• East Asian mathematical journal
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• 제18권1호
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• 대한기계학회논문집A
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• 제32권6호
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• pp.519-525
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• 2008

For this study, SM45C steel rods using generally for power transmission shafts and machine components was selected and welded by butt-GMAW method. And then it was studied about estimation of fatigue strength and the region of infinite life by Haigh diagram using Goodman's equation. Fatigue strength in weld zone presents highly in order of the boundary between deposited metal zone and heat affected zone, deposited metal zone, heat affected zone. This result agrees with distribution of hardness in weld zone. Fatigue strength in base metal zone presents highly compared with weld zone in low cycles between $10^4$ cycles and $10^6$cycles, but it presents the lowest fatigue strength on the order of heat affected zone in the vicinity of $10^6$cycles. It is the result that the first high compressive residual stress distributed by drawing process of the steel rods is released and the base metal is softened by alternating stresses. The region of infinite life by Haigh diagram presents highly in order of the boundary between deposited metal zone and heat affected zone, deposited metal zone, heat affected zone. From this results, it is demanded that the stress for safety design of machine components using SM45C butt-welded steel rods must be selected in the region of the lowest infinite life of heat affected zone.

• Communications for Statistical Applications and Methods
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• 제24권4호
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• pp.367-382
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• 2017

We consider an infinite-order long-memory heterogeneous autoregressive (HAR) model, which is motivated by a long-memory property of realized volatilities (RVs), as an extension of the finite order HAR-RV model. We develop bootstrap tests for structural mean or variance changes in the infinite-order HAR model via stationary bootstrapping. A functional central limit theorem is proved for stationary bootstrap sample, which enables us to develop stationary bootstrap cumulative sum (CUSUM) tests: a bootstrap test for mean break and a bootstrap test for variance break. Consistencies of the bootstrap null distributions of the CUSUM tests are proved. Consistencies of the bootstrap CUSUM tests are also proved under alternative hypotheses of mean or variance changes. A Monte-Carlo simulation shows that stationary bootstrapping improves the sizes of existing tests.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.304-309
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• 2003

A new modal analysis method for rotor systems with periodically time-varying parameters is proposed. The essence of method is to introduce modulated coordinates to derive the equivalent time-invariant equation. This paper presents a modal analysis method using modulated coordinates fur general rotors, of which rotating and stationary parts both possess asymmetric properties. The equation of motion with time-varying parameters is transformed to an infinite order matrix equation with the time-invariant parameters. A theory of modal analysis for the system is presented with the infinite order equation and a couple of reduced order equations. A numerical example with simple asymmetric rotor is provided to demonstrate the effectiveness of the proposed method

• International Journal of Safety
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• 제2권1호
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• pp.17-22
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• 2003

In order to analyze general three dimensional cracks in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear is used. A crack is modelled as distribution of displacement discontinuities, and the governing equation is formulated as singularity-reduced integral equations. With the proposed method several example problems for three dimensional cracks in an infinite solid, as well as their growth under fatigue, are solved and the accuracy and efficiency of the method are demonstrated.

• 대한수학회지
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• 제54권2호
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• pp.417-426
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• 2017

We explicitly determine fundamental units and regulators of an infinite family of cyclic quartic function fields $L_h$ of unit rank 3 with a parameter h in a polynomial ring $\mathbb{F}_q[t]$, where $\mathbb{F}_q$ is the finite field of order q with characteristic not equal to 2. This result resolves the second part of Lehmer's project for the function field case.

• 논리연구
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• 제9권2호
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• pp.1-30
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• 2006

This paper investigates algebraic semantics for some weak Boolean (wB) logics, which may be regarded as left-continuous t-norm based logics (or monoidal t-norm based logics (MTLs)). We investigate as infinite-valued logics each of wB-LC and wB-sKD, and each corresponding first order extension $wB-LC\forall$ and $wB-sKD\forall$. We give algebraic completeness for each of them.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.351-360
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• 2006

In this paper, we develop an inexact-Newton method for solving nonsmooth operator equations in infinite-dimensional spaces. The linear convergence and superlinear convergence of inexact-Newton method under some conditions are shown. Then, we characterize the order of convergence in terms of the rate of convergence of the relative residuals. The present inexact-Newton method could be viewed as the extensions of previous ones with same convergent results in finite-dimensional spaces.

• Korean Journal of Mathematics
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• 제32권3호
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• pp.521-531
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• 2024

The main purpose of this study is to shed light on whether new types of uncertain variable sequences can be defined with the help of an infinite matrix. For this purpose, the first-order Cesàro matrix was used as an infinite matrix, and new types of uncertain variable sequences, called Cesàro-type uncertain variable sequences, were obtained. Theorems about uncertain variable sequences of Cesàro type have been included in this study, and some comparisons have been made. Thus, the gaps in the existing literature were filled.

• Kyungpook Mathematical Journal
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• 제16권2호
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• pp.219-223
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• 1976