• Journal of information and communication convergence engineering
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• v.14 no.1
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• pp.40-44
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• 2016

The device coupling between the stacked top/bottom field-effect transistors (FETs) in two types of monolithic 3D inverter (M3INV) with/without a metal layer in the bottom tier is investigated, and then the regime of the thickness T_ILD and dielectric constant ε_r of the inter-layer distance (ILD), the doping concentration N_d (N_a), and length L_g of the channel, and the side-wall length L_SW where the stacked FETs are coupled are studied. When N_d (N_a) < 10¹⁶ cm^-3 and L_SW < 20 nm, the threshold voltage shift of the top FET varies almost constantly by the gate voltage of the bottom FET, but when N_d (N_a) > 10¹⁶ cm^-3 or L_SW > 20 nm, the shift decreases and increases, respectively. M3INVs with T_ILD ≥ 50 nm and ε_r ≤ 3.9 can neglect the interaction between the stacked FETs, but when T_ILD or ε_r do not meet the above conditions, the interaction must be taken into consideration.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.73-84
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• 2011

Let f, g, h, k : $\mathbb{R}^n{\rightarrow}\mathbb{C}$ be locally integrable functions. We deal with the $L^{\infty}$-version of the Hyers-Ulam stability of the quadratic functional inequality and the Pexiderized quadratic functional inequality $${\parallel}f(x + y) + f(x - y) -2f(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ $${\parallel}f(x + y) + g(x - y) -2h(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ based on the concept of linear functionals on the space of smooth functions with compact support.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.235-251
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• 2021

We consider the Schrödinger type operator ��k = (-∆)k+Vk on ℝn(n ≥ 2k + 1), where k = 1, 2 and the nonnegative potential V belongs to the reverse Hölder class RHs with n/2 < s < n. In this paper, we establish the (Lp, Lq)-boundedness of the higher order Riesz transform T��,�� = V2��∇2��-��2 (0 ≤ �� ≤ 1/2 < �� ≤ 1, �� - �� ≥ 1/2) and its adjoint operator T∗��,�� respectively. We show that T��,�� is bounded from Hardy type space $H^1_{\mathcal{L}_2}({\mathbb{R}}_n)$ into Lp2 (ℝn) and T∗��,�� is bounded from ��p1 (ℝn) into BMO type space $BMO_{\mathcal{L}_1}$ (ℝn) when �� - �� > 1/2, where $p_1={\frac{n}{4({\beta}-{\alpha})-2}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})+2}}$. Moreover, we prove that T��,�� is bounded from $BMO_{\mathcal{L}_1}({\mathbb{R}}_n)$ to itself when �� - �� = 1/2.

• Animal cells and systems
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• v.4 no.1
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• pp.51-55
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• 2000

Mass loss and changes of mineral nutrients during the decomposition of mushrooms, Russula alboareolata and Lactarius violascens, were investigated for 7d from June 29 to July 5 in 1999 in an oak stand in Kongju, Korea. At 7d after installation of litterbags, the remaining mass of R. alboareolata and L. violaxcens was 9.4% and 25.9%, respectively. The mass loss rate of R. alboareolata was significantly higher than that of L. violascens. Concentration of N, P, K, Ca and Mg of R. alboareolata and L. violascens were 37.7 mg/g, 0.97mg/g, 38.25 mg/g, 0.04 mg/g, and 0.75 mg/g for R. alboareolata and 45.7 mg/g, 1.31mg/g, 24.0 mg/g, 0.06 mg/g, and 0.80 mg/g for L. violascens, respectively. Concentrations of nutrients in R. alboareolata and L. violascens were much higher than those in the surrounding leaf litter. N, P, Ca and Mg concentrations in the decomposing mushroom tissue were higher during the experimental period in both species than initial concentrations. Potassium increased during the first 3 d and then decreased in both species. Potassium contents in the mushroom were much greater than those of Ca and Mg. Except for Ca, there was no immobilization period in all the nutrients during decomposition. At 7 d after installation of litterbags, the remaining N, P, K, Ca and Mg of R. alboareolata and L. violascens were 9.8%, 8.9%, 2.7%, 47.7%, and 14.8% of the initial contents for R. alboareolata and 28.2%,30.5%, 19.6%, 199.9%, and 02.1% for L. violascens, respectively. Nutrients could be relocated spatially during the formation and decomposition of the Basidiomycetes fruiting body.

• East Asian mathematical journal
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• v.19 no.2
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• pp.317-335
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• 2003

In this paper, we characterize SL(2, $\mathbb{C}$)-representations of an n-periodic link $\tilde{L}$ in terms of SL(2, $\mathbb{C}$)-representations of its quotient link L and express the SL(2, $\mathbb{C}$)-representation variety R($\tilde{L}$) of $\tilde{L}$ as the union of n affine algebraic subsets which have the same dimension. Also, we show that the dimension of R($\tilde{L}$) is bounded by the dimensions of affine algebraic subsets of the SL(2, $\mathbb{C}$)-representation variety R(L) of its quotient link L.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.593-601
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• 2015

Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1117-1130
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• 2010

The main goal for this paper is consider the necessary conditions and sufficient conditions of wavelet frames in higher dimensions with an arbitrary expanding matrix dilation. At first, we give a necessary condition of wavelet frame in $L^2(R^n)$, which generalizes the univariate results of Shi from one dimension with an arbitrary real number a(a > 1) dilation to higher dimension with an arbitrary expansive matrix dilation. Secondly, we deduce a necessary condition for wavelet frames in $L^2(R^n)$ when the function $\psi$ satisfies some property of the decay. For the case n = 1, we obtain a corollary which has weaker condition comparing with existing result.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.405-434
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• 2005

We establish appropriate $L^p$ estimates for a class of maximal operators $S_{\Omega}^{(\gamma)}$ on the product space $R^n\;\times\;R^m\;when\;\Omega$ lacks regularity and $1\;\le\;\gamma\;\le\;2.\;Also,\;when\;\gamma\;=\;2$, we prove the $L^p\;(2\;{\le}\;P\;<\;\infty)\;boundedness\;of\;S_{\Omega}^{(\gamma)}\;whenever\;\Omega$ is a function in a certain block space $B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ (for some q > 1). Moreover, we show that the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is nearly optimal in the sense that the operator $S_{\Omega}^{(2)}$ may fail to be bounded on $L^2$ if the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is replaced by the weaker conditions $\Omega\;{\in}\;B_q^{(0,\varepsilon)}(S^{n-1}\;\times\;S^{m-1})\;for\;any\;-1\;<\;\varepsilon\;<\;0.$

• Journal of the Korean Chemical Society
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• v.14 no.2
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• pp.155-160
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• 1970

The kinetics of the pepsin-catalyzed hydrolysis of N-carbobenzoxy-L-glutamyl-L-tyrosine at pH 3.5 and $37^{\circ}C$ were determined by a spectrophotometric technique. The pepsin used was further purified on a Sephadex G-75 column. The kinetics data were Km = l.7 ${\times}10^{-3}M,\;-{\Delta}F^{\circ}$ = 3.99Kcal/mole, and $k^3=\;2.1{\times}10^{-2}\;sec^{-1}$. An analysis of the above data and other investigators' data obtained from some dipeptides led to the following conclusions. (1) Phenylalanyl residues in a synthetic peptide are bound to pepsin more strongly than glutamyl or tyrosyl residues, supporting the theory that a part of the binding region of the active center is hydrophobic. (2) Dipeptides are bound to pepsin principally through their side chains and the binding involves both side-chain residues. (3) The nature of amino acids in dipeptides $R_2-R_1,\;affect\;the\;k_3$ values.