Search results for: Strong and weak convergence

Authors: Safeer Hussain Khan

Abstract:

In this paper, we consider an iteration process for approximating common fixed points of two asymptotically quasinonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

Keywords: Asypmtotically quasi-nonexpansive mappings, Commonfixed point, Strong and weak convergence, Iteration process.

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Authors: C.Natarajan, S.K.Ayyaswamy

Abstract:

Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)γwf (G). In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.

Keywords: Fuzzy graphs, fuzzy domination, strong (weak) fuzzy domination number.

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.

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Authors: Alemayehu Geremew Negash

Abstract:

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: Mona Taheri

Abstract:

For the purpose of finding the quotient structure of multiple algebras such as groups, Abelian groups and rings, we will state concepts of ( strong or weak ) equalities on multiple algebras, which will lead us to research on how ( strong or weak) are equalities defined on a multiple algebra over the quotients obtained from it. In order to find a quotient structure of multiple algebras such as groups, Abelian groups and loops, a part of this article has been allocated to the concepts of equalities (strong and weak) of the defined multiple functions on multiple algebras. This leads us to do research on how defined equalities (strong and weak) are made in the multiple algebra on its resulted quotient.

Keywords: Multiple algebra, mathematics, universal algebra.

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Authors: Yan-zhao Yang

Abstract:

In this paper, some limit properties for mixing random variables sequences were studied and some results on weak law of large number for mixing random variables sequences were presented. Some complete convergence theorems were also obtained. The results extended and improved the corresponding theorems in i.i.d random variables sequences.

Keywords: Complete convergence, mixing random variables, weak law of large numbers.

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Authors: Safeer Hussain Khan

Abstract:

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

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

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Authors: Bainian Li, Kongsheng Zhang

Abstract:

Strong law of large numbers and complete convergence for sequences of *-mixing random variables are investigated. In particular, Teicher-s strong law of large numbers for independent random variables are generalized to the case of *-mixing random sequences and extended to independent and identically distributed Marcinkiewicz Law of large numbers for *-mixing.

Keywords: mixing squences, strong law of large numbers, martingale differences, Lacunary System

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Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia

Abstract:

The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: Conjugate Dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums.

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Authors: Khalid Bouras, Mohammed Moussa

Abstract:

We introduce and study the class of weak almost Dunford-Pettis operators. As an application, we characterize Banach lattices with the weak Dunford-Pettis property. Also, we establish some sufficient conditions for which each weak almost Dunford-Pettis operator is weak Dunford-Pettis. Finally, we derive some interesting results.

Keywords: Almost Dunford-Pettis operator, weak Dunford-Pettis operator, eak almost Dunford-Pettis operator, almost Dunford-Pettis operator, weak Dunford-Pettis operator

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: Contractive-like operator, iterative algorithm, fixed point, strong convergence.

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Authors: Raphael Zanella

Abstract:

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit time marching. The code is verified by space and time convergence tests using a manufactured solution. An example problem is solved with an axisymmetric formulation and with a 3D formulation. Both formulations lead to the same result but the code based on the axisymmetric formulation is mush faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest of using an axisymmetric formulation when it is possible.

Keywords: Axisymmetric problem, continuous finite elements, heat equation, weak formulation.

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Authors: Snehasis Kundu, Koeli Ghoshal

Abstract:

In this paper, based on flume experimental data, the velocity distribution in open channel flows is re-investigated. From the analysis, it is proposed that the wake layer in outer region may be divided into two regions, the relatively weak outer region and the relatively strong outer region. Combining the log law for inner region and the parabolic law for relatively strong outer region, an explicit equation for mean velocity distribution of steady and uniform turbulent flow through straight open channels is proposed and verified with the experimental data. It is found that the sediment concentration has significant effect on velocity distribution in the relatively weak outer region.

Keywords: Inner and outer region, Log law, Parabolic law, Richardson number.

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Authors: Libin Wu, Bainian Li

Abstract:

In This Article We establish moment inequality of dependent random variables,furthermore some theorems of strong law of large numbers and complete convergence for sequences of dependent random variables. In particular, independent and identically distributed Marcinkiewicz Law of large numbers are generalized to the case of m0-dependent sequences.

Keywords: Lacunary System, Generalized Gaussian, NA sequences, strong law of large numbers.

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Authors: Eatedal A. Alabdulkreem, Hamed S. Al-Raweshidy, Maysam F. Abbod

Abstract:

Border Gateway Protocol (BGP) is the standard routing protocol between various autonomous systems (AS) in the internet. In the event of failure, a considerable delay in the BGP convergence has been shown by empirical measurements. During the convergence time the BGP will repeatedly advertise new routes to some destination and withdraw old ones until it reach a stable state. It has been found that the KEEPALIVE message timer and the HOLD time are tow parameters affecting the convergence speed. This paper aims to find the optimum value for the KEEPALIVE timer and the HOLD time that maximally reduces the convergence time without increasing the traffic. The KEEPALIVE message timer optimal value founded by this paper is 30 second instead of 60 seconds, and the optimal value for the HOLD time is 90 seconds instead of 180 seconds.

Keywords: BGP, Convergence Time, HOLD time, Keep alive.

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Authors: Y.Ben Jemaa, M.Jaidane

Abstract:

In wireless communication system, a Decision Feedback Equalizer (DFE) to cancel the intersymbol interference (ISI) is required. In this paper, an exact convergence analysis of the (DFE) adapted by the Least Mean Square (LMS) algorithm during the training phase is derived by taking into account the finite alphabet context of data transmission. This allows us to determine the shortest training sequence that allows to reach a given Mean Square Error (MSE). With the intention of avoiding the problem of ill-convergence, the paper proposes an initialization strategy for the blind decision directed (DD) algorithm. This then yields a semi-blind DFE with high speed and good convergence.

Keywords: Adaptive Decision Feedback Equalizer, PerformanceAnalysis, Finite Alphabet Case, Ill-Convergence, Convergence speed.

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Authors: H. Daoud Dammak, S. Bensalem, S. Zouari, M. Loulou

Abstract:

This paper presents an optimized methodology to folded cascode operational transconductance amplifier (OTA) design. The design is done in different regions of operation, weak inversion, strong inversion and moderate inversion using the gm/ID methodology in order to optimize MOS transistor sizing. Using 0.35μm CMOS process, the designed folded cascode OTA achieves a DC gain of 77.5dB and a unity-gain frequency of 430MHz in strong inversion mode. In moderate inversion mode, it has a 92dB DC gain and provides a gain bandwidth product of around 69MHz. The OTA circuit has a DC gain of 75.5dB and unity-gain frequency limited to 19.14MHZ in weak inversion region.

Keywords: CMOS IC design, Folded Cascode OTA, gm/ID methodology, optimization.

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Authors: Guiding Gu, Guo Liu

Abstract:

We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f. Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I + H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. Numerical experiments show such convergence properties.

Keywords: complex shifted linear system, Hermitian matrix, MINRES method.

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Authors: Dalhatu, Musa Yusha’u, Shuaibu Sidi Safiyanu, Haliru Musa Hussaini

Abstract:

This study examined budget and performance of public enterprises in Nasarawa State, Nigeria in a period of 2009-2013. The study utilized secondary sources of data obtained from four selected parastatals’ budget allocation and revenue generation for the period under review. The simple correlation coefficient was used to analyze the extent of the relationship between budget allocation and revenue generation of the parastatals. Findings revealed varying results. There was positive (0.21) and weak correlation between expenditure and revenue of Nasarawa Investment and Property Development Company (NIPDC). However, the study further revealed that there was strong and weak negative relationship in the revenue and expenditure of the following parastatals over the period under review. Viz: Nasarawa State Water Board, -0.27 (weak), Nasarawa State Broadcasting Service, -0.52 (Strong) and Nasarawa State College of Agriculture, -0.36 (weak). The study therefore, recommends that government should increase its investments in NIPDC to enhance efficiency and profitability. It also recommends that government should strengthen its fiscal responsibility, accountability and transparency in public parastatals.

Keywords: Allocation, Budget, Public Enterprises, Parastatals, Performance.

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Authors: Liang Chen

Abstract:

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.

Keywords: Nonlinear equations, Secant method, Convergence order, Secant-like method.

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Authors: Chong Zhang, Mu-Xuan Tao

Abstract:

In several earthquakes, numerous reinforced concrete (RC) frames subjected to seismic excitation demonstrated a collapse pattern characterized by column hinges, though designed according to the Strong-Column-Weak-Beam (S-C-W-B) criteria. The effect of biaxial seismic excitation on the disparity between design and actual performance is carefully investigated in this article. First, a modified load contour method is proposed to derive a closed-form equation of biaxial bending moment strength, which is verified by numerical and experimental tests. Afterwards, a group of time history analyses of a simple frame modeled by fiber beam-column elements subjected to biaxial seismic excitation are conducted to verify that the current S-C-W-B criteria are not adequate to prevent the occurrence of column hinges. A biaxial over-strength factor is developed based on the proposed equation, and the reinforcement of columns is appropriately amplified with this factor to prevent the occurrence of column hinges under biaxial excitation, which is proved to be effective by another group of time history analyses.

Keywords: Biaxial bending moment strength, biaxial seismic excitation, fiber beam-column model, load contour method, strong-column-weak-beam.

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Authors: Nuanwan Soonthornphisaj, Boonserm Kijsirikul

Abstract:

This paper presents a semi-supervised learning algorithm called Iterative-Cross Training (ICT) to solve the Web pages classification problems. We apply Inductive logic programming (ILP) as a strong learner in ICT. The objective of this research is to evaluate the potential of the strong learner in order to boost the performance of the weak learner of ICT. We compare the result with the supervised Naive Bayes, which is the well-known algorithm for the text classification problem. The performance of our learning algorithm is also compare with other semi-supervised learning algorithms which are Co-Training and EM. The experimental results show that ICT algorithm outperforms those algorithms and the performance of the weak learner can be enhanced by ILP system.

Keywords: Inductive Logic Programming, Semi-supervisedLearning, Web Page Categorization

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Authors: N. Moradian, E. Timofeev, R. Tahir

Abstract:

In this work, startability of the Busemann intake family with weak/strong conical shock, as most efficient intakes, via overboard mass spillage method is theoretically analyzed. Masterix and Candifix codes are used to numerically simulate few models of this type of intake and verify the theoretical results. Portions of the intake corresponding to various flow capture angles are considered to have mass spillage in the starting process of this intake. This approach allows for overboard mass spillage via a V-shaped slot with the tip of V coinciding with the focal point of the Busemann flow. The theoretical results, achieved using two different theories, of self-started Busemann takes with weak/strong conical shock show that significant improve in intake startability using overboard spillage technique. The starting phenomena of Busemann intakes with weak conical shock and seven different capture angles are numerically simulated at freestream Mach number of 3 to find the minimum area ratios of self-started intakes. The numerical results confirm the theoretical ones achieved by authors.

Keywords: Busemann intake, conical shock, overboard spillage, startability.

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Authors: Giseob Byun, Ji Yeon Cho, Bong Gyou Lee

Abstract:

The purpose of this study is to analyze Green IT industry in major developed countries and to suggest overall directions for IT-Energy convergence industry. Recently, IT industry is pointed out as a problem such as environmental pollution, energy exhaustion, and high energy consumption. Therefore, Green IT gets focused which concerns as solution of these problems. However, since it is a beginning stage of this convergence area, there are only a few studies of IT-Energy convergence industry. According to this, this study examined the major developed countries in terms of institution arrangements, resources, markets and companies based on Van de Ven(1999)'s social system framework that shows relationship among key components of industrial infrastructure. Subsequently, the direction of the future study of convergence on IT and Energy industry is proposed.

Keywords: Green IT, Energy industry, Convergence, Social System Framework.

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Authors: Jeng-Shin Sheu, Jenn-Kaie Lain, Tai-Kuo Woo, Jyh-Horng Wen

Abstract:

The least mean square (LMS) algorithmis one of the most well-known algorithms for mobile communication systems due to its implementation simplicity. However, the main limitation is its relatively slow convergence rate. In this paper, a booster using the concept of Markov chains is proposed to speed up the convergence rate of LMS algorithms. The nature of Markov chains makes it possible to exploit the past information in the updating process. Moreover, since the transition matrix has a smaller variance than that of the weight itself by the central limit theorem, the weight transition matrix converges faster than the weight itself. Accordingly, the proposed Markov-chain based booster thus has the ability to track variations in signal characteristics, and meanwhile, it can accelerate the rate of convergence for LMS algorithms. Simulation results show that the LMS algorithm can effectively increase the convergence rate and meantime further approach the Wiener solution, if the Markov-chain based booster is applied. The mean square error is also remarkably reduced, while the convergence rate is improved.

Keywords: LMS, Markov chain, convergence rate, accelerator.

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Authors: Chenxue Yang, Mao Ye, Zijian Liu, Tao Li, Jiao Bao

Abstract:

Non-negative matrix factorization (NMF) is a useful computational method to find basis information of multivariate nonnegative data. A popular approach to solve the NMF problem is the multiplicative update (MU) algorithm. But, it has some defects. So the columnwisely alternating gradient (cAG) algorithm was proposed. In this paper, we analyze convergence of the cAG algorithm and show advantages over the MU algorithm. The stability of the equilibrium point is used to prove the convergence of the cAG algorithm. A classic model is used to obtain the equilibrium point and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the cAG algorithm are obtained, which help reducing the evaluation time and is confirmed in the experiments. By using the same method, the MU algorithm has zero divisor and is convergent at zero has been verified. In addition, the convergence conditions of the MU algorithm at zero are similar to that of the cAG algorithm at non-zero. However, it is meaningless to discuss the convergence at zero, which is not always the result that we want for NMF. Thus, we theoretically illustrate the advantages of the cAG algorithm.

Keywords: Non-negative matrix factorizations, convergence, cAG algorithm, equilibrium point, stability.

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Authors: Kankesu Jayanthakumaran, Shao-Wei Lee

Abstract:

This paper proposes the hypothesis that multilateralism and regionalism are complementary, and that regional income convergence is likely with a like minded and committed regionalism that often has links geographically and culturally. The association between international trade, income per capita, and regional income convergence in founder members of ASEAN and SAARC, is explored by applying the Lumsdaine, and Papell approach. The causal relationships between the above variables are also studied in respective trade blocs by using Granger causality tests. The conclusion is that global reforms have had a greater impact on increasing trade for both trade blocs and induced convergence only in ASEAN-5 countries. The experience of ASEAN countries shows a two-way causal relationship between the flow from trade to regional income convergence, and vice versa. There is no evidence in SAARC countries for income convergence and causality.

Keywords: ASEAN-5, SAARC-5, trade liberalisation, incomeconvergence, structural breaks and causality.

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Authors: Miloje S. Radenkovic, Tamal Bose

Abstract:

This paper presents the convergence analysis of a prediction based blind equalizer for IIR channels. Predictor parameters are estimated by using the recursive least squares algorithm. It is shown that the prediction error converges almost surely (a.s.) toward a scalar multiple of the unknown input symbol sequence. It is also proved that the convergence rate of the parameter estimation error is of the same order as that in the iterated logarithm law.

Keywords: Adaptive blind equalizer, Recursive leastsquares, Adaptive Filtering, Convergence analysis.

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Authors: Rado Flajs, Miran Saje

Abstract:

In the present paper the displacement-based nonconforming quadrilateral affine thin plate bending finite element ARPQ4 is presented, derived directly from non-conforming quadrilateral thin plate bending finite element RPQ4 proposed by Wanji and Cheung [19]. It is found, however, that element RPQ4 is only conditionally unisolvent. The new element is shown to be inherently unisolvent. This convenient property results in the element ARPQ4 being more robust and thus better suited for computations than its predecessor. The convergence is proved and the rate of convergence estimated. The mathematically rigorous proof of convergence presented in the paper is based on Stummel-s generalized patch test and the consideration of the element approximability condition, which are both necessary and sufficient for convergence.

Keywords: Quadrilateral thin plate bending element, convergence, generalized patch test.

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Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

Abstract:

In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Hölder continuity condition, Fréchet derivative, fifth order convergence, recurrence relations.

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