• Title/Summary/Keyword: unique solution

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ON THE CONVERGENCE OF INEXACT TWO-STEP NEWTON-TYPE METHODS USING RECURRENT FUNCTIONS

  • Argyros, Ioannis K.;Hilou, Said
    • East Asian mathematical journal
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    • v.27 no.3
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    • pp.319-337
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    • 2011
  • We approximate a locally unique solution of a nonlinear equation in a Banach space setting using an inexact two-step Newton-type method. It turn out that under our new idea of recurrent functions, our semilocal analysis provides tighter error bounds than before, and in many interesting cases, weaker sufficient convergence conditions. Applications including the solution of nonlinear Chandrasekhar-type integral equations appearing in radiative transfer and two point boundary value problems are also provided in this study.

A Solution Procedure Based on Analytical Solutions for Laplace's Equation on Convex Polygons (해석해를 이용한 단순볼록 다각형에서의 라프라스방정식의 해법)

  • 김윤영;윤민수
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.11
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    • pp.2773-2781
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    • 1993
  • Laplace's equation is, perhaps, the most important equation, which governs various kinds of physical phenomena. Due to its importance, there have been several numerical techniques such as the finite element method, the finite difference method, and the boundary element method. However, these techniques do not appear very effective as they require a substantial amount of numerical calculation. In this paper, we develop a new most efficient technique based on analytic solutions for Laplace's equation in some convex polygons. Although a similar approach was used for the same problem, the present technique is unique as it solves directly Laplace's equation with the utilization of analytical solutions.

Perspectivism on Probability (확률에 대한 관점주의)

  • Kim, Han-Seung
    • Korean Journal of Logic
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    • v.14 no.3
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    • pp.59-84
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    • 2011
  • Professor Song criticizes my view on the Sleeping Beauty problem in his recent paper which endorses the thirder solution. I shall argue that his criticism is based upon a strong interpretation on my view and that this interpretation is neither unique nor proper. Critically examining recent discussions on observer-relativity of probability I shall claim that my perspectivistic solution to the Sleeping Beauty problem is still plausible.

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An Explicit Solution of the Cubic Spline Interpolation for Polynomials

  • Moon, Byung Soo
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.1 no.1
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    • pp.75-82
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    • 1997
  • An algorithm for computing the cubic spline interpolation coefficients for polynomials is presented in this paper. The matrix equation involved is solved analytically so that numerical inversion of the coefficient matrix is not required. For $f(t)=t^m$, a set of constants along with the degree of polynomial m are used to compute the coefficients so that they satisfy the interpolation constraints but not necessarily the derivative constraints. Then, another matrix equation is solved analytically to take care of the derivative constraints. The results are combined linearly to obtain the unique solution of the original matrix equation. This algorithm is tested and verified numerically for various examples.

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An Ant System Extrapolated Genetic Algorithm (개미 알고리즘을 융합한 적응형 유전알고리즘)

  • Kim Joong Hang;Lee Se-Young;Chang Hyeong Soo
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.8
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    • pp.399-410
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    • 2005
  • This paper Proposes a novel adaptive genetic algorithm (GA) extrapolated by an ant colony optimization. We first prove that the algorithm converges to the unique global optimal solution with probability arbitrarily close to one and then, by experimental studies, show that the algorithm converges faster to the optimal solution than GA with elitism and the population average fitness value also converges to the optimal fitness value. We further discuss controlling the tradeoff of exploration and exploitation by a parameter associated with the proposed algorithm.

Solution-State Structure of Native Coenzyme F430 by NMR Methods

  • 원호식;Karl D. Olson;박지석;Ralph S. Wolfe;Dennis R. Hare;Michael F. Summers
    • Bulletin of the Korean Chemical Society
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    • v.16 no.7
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    • pp.649-653
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    • 1995
  • Solution-state structure of native F430 was determined by using NMR methods and NMR-based distance geometry (DG) computations. Structures were generated with loose NOE-derived interproton distance restraints (2.0-2.5 Å, 2.0-3.5 Å and 2.0-4.5 Å for strong, medium, and weak NOE cross-peak intensities, respectively). 2D NOESY back-calculations of structures were subsequently carried out for establishing the consistence between experimental data and DG-model structures. The back-calculated 2D NOESY spectra of resulting DG structures were well consistent with experimental 2D NOESY spectra. Superposition of 20 independent structures with macrocyclic ring atoms and all atoms of F430 afforded pairwise root mean square deviations (RMSD) of 0.025-0.125 Å and 0.64-1.3 Å, respectively. The macrocyclic rings of structures are well converged to a unique conformation with saddle-shaped deformation whereas most of side chains are not converged. The average dihedral angle (N1-N2-N3-N4, 27.78±1.50°) of 20 DG-structures exhibits that the macrocyclic ring conformation is puckered as much as 12,13-diepimeric F430 (28.75±4.07°).

A Brief Review on 2-Dimensional Dielectric Nanosheets (이차원 유전체 나노시트의 개발 동향)

  • Yim, Haena;Choi, Ji-Won
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.35 no.1
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    • pp.1-10
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    • 2022
  • Two-dimensional materials have shown a great promise for the next-generation electronic materials due to their unique optical, physical, and chemical properties that are distinct from their bulk counterparts. Their atomic-level thickness, the feature for flexible tenability, and exposed huge surface allow various approaches for high-performance nanoscale devices. Especially, this review highlights the recent progress on two-dimensional dielectric nanosheets, which are obtained by cheap and massproducible solution-based exfoliation process, accompanied by the preparation methods, various deposition methods, and the characteristics of devices using a dielectric nanosheet thin films. We also present a perspective on the advantages offered by this two-dimensional dielectric nanosheets for the upcoming future nanoelectonics.

THE N-ORDER ITERATIVE SCHEME FOR A SYSTEM OF NONLINEAR WAVE EQUATIONS ASSOCIATED WITH THE HELICAL FLOWS OF MAXWELL FLUID

  • Ngoc, Le Thi Phuong;Dzung, Nguyen Vu;Long, Nguyen Thanh
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.3
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    • pp.471-497
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    • 2022
  • In this paper, we study a system of nonlinear wave equations associated with the helical flows of Maxwell fluid. By constructing a N-order iterative scheme, we prove the local existence and uniqueness of a weak solution. Furthermore, we show that the sequence associated with N-order iterative scheme converges to the unique weak solution at a rate of N-order.

Development and application of ex-solution nanocatalyst (용출 현상 기반 나노촉매의 개발 및 응용)

  • Kim, Jun Hyuk;Kim, Jun Kyu;Jung, WooChul
    • Ceramist
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    • v.23 no.2
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    • pp.200-210
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    • 2020
  • Supported catalysts are at the heart of manufacturing essential chemical, agricultural and pharmaceutical products. While the longevity of such systems is critically hinged on the durability of metal nanoparticles, the conventional deposition/dispersion techniques are difficult to enhance the stability of the metal nanoparticles due to the lack of control over the interaction between metal-support. Regarding this matter, ex-solution has begun to be recognized as one of the most promising methodologies to develop thermally and chemically robust nanoparticles. By dissolving desired catalysts as a cation form into a parent oxide, fine and uniformly distributed metal nano-catalysts can be subsequently grown in situ under reductive heat treatment, which is referred to ex-solution. Over the several years, ex-solved analog has resulted in tremendous progress in the chemical-electrochemical applications due to the exceptional robustness coupled with ease synthesis. Herein, we describe the ex-solution process in detail which therein introducing the unique characteristics of ex-solved particles that distinguish them from conventionally dispersed nanoparticles. We then go through the history of science regarding the ex-solution phenomena and summarize several major research achievements which embrace the ex-solved nanoparticles to markedly promote the catalytic performances. In conclusion, we address the remaining challenges and the future perspectives of this rapidly growing field.

Real-time hacking, detection and tracking ICT Convergence Security Solutions Test and Evaluation (실시간 해킹, 탐지 및 추적관리 ICT 융합 보안 솔루션 시험평가)

  • Kim, Seung-Bum;Yang, Hae-Sool
    • Journal of Digital Convergence
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    • v.13 no.4
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    • pp.235-246
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    • 2015
  • Understanding the various unspecified hacking and repeated cyber DDoS attacks, finally was able to find a solution in the methods of attacks. Freely researching approach that combines the attacker and defender, offensive and defensive techniques can be called a challenge to discover the potential in whimsy. In this paper we test and evaluate "KWON-GA", global white hackers team has made by many years of experiences in infiltration and diagnosis under guise of offence is the best defence. And it is knowledge information ICT Convergence security solution which is developed for the purpose of defence, it provide customization policy that can be fit to customer's system environment with needed techniques and it is processed with unique proprietary technology so that it's not possible to scan. And even if it has leaked internally it's impossible to analyze so hackers can't analyze vulnerability, also it can't be abused as hacking tools.