional displacement field which leads to large plastic deformations, no assumptions are made such as plane stress or plane strain although only pressure-independent plasticity is considered. Moreover the equilibrium equation is written in terms of the deviatoric stress tensor that can be directly computed from the strain field without iterations. Thanks to this, the identification routine is much faster compared to other inverse methods such as finite element updating. The proposed method can be a valid tool to study complex phenomena which involve severe plastic deformation and where the state of stress is completely triaxial, e.g. strain localization or necking occurrence. The procedure has been validated using a three dimensional displacement field obtained from a simulated experiment. The main potentialities as well as a first sensitivity study on the influence of measurement errors are illustrated. [ABSTRACT FROM AUTHOR]

The 1985 paper by Carlos Alchourrón (1931-1996), Peter Gärdenfors, and David Makinson (AGM), 'On the Logic of Theory Change: Partial Meet Contraction and Revision Functions' was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twenty-five years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, computatibility of AGM operations, and criticism of the model. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm using binary trees is developed to detect the change points of a data set in which the data are assumed to be normally distributed. Usual BIC-type criteria are considered in the binary searching procedures when the number of change points is unknown. The algorithm is also extended to the switching regression models. Simulation study confirms that our algorithm is efficient compared with the ML-method. A real data example also verifies that the proposed procedure is appropriate. [ABSTRACT FROM AUTHOR]

Abstract  Suppressed fuzzy c-means (s-FCM) clustering was introduced in Fan et al. (Pattern Recogn Lett 24:1607–1612, 2003) with the intention of combining the higher speed of hard c-means (HCM) clustering with the better classification properties of fuzzy c-means (FCM) algorithm. The authors modified the FCM iteration to create a competition among clusters: lower degrees of memberships were diminished according to a previously set suppression rate, while the largest fuzzy membership grew by swallowing all the suppressed parts of the small ones. Suppressing the FCM algorithm was found successful in the terms of accuracy and working time, but the authors failed to answer a series of important questions. In this paper, we clarify the view upon the optimality and the competitive behavior of s-FCM via analytical computations and numerical analysis. A quasi competitive learning rate (QLR) is introduced first, in order to quantify the effect of suppression. As the investigation of s-FCM’s optimality did not provide a precise result, an alternative, optimally suppressed FCM (Os-FCM) algorithm is proposed as a hybridization of FCM and HCM. Both the suppressed and optimally suppressed FCM algorithms underwent the same analytical and numerical evaluations, their properties were analyzed using the QLR. We found the newly introduced Os-FCM algorithm quicker than s-FCM at any nontrivial suppression level. Os-FCM should also be favored because of its guaranteed optimality. [ABSTRACT FROM AUTHOR]

In this paper, for a Lipschitz pseudocontractive mapping T, we study the strong convergence of iterative schemes generated by , where f is a Lipschitz strong pseudocontractive mapping and { β n}, { α n} satisfy (i) $$\lim\limits_{n\to\infty}\alpha_n = 0$$; (ii) $$ \sum\limits_{n=1}^\infty \alpha_n = \infty$$; (iii) $$\lim\limits_{n\to\infty}\frac{\beta_n^2}{\alpha_n} = 0$$. [ABSTRACT FROM AUTHOR]

This paper presents a general mixed-norm minisum problem for locating a single facility in continuous space. It is assumed that several transportation modes exist between the new facility and a given set of fixed points (the customers), each mode being represented by a different ℓ p norm. A simple extension of Weiszfeld’s well known iterative procedure is proposed to solve the model. Convergence properties and optimality criteria are derived, and computational results are given. [ABSTRACT FROM AUTHOR]

Abstract  A mathematical model of amperometric biosensors has been developed. In this paper, He’s variational iteration method is implemented to give approximate and analytical solutions of non-linear reaction diffusion equations containing a non linear term related to Michaelis–Menten kinetic of the enzymatic reaction. The variational iteration method which produces the solutions in terms of convergent series, requiring no linearization or small perturbation. These analytical results are compared with available limiting case result and are found to be in good agreement. [ABSTRACT FROM AUTHOR]

In this paper, we give details of results of Shelah concerning iterated Namba forcing over a ground model of CH and iteration of P[ W] where W is a stationary subset of ω 2 concentrating on points of countable cofinality. [ABSTRACT FROM AUTHOR]

Abstract  In this paper a spectral method and a numerical continuation algorithm for solving eigenvalue problems for the rectangular von Kármán plate with different boundary conditions (simply supported, partially or totally clamped) and physical parameters are introduced. The solution of these problems has a postbuckling behaviour. The spectral method is based on a variational principle (Galerkin’s approach) with a choice of global basis functions which are combinations of trigonometric functions. Convergence results of this method are proved and the rate of convergence is estimated. The discretized nonlinear model is treated by Newton’s iterative scheme and numerical continuation. Branches of eigenfunctions found by the algorithm are traced. Numerical results of solving the problems for polygonal and ferroconcrete plates are presented. [ABSTRACT FROM AUTHOR]

Let { X n , n ≥ 0} be an AR(1) process. Let Q( n) be the rescaled range statistic, or the R/ S statistic for { X n } which is given by $$ (\max _{{1 \leqslant k \leqslant n}} ({\sum\nolimits_{j = 1}^k {(X_{j} - \bar{X}_{n} )) - \min _{{1 \leqslant k \leqslant n}} ({\sum\nolimits_{j = 1}^k {(X_{j} - \bar{X}_{n} )))/(n^{{ - 1}} {\sum\nolimits_{j = 1}^n {(X_{j} - \bar{X}_{n} )^{2} )^{{1/2}} } }} }} } $$ where $$ \bar{X}_{n} = n^{{ - 1}} {\sum\nolimits_{j = 1}^n {X_{j} .} } $$ In this paper we show a law of iterated logarithm for rescaled range statistics Q( n) for AR(1) model. [ABSTRACT FROM AUTHOR]

The steady partially cavitating flow around two-dimensional hydrofoils was simulated numerically by the low-order potential-based boundary integration method. The cavity shape and length are determined for given cavitating numbers in the course of iteration by satisfying the kinematic and dynamic boundary conditions. The re-entrant jet model and the pressure-recovery close model are adopted to replace the high turbulent and two-phase wake forming behind the cavity. The results are compared with the other published numerical ones. [ABSTRACT FROM AUTHOR]

The proximal gradient algorithm is an appealing approach in finding solutions of non-smooth composite optimization problems, which may only has weak convergence in the infinite-dimensional setting. In this paper, we introduce a modified proximal gradient algorithm with outer perturbations in Hilbert space and prove that the algorithm converges strongly to a solution of the composite optimization problem. We also discuss the bounded perturbation resilience of the basic algorithm of this iterative scheme and illustrate it with an application. [ABSTRACT FROM AUTHOR]

Powder hot isostatic pressing is a resource-efficient approach for net-shape manufacture of high-value nickel-based superalloy structures. One of the key challenges to its application is the availability of modelling tools that can predict the geometrical changes that occur during the consolidation process in order to design the tooling required. In this work, the utility of a finite element code, based on the plastic collapse model, was assessed. The finite element model was then combined with an optimisation toolbox to design (in an iterative process) the tooling required to accommodate the powder consolidation process. The model was validated for IN718 superalloy using a demonstrator with complex features. Microstructural characterisation was also performed to assess the degree of densification. Although the finite element model did not account for creep deformation, good predictions were obtained. Nevertheless, predictions of the dimensions of consolidated samples were obtained, which were typically within 1 % of the observations, suggesting that plastic collapse accounts for 99 % of the geometrical changes due to the densification process for the range of hot isostatic pressing parameters investigated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of generalized nonexpansive mappings which is wider than the class of mappings satisfying (C) condition. Different properties and some fixed point results for these mappings are obtained here. The convergence of some iteration schemes to the fixed point is also discussed with suitable examples. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new methodology to automatically find a model that fits on an experimental variogram. Starting with a linear combination of some basic authorized structures (for instance, spherical and exponential), a numerical algorithm is used to compute the parameters, which minimize a distance between the model and the experimental variogram. The initial values are automatically chosen and the algorithm is iterative. After this first step, parameters with a negligible influence are discarded from the model and the more parsimonious model is estimated by using the numerical algorithm again. This process is iterated until no more parameters can be discarded. A procedure based on a profiled cost function is also developed in order to use the numerical algorithm for multivariate data sets (possibly with a lot of variables) modeled in the scope of a linear model of coregionalization. The efficiency of the method is illustrated on several examples (including variogram maps) and on two multivariate cases. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy (even that of the optimal dividend strategy). Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang (2) and compound Poisson risk models are also given. [ABSTRACT FROM AUTHOR]