• 호남수학학술지
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• 제39권2호
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• pp.307-315
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• 2017

In this paper, we aim to compare the differentials with the regularity of the hypercomplex valued functions in Clifford analysis. For three kinds of conjugation of the bicomplex numbers, we define the differentials of the bicomplex number functions by the naive approach. And we investigate some relations of the corresponding Cauchy-Riemann system and the conditions of the differentiable functions in the bicomplex number system.

• 호남수학학술지
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• 제30권4호
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• pp.671-676
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• 2008

We give the relation between the Riemann-Stieltjes integrals with respect to the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) distribution $H_{a,p}$ satisfying the equation a = $(1-a)^m$ and those with respect to the dual RNT distribution $H_{1-a,1-p}$, which leads to a generalization of recent results for a = $\frac{1}{2}$.

• 대한수학회보
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• 제53권2호
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• pp.507-518
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• 2016

In this paper, using forms of conjugations, we give some algebraic properties of bicomplex numbers. We research differential operators, elementary functions and the analogous Cauchy-Riemann system in bicomplex number systems. Also, we investigate the definition and properties of regular functions with values in bicomplex settings in Clifford analysis.

• 대한수학회보
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• 제58권3호
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• pp.537-557
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• 2021

In this paper, we investigate the curvature behavior of complete noncompact gradient expanding Ricci solitons with nonnegative Ricci curvature. For such a soliton in dimension four, it is shown that the Riemann curvature tensor and its covariant derivatives are bounded. Moreover, the Ricci curvature is controlled by the scalar curvature. In higher dimensions, we prove that the Riemann curvature tensor grows at most polynomially in the distance function.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.47-56
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• 2024

It is well known that inequalities enable us to analyze and solve complex problems with precision and efficiency. The inequalities provide powerful tools for establishing bounds, optimizing solutions, and deepening our understanding of mathematical concepts, paving the way for advancements in areas such as optimization, analysis, and probability theory. In this paper, we present some properties for Hadamard-Simpsons type inequalities in the classic integral and Riemann-Liouville fractional integral. We use the convexity of the given function and its first derivative.

• East Asian mathematical journal
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• 제12권2호
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• pp.203-211
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• 1996

• East Asian mathematical journal
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• 제16권2호
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• pp.233-237
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• 2000

Since the time of Euler, there have been many proofs giving the value of $\zeta(2n)$. We also give an evaluation of $\zeta(2n)$ by analyzing the generating function of Bernoulli numbers.

• 대한수학회논문집
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• 제35권1호
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• pp.161-184
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• 2020

In this article, we establish some new weighted Hardy-type inequalities involving some variants of extended Riemann-Liouville fractional derivative operators, using convex and increasing functions. As special cases of the main results, we obtain the results of [18,19]. We also prove the boundedness of the k-fractional integral operator on L_p[a, b].

• 충청수학회지
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• 제24권2호
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• pp.247-252
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• 2011

We study some properties of the Riemann-Stieltjes integrals with respect to the Riesz-$N\acute{a}gy$-$Tak\acute{a}cs$ distribution $H_{a,p}$ and its inverse $H_{p,a}$ on the unit interval satisfying the equation 1 - a = $a^2$ and p = 1 - a. Using the properties of the dual distributions $H_{a,p}$ and $H_{p,a}$, we compare the Riemann-Stieltjes integrals of $H_{a,p}$ over some essential intervals with that of its inverse $H_{p,a}$ over the related intervals.

• 대한토목학회논문집
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• 제32권1B호
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• pp.21-27
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• 2012

T. Linde가 제안한 HLLL 기법에서는 일반화된 엔트로피 함수의 도입으로 중앙파가 평가되므로 모든 파속이 초기 상태로부터 결정된다. HLLE 기법과 달리 Roe의 선형화 기법과 완전히 결별되고 HLLC 기법과 달리 정확해에 의존되지 않으므로 모태인 HLL 기법의 온전한 계승으로 볼 수 있다. 이 연구에서는 생성항이 없는 1차원 천수방정식에 농도와 관련된 보존변수를 추가한 지배방정식에 대해 총 에너지를 일반화된 엔트로피 함수로 두고 HLLL 기법을 적용하여 모형을 구성하였다. 정확해가 알려진 세 경우에 대해 모의한 결과, 1차 정확도 수치해의 한계에도 불구하고, 대체로 정확해와 잘 일치하였다. HLLL 기법은 그 외 HLL 형 기법에 비해 우수한 것으로 나타났다. 특히, 물이 빠져 바닥이 드러나는 경우에서 그 전선이 비교적 정확하게 포착되었다. 다만, 그 외 기법에 비해 계산 시간이 더 오래 걸리는 단점이 드러났다.