• Honam Mathematical Journal
• /
• 제16권1호
• /
• pp.119-135
• /
• 1994

Let $Q_{n+p-1}(\alpha)$ denote the- dass of functions $$f(z)=z^{P}-\sum_{n=0}^\infty{a_{(p+k)}z^{p+k}$$ ($a_{p+k}{\geq}0$, $p{\in}N=\left{1,2,{\cdots}\right}$) which are analytic and p-valent in the unit disc $U=\left{z:{\mid}z:{\mid}<1\right}$ and satisfying $Re\left{\frac{D^{n+p-1}f(\approx))^{\prime}}{pz^{p-a}\right}>{\alpha},0{\leq}{\alpha}<1,n>-p,z{\in}U.$ In this paper we obtain sharp results concerning coefficient estimates, distortion theorem, closure theorems and radii of p-valent close-to- convexity, starlikeness and convexity for the class $Q_{n+p-1}$ ($\alpha$). We also obtain class preserving integral operators of the form $F(z)=\frac{c+p}{z^{c}}\int_{o}^{z}t^{c-1}f(t)dt.$ c>-p $F\left(z\right)=\frac{c+p}{z^{c}}\int_{0}^{z} t^{c-1}f\left(t \right)dt. \qquad c>-p$ for the class $Q_{n+p-1}$ ($\alpha$). Conversely when $F(z){\in}Q_{n+p-1}(\alpha)$, radius of p-valence of f(z) has been determined.

• The Korean Journal of Malacology
• /
• 제24권2호
• /
• pp.143-151
• /
• 2008

We studied the management policy for Haliotis diversicolor fisheries in the coastal area of Sungsanpo using Yield-per-recruit model from 2004 to 2006. The age at first capture($t_c$) and fishing mortality(F) annually estimated during the study period decreased and increased, respectively. The maximum yield-per-recruit in 2004 was increased by increasing $t_c$ from the 2.012 year of current $t_c$ to 2.7 year or increasing F from the 0.574/year of current F to 0.800/year, and that in 2005 was increased by increasing $t_c$ from the 1.946 year of current $t_c$ to 2.5 year or increasing F from the 0.578/year of current F to 0.880/year. In 2006, the maximum yield-per-recruit was increased by increasing $t_c$ from the 1.926year of current $t_c$ to 3.1 year or decreasing F from the 1.088/year of current F to 0.810/year. Further, although the current F in 2004 and 2005 was lower than the estimated $F_{MAX}$, that in 2006 was higher than the estimated $F_{MAX}$. These results indicate that the likelihood of growth overfishing with increasing catch of smaller H. diversicolor in 2006 was greater than in 2004 and 2005. As action that could prevent growth overfishing in fisheries management of H. diversicolor, increasing for the current $t_c$ could be a more appropriate policy because the artificial decrease of the number of woman divers related F is actually difficult.

• The Pure and Applied Mathematics
• /
• 제25권1호
• /
• pp.49-57
• /
• 2018

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then $C({\subseteq}X)$ is functionally convex (briefly, F-convex), if $T(C){\subseteq}{\mathbb{R}}$ is convex for all bounded linear transformations $T{\in}B$(X, R); and $K({\subseteq}X)$ is functionally closed (briefly, F-closed), if $T(K){\subseteq}{\mathbb{R}}$ is closed for all bounded linear transformations $T{\in}B$(X, R). By using these new notions, the Alaoglu-Bourbaki-Eberlein-${\check{S}}muljan$ theorem has been generalized. Moreover, we show that X is reflexive if and only if the closed unit ball of X is F-closed. James showed that for every closed convex subset C of a Banach space X, C is weakly compact if and only if every $f{\in}X^{\ast}$ attains its supremum over C at some point of C. Now, we show that if A is an F-convex subset of a Banach space X, then A is bounded and F-closed if and only if every element of $X^{\ast}$ attains its supremum over A at some point of A.

• Communications for Statistical Applications and Methods
• /
• 제12권3호
• /
• pp.545-556
• /
• 2005

Hjort(1990) obtained the nonparametric Bayes estimator $\^{F}_{c,a}$ of $F_0$ with respect to beta processes in the random censorship model. Let $X_1,{\cdots},X_n$ be i.i.d. $F_0$ and let $C_1,{\cdot},\;C_n$ be i.i.d. G. Assume that $F_0$ and G are continuous. This paper shows that {$\^{F}_{c,a}$(u){\|}0 < u < T} converges weakly to a Gaussian process whenever T < $\infty$ and $\~{F}_0({\tau})\;<\;1$.

• The Pure and Applied Mathematics
• /
• 제30권2호
• /
• pp.109-129
• /
• 2023

In this paper, we introduce a second order linear differential operator ^T□: C^∞ (M) → C^∞ (M) as a natural generalization of Cheng-Yau operator, [8], where T is a (1, 1)-tensor on Riemannian manifold (M, h), and then we show on compact Riemannian manifolds, divT = divT^t, and if divT = 0, and f be a smooth function on M, the condition ^T□ f = 0 implies that f is constant. Hereafter, we introduce T-energy functionals and by deriving variations of these functionals, we define T-harmonic maps between Riemannian manifolds, which is a generalization of L_k-harmonic maps introduced in [3]. Also we have studied fT-harmonic maps for conformal immersions and as application of it, we consider fL_k-harmonic hypersurfaces in space forms, and after that we classify complete fL₁-harmonic surfaces, some fL_k-harmonic isoparametric hypersurfaces, fL_k-harmonic weakly convex hypersurfaces, and we show that there exists no compact fL_k-harmonic hypersurface either in the Euclidean space or in the hyperbolic space or in the Euclidean hemisphere. As well, some properties and examples of these definitions are given.

• Journal of the Korean Mathematical Society
• /
• 제47권6호
• /
• pp.1147-1165
• /
• 2010

In this paper we compare a torsion free sheaf F on $P^N$ and the free vector bundle $\oplus^n_{i=1}O_{P^N}(b_i)$ having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of F. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes $c_i$(F(t)) of twists of F, only depending on some numerical invariants of F. Especially, we prove for rank n torsion free sheaves on $P^N$, whose splitting type has no gap (i.e., $b_i{\geq}b_{i+1}{\geq}b_i-1$ 1 for every i = 1,$\ldots$,n-1), the following formula for the discriminant: $$\Delta(F):=2_{nc_2}-(n-1)c^2_1\geq-\frac{1}{12}n^2(n^2-1)$$. Finally in the case of rank n reflexive sheaves we obtain polynomial upper bounds for the absolute value of the higher Chern classes $c_3$(F(t)),$\ldots$,$c_n$(F(t)) for the dimension of the cohomology modules $H^iF(t)$ and for the Castelnuovo-Mumford regularity of F; these polynomial bounds only depend only on $c_1(F)$, $c_2(F)$, the splitting type of F and t.

• Communications of the Korean Mathematical Society
• /
• 제9권3호
• /
• pp.731-737
• /
• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 한국전기전자재료학회 2003년도 하계학술대회 논문집 Vol.4 No.2
• /
• pp.1034-1037
• /
• 2003

Microcrystalline silicon(c-Si:H) thin-film solar cells are prepared with intrinsic Si-layer by hot wire CVD. The operating parameters of solar cells are strongly affected by the filament temperature ($T_f$) during intrinsic layer. Jsc and efficiency abruptly decreases with elevated $T_f$ to $1400^{\circ}C$. This deterioration of solar cell parameters are resulted from increase of crystalline volume fraction and corresponding defect density at high $T_f$. The heater temperature ($T_h$) are also critical parameter that controls device operations. Solar cells prepared at low $T_h$ ($<200^{\circ}C$) shows a similar operating properties with devices prepared at high $T_f$, i.e. low Jsc, Voc and efficiency. The origins for this result, however, are different with that of inferior device performances at high $T_f$. In addition the phase transition of the silicon films occurs at different silane concentration (SC) by varying filament temperature, by which highest efficiency with SC varies with $T_f$.

• Proceedings of the KIEE Conference
• /
• 대한전기학회 2003년도 하계학술대회 논문집 C
• /
• pp.1598-1600
• /
• 2003

Microcrystalline silicon(c-Si:H) thin-film solar cells are prepared with intrinsic Si-layer by hot wire CVD. The operating parameters of solar cells are strongly affected by the filament temperature ($T_f$) during intrinsic layer. Jsc and efficiency abruptly decreases with elevated $T_f$ to $1400^{\circ}C$. This deterioration of solar cell parameters are resulted from increase of crystalline volume fraction and corresponding defect density at high $T_f$ The heater temperature ($T_h$) are also critical parameter that controls device operations. Solar cells prepared at low $T_h$ (<$200^{\circ}C$) shows a similar operating properties with devices prepared at high $T_f$, i.e. low Jsc, Voc and efficiency. The origins for this result, however, are different with that of inferior device performances at high $T_f$. In addition the phase transition of the silicon films occurs at different silane concentration (SC) by varying filament temperature, by which highest efficiency with SC vanes with $T_f$.

• Journal of the Korean Mathematical Society
• /
• 제57권1호
• /
• pp.145-169
• /
• 2020

Let k be a field of characteristic 0. Let ${\mathfrak{C}}=Spec(k[x,y]/{\langle}f{\rangle})$ be a weighted homogeneous plane curve singularity with tangent space ${\pi}_{\mathfrak{C}}:T_{{\mathfrak{C}}/k}{\rightarrow}{\mathfrak{C}$. In this article, we study, from a computational point of view, the Zariski closure ${\mathfrak{G}}({\mathfrak{C}})$ of the set of the 1-jets on ${\mathfrak{C}}$ which define formal solutions (in F[[t]]² for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal ${\mathcal{N}}_1({\mathfrak{C}})$ defining ${\mathfrak{G}}({\mathfrak{C}})$ as a reduced closed subscheme of $T_{{\mathfrak{C}}/k}$ and obtain applications in terms of logarithmic differential operators (in the plane) along ${\mathfrak{C}}$.