• 대한수학회논문집
• /
• 제21권2호
• /
• pp.363-374
• /
• 2006

A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.

• 대한수학회지
• /
• 제44권2호
• /
• pp.343-371
• /
• 2007

We find the super-replication formulae which would be a generalization of replication formulae. And we apply the formulae to derive periodically vanishing property in the Fourier coefficients of the Hauptmodul $\aleph(j_{1,N})$ as a super-replicable function.

• 충청수학회지
• /
• 제24권3호
• /
• pp.529-531
• /
• 2011

We show that for all $N{\geq}1$, the modular function field $K(X_0^+(N))$ is generated by j(z)j(Nz) and j(z) + j(Nz) over ${\mathbb{C}}$, where j(z) is the modular invariant. Moreover we derive the defining equation of the the modular function field $K(X_0^+(N))$ from the classical modular polynomial ${\Phi}_N(X, Y )$.

• Kyungpook Mathematical Journal
• /
• 제58권4호
• /
• pp.615-625
• /
• 2018

In this paper, we discuss the connection between the 5-dimensional complex Lie algebra ${\mathcal{K}} _5$ and Special functions. We construct certain two variable models of the irreducible representations of ${\mathcal{K}}_5$. We also use an Euler type integral transformation to obtain the new transformed models, in which the basis function appears as $_2F_1$. Further, we utilize these models to get some generating functions and recurrence relations.

• Journal of applied mathematics & informatics
• /
• 제37권5_6호
• /
• pp.481-489
• /
• 2019

In this manuscript, we provide some new results with short proofs for the existence of Picard-Jungck operators in the framework of generalized metric spaces using $C_G$-simulation functions. An example is also provided to illustrate the usability of the results.

• 대한수학회보
• /
• 제59권4호
• /
• pp.801-810
• /
• 2022

In this paper, we prove that any orthogonal almost complex structure on a warped product manifold of any oriented closed surface and a round 4-sphere for a concircular warping function on the sphere is never integrable. This gives a partial answer to Calabi's problem.

• Nonlinear Functional Analysis and Applications
• /
• 제28권1호
• /
• pp.81-93
• /
• 2023

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ A_p using this operator.

• 대한수학회논문집
• /
• 제38권2호
• /
• pp.355-364
• /
• 2023

In this paper, we investigate the sums of the elements in the finite set $\{x^k:1{\leq}x{\leq}{\frac{n}{m}},\;gcd_u(x,n)=1\}$, where k, m and n are positive integers and gcd_u(x, n) is the unitary greatest common divisor of x and n. Moreover, for some cases of k and m, we can give the explicit formulae for the sums involving some well-known arithmetic functions.

• 천문학회지
• /
• 제48권4호
• /
• pp.213-228
• /
• 2015

The Horizon Run 4 is a cosmological N-body simulation designed for the study of coupled evolution between galaxies and large-scale structures of the Universe, and for the test of galaxy formation models. Using 6300³ gravitating particles in a cubic box of L_box = 3150 h⁻¹Mpc, we build a dense forest of halo merger trees to trace the halo merger history with a halo mass resolution scale down to M_s = 2.7 × 10¹¹h⁻¹M_⊙. We build a set of particle and halo data, which can serve as testbeds for comparison of cosmological models and gravitational theories with observations. We find that the FoF halo mass function shows a substantial deviation from the universal form with tangible redshift evolution of amplitude and shape. At higher redshifts, the amplitude of the mass function is lower, and the functional form is shifted toward larger values of ln(1/σ). We also find that the baryonic acoustic oscillation feature in the two-point correlation function of mock galaxies becomes broader with a peak position moving to smaller scales and the peak amplitude decreasing for increasing directional cosine μ compared to the linear predictions. From the halo merger trees built from halo data at 75 redshifts, we measure the half-mass epoch of halos and find that less massive halos tend to reach half of their current mass at higher redshifts. Simulation outputs including snapshot data, past lightcone space data, and halo merger data are available at http://sdss.kias.re.kr/astro/Horizon-Run4.

• Biomolecules & Therapeutics
• /
• 제28권3호
• /
• pp.250-258
• /
• 2020

Emphysema, a major component of chronic obstructive pulmonary disease (COPD), is a leading cause of human death worldwide. The progressive deterioration of lung function that occurs in the disease is caused by chronic inflammation of the airway and destruction of the lung parenchyma. Despite the main impact of inflammation on the pathogenesis of emphysema, current therapeutic regimens mainly offer symptomatic relief and preservation of lung function with little therapeutic impact. In the present study, we aimed to discover novel therapeutics that suppress the pathogenesis of emphysema. Here, we show that LJ-2698, a novel and highly selective antagonist of the adenosine A₃ receptor, a G protein-coupled receptor involved in various inflammatory diseases, significantly reversed the elastase-induced destructive changes in murine lungs. We found that LJ-2698 significantly prevented elastase-induced airspace enlargement, resulting in restoration of pulmonary function without causing any obvious changes in body weight in mice. LJ-2698 was found to inhibit matrix metalloproteinase activity and pulmonary cell apoptosis in the murine lung. LJ-2698 treatment induced increases in anti-inflammatory cytokines in macrophages at doses that displayed no significant cytotoxicity in normal cell lines derived from various organs. Treatment with LJ-2698 significantly increased the number of anti-inflammatory M2 macrophages in the lungs. These results implicate the adenosine A₃ receptor in the pathogenesis of emphysema. Our findings also demonstrate the potential of LJ-2698 as a novel therapeutic/preventive agent in suppressing disease development with limited toxicity.