• Journal of the Korean Physical Society
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• 제73권12호
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• pp.1840-1844
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• 2018

Working in an arbitrary Lorentz frame, we address the question of formulating the covariant variational principle for classical, single-particle, dissipative, relativistic mechanics. First, within a Minkowskian geometry, the basic properties of the proper time ${\tau}$ and the covariant velocity $u_{\mu}$ are recapitulated. Next, using a scalar function ${\psi}(x)$ and its negative derivatives ${\varphi}_{\mu}{^{\prime}}s$, we construct a covariant Lagrangian ${\Lambda}$ that generalizes the famous Bateman-Caldirola-Kanai Lagrangian of nonrelativistic frictional mechanics. Finally, we propose a deterministic model for ${\psi}$ (involving the drag coefficient A) whose explicit solution leads to relativistic damped Rayleigh motion in the rest frame of the medium.

• 대한화학회지
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• 제17권1호
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• pp.1-9
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• 1973

區區한 Diels-Alder 反應의 구조를 규명하기 위하여 Diels-Alder 反應 基 自體의 本質에 가장 가깝다고 생각한 새로운 擬似分子化合物이라는 遷移狀態의 模型을 假定하여 Mulliken의 分子化合物의 量子力學을 適用하였다. 이 擬似分子化合物은 이온성과 Radical성을 지닌 混成體이다. 이 混成體의 波動函數는 다음 식으로 표현된다. ${\psi}_{complex} = {\psi}(R,S) + {\rho}{\psi}(R^+,S^-)$ 여기 ${\rho}$는 擬似分子化合物의 極性程度를 나타내는 것이고 이 ${\rho}$가 Diene과 Dienpohile의 反應中心原子들의 自由原子價의 차 $({\Delta}F)$에 關係함을 밝혔다. 아울러 이 ${\Delta}F$量이 Brown氏의 Lp量 및 Dewar氏의 ${\Delta}E_{deloc}$量과 直線성이 있음을 알았다. Diels-Alder反應의 可能性與否를 24組의 反應組에 對하여 豫言하였다. 따라서 우리가 假定한 遷移狀態의 模型이 眞實에 가깝다고 볼 수 있으며 결국 Diels-Alder 反應은 同時附加로 융합된 ionic-Radical mechanism으로 反應이 進行한다고 볼 수 있다.

• 호남수학학술지
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• 제33권3호
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• pp.321-333
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• 2011

During the last three decades, the problem of evaluation of the determinants of the Laplacians on Riemann manifolds has received considerable attention by many authors. The functional determinant for the n-dimensional sphere $S^n$ with the standard metric has been computed in several ways. Here we aim at computing the determinants of the Laplacians on $S^n$ (n = 8, 9) by mainly using ceratin known closed-form evaluations of series involving Zeta function.

• 대한수학회보
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• 제60권4호
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• 호남수학학술지
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• 제35권4호
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• pp.667-677
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• 2013

A remarkably large number of integrals involving a product of certain combinations of Bessel functions of several kinds as well as Bessel functions, themselves, have been investigated by many authors. Motivated the works of both Garg and Mittal and Ali, very recently, Choi and Agarwal gave two interesting unified integrals involving the Bessel function of the first kind $J_{\nu}(z)$. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present two generalized integral formulas involving a product of Bessel functions of the first kind, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. Some interesting special cases and (potential) usefulness of our main results are also considered and remarked, respectively.

• East Asian mathematical journal
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• 제31권1호
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• pp.41-53
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• 2015

A large number of series and integral representations for the Stieltjes constants (or generalized Euler-Mascheroni constants) ${\gamma}_k$ and the generalized Stieltjes constants ${\gamma}_k(a)$ have been investigated. Here we aim at presenting certain integral representations for the generalized Stieltjes constants ${\gamma}_k(a)$ by choosing to use four known integral representations for the generalized zeta function ${\zeta}(s,a)$. As a by-product, our main results are easily seen to specialize to yield those corresponding integral representations for the Stieltjes constants ${\gamma}_k$. Some relevant connections of certain special cases of our results presented here with those in earlier works are also pointed out.

• 대한수학회논문집
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• 제34권2호
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• pp.523-532
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• 2019

Integrals involving a finite product of the generalized Bessel functions have recently been studied by Choi et al. [2, 3]. Motivated by these results, we establish certain unified integral formulas involving a finite product of the generalized k-Bessel functions. Also, we consider some integral formulas of the (p, q)-extended Bessel functions $J_{{\nu},p,q}(z)$ and the Delerue hyper-Bessel function which are proved in terms of (p, q)-extended generalized hypergeometric functions, and the generalized Wright hypergeometric functions, respectively.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.119-129
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• 2019

Balance function is one of the joint factors to determine fall in risk theory. It helps to moderate the progression and riskiness of falls for detecting balance and fall risk factors. Nevertheless, the objective measures for balance function require expensive equipment with the assessment of any expertise. We establish the existence and uniqueness of a multi-order fractional differential equations based on ${\psi}$-Hilfer operator on time scales with balance function. This class describes the dynamic of time scales derivative. Our tool is based on the Schauder fixed point theorem. Here, sufficient conditions for Ulam-stability are given.

• Asian-Australasian Journal of Animal Sciences
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• 제24권6호
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• pp.857-866
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• 2011

This study examined the metabolism of free radicals in hepatic mitochondria of goats induced by lipopolysaccharide (LPS), and investigated the effects of melatonin (MT). Forty-eight healthy goats ($10{\pm}1.2\;kg$) were randomly selected and divided into four groups: saline control, LPS, MT+LPS and MT. The goats within each group were3 sacrificed either 3 or 6 h after treatment and the livers removed to isolate mitochondria. The respiration control ratio (RCR), the ADP:O ratio, the oxidative phosphorylation ratio (OPR), the concentration of $H_2O_2$ and the activities of Complex I-IV were determined. The mitochondrial membrane potential ($\Delta\psi_m$) was analyzed by flow cytometry. The results showed that RCR, O/P and OPR of the LPS group decreased (p<0.05), as well as activities of respiratory complexes, whereas the generation of $H_2O_2$ in Complex III increased (p<0.05) after 3 h, while Complex II and III increased after 6 h. Also, it was found that the mitochondrial membrane potential of the LPS group declined (p<0.05). However, pre-treatment with MT attenuated the injury induced by LPS, which not only presented higher (p<0.05) RCR, O/P, OPR, and respiratory complex activities, but also maintained the $\Delta\psi_m$. Interestingly, it is revealed that, in the MT+LPS group, the generation of $H_2O_2$ increased firstly in 3 h, and then significantly (p<0.05).decreased after 6 h. In the MT group, the function of mitochondria, the transmenbrane potential and the generation of $H_2O_2$ were obviously improved compared to the control group. Conclusion: melatonin prevents damage caused by LPS on hepatic mitochondria of goats.

• 한국지반신소재학회논문집
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• 제22권2호
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• pp.71-83
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• 2023

해안구조물의 기능 유지를 위해서 침하량을 예측하는 것은 매우 중요하다. 이를 위한 방법으로는 유한요소해석법이나 실물 및 모형실험 등을 들 수 있지만, 이는 비용과 시간이 많이 소요된다는 단점을 가지고 있다. 따라서 본 연구는 케이슨식 안벽구조물의 침하량을 간편하게 예측할 수 있는 간편식 제안을 목적으로 연구가 진행되었다. 연구 진행 과정은 속도의 PSI(Power Spectrum Intensity)를 산정 후, 기존 중력식 방파제의 간편식에 대입하여 구조물의 침하량을 구한다. 이를 수치해석을 통해 얻은 구조물의 침하량과 비교 분석하여 기존 간편식 침하량과 수치해석 침하량 간의 오차가 다소 큰 것을 확인하였고, 이는 기존 간편식의 경우 배후지반에 대해 고려할 수 없었기 때문임을 확인하였다. 따라서 본 연구는 안벽구조물의 배후지반에 대한 보정계수를 제안함으로써 케이슨식 안벽구조물의 침하량을 구할 수 있는 간편식을 나타내었다. 수치해석 침하량과 비교하였을 때, 이 간편식은 케이슨식 안벽 침하량을 산정하는데에 충분한 정밀도를 가지고 있다고 판단하였다. 또한 시간과 비용이 부족한 상황에서 내진성에 취약한 시설을 간편하게 추출할 수 있으며, 스크리닝 기법으로 활용될 수 있을 것으로 기대된다.