• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.769-788
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• 2003

In this paper, we study the optimal control for the damped semilinear hyperbolic systems with unknown parameters (C(t)y')'＋ $A_2$(t, q)y'＋ $A_1$(t, q)y = f(t, q, y, u). We will prove the existence of weak solution of this system and is to find the optimal control pair (q, u) $\in$ $Q_{t}$ ${\times}$ $U_{ad}$ such that in $f_{u}$$\in$ $Q_{t}$/ J(q, u) = J(q, u).$_{t}$/ J(q, u) = J(q, u).

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1175-1199
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• 2019

We construct a general bi-basic inverse series relation which provides extension to several q-polynomials including the Askey-Wilson polynomials and the q-Racah polynomials. We introduce a general class of polynomials suggested by this general inverse pair which would unify certain polynomials such as the q-extended Jacobi polynomials and q-Konhauser polynomials. We then emphasize on applications of the general inverse pair and obtain the generating function relations, summation formulas involving the associated polynomials and derive the p-deformation of some of the q-analogues of Riordan's classes of inverse series relations. We also illustrate the companion matrix corresponding to the general class of polynomials; this is followed by a chart showing the reducibility of the extended p-deformed Askey-Wilson polynomials as well as the extended p-deformed q-Racah polynomials.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.753-763
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• 2023

In this paper, we introduce a fully modified (p, q)-poly tangent polynomials and numbers of the first type. We investigate analytic properties that is related with (p, q)-Gaussian binomial coefficients. We also define (p, q)-Stirling numbers of the second kind and fully modified (p, q)-poly tangent polynomials and numbers of the first type with two variables. Moreover, we derive some identities are concerned with the modified tangent polynomials and the (p, q)-Stirling numbers.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1111-1126
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• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• Journal of the Society of Cosmetic Scientists of Korea
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• v.26 no.1
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• pp.149-162
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• 2000

Coenzyme Q10 is found in all tissues including skin and it is the well-known coenzyme for mitochondrial enzymes. The electron and proton transfer functions of the quinone ring are of fundamental importance for the oxidative phosphorylation pathway to generate energy in the cells. Coenzyme Q10 has been studied as a potent antioxidant molecule in the skin. It is involved in the skin's response to UVR irradiation. The concentration of this antioxidant in UVR exposed skin is higher than in non-exposed skin. However, recent studies have also shown that coenzyme Q10 is one of the first antioxidants to be depleted when skin is UVR-irradiated. This indicates that coenzyme Q10 is primarily involved in defense mechanisms of the skin. Therefore, we questioned whether coenzyme Q10 shows reulatory effect of melanogenesis. Here we report that coenzyme Q10 inhibits melanin neosynthesis of normal human melanocytes grown in culture, and lightens UVB-induced hyperpigmentation of the guinea pig skin in vivo. We treated human melanocytes with 0.05mM to 0.5mM of coenzyme Q10 for a total of two days. This inhibited melanin neosynthesis of cultured human melanocytes dose-dependently. The inhibitory effect of coenzyme Q10 was as effective as kojic acid or vitamin C on cultured human melanocytes. CoQ10 didn't have direct inhibitory effect on tyrosinase activity in in vitro tyrosine hydroxylase activity To further clarify the effect of coenzyme Q10 on the melanogenesis, we established UVB-induced hyperpigmentation on the shaved backs of brownish guinea pigs. The UVB intensity was 500mJ/$\textrm{cm}^2$ and the total energy dose was 1,500 mJ/$\textrm{cm}^2$. The animals were exposed to UVB radiation one times a week for three consecutive weeks. Coenzyme Q10, kojic acid, Arbutin, vitamin C(1% in vehicle) or vehicle alone as a control were then topically applied daily to the hyperpigmented areas twelve times per week far four successive weeks. The lightening effect was evaluated by visual scoring, chromameter and immunohistochemistry. Coenzyme Q10 had lightening effect on the UVB-induced hyperpigmentation without any other side effects, whereas another compounds showed weak lightening efficacies. Therefore, these results suggest that coenzyme Q10 may be useful for solving physiological hyperpigmenting problems for cosmetic purposes.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.43-57
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• 2024

Given a domain X and a collection H of functions h : X → {0, 1}, the Vapnik-Chervonenkis (VC) dimension of H measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical learning says that a hypothesis class with finite VC-dimension is PAC learnable. Recent work by Fitzpatrick, Wyman, the fourth and seventh named authors studied the VC-dimension of a natural family of functions ℋ'²_t(E) : 𝔽²_q → {0, 1}, corresponding to indicator functions of circles centered at points in a subset E ⊆ 𝔽²_q. They showed that when |E| is large enough, the VC-dimension of ℋ'²_t(E) is the same as in the case that E = 𝔽²_q. We study a related hypothesis class, ℋ^d_t(E), corresponding to intersections of spheres in 𝔽^d_q, and ask how large E ⊆ 𝔽^d_q needs to be to ensure the maximum possible VC-dimension. We resolve this problem in all dimensions, proving that whenever |E| ≥ C_dq^d-1/(d-1) for d ≥ 3, the VC-dimension of ℋ^d_t(E) is as large as possible. We get a slightly stronger result if d = 3: this result holds as long as |E| ≥ C_3q^7/3. Furthermore, when d = 2 the result holds when |E| ≥ C_2q^7/4.

• Korean Journal of Ecology and Environment
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• v.52 no.3
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• pp.210-220
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• 2019

Population growth and the increase of energy consumption due to civilization caused global warming. Temperature on the Earth rose about $0.7^{\circ}C$ for the last 100 years, the rate is accelerated since 2000. Temperature is a factor, which determines physiological action, growth and development, survival, etc. of the plant together with light intensity and precipitation. Therefore, it is expected that global warming would affect broadly geographic distribution of the plant as well as structure and function ecosystem. In order to understand the effect of global warming on the ecosystem, a study about the effect of temperature rise on germination and growth in the plant is required necessarily. This study was carried out to investigate the effects of experimental warming on the germination and growth of two oak species(Quercus mongolica and Q. serrata) in temperature gradient chamber(TGC). This study was conducted in control, medium warming treatment($+1.7^{\circ}C$; Tm), and high warming treatment ($+3.2^{\circ}C$; Th) conditions. The final germination percentage, mean germination time and germination rate of two oak species increased by the warming treatment, and the increase in Q. serrata was higher than that in Q. mongolica. Root collar diameter, seedling height, leaf dry weight, stem dry weight, root dry weight, and total biomass were the highest in Tm treatment. Butthey were not significantly different in the Th treatment. In the Th treatment, Q. serrata had significantly higher H/D ratio, S/R ratio, and low root mass ratio (RMR) compared with control plot. Q. mongolica had lower RMR and higher S/R ratio in the Tm and Th treatments compared with control plot. Therefore, growth of Q. mongolica are expected to be more vulnerable to warming than that of Q. serrata. The main findings of this study, species-specific responses to experimental warming, could be applied to predict ecosystem changes from global warming. From the result of this study, we could deduce that temperature rise would increase germination of Q. serrata and Q. mongolica and consequently contribute to increase establishment rate in the early growth stage of the plants. But we have to consider diverse variables to understand properly the effects that global warming influences germination in natural condition. Treatment of global warming in the medium level increased the growth and the biomass of both Q. serrata and Q. mongolica. But the result of treatment in the high level showed different aspects. In particular, Q. mongolica, which grows in cooler zones of higher elevation on mountains or northward in latitude, responded more sensitively. Synthesized the results mentioned above, continuous global warming would function in stable establishment of both plants unfavorably. Compared the responses of both sample plants on temperature rise, Q. serrata increased germination rate more than Q. mongolica and Q. mongolica responded more sensitively than Q. serrata in biomass allocation with the increase of temperature. It was estimated that these results would due to a difference of microclimate originated from the spatial distribution of both plants.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.127-134
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• 1998

This paper presents d new algorithm to compute the offlet curve of a given planar parametric curve. We reduce the problem of computing an offset curve to that of intersecting a surface to a paraboloid. Given an input curve C(t)=(x(t), y(t))∈R², the corresponding surface D/sub c(t)/ is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid Q:z=x²+y²along a lifted curve C(t)=(x(t), y(t), x(t)²+y(t)²∈Q. Given an offset distance d∈R, the offset curve C/sub d/(t) is obtained by the projection of the intersection curve of D/sub c(t)/ and a paraboloid Q:z=x²+y²-d² into the xy-plane.

• Journal of Applied Biological Chemistry
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• v.48 no.4
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• pp.183-186
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• 2005

Arabidopsis AHL gene encodes a 3'(2')-phosphoadenosine 5'-phosphate (PAP)-specific phosphatase that plays a role in the sulfate activation pathway. We complemented E. coli cysQ mutant defective in cysteine biosynthesis with the AHL gene. AHL cDNA was cloned into the prokaryotic expression vector pKK388-1 and transformed into the bacterial mutant. Since cysQ mutant is a leaky cysteine auxotroph only under aerobic conditions, the bacteria were grown in liquid media with vigorous shaking to provide more aeration. In cysteine-free medium, cysQ mutant and the mutant harboring empty vector did not grow well, whereas cells harboring AHL cDNA exhibited significantly improved growth with doubling time of approximately 3 h. cysQ is known to encode a 3'(2'),5'-diphosphonucleoside 3'(2')-phosphohydrolase (DPNPase). However, our data suggest that cysQ protein has PAP-specific phosphatase activity in addition to DPNPase activity. Microbial complementation procedure described in this paper is useful for structure-activity studies of PAP-specific phosphatases identified from microbes and plants.