Search results for: rate of convergence

Authors: Andreas Aceranti, Guido Bighiani, Francesca Crotto, Marco Colorato, Stefania Zaghi, Marino Zanetti, Simonetta Vernocchi

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The management of eye parameters such as convergence, accommodation, and miosis is very complex; in fact, both the neurovegetative system and the complex Oculocephalgiria system come into play. We have found the effectiveness of the "highvelocity low amplitude" technique directed on C7-T1 (where the cilio-spinal nucleus of the budge is located) in improving the convergence parameter through the measurement of the point of maximum convergence. With this research, we set out to investigate whether the improvement obtained through the High Velocity Low Amplitude maneuver lasts over time, carrying out a pre-manipulation measurement, one immediately after manipulation and one month after manipulation. We took a population of 30 subjects with both refractive and non-refractive problems. Of the 30 patients tested, 27 gave a positive result after the High Velocity Low Amplitude maneuver, giving an improvement in the point of maximum convergence. After a month, we retested all 27 subjects: some further improved the result, others kept, and three subjects slightly lost the gain obtained. None of the re-tested patients returned to the point of maximum convergence starting pre-manipulation. This result opens the door to a multidisciplinary approach between ophthalmologists and osteopaths with the aim of addressing oculomotricity and convergence deficits that increasingly afflict our society due to the massive use of devices and for the conduct of life in closed and restricted environments.

Keywords: point of maximum convergence, HVLA, improvement in PPC, convergence

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Authors: Reza Mollapourasl, Majid Haghi

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In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: radial basis functions, Hermite finite difference, Helmholtz equation, stability

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Authors: R. Sabre

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This work focuses on the symmetric alpha stable process with continuous time frequently used in modeling the signal with indefinitely growing variance, often observed with an unknown additive error. The objective of this paper is to estimate this error from discrete observations of the signal. For that, we propose a method based on the smoothing of the observations via Jackson polynomial kernel and taking into account the width of the interval where the spectral density is non-zero. This technique allows avoiding the “Aliasing phenomenon” encountered when the estimation is made from the discrete observations of a process with continuous time. We have studied the convergence rate of the estimator and have shown that the convergence rate improves in the case where the spectral density is zero at the origin. Thus, we set up an estimator of the additive error that can be subtracted for approaching the original signal without error.

Keywords: spectral density, stable processes, aliasing, non parametric

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Authors: Sharfi Dirar, Shihab Elhaj, Ahmed El Fatih

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Computational fluid dynamics were used to simulate and study the heated water boiler tube for both normal and rifled tube with a refinement of the mesh to check the convergence. The operation condition was taken from GARRI power station and used in a boundary condition accordingly. The result indicates the rifled tube has higher heat transfer efficiency than the normal tube.

Keywords: boiler tube, convergence check, normal tube, rifled tube

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Authors: Vishal Jaunky, Jonas Grafström

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The development of the European Union’s (EU) single economic market and rapid technological change has resulted in major structural changes in EU’s member states economies. The general liberalization process that the countries has undergone together has convinced the governments of the member states of need to upgrade their economic and training systems in order to be able to face the economic globalization. Several signs of economic convergence have been found but less is known about the knowledge production. This paper addresses the convergence pattern of technological innovation in 13 European Union (EU) states over the time period 1990-2011 by means of parametric and non-parametric techniques. Parametric approaches revolve around the neoclassical convergence theories. This paper reveals divergence of both the β and σ types. Further, we found evidence of stochastic divergence and non-parametric convergence approach such as distribution dynamics shows a tendency towards divergence. This result is supported with the occurrence of γ-divergence. The policies of the EU to reduce technological gap among its member states seem to be missing its target, something that can have negative long run consequences for the market.

Keywords: convergence, patents, panel data, European union

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Authors: Manideepa Saha, Jahnavi Chakrabarty

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Generalized Jacobi (GJ) and Generalized Gauss-Seidel (GGS) methods are most effective than conventional Jacobi and Gauss-Seidel methods for solving linear system of equations. It is known that GJ and GGS methods converge for strictly diagonally dominant (SDD) and for M-matrices. In this paper, we study the convergence of GJ and GGS converge for symmetric positive definite (SPD) matrices, L-matrices and H-matrices. We introduce a generalization of successive overrelaxation (SOR) method for solving linear systems and discuss its convergence for the classes of SDD matrices, SPD matrices, M-matrices, L-matrices and for H-matrices. Advantages of generalized SOR method are established through numerical experiments over GJ, GGS, and SOR methods.

Keywords: convergence, Gauss-Seidel, iterative method, Jacobi, SOR

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Authors: Mubarak Alhajri

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This paper addresses certain inherent limitations of local priority hysteresis switching logic. Our main result establishes that under persistent excitation assumption, it is possible to relax constraints requiring strict positivity of local priority and hysteresis switching constants. Relaxing these constraints allows the adaptive system to reach optimality which implies the performance improvement. The unconstrained local priority hysteresis switching logic is examined and conditions for global convergence are derived.

Keywords: adaptive control, convergence, hysteresis constant, hysteresis switching

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Authors: Francis O. Nwawuru, Jeremiah N. Ezeora

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In this paper, a new algorithm for solving the system of split equilibrium and fixed point problems in real Hilbert spaces is considered. The equilibrium bifunction involves a nite family of pseudo-monotone mappings, which is an improvement over monotone operators. More so, it turns out that the solution of the finite family of nonexpansive mappings. The regularized parameters do not depend on Lipschitz constants. Also, the computations of the stepsize, which plays a crucial role in the convergence analysis of the proposed method, do require prior knowledge of the norm of the involved bounded linear map. Furthermore, to speed up the rate of convergence, an inertial term technique is introduced in the proposed method. Under standard assumptions on the operators and the control sequences, using a modified Halpern iteration method, we establish strong convergence, a desired result in applications. Finally, the proposed scheme is applied to solve some optimization problems. The result obtained improves numerous results announced earlier in this direction.

Keywords: equilibrium, Hilbert spaces, fixed point, nonexpansive mapping, extragradient method, regularized equilibrium

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Authors: Saleh Maina

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There is an on-going debate among intellectuals and scholars of international relations and world politics over the direction which the world is heading particularly in the current era of globalization. On the one hand are adherents to the convergence thesis which is premised on the assumption that global social order is tending toward universalism which could translate into the possible end of the classical state system and the unification of world societies under a single and common ideological dispensation. The convergence thesis is hinged on the globalization process which is gradually reducing world societies into a 'global village'. On the other hand are intellectuals who hold the view that despite advances made in communication technology which appear to threaten the survival of the classical state system. Invariance, as expressed in the survival of the existing state system and the diverse social traditions in world societies, remain a realistic possibility contrary to the conclusions of the convergence thesis. The invariance thesis has been advanced by scholars like Samuel P. Huntington whose work on clash of civilizations suggests that world peace can only be sustained through the co-habitation of diverse civilizations across the world. The purpose of this paper is to examine both sides of the debate with the aim of making a realistic assessment on where world societies are headed, between convergence and invariance. Using the realist theory of international relations as our theoretical premise the paper argues that while there is sufficient ground to predict the future direction of world societies as headed towards some form of convergence, invariance as expressed in the co-existence of diverse civilizations will for a long time remain a major feature of the international system.

Keywords: convergence, invariance, clash of civilization, classical state system, universalism

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Authors: Alemayehu Geremew Geremew

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We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.

Keywords: common fixed point, Mann iteration, multivalued mapping, weak convergence

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Authors: Gulay Aras, Isil Kutluturk Karagoz, Z. Candan Algun

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Background: Hypermetropia in school-age is a pathology that responds to treatment. In the literature, there has been no study of exercise practice in hypermetropia treatment. Objective: The purpose of this study was to investigate the effects of eye exercises and convergence exercise on visual acuity in school-age children with hypermetropia. Methods: Forty volunteer school-age children with hypermetropia (30 girls, 30 boys, between 7-17 years of age) were included in the study. Sociodemographic information and clinical characteristics were evaluated. 40 participants were randomly divided into two groups: eye exercises and convergence exercises. Home exercise protocols were given to all groups for six weeks, and regular phone calls were made once a week. Individuals performed eye exercises 10 times, convergence exercises 5 min. for two sessions per day for six weeks. The right and left eyes of all the subjects participating in the study were assessed separately by the eye doctor with a Snellen chart. The participants' quality of life was assessed using Pediatric Quality of Life Inventory Version 4.0. Physical health total score (PHTS) and scale total score (STS), which were obtained by evaluating Psychosocial health total score (PSHTS) school, emotional and social functioning, were calculated separately in the scores. At the end of the exercise program, the assessment tests applied at the beginning of the study were reapplied to all individuals. Results: There was no statistically significant difference between the pre- and post-Snellen chart measurements and quality of life in the eye exercises group (p > 0,05). There was a statistically significant difference in visual acuity of right and left eyes (p=0,004, p=0,014) and quality of life in PHTS, PSHTS and STS in the convergence exercise group (p=0,001, p=0,017, p=0,001). Conclusions: In school-age children, convergence exercises were found to be effective on visual acuity and health-related quality of life. Convergence exercises are recommended for the treatment of school-aged children with hypermetropia.

Keywords: convergence exercise, eye exercises, hypermetropia, school-age children

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Authors: Paula Verdugo-Hernandez, Patricio Cumsille

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We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of mathematical working spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.

Keywords: convergence, graphical representations, mathematical working spaces, paradigms of real analysis, real number sequences

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Authors: Badoiu Mihaela Catalina

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Main focus of COHESION policy was reducing social and economic disparities between member states and regions, sustainable development and equal opportunities. In this perspective, the present study intend to analyze the evolution of the European architecture and its direct impact over the real convergence in the member states.

Keywords: cooperation, European union, member states, cohesion policy

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Authors: Bastien Batardière, Joon Kwon

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For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past gradients and thereby adapt to the geometry of the objective function. Variants such as RMSprop and Adam demonstrate outstanding practical performance that have contributed to the success of deep learning. In this work, we present AdaLVR, which combines the AdaGrad algorithm with loopless variance-reduced gradient estimators such as SAGA or L-SVRG that benefits from a straightforward construction and a streamlined analysis. We assess that AdaLVR inherits both good convergence properties from VR methods and the adaptive nature of AdaGrad: in the case of L-smooth convex functions we establish a gradient complexity of O(n + (L + √ nL)/ε) without prior knowledge of L. Numerical experiments demonstrate the superiority of AdaLVR over state-of-the-art methods. Moreover, we empirically show that the RMSprop and Adam algorithm combined with variance-reduced gradients estimators achieve even faster convergence.

Keywords: convex optimization, variance reduction, adaptive algorithms, loopless

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Authors: Young Hee Geum

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We compare optimal quartic order method for the multiple zeros of nonlinear equations illustrating the basins of attraction. To construct basins of attraction effectively, we take a 600×600 uniform grid points at the origin of the complex plane and paint the initial values on the basins of attraction with different colors according to the iteration number required for convergence.

Keywords: basins of attraction, convergence, multiple-root, nonlinear equation

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Authors: Giorgi Dalakishvili, Goderdzi G. Didebulidze, Maya Todua

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The possibility of sporadic E (Es) layer formation in the mid-latitude nighttime lower thermosphere by horizontal homogeneous and inhomogeneous (vertically and horizontally changing) winds is investigated in 3D by analytical and numerical solutions of continuity equation for dominant heavy metallic ions Fe+. The theory of influence of wind velocity direction, value, and its shear on formation of sporadic E is developed in case of presence the effect of horizontally changing wind (the effect of horizontal convergence). In this case, the horizontal wind with horizontal shear, characterized by compressibility and/or vortices, can provide an additional influence on heavy metallic ions Fe+ horizontal convergence and Es layers density, which can be formed by their vertical convergence caused as by wind direction and values and by its horizontal shear as well. The horizontal wind value and direction have significant influence on ion vertical drift velocity and its minimal negative values of divergence necessary for development of ion vertical convergence into sporadic E type layer. The horizontal wind horizontal shear, in addition to its vertical shear, also influences the ion drift velocity value and its vertical changes and correspondingly on formation of sporadic E layer and its density. The atmospheric gravity waves (AGWs), with relatively smaller horizontal wave length than planetary waves and tidal motion, can significantly influence location of ion vertical drift velocity nodes (where Es layers formation expectable) and its vertical and horizontal shear providing ion vertical convergence into thin layer. Horizontal shear can cause additional influence in the Es layers density than in the case of only wind value and vertical shear only. In this case, depending on wind direction and value in the height region of the lower thermosphere about 90-150 km occurs heavy metallic ions (Fe+) vertical convergence into thin sporadic E type layer. The horizontal wind horizontal shear also can influence on ions horizontal convergence and density and location Es layers. The AGWs modulate the horizontal wind direction and values and causes ion additional horizontal convergence, while the vertical changes (shear) causes additional vertical convergence than in the case without vertical shear. Influence of horizontal shear on sporadic E density and the importance of vertical compressibility of the lower thermosphere, which also can be influenced by AGWs, is demonstrated numerically. For the given wavelength and background wind, the predictability of formation Es layers and its possible location regions are shown. Acknowledgements: This study was funded by Georgian Shota Rustaveli National Science Foundation Grant no. FR17-357.

Keywords: in-homogeneous, sporadic E, thermosphere, wind

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Authors: Kuniyoshi Abe

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Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear equations Ax = b, for x, where A is a given n-by-n matrix, and b is a given n-vector. Typically, the dimension of the linear equation is high and the matrix is sparse. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG stabilized (Bi-CGSTAB), BiCGStab2, and BiCGstab(l) have been developed to improve the convergence of Bi-CG. Bi-CGSTAB has been most often used for efficiently solving the linear equation, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the Bi-CG coefficients, has been proposed. It may avoid stagnation and lead to faster computation. Motivated by a large number of processors in present petascale high-performance computing hardware, the scalability of Krylov subspace methods on parallel computers has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The resulting global synchronization phases cause communication overhead on parallel computers. The parallel variants of Krylov subspace methods reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants of Bi-CGSTAB may become worse than that of the standard Bi-CGSTAB. In this paper, therefore, we compare the convergence speed between the standard Bi-CGSTAB and the parallel variants by numerical experiments and show that the convergence speed of the standard Bi-CGSTAB is faster than the parallel variants. Moreover, we propose the stabilization strategy for the parallel variants.

Keywords: bi-conjugate gradient stabilized method, convergence speed, Krylov subspace methods, linear equations, parallel variant

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Authors: Sadegh Sadeghi, Negar Shabani

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From a thermal point of view, zeotropic mixtures are likely to be more efficient than azeotropic fluids in low-temperature thermodynamic cycles due to their suitable boiling characteristics. In this study, performance of a low-temperature Kalina cycle with R717/water working fluid used in different existing power plants is mathematically investigated. To analyze the behavior of the cycle, mass conservation, energy conservation, and exergy balance equations are presented. With regard to the similarity in molar mass of R717 (17.03 gr/mol) and water (18.01 gr/mol), there is no need to alter the size of Kalina system components such as turbine and pump. To optimize the cycle energy and exergy efficiencies simultaneously, a constrained multi-objective optimization is carried out applying an Artificial Bee Colony algorithm. The main motivation behind using this algorithm lies on its robustness, reliability, remarkable precision and high–speed convergence rate in dealing with complicated constrained multi-objective problems. Convergence rates of the algorithm for calculating the optimal energy and exergy efficiencies are presented. Subsequently, due to the importance of exergy concept in Kalina cycles, exergy destructions occurring in the components are computed. Finally, the impacts of pressure, temperature, mass fraction and mass flow rate on the energy and exergy efficiencies are elaborately studied.

Keywords: artificial bee colony algorithm, binary zeotropic mixture, constrained multi-objective optimization, energy efficiency, exergy efficiency, Kalina cycle

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Authors: Agrinë Baraku

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This paper focuses on the convergence of the internet, fake news, and democracy. This paper will examine the convergence of these concepts, the tenets of democracy which are affected by the ever-increasing exposure to fake news, and whether the impact strengthens or can further weaken countries with fragile democracies. To demonstrate the convergence and the impact and to further the discussion about this topic, the case of Kosovo is explored. Its position in the Western Balkans makes it even more susceptible to the pressure stemming from geopolitical interests, which intersect with the generation of fake news by different international actors. Domestically, through data generated by Kantar (Index) Kosova Longitudinal Study on Media Measurement Survey (MMS), which focused on media viewership, the trend among Kosovar citizens is traced and then inserted into a bigger landscape, which is compounded by tenuous circumstances and challenges that Kosovo faces. Attention will be paid to what this can tell about where Kosovo currently is and the possibilities of what can be done regarding the phenomenon that is taking place.

Keywords: democracy, disinformation, internet, social media, fake news

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Authors: Philippe Gugler

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This contribution reflects some important questions regarding inter alia the economic development occurring in the light of the ASEAN’s goal of creating the ASEAN Economic Community (AEC) by 2015. We observe a continuing economic growth of GDP per capita over recent years despite the negative effects of the world economic crisis. IMF forecasts indicate that this trend will continue. The paper focuses on the analysis and comparison of economic growth trends of ASEAN countries.

Keywords: ASEAN, convergence, divergence, economic growth, globalization, integration

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Authors: Preeti Sharma

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This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

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Authors: Safeer Hussain Khan

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In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves and generalizes corresponding results in the literature in two ways: the iterative process is faster, operators are more general. In the end, we indicate that the results can also be proved with the iterative process with error terms.

Keywords: contractive-like operator, iterative process, fixed point, strong convergence

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Authors: Malika El Kyal, Ahmed Machmoum

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We prove the superlinear convergence of asynchronous multi-splitting methods applied to differential equations. This study is based on the technique of nested sets. It permits to specify kind of the convergence in the asynchronous mode.The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, ODE

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Authors: Helmi Temimi

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In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

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Authors: M. S. Turan, Dimple

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Due to implementation of IFRS by several developed and developing countries, India has no option other than to converge their accounting standards with IFRS. There are over 10,000 listed companies required to implement IFRS in India. IFRS based financial information presented by a company is different from the same information provided by Indian GAAPs. In this study, we have brought out and analyzed the effect of IFRS reporting on the financial statements of selected companies. The results reveal that convergence with IFRS brought prominent positive variations in the values of quick ratio, debt/equity ratio, proprietary ratio and net profit ratio, while negative variation is brought in the values of current ratio, debt to total assets ratio, operating profit ratio, return on capital employed and return on shareholders’ equity ratios. It also presents significant changes in the values of items of balance sheet, profit and loss account and cash flow statement.

Keywords: IFRS, reporting standards, convergence process, results

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Authors: O. M. Bamigbola, A. A. Ibrahim

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Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined a priori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss-Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss-Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: linear algebraic system, Gauss-Seidel iteration, algebraic structure, convergence

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Authors: Farangiz Davranbekova

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Subject: The study explores the impact of Over-the-Top services in the sports rights market, focusing on football games. This impact is analysed in the big five European football markets. The research entails how the pay-TV market is combating the disruptors' entry, how the fans are adjusting to these changes and how leagues and football clubs are orienting in the transitional period of more choice. Aims and methods: The research aims to offer a general overview of the impact of OTT players in the football rights market. A theoretical framework of Jenkins’ five layers of convergence is implemented to analyse the transition the sports rights market is witnessing from various angles. The empirical analysis consists of secondary research data as and seven expert interviews from three different clusters. The findings are bound by the combination of the two methods offering general statements. Findings: The combined secondary data as well as expert interviews, conducted on five layers of convergence found: 1. Technological convergence presents that football content is accessible through various devices with innovative digital features, unlike the traditional TV set box. 2. Social convergence demonstrates that football fans multitask using various devices on social media when watching the games. These activities are complementary to traditional TV viewing. 3. Cultural convergence points that football fans have a new layer of fan engagement with leagues, clubs and other fans using social media. Additionally, production and consumption lines are blurred. 4. Economic convergence finds that content distribution is diversifying and/or eroding. Consumers now have more choices, albeit this can be harmful to them. Entry barriers are decreased, and bigger clubs feel more powerful. 5. Global convergence shows that football fans are engaging with not only local fans but with fans around the world that social media sites enable. Recommendation: A study on smaller markets such as Belgium or the Netherlands would benefit the study on the impact of OTT. Additionally, examination of other sports will shed light on this matter. Lastly, once the direct-to-consumer model is fully taken off in Europe, it will be of importance to examine the impact of such transformation in the market.

Keywords: sports rights, OTT, pay TV, football

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Authors: Maryam Moosavi, Hadi Khatibzadeh

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The main purpose of this paper is to study the proximal point algorithm for quasi-nonexpansive mappings in Hadamard spaces. △-convergence and strong convergence of cyclic resolvents for a finite family of quasi-nonexpansive mappings one to a fixed point of the mappings are established

Keywords: Fixed point, Hadamard space, Proximal point algorithm, Quasi-nonexpansive sequence of mappings, Resolvent

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Authors: Bharti Gupta, V. K. Kukreja

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A comprehensive numerical study is presented for the solution of time-dependent advection diffusion problems by using cubic B-spline collocation method. The linear combination of cubic B-spline basis, taken as approximating function, is evaluated using the zeros of shifted Chebyshev polynomials as collocation points in each element to obtain the best approximation. A comparison, on the basis of efficiency and accuracy, with the previous techniques is made which confirms the superiority of the proposed method. An asymptotic convergence analysis of technique is also discussed, and the method is found to be of order two. The theoretical analysis is supported with suitable examples to show second order convergence of technique. Different numerical examples are simulated using MATLAB in which the 3-D graphical presentation has taken at different time steps as well as different domain of interest.

Keywords: cubic B-spline basis, spectral norms, shifted Chebyshev polynomials, collocation points, error estimates

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Authors: Alina Mirza, Sumrin M. Kabir, Shahzad A. Sheikh

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The Orthogonal Frequency Division Multiplexing (OFDM) with high data rate, high spectral efficiency and its ability to mitigate the effects of multipath makes them most suitable in wireless application. Impulsive noise distorts the OFDM transmission and therefore methods must be investigated to suppress this noise. In this paper, a State Space Recursive Least Square (SSRLS) algorithm based adaptive impulsive noise suppressor for OFDM communication system is proposed. And a comparison with another adaptive algorithm is conducted. The state space model-dependent recursive parameters of proposed scheme enables to achieve steady state mean squared error (MSE), low bit error rate (BER), and faster convergence than that of some of existing algorithm.

Keywords: OFDM, impulsive noise, SSRLS, BER

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