Search results for: convergence analysis

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: 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: 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: Omenogor, Happy Dumbi

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This paper examines the areas of convergence and divergence between English and Ųkwųanį (a language in Nigeria) vowel systems with particular emphasis on the front vowels. It specifies areas of difficulty for the average Ųkwųanį users of English and Ųkwųanį L1 users of English as a second language. The paper explains the nature of contrastive analysis, the geographical locations where Ųkwųanį is spoken as mother tongue as well as English and Ųkwųanį front vowels. The principles of establishing phonemes, minimal pairs in Ųkwųanį as well as the vowel charts in both languages are among the issues highlighted in this paper.

Keywords: convergence, divergence, English, Ukwųanį

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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: 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: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Arbolino Roberta, Boffardi Raffaele

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Achieving the highest effectiveness for the National Plans for Recovery and Resilience (NPRR) while strengthening the objectives of cohesion and reduction of intra-EU unbalances is only possible by means of strategic, coordinated, and coherent policy planning. Therefore, the present research aims at assessing and quantifying the potential impact of NPRRs across the twenty-seven European Member States in terms of economic convergence, considering disaggregated data on industrial, construction, and service sectors. The first step of the research involves a performance analysis of the main macroeconomic indicators describing the trends of twenty-seven EU economies before the pandemic outbreak. Subsequently, in order to define the potential effect of the resources allocated, we perform an impact analysis of previous similar EU investment policies, estimating national-level sectoral elasticity associated with the expenditure of the 2007-2013 and 2014-2020 Cohesion programmes funds. These coefficients are then exploited to construct adjustment scenarios. Finally, convergence analysis is performed on the data used for constructing scenarios in order to understand whether the expenditure of funds might be useful to foster economic convergence besides driving recovery. The results of our analysis show that the allocation of resources largely mirrors the aims of the policy framework underlying the NPRR, thus reporting the largest investments in both those sectors most affected by the economic shock (services) and those considered fundamental for the digital and green transition. Notwithstanding an overall positive effect, large differences exist among European countries, while no convergence process seems to be activated or fostered by these interventions.

Keywords: NPRR, policy evaluation, cohesion policy, scenario Nalsysi

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Authors: Salah Al-Din I. Badran, Samad Ahmadi, Dylan Menzies, Ismail Shahin

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This paper describes a new efficient blind source separation method; in this method we use a non-uniform filter bank and a new structure with different sub-bands. This method provides a reduced permutation and increased convergence speed comparing to the full-band algorithm. Recently, some structures have been suggested to deal with two problems: reducing permutation and increasing the speed of convergence of the adaptive algorithm for correlated input signals. The permutation problem is avoided with the use of adaptive filters of orders less than the full-band adaptive filter, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each sub-band than the input signal at full-band, and can promote better rates of convergence.

Keywords: Blind source separation, estimates, full-band, mixtures, sub-band

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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: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Cemil Turan, Mohammad Shukri Salman

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The convergence rate of the least-mean-square (LMS) algorithm deteriorates if the input signal to the filter is correlated. In a system identification problem, this convergence rate can be improved if the signal is white and/or if the system is sparse. We recently proposed a sparse transform domain LMS-type algorithm that uses a variable step-size for a sparse system identification. The proposed algorithm provided high performance even if the input signal is highly correlated. In this work, we investigate the performance of the proposed TD-LMS algorithm for a large number of filter tap which is also a critical issue for standard LMS algorithm. Additionally, the optimum value of the most important parameter is calculated for all experiments. Moreover, the convergence analysis of the proposed algorithm is provided. The performance of the proposed algorithm has been compared to different algorithms in a sparse system identification setting of different sparsity levels and different number of filter taps. Simulations have shown that the proposed algorithm has prominent performance compared to the other algorithms.

Keywords: adaptive filtering, sparse system identification, TD-LMS algorithm, VSSLMS algorithm

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Authors: Harendra Singh, Rajesh Pandey

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The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.

Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis

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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: Hassan Samadi, Mustapha El Jarroudi

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In this work, we consider the homogenization of a non-linear problem in periodic medium with two periodic connected media exchanging a heat flux throughout their common interface. The interfacial exchange coefficient λ is assumed to tend to zero or to infinity following a rate λ=λ(ε) when the size ε of the basic cell tends to zero. Three homogenized problems are determined according to some critical value depending of λ and ε. Our method is based on Γ-Convergence techniques.

Keywords: variational methods, epiconvergence, homogenization, convergence technique

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Authors: Mandy Tao Benec

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Propaganda, understood as a ‘deliberate attempt to persuade people to think and behave in a desired way’, contributes to the fabric of mass media discourse as an important component, albeit often under various alternative expressions except ‘propaganda’. When the word ‘propaganda’ does appear in the mainstream media of the West, it is often selectively applied upon undesiring parties such as China, the North Korea, Russia’s Putin, or terrorists, etc.. This attitude reveals an ‘us verse them’ mentality; and a presupposition that propaganda is something only ‘they’ do whilst ‘we’ do not. This phenomenon not only runs in danger of generating political naivety, but also calls for the necessity of re-examining propaganda which will benefit from analysing it in contrasting social and political environments. Therefore, this paper aims to compare how propaganda has been understood and put in practice both in the Anglo-American context and by the Chinese Communist Party (CCP). By revealing the convergence and divergence of the propaganda discourses between China and the West, it will help clarify the misconception and misunderstanding of the term. Historical narrative analysis and critical discourse analysis are the main methodologies. By carefully examining data from academic research on propaganda in both English and Chinese, the landscape of how propaganda is defined throughout different eras is mapped, with special attention paid to analysing the parallelism and/or correspondence between China and the West when applicable. Meanwhile, critically analysing the official documents such as speeches and guidelines for propaganda administration given by top-rank CCP leaders will help reveal that in contrast to the West’s ‘us-them’ mentality, China sees oneself in no difference with the Western democracies when propaganda is concerned. Major findings of this study will identify a series of convergence and divergence between Chinese and Western propaganda discourses, and the relationship between propaganda the ‘signified’ (its essence) and propaganda the ‘signifier’ (the term itself), including (yet not limited to): 1) convergence in China catching up with the West, acknowledging the perceived pejorative connotation of the term 2) divergence in propaganda activities disassociated from the term in the West; and convergence in adopting such practice when China following suit in its external propaganda towards the West 3) convergence in utilising alternative notions to replace ‘propaganda’, first by the West, then imported and incorporated enthusiastically by China into its propaganda discourse 4) divergence between China’s internal and external propaganda and the subsequent differentiation between in which contexts the CCP sees fit to utilise the concept 5) convergence between China and the West in their English language propaganda discourses, whilst simultaneous divergence in their presuppositions: ‘usthem’ by the West and ‘we are the same’ by China. To conclude, this paper will contribute to the study of propaganda and its discourse by analysing how propaganda is understood and utilised in both worlds, and hence to uncover the discourse power struggle between the two, which contributes to the propaganda discourse itself. Hence, to untie the misconception of propaganda.

Keywords: China, discourse, power, propaganda

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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: Jinhui Bak, Bumjin Kim

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The purpose of this study is to analyze how the scientific and mathematical fields (STEM) and liberal arts (A) work together in the STEAM program. In the future STEAM programs that have been designed and developed, the humanities will act not just as a 'tool' for science technology and mathematics, but as a 'core' content to have an equivalent status. STEAM was first introduced to the Republic of Korea in 2011 when the Ministry of Education emphasized fostering creative convergence talent. Many programs have since been developed under the name STEAM, but with the majority of programs focusing on technology education, arts and humanities are considered secondary. As a result, arts is most likely to be accepted as an option that can be excluded from the teachers who run the STEAM program. If what we ultimately pursue through STEAM education is in fostering STEAM literacy, we should no longer turn arts into a tooling area for STEM. Based on this consciousness, this study analyzed over 160 STEAM programs in middle and high schools, which were produced and distributed by the Ministry of Education and the Korea Science and Technology Foundation from 2012 to 2017. The framework of analyses referenced two criteria presented in the related prior studies: normative convergence and technological convergence. In addition, we divide Arts into fine arts and liberal arts and focused on Korean Language Course which is in liberal arts and analyzed what kind of curriculum standards were selected, and what kind of process the Korean language department participated in teaching and learning. In this study, to ensure the reliability of the analysis results, we have chosen to cross-check the individual analysis results of the two researchers and only if they are consistent. We also conducted a reliability check on the analysis results of three middle and high school teachers involved in the STEAM education program. Analyzing 10 programs selected randomly from the analyzed programs, Cronbach's α .853 showed a reliable level. The results of this study are summarized as follows. First, the convergence ratio of the liberal arts was lowest in the department of moral at 14.58%. Second, the normative convergence is 28.19%, which is lower than that of the technological convergence. Third, the language and achievement criteria selected for the program were limited to functional areas such as listening, talking, reading and writing. This means that the convergence of Korean language departments is made only by the necessary tools to communicate opinions or promote scientific products. In this study, we intend to compare these results with the STEAM programs in the United States and abroad to explore what elements or key concepts are required for the achievement criteria for Korean language and curriculum. This is meaningful in that the humanities field (A), including Korean, provides basic data that can be fused into 'equivalent qualifications' with science (S), technical engineering (TE) and mathematics (M).

Keywords: Korean STEAM Programme, liberal arts, STEAM curriculum, STEAM Literacy, STEM

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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: 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: Jiaqi Huang, Lu Jin

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Pervious concrete features with high water permeability rate. However, due to the lack of fine aggregates, the compressive strength is usually lower than other conventional concrete products. Optimization of pervious concrete mix design has long been recognized as an effective mechanism to achieve high compressive strength while maintaining desired permeability rate. In this paper, a Gibbs Sampling based algorithm is proposed to approximate the optimal mix design to achieve a high compressive strength of pervious concrete. We prove that the proposed algorithm efficiently converges to the set of global optimal solutions. The convergence rate and accuracy depend on a control parameter employed in the proposed algorithm. The simulation results show that, by using the proposed approach, the system converges to the optimal solution quickly and the derived optimal mix design achieves the maximum compressive strength while maintaining the desired permeability rate.

Keywords: convergence, Gibbs Sampling, high compressive strength, optimal mix design, pervious concrete

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Authors: Sahar Mobeen, Anam Rafique, Irum Baig

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Acoustic echo cancellation in multichannel is a system identification application. In real time environment, signal changes very rapidly which required adaptive algorithms such as Least Mean Square (LMS), Leaky Least Mean Square (LLMS), Normalized Least Mean square (NLMS) and average (AFA) having high convergence rate and stable. LMS and NLMS are widely used adaptive algorithm due to less computational complexity and AFA used of its high convergence rate. This research is based on comparison of acoustic echo (generated in a room) cancellation thorough LMS, LLMS, NLMS, AFA and newly proposed average normalized leaky least mean square (ANLLMS) adaptive filters.

Keywords: LMS, LLMS, NLMS, AFA, ANLLMS

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Authors: Bruna Luisa Ramos Prado Vasques, Mariane Rembold Petraglia, Antonio Petraglia

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This paper investigates MIMO (Multiple-Input Multiple-Output) adaptive filtering techniques for the application of supervised source separation in the context of convolutive mixtures. From the observation that there is correlation among the signals of the different mixtures, an improvement in the NSAF (Normalized Subband Adaptive Filter) algorithm is proposed in order to accelerate its convergence rate. Simulation results with mixtures of speech signals in reverberant environments show the superior performance of the proposed algorithm with respect to the performances of the NLMS (Normalized Least-Mean-Square) and conventional NSAF, considering both the convergence speed and SIR (Signal-to-Interference Ratio) after convergence.

Keywords: adaptive filtering, multi-rate processing, normalized subband adaptive filter, source separation

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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: Hudson Akewe

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This research presents complementary results with wider applications on convergence and rate of convergence of classical fixed point theory in Banach spaces to the world of the theory of fixed points of mappings defined in classes of spaces of measurable functions, known in the literature as modular function spaces. The study gives a comprehensive survey of various iterative fixed point results for the classes of multivalued ρ-contractive-like, ρ-quasi-contractive-like, ρ-quasi-contractive, ρ-Zamfirescu and ρ-contraction mappings in the framework of modular function spaces. An example is presented to demonstrate the applicability of the implicit-type iterative schemes to the system of ordinary differential equations. Furthermore, numerical examples are given to show the rate of convergence of the various explicit Kirk-type and implicit Kirk-type iterative schemes under consideration. Our results complement the results obtained on normed and metric spaces in the literature. Also, our methods of proof serve as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive, and accretive type mappings.

Keywords: implicit Kirk-type iterative schemes, multivalued mappings, convergence results, fixed point

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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: 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: 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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