• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• 한국정보과학회논문지:시스템및이론
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• 제30권5_6호
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• pp.319-323
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• 2003

이차원 평면에 주어진 n개의 점 집합 P에 대한, 최소 신장 트리(minimum spanning tree, MST)는 P의 점들을 연결한 신장 트리 중에서 에지 길이의 총합이 최소가 되는 트리로 정의된다. P에 대한 신장 트리의 지름(diameter)은 트리의 두 점을 연결한 트리 경로 중에서 최장 경로의 길이로 정의되며, 최소 지름 신장 트리(minimum-diameter spanning tree, MDST)는 P에 대한 신장 트리 중에서 지름이 가장 작은 트리를 의미한다. 현재까지 알려진 가장 좋은 알고리즘[3]은 MDST를 O(n$^3$) 시간에 구한다. 본 논문에서는 MDST의 지름보다 최대 5/4배 이내의 지름을 보장하는 신장 트리를 구하는 $O(n^2)$ 시간 근사 알고리즘(approximation algorithm)을 제시한다. 이것은 MDST 문제에 관한 첫 번째 근사 알고리즘이다.

• 대한수학회논문집
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• 제12권2호
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• pp.403-403
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• 1997

• Journal of applied mathematics & informatics
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• 제41권5호
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• pp.1057-1069
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• 2023

In this paper, we have determined the degree of approximation of function belonging of Lipschitz class by using Deferred-Generalized Nörlund (D^𝛾_𝛽.N_pq) means of Fourier series and conjugate series of Fourier series, where {p_n} and {q_n} is a non-increasing sequence. So that results of DEGER and BAYINDIR [23] become special cases of our results.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.365-382
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• 2023

In this paper we prove the existence and uniqueness of solution of stochastic fractional neutral differential equations with Gaussian noise or Lévy noise by using the Picard-Lindelöf successive approximation scheme. Further stability results of nonlinear stochastic fractional dynamical system with Gaussian and Lévy noises are established. Examples are provided to illustrate the theoretical results.

• 설비공학논문집
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• 제4권1호
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• pp.20-32
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• 1992

A numerical solution for heat transfer in the flue tube of a pulse combustion water heater was presented. The $k-{\varepsilon}$ turbulent model was adopted to describe turbulent characteristics and radiative heat transfer was calculated by P-N approximation. Three pulsating conditions equivalent to existing experimental studies were used for analysis. Pulsating pressure was specified at the inlet and outlet of flue tube and numerical procedure using control volume method and pressure boundary condition was presented. It was found that the present mathematical model and numerical method could predict effectively the flow field and heat transfer for the flue tube in pulse combustor.

• East Asian mathematical journal
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• 제28권5호
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• pp.597-604
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• 2012

Let C be a nonempty closed convex subset of real Hilbert space H and F = $\{S(t):t{\geq}0\}$ a nonexpansive self-mapping semigroup of C, and $f:C{\rightarrow}C$ is a fixed contractive mapping. Consider the process {$x_n$} : $$\{{x_{n+1}={\beta}_nx_n+(1-{\beta}_n)z_n\\z_n={\alpha}_nf(x_n)+(1-{\alpha}_n)S(t_n)P_C(x_n-r_nAx_n)$$. It is shown that {$x_n$} converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.

• Journal of Advanced Marine Engineering and Technology
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• 제26권2호
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• pp.219-225
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• 2002

Parameter tuning methods by Ziegler-Nichols for PID controllers are generally classified into Z-N(1) and Z-N(2). The purpose of this paper is to describe what relations exist between the methods of Z-N(1) and Z-N(2), or how Z-N(1) can be originated from Z-N(2) by analyzing one loop control system composing of P or PI controller and time delay process. In this paper, for the first step to seek mutual relations, the simple formulas of Z-N(2) are transformed into those composing of the same parameters as Z-N(1) which is derived from the analysis of frequency characteristics. Then, the approximation of the actual ultimate frequency is proposed as important premise in the translation between Z-N(1) and (2). Such equalization and approximation brings a simple approximated formula which can explain how Z-N(1) is originated from the Z-N(2) in the form of formula.

• 대한수학회지
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• 제24권2호
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• pp.239-245
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• 1987

• 대한기계학회논문집
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• 제12권6호
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• pp.1428-1437
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• 1988

본 연구에서는 흡수, 방사 및 비등방성 산란을 하는 축대칭 유한원통형매질에 서의 형식해로부터 Gaussian Quadrature를 이용하여 수치적으로 엄밀해를 구하고 P-1 과 P-3근사해법을 통하여 얻어진 해와 비교하여 P-1과 P-3근사해법의 타당성을 검토하 였다.또한 매질의 광학두께, 산란알베도, 벽면방사율, 형상계수 등을 주요 파라미 터로 하여 이들의 영향에 대하여 고찰하였다.