• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.757-771
• /
• 2022

In this paper, we present some fixed point theorems for rational type contractive conditions in the setting of a complete metric space via a cyclic (𝛼, 𝛽)-admissible mapping imbedded in simulation function. Our results extend and generalize some previous works from the existing literature. We also give some examples to illustrate the obtained results.

• Journal of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.287-304
• /
• 2016

In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of ${\mathbb{R}}^n$, $n{\geq}3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is ${\beta}{\in}[1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.

• Journal of applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.275-282
• /
• 2008

Our aim in this paper is to investigate the global attractivity of the recursive sequence $x_{n+1}$ = $\frac{\alpha-{\beta}x_{n-1}}{\gamma+g(x_n)}$ under specified conditions. We show that the positive (or zero for $\alpha$ = 0) equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients and the function g(x).

• Journal of applied mathematics & informatics
• /
• v.36 no.1_2
• /
• pp.15-28
• /
• 2018

In this paper, we introduce a Stancu type generalization of genuine LupaŞ-Beta operators of integral type. We establish some moment estimates and the direct results in terms of classical modulus of continuity, Voronovskaja-type asymptotic theorem, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Lastly, we propose a king type modification of these operators to obtain better estimates.

• Kyungpook Mathematical Journal
• /
• v.55 no.1
• /
• pp.109-118
• /
• 2015

In the present paper, a new analytic function valued integral operator is introduced which is defined on n-copies of a subset of the class of normalized analytic functions on the unit disc of the complex plane. This operator, which is denoted here by $\mathfrak{J}^{{\alpha}_i,{\beta}_i}(f_1,{\ldots},f_n)$, unifies and generalizes several integral operators studied earlier. Interesting sufficient conditions are derived for the univalent starlikeness of $\mathfrak{J}^{{\alpha}_i,{\beta}_i}(f_1,{\ldots},f_n)$.

• Journal of the Chungcheong Mathematical Society
• /
• v.5 no.1
• /
• pp.87-97
• /
• 1992

Sequential procedure with ${\beta}$-protection for the mean vector ${\mu}(\theta)$ of a p(> 1)-variate multivariate distribution $P_{\theta}$, ${\theta}{\in}{\Theta}$, with covariance matrix ${\sum}(\theta)$ is considered when the only nuisance parameters is ${\sum}(\theta)$. We obtain a confidence set for ${\mu}(\theta)$ with coverage probability condition and ${\beta}$-protection at ${\mu}-{\delta}(\mu)$ for some imprecision function ${\delta}:\mathbb{R}^p{\rightarrow}\mathbb{R}^p$.

• The Bulletin of The Korean Astronomical Society
• /
• v.37 no.2
• /
• pp.79.1-79.1
• /
• 2012

Due to the quantum interference of many atomic levels, the exact scattering cross section around a given resonance transition deviates from the Lorentz function when the frequency of the incident radiation is quite far from the resonance frequency. This atomic effect is quite significant in the case of damped Ly alpha systems, where HI column density is in excess of 10^20 cm^-2. In this poster, we present the deviation quantitatively taking into consideration of the Rayleigh and Raman scattering around Lyman alpha and Lyman beta.

• Communications for Statistical Applications and Methods
• /
• v.1 no.1
• /
• pp.81-86
• /
• 1994

A Chi-square approximation to the distribution of product of independent Beta variates denoted by U is developed. The distribution is commonly used as a test criterion for the general linear hypothesis about the multivariate linear models. The approximation is obtained by fitting a logarithmic function of U to a Chi-square variate in terms of the first three moments. It is compared with the well known approximations due to Box(1949), Rao(1948), and Mudholkar and Trivedi(1980). It is found that the Chi-square approximation compares favorably with the other three approximations.

• The Pure and Applied Mathematics
• /
• v.29 no.2
• /
• pp.125-139
• /
• 2022

In this paper we wish to establish some results relating to the growths of composition of two entire functions with their corresponding left and right factors on the basis of their generalized relative order (α, β) and generalized relative lower order (α, β) where α and β are continuous non-negative functions defined on (-∞, +∞).

• Molecular & Cellular Toxicology
• /
• v.4 no.2
• /
• pp.157-163
• /
• 2008

Formation of ${\beta}$-amyloid $(A{\beta})$ fibrils has been identified as one of the major characteristics of Alzheimer's disease (AD). Inhibition of $A{\beta}$ fibril formation in the CNS would be attractive therapeutic targets for the treatment of AD. Several small compounds that inhibit amyloid formation or amyloid neurotoxicity in vitro have been known. Citrate has surfactant function effect because of its molecular structure having high anionic charge density, in addition to the well-known antibacterial and antioxidant properties. Therefore, we hypothesized that citrate might have the inhibitory effect against $A{\beta}$ fibril formation in vitro and have the protective effect against $A{\beta}$-induced neurotoxicity in PC12 cells. We examined the effect of citrate against the formation of $A{\beta}$ fibrils by measuring the intensity of fluorescence in thioflavin-T (Th-T) assay of between $A{\beta}_{25-35}$ groups treated with citrate and the control with $A{\beta}_{25-35}$ alone. The neuroprotective effect of citrate against $A{\beta}$-induced toxicity in PC12 cells was investigated using the WST-1 assay. Fluorescence spectroscopy showed that citrate inhibited dose-dependently the formation of $A{\beta}$ fibrils from ${\beta}$-amyloid peptides. The inhibition percentages of $A{\beta}$ fibril formation by citrate (1, 2.5, and 5 mM) were 31%, 60%, and 68% at 7 days, respectively in thioflavin-T (Th-T) assay. WST-1 assay revealed that the toxic effect of $A{\beta}_{25-35}$ was reduced, in a dose-dependent manner to citrate. The percentages of neuroprotection by citrate (1, 2.5, and 5 mM) against $A{\beta}-induced$ toxicity were 19%, 31 %, and 34%, respectively. We report that citrate inhibits the formation of $A{\beta}$ fibrils in vitro and has neuroprotective effect against $A{\beta}$-induced toxicity in PC12 cells. Neuroprotective effects of citrate against $A{\beta}$ might be, to some extent, attributable to its inhibition of $A{\beta}$ fibril formation. Although the mechanism of anti-amyloidogenic activity is not clear, the possible mechanism is that citrate might have two effects, salting-in and surfactant effects. These results suggest that citrate could be of potential therapeutic value in Alzheimer's disease.