• Journal of IKEEE
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• v.27 no.4
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• pp.399-404
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• 2023

In this paper, we analyzed the current path in the O/N/O (Oxide/Nitride/Oxide) structure of 3D NAND Flash memory and in the O/N/F (Oxide/Nitride/Ferroelectric) structure where the blocking oxide is replaced by a ferroelectric. In the O/N/O structure, when V_read is applied, a current path is formed on the backside of the channel due to the E-fields of neighboring cells. In contrast, the O/N/F structure exhibits a current path formed on the front side due to the polarization of the ferroelectric material, causing electrons to move toward the channel front. Additionally, we performed an examination of device characteristics considering channel thickness and channel length. The analysis results showed that the front electron current density in the O/N/F structure increased by 2.8 times compared to the O/N/O structure, and the front electron current density ratio of the O/N/F structure was 17.7% higher. Therefore, the front current path is formed more effectively in the O/N/F structure than in the O/N/O structure.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.557-569
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• 2010

Suppose that n is a positive integer. For any real number $\alpha$($\beta$ resp.) with $\alpha$ < 1 ($\beta$ > 1 resp.), let $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) be the class of analytic functions in the unit disk $\mathbb{D}$ with f(0) = f'(0) = $\cdots$ = $f^{(n-1)}(0)$ = $f^{(n)}(0)-1\;=\;0$, Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) > $\alpha$ (Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) < $\beta$ resp.) in $\mathbb{D}$, and for any ${\lambda}\;{\in}\;\bar{\mathbb{D}}$, let $K^{(n)}({\alpha},\;{\lambda})$ $K^{(n)}({\beta},\;{\lambda})$ resp.) denote a subclass of $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) whose elements satisfy some condition about derivatives. For any fixed $z_0\;{\in}\;\mathbb{D}$, we shall determine the two regions of variability $V^{(n)}(z_0,\;{\alpha})$, ($V^{(n)}(z_0,\;{\beta})$ resp.) and $V^{(n)}(z_0,\;{\alpha},\;{\lambda})$ ($V^{(n)}(z_0,\;{\beta},\;{\lambda})$ resp.). Also we shall determine the extreme points of the families of analytic functions which satisfy $f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\alpha})$ ($f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\beta})$ resp.) when f ranges over the classes $K^{(n)}(\alpha)$ ($K^{(n)(\beta)$ resp.) and $K^{(n)}({\alpha},\;{\lambda})$ ($K^{(n)}({\beta},\;{\lambda})$ resp.), respectively.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.659-666
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• 2014

Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1315-1322
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• 2010

Let D be a plane domain whose boundary consists of n components and $C_1$, $C_2$ two boundary components of D. We consider the family $F_1$ of conformal mappings f satisfying f(D) $\subset$ {1 < |w| < ${\mu}(f)$}, $f(C_1)=\{|w|=1\}$, $f(C_2)=\{|w|={\mu}(f)\}$. There are conformal mappings $g_0$, $g_1({\in}F_1)$ onto a radial and a circular slit annulus respectively. We obtain the following theorem, $$\{{\mu}(f)|f\;{\in}\;F_1\}=\{\mu|\mu(g_1)\;{\leq}\;{\mu}\;{\leq}\;{\mu}(g_0)\}$$. And we consider the family $F_n$ of conformal mappings $\tilde{f}$ from D onto a covering surfaces of the Riemann sphere satisfying some conditions. We obtain the following theorems, {$\mu|1$ < ${\mu}\;{\leq}\;{\mu}(g_1)$} ${\subset}\;\{{\mu}(\tilde{f})|\tilde{f}\;{\in}\;F_2\}\;{\subset}\;\{{\mu}(\tilde{f})|\tilde{f}\;{\in}\;F_n\}$ and ${\mu}(\tilde{f})\;{\leq}\;{\mu}(g_0)^n$.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.43-65
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• 2023

In this paper, by using the difference analogue of Nevanlinna's theory, the authors study the shared-value problem concerning two higher order difference operators of a transcendental entire function with finite order. The following conclusion is proved: Let f(z) be a finite order transcendental entire function such that λ(f - a(z)) < ρ(f), where a(z)(∈ S(f)) is an entire function and satisfies ρ(a(z)) < 1, and let 𝜂(∈ ℂ) be a constant such that ∆_𝜂ⁿ⁺¹ f(z) ≢ 0. If ∆_𝜂ⁿ⁺¹ f(z) and ∆_𝜂ⁿ f(z) share ∆_𝜂ⁿ a(z) CM, where ∆_𝜂ⁿ a(z) ∈ S ∆_𝜂ⁿ⁺¹ f(z), then f(z) has a specific expression f(z) = a(z) + Be^Az, where A and B are two non-zero constants and a(z) reduces to a constant.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.539-545
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• 1994

Let $q = p^r$, where p is a prime. A polynomial $f(x) \in GF(q)[x]$ is called a permutation polynomial (PP) over GF(q) if the numbers f(a) where $a \in GF(Q)$ are a permutation of the a's. In other words, the equation f(x) = a has a unique solution in GF(q) for each $a \in GF(q)$. More generally, $f(x_1, \cdots, x_n)$ is a PP in n variables if $f(x_1,\cdots,x_n) = \alpha$ has exactly $q^{n-1}$ solutions in $GF(q)^n$ for each $\alpha \in GF(q)$. Mullen ([3], [4], [5]) has studied the concepts of local permutation polynomials (LPP's) over finite fields. A polynomial $f(x_i, x_2, \cdots, x_n) \in GF(q)[x_i, \codts,x_n]$ is called a LPP if for each i = 1,\cdots, n, f(a_i,\cdots,x_n]$ is a PP in $x_i$ for all $a_j \in GF(q), j \neq 1$.Mullen ([3],[4]) found a set of necessary and three variables over GF(q) in order that f be a LPP. As examples, there are 12 LPP's over GF(3) in two indeterminates ; $f(x_1, x_2) = a_{10}x_1 + a_{10}x_2 + a_{00}$ where $a_{10} = 1$ or 2, $a_{01} = 1$ or x, $a_{00} = 0,1$, or 2. There are 24 LPP's over GF(3) of three indeterminates ; $F(x_1, x_2, x_3) = ax_1 + bx_2 +cx_3 +d$ where a,b and c = 1 or 2, d = 0,1, or 2.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.845-852
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• 2010

A nonlinear algebraic equation f(x) = 0 is considered to find a root with integer multiplicity $m{\geq}1$. A variant of Newton-secant method for a multiple root is proposed below: for n = 0, 1, $2{\cdots}$ $$x_{n+1}=x_n-\frac{f(x_n)^2}{f^{\prime}(x_n)\{f(x_n)-{\lambda}f(x_n-\frac{f(x_n)}{f^{\prime}(x_n)})\}$$, $$\lambda=\{_{1,\;if\;m=1.}^{(\frac{m}{m-1})^{m-1},\;if\;m{\geq}2$$ It is shown that the method has third-order convergence and its asymptotic error constant is expressed in terms of m. Numerical examples successfully verified the proposed scheme with high-precision Mathematica programming.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.513-519
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Jensen's functional equation $$2f(\frac{x_1+y_1}{2},\;\cdots,\;\frac{x_n+y_n}{2})=f(x_1,\;\cdots,\;x_n)+f(y_1,\;\cdots,\;y_n)$$. The function f given by $f(x_1,\;\cdots,\;x_n)=a_1x_1+{\cdots}+a_nx_n+b$ is a solution of the above functional equation.

• Korean Journal of Plant Tissue Culture
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• v.25 no.2
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• pp.135-139
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• 1998

Reciprocal interspecific hybrids between N. glauca(2n=24) and N. langsdorffii(2n=18) were obtained by intercrossing. One hundred percent of F$_1$ seeds was produced from intercrossing of N. glauca $\times$ N. langsdorffii, whereas the frequency of F$_1$ hybrid seed formation from N. langsdorffii $\times$ N. glauca was very low. However, all the hybrid seeds were germinated well and then grown to normal plantlets. All the plants of F$_1$ hybrids have chromosome number of interspecific hybrids (2n=21). From observation of morphological characteristic, the structure of petrol, leaf, flower, and the morphology of pollen have characteristics of F1 hybrid. Spontaneous tumors (genetic tumor) were formed from each F$_1$ hybrid; the genetic tumor arose at the reproductive phase when the maternal type of F$_1$ hybrid came from N. glauca, while the genetic tumor arose only after reproductive phase when the maternal type of F$_1$ hybrid came from N. langsdorffii. The genetic tumor actively proliferated on hormone-free medium and produced numerous teratoma shoots. In addition, normal leaf or stem explants of F$_1$ hybrid produced calli on hormone-free medium after 15 days of culture, the calli produced new numerous teratoma shoots after 30 days. The frequency of teratoma shoot formation from rnterspecific hybrid was higher in the N. glauca $\times$ N. langsdorffii than in the N. langsdorffii $\times$ N. glauca. Root development from the teratoma shoots was hardly obtained. Teratoma shoots without roots in vitro can form genetic tumor at the vegetative growth phase after tissue culture.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1147-1165
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• 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.