• 대한수학회지
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• 제51권6호
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• pp.1291-1304
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• 2014

In 2005 Kadiri proved that the Riemann zeta function ${\zeta}(s)$ does not vanish in the region $$Re(s){\geq}1-\frac{1}{R_0\;{\log}\;{\mid}Im(s){\mid}},\;{\mid}Im(s){\mid}{\geq}2$$ with $R_0=5.69693$. In this paper we will show that $R_0$ can be taken $R_0=5.68371$ using Kadiri's method together with Platt's numerical verification of Riemann Hypothesis.

• 대한수학회논문집
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• 제11권1호
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• pp.57-62
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• 1996

For $1 < p \leq 2$ it is shown that a certain sequence of functions converges to -1 in $L^{p-\varepsilon}(0, 1)$ for any small $\varepsilon > 0$ if and only if the Riemann zeta function satisfies $\zeta(s) \neq 0$ for $\sigma = Re s > 1/p$.

• 대한수학회지
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• 제59권4호
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• pp.775-787
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• 2022

Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some recent results on Jensen polynomials, relevant to the Riemann hypothesis, are extended and improved.

• 대한수학회지
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• 제40권4호
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• pp.747-756
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• 2003

We establish a vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds. The hypothesis needed for this result is a growth condition on a primitive of the Kaehler form.

• 대한기계학회논문집B
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• 제30권7호
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• pp.671-681
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• 2006

This study focuses on the development of numerical procedure to analyze the nonlinear combustion instabilities in liquid rocket engine. Nonlinear behaviors of acoustic instabilities are characterized by the existence of limit cycle in linearly unstable engines and nonlinear or triggering instability in linearly stable engines. To discretize convective fluxes with high accuracy and robustness, approximated Riemann solver based on characteristics and Euler-characteristic boundary conditions are employed. The present procedure predicts well the transition processes from initial harmonic pressure disturbance to N-like steep-fronted shock wave in a resonant pipe. Longitudinal pressure oscillations within the SSME(Space Shuttle Main Engine) engine have been analyzed using the pressure-sensitive time lag model to account for unsteady combustion response. It is observed that the pressure oscillations reach a limit cycle which is independent of the characteristics of the initial disturbances and depends only on combustion parameters and operating conditions.

• 대한수학회지
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• 제58권6호
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• pp.1529-1547
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• 2021

In this series, we investigate the calculation of mean values of derivatives of Dirichlet L-functions in function fields using the analogue of the approximate functional equation and the Riemann Hypothesis for curves over finite fields. The present paper generalizes the results obtained in the first paper. For µ ≥ 1 an integer, we compute the mean value of the µ-th derivative of quadratic Dirichlet L-functions over the rational function field. We obtain the full polynomial in the asymptotic formulae for these mean values where we can see the arithmetic dependence of the lower order terms that appears in the asymptotic expansion.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.601-612
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• 2023

The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2005년도 제24회 춘계학술대회논문집
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• pp.281-287
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• 2005

연소불안정에서 흔히 수반되는 충격파와 한계사이클 같은 비선형적 거동을 수치해석을 통해 고찰하였다. 공진관에 가해진 초기 압력교란이 충격파로 천이되는 과정을 해석함으로서 비선형 음향특성에 대한 이해를 돕는 동시에 수치해석기법의 정확성을 검증하였다. ${\eta}-{\tau}$ 연소응답모델을 이용한 SSME의 해석결과는 선형불안정 영역에서 한계사이클의 특성은 연소파라미터와 작동조건에 의존할 뿐 초기 교란의 특성과는 무관함을 밝혔다. 또한 1.5 MW급 가스발생기의 개발 과정에서 겪은 연소불안정 문제에 적용하여 예측된 안정성 경향을 연소시험 결과와 비교함으로서, 향후 수치해석을 통한 연소불안정 예측기법에 대해 가능성을 확인하는 동시에 향후 연구방향을 모색하였다.