• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1293-1307
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• 2017

General (${\alpha},{\beta}$)-metrics form a rich class of Finsler metrics. They include many important Finsler metrics, such as Randers metrics, square metrics and spherically symmetric metrics. In this paper, we find equations which are necessary and sufficient conditions for such Finsler metric to be locally projectively flat. By solving these equations, we obtain all of locally projectively flat general (${\alpha},{\beta}$)-metrics under certain condition. Finally, we manufacture explicitly new locally projectively flat Finsler metrics.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.155-185
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• 2021

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of generalized relative order (𝛼, 𝛽), generalized relative type (𝛼, 𝛽) and generalized relative weak type (𝛼, 𝛽) of entire functions with respect to another entire function where 𝛼, 𝛽 are continuous non-negative functions on (-∞, +∞).

• Bulletin of the Korean Chemical Society
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• v.31 no.3
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• pp.620-623
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• 2010

A brush type chiral stationary phase (CSP 2) derived from ${\alpha}$-amino ${\beta}$-lactam was prepared for the separation of the enantiomers of ${\beta}$-blockers. Compared to the CSP derived from ${\alpha}$-amino phosphonate (CSP 1), in general, the conformationally rigid CSP 2 showed greater scope and much enhanced enantioselectivity for the resolution of ${\beta}$-blockers. The effect of various salt additives on enantioseparation of ${\beta}$-blockers in the mobile phase was investigated. The unusual effect of temperature on the chromatographic behaviors was observed on CSP 2. It also afforded appreciable increases in enantioselectivity without significantly affecting resolution, as the column temperature was reduced.

• Applied Biological Chemistry
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• v.9
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• pp.153-159
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• 1968

In this paper the auther investigated the chemical properties, process of humification and type of humic acid in soils which were reclaimed by farming for cultivation in Kangwondo. The results obtained in this studies were summarized as follows: 1. General chemical components of these soil were similar to the ordinary soil but C.E.C. and humus contents were found much more 2. Humic acid and fulvic acid which were extracted with NaOH from soil were greater than those of Na-pyrophosphate(Na-p.) and NaF. Hmus contents and PQ% were increased much more in the upper layer than in the lower layer. 3. Degree of humification of humic acid extracted with NaOH. was very similar to those extracted with Na-pyrophosphate. Humification degree of humic acid extracted with NaF was lower than humic acid which were extracted with NaOH and Na-pyrophosphate. But humification degree of humic acid extracted with NaOH was similar to that with Na-pyrophosphate. Humic acid in B soil and the upper layer was higher than A, C soil and the lower layer of soil, in humification degree. 4. Humic acids extracted with NaOH and Na-pyrophosphate from soil were fractionated by Mg into two parts ${\alpha}$ type and ${\beta}$ type humic acid. Humic acids of ${\alpha}$ and ${\beta}$ type extracted with NaOH were higher than these of Na-pyrophosphate in humification degree. In this soil the humification degree of humic acid was not changed during the period of cultivation. 5. ${\alpha}$, ${\beta}$ type humic acid extracted with NaOH were very similar to the humic acid extracted with Na-pyrophosphate in shapes of absorption curves.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.583-588
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• 2013

In this paper, we introduce the $q$-analogue of $p$-adic log gamma functions with weight alpha. Moreover, we give a relationship between weighted $p$-adic $q$-log gamma functions and $q$-extension of Genocchi and Euler numbers with weight alpha.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.663-684
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• 2021

In this paper, we present some fixed point results for a general class of nonexpansive mappings in the framework of Banach space and also proposed a new iterative scheme for approximating the fixed point of this class of mappings in the frame work of uniformly convex Banach spaces. Furthermore, we establish some basic properties and convergence results for our new class of mappings in uniformly convex Banach spaces. Finally, we present an application to nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper improve, extend and unify some related results in the literature.

• Molecules and Cells
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• v.40 no.6
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• pp.393-400
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• 2017

Type 2 diabetes mellitus (T2DM) is a chronic metabolic disease characterized by lack of insulin and high glucose levels. T2DM can cause bone loss and fracture, thus leading to diabetic osteoporosis. Promoting osteogenic differentiation of osteoblasts may effectively treat diabetic osteoporosis. We previously reported that Sirtuin 1 (Sirt1), a $NAD^+$-dependent deacetylase, promotes osteogenic differentiation through downregulation of peroxisome proliferator-activated receptor (PPAR) ${\gamma}$. We also found that miR-132 regulates osteogenic differentiation by downregulating Sirt1 in a $PPAR{\beta}/{\delta}$-dependent manner. The ligand-activated transcription factor, $PPAR{\alpha}$, is another isotype of the peroxisome proliferator-activated receptor family that helps maintain bone homeostasis and promot bone formation. Whether the regulatory role of $PPAR{\alpha}$ in osteogenic differentiation is mediated via Sirt1 remains unclear. In the present study, we aimed to determine this role and the underlying mechanism by using high glucose (HG) and free fatty acids (FFA) to mimic T2DM in MC3T3-E1 cells. The results showed that HG-FFA significantly inhibited expression of $PPAR{\alpha}$, Sirt1 and osteogenic differentiation, but these effects were markedly reversed by $PPAR{\alpha}$ overexpression. Moreover, siSirt1 attenuated the positive effects of $PPAR{\alpha}$ on osteogenic differentiation, suggesting that $PPAR{\alpha}$ promotes osteogenic differentiation in a Sirt1-dependent manner. Luciferase activity assay confirmed interactions between $PPAR{\alpha}$ and Sirt1. These findings indicate that $PPAR{\alpha}$ promotes osteogenic differentiation via the Sirt1-dependent signaling pathway.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.1-22
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• 1997

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.

• Bulletin of the Korean Chemical Society
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• v.3 no.3
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• pp.83-88
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• 1982

Viscosity and zeta-potential of 11.0 wt. % aqueous bentonite suspension containing various electrolytes and hydrogen-ion concentration were measured by using a Couette type automatic rotational viscometer and Zeta Meter, respectively. The effects of pH and elcctrolytes on the rheological properties of the suspension were investigated. A system, which has a large zeta-potcntial, has a small intrinsic relaxation time ${\beta}$ and a small intrinsic shear modulus $1/{\alpha}$ in the Ree-Eyring generalized viscosity equation, i.e., such a system has a small viscosity value, since ${\eta}={\beta}/{\alpha}$. In general, a stable suspension system has large zeta-potential. The stability condition of clay-water suspension can be estimated by viscometric method since stable suspension generally has small viscosity. The correlation between the stability, viscosity and zeta-potential has been explained by the Ree-Eyring theory of viscous flow.

• Journal of the Korean Mathematical Society
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• v.8 no.1
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• pp.25-30
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• 1971

Put ($$^*$$) $$G[x,y]={\sum}\limits^{p+q=n}_{p,q=0}[-n]_{p+q}c_{p,q}x^py^q$$, where $[{\lambda}]_m$ is the Pocbhammer symbol and the $c_{p,q}$ are arbitrary constants. Making use of the specialized forms of some of his earlier results (see [8] and [9] the author derives here bilateral generating functions of the type ($$^{**}$$) $${\sum}\limits^{\infty}_{n=0}{\frac{[\lambda]_n}{n!}}_2F_1[\array{{\rho}-n,\;{\alpha};\\{\lambda}+{\rho};}x]\;G[y,z]t^n$$ where ${\alpha}$, ${\rho}$ and ${\lambda}$ are arbitrary complex numbers. In particular, it is shown that when G[y, z] is a double hypergeometric polynomial, the right-band member of ($^{**}$) belongs to a class of general triple hypergeometric functions introduced by the author [7]. An interesting special case of ($^{**}$) when ${\rho}=-m,\;m$ being a nonnegative integer, yields a class of bilateral generating functions for the Jacobi polynomials $\{P_n{^{{\alpha},{\beta}}}(x)\}$ in the form ($$^{***}$$) $${\sum\limits^{\infty}_{n=0}}\(\array{m+n\\n}\)P{^{({\alpha}-n,{\beta}-n)}_{m+n}(x)\;G[y,z]{\frac{t^n}{n!}}$$, which provides a unification of several known results. Further extensions of ($^{**}$) and ($^{***}$) with G[y, z] replaced by an analogous multiple sum $H\[y_1,{\cdots},y_m\]$ are also discussed.