• Title/Summary/Keyword: Space Convergence

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CONVERGENCE OF VISCOSITY APPROXIMATIONS TO FIXED POINTS OF NONEXPANSIVE NONSELF-MAPPINGS IN BANACH SPACES

  • Jung, Jong-Soo
    • East Asian mathematical journal
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    • v.24 no.1
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    • pp.81-95
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    • 2008
  • Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

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ORLICZ SEQUENCE SPACES OF FOUR DIMENSIONAL REGULAR MATRIX AND THEIR CLOSED IDEAL

  • Raj, Kuldip;Pandoh, Suruchi;Choudhary, Anu
    • Honam Mathematical Journal
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    • v.41 no.4
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    • pp.725-744
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    • 2019
  • In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices A = (artkl). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space 𝑙2.

THE EFFECT OF ROUNDING ERRORS ON NEWTON METHODS

  • Argyros, Ioannis K.
    • Journal of applied mathematics & informatics
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    • v.7 no.3
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    • pp.765-772
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    • 2000
  • In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the second Frechet-derivative instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover, we show that the ratio of convergence improves under our conditions. Furthermore, we provide a wider choice of initial guesses than before. Finally, a numerical example is provided to show that our results compare favorably with earlier ones.

ON SOLVABILITY OF GENERALIZED NONLINEAR VARIATIONAL-LIKE INEQUALITIES

  • Zhang, Lili;Liu, Zeqing;Kang, Shin-Min
    • Journal of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.163-176
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    • 2008
  • In this paper, we introduce and study a new class of generalized nonlinear variational-like inequalities. By employing the auxiliary principle technique we suggest an iterative algorithm to compute approximate solutions of the generalized nonlinear variational-like inequalities. We discuss the convergence of the iterative sequences generated by the algorithm in Banach spaces and prove the existence of solutions and convergence of the algorithm for the generalized nonlinear variational-like inequalities in Hilbert spaces, respectively. Our results extend, improve and unify several known results due to Ding, Liu et al, and Zeng, and others.

Dual Diversity over Correlated Ricean Fading Channels

  • Bithas Petros S.;Sagias Nikos C.;Mathiopoulos P. Takis
    • Journal of Communications and Networks
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    • v.9 no.1
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    • pp.67-74
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    • 2007
  • The performance of dual diversity receivers operating over correlated Ricean fading channels is analyzed. Using a previously derived rapidly converging infinite series representation for the bivariate Ricean probability density function, analytical expressions for the statistics of dual-branch selection combining, maximal-ratio combining, and equal-gain combining output signal-to-noise ratio (SNR) are derived. These expressions are employed to obtain novel analytical formulae for the average output SNR, amount of fading, average bit error probability, and outage probability. The proposed mathematical analysis is used to study various novel performance evaluation results with parameters of interest the fading severity, average input SNRs, and the correlation coefficient. The series convergence rate is also examined verifying the fast convergence of the analytical expressions. The accuracy of most of the theoretical performance evaluation results are validated by means of computer simulations.

Navier-Stokes Analysis of Pitching Delta Wings in a Wind Tunnel

  • Lee, Yung-Gyo
    • International Journal of Aeronautical and Space Sciences
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    • v.2 no.2
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    • pp.28-38
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    • 2001
  • A numerical method for the assessment and correction of tunnel wall interference effects on forced-oscillation testing is presented. The method is based on the wall pressure signature method using computed wall pressure distributions. The wall pressure field is computed using unsteady three-dimensional full Navier-Stokes solver for a 70-degree pitching delta wing in a wind tunnel. Approximately-factorized alternate direction implicit (AF-ADI) scheme is advanced in time by solving block tri-diagonal matrices. The algebraic Baldwin-Lomax turbulence, model is included to simulate the turbulent flow effect. Also, dual time sub-iteration with, local, time stepping is implemented to improve the convergence. The computed wall pressure field is then imposed as boundary conditions for Euler re-simulation to obtain the interference flow field. The static computation shows good agreement with experiments. The dynamic computation demonstrates reasonable physical phenomena with a good convergence history. The effects of the tunnel wall in upwash and blockage are analyzed using the computed interference flow field for several reduced frequencies and amplitudes. The corrected results by pressure signature method agree well with the results of free air conditions.

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Path-smoothing for a robot arm manipulator using a Gaussian process

  • Park, So-Youn;Lee, Ju-Jang
    • Journal of the Korean Society of Industry Convergence
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    • v.18 no.4
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    • pp.191-196
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    • 2015
  • In this paper, we present a path-smoothing algorithm for a robot arm manipulator that finds the path using a joint space-based rapidly-exploring random tree. Unlike other smoothing algorithms which require complex mathematical computation, the proposed path-smoothing algorithm is done using a Gaussian process. To find the optimal hyperparameters of the Gaussian process, we use differential evolution hybridized with opposition-based learning. The simulation result indicates that the Gaussian process whose hyperparameters were optimized by hybrid differential evolution successfully smoothed the path generated by the joint space-based rapidly-exploring random tree.

A Study on the Planning Factor Evaluation of Environmental Friendiness by Apartment Residents (공동주택단지 거주자의 환경친화 계획요소 평가에 관한 연구)

  • Kim, Ick-Hwan
    • Journal of the Korean Society of Industry Convergence
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    • v.10 no.1
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    • pp.55-63
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    • 2007
  • The purpose of this study is to extract the main planning factors of environment friendly apartment complex through the residents' evaluations on importance levels of the planning factors. The major findings of this study are as follows; 1) Understanding on the environment friendly apartment complex is lacking, and the satisfaction level on the living space as the environment friendly apartment is very low. 2) The residents in the low-storied apartments want the introduction of facilities for energy saving, and those in the high-storied apartments demand to develop to green area. 3) In evaluating the importance of the environment friendly planning factors and the image of the apartment complex, the guarantee of green area and the development of water friendly space are closely related with the image of the apartment complex. So, they are the planning factors that should be handled importantly.

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Development Method of Open BIM Data for Facility Space Management (시설물 공간관리를 위한 개방형 BIM 데이터 구축 방안)

  • Cho, Geun-Ha;Ju, Ki-Beom
    • Proceedings of the Korean Society of Computer Information Conference
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    • 2015.07a
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    • pp.321-322
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    • 2015
  • 본 연구는 BIM의 최종 모델(As-built Model)이 BIM기반 유지관리 시스템(Facility Management System)에 활용되는 것을 전제로 하며 유지관리 분야 중 공간관리 분야에서 활용되는 BIM 모델을 구축하기 위한 방안을 제시한다. 연구의 최종 결과물인 BIM 유지관리 가이드라인은 향후 BIM 발주 지침에 반영되어 건설과정에서 구축된 BIM 정보를 유지관리 단계까지 지속적으로 활용하도록 유도할 것이라 기대한다.

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Design of Adaptive Population-size on Bias in Genetic Algorithms (유전자 알고리즘에서 bias에 의한 adaptive한 개체군 크기의 설정)

  • 김용범;오충환
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.18 no.36
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    • pp.133-141
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    • 1995
  • One of the problems brought up in the effective execution of genetic algorithms is that if they come under any influences according as the population size is large or small. In the case of small population size the opportunities of premature convergence are increased when the greatly powerful or no good individual is generated during search of the solution space. And searching the solution space in the case of large population size, the difficulties under the execution cause to searching all for one by one individual in every generation applied is limited, this gives the many interruptions to the convergence of final solution. Now this paper gives a suggestion to set up the adaptive population size which could compute the more correct solution and simplify the development of computation performance.

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