• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.471-479
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• 2015

In this paper, we prove that any stable f-harmonic map ${\psi}$ from ${\mathbb{S}}^2$ to N is a holomorphic or anti-holomorphic map, where N is a $K{\ddot{a}}hlerian$ manifold with non-positive holomorphic bisectional curvature and f is a smooth positive function on the sphere ${\mathbb{S}}^2$with Hess $f{\leq}0$. We also prove that any stable f-harmonic map ${\psi}$ from sphere ${\mathbb{S}}^n$ (n > 2) to Riemannian manifold N is constant.

• Journal of the Korean Physical Society
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• v.73 no.12
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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.

• Journal of the Korean Chemical Society
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• v.17 no.1
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• pp.1-9
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• 1973

The purpose of this paper is to investigate the mechanism of Diels-Alder reaction by assuming pseudo molecular complex (PMC) which has characters both of ionic and radical bonds. We treated this complex quantum-chemically as an intermediate between the configuration without charge transfer (radical bond character) and the configuration corresponding to the charge transfer from Diene (R) to Dienophile (S) (ionic bond character). The wave function for the complex could be expressed as: ${\psi}_{complex} = {\psi}(R,S) +{ \rho}{\psi}(R^+,S^-)$ where ${\rho}$ is the extent of charge transfer which is a constant to measure the ionic character of PMC. It has been noticed that${\rho}$is related to the difference between Fr + Fr' and Fs + Fs' in free valence (F) when R is united to S through atom r in R to atom s in S and atom r' in R to atom s' in S, That is, ${\rho}{\alpha}$ ${\Delta}F = (Fr + Fr') - (Fs + Fs')$. We have calculated ${\Delta}F$values for more than forty Diels-Alder reactions. The calculated values of ${\Delta}F$ is reversely proportional to the values of Brown's paralocalization energy (Lp) as well as Dewar's differences of delocalization energy$({\Delta}Edeloc.)$ with good linearity. This approach also presents a way of predicting the possibility and the easiness of diene synthesis between any two conjugate compounds. According to the considerations, it could be concluded that Diels-Alder reaction takes place through the united ionic-radical mechanism rather than the separated ionic or radical mechanism.

• Honam Mathematical Journal
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• v.33 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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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.

• Honam Mathematical Journal
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• v.35 no.4
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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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• v.31 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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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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• v.27 no.1
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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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• v.24 no.6
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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.