• 대한수학회보
• /
• 제56권4호
• /
• pp.885-898
• /
• 2019

This paper gives a counterexample to show that the first order commutator $C_2$ is not bounded from $H^1({\mathbb{R}}){\times}H^1({\mathbb{R}})$ into $L^{1/2}({\mathbb{R}})$. Then we introduce the atomic definition of abstract weighted Hardy spaces $H^1_{ato,{\omega}}$$({\mathbb{R}})$ and study its properties. At last, we prove that $C_2$ maps $H^1_{ato,{\omega}}$$({\mathbb{R}}){\times}H^1_{ato,{\omega}}$$({\mathbb{R}})$ into $L^{1/2}_{\omega}$$({\mathbb{R}})$.

• 대한수학회논문집
• /
• 제10권1호
• /
• pp.207-213
• /
• 1995

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measure 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 $\Vert \gamma \Vert = sup_{s \in J}$\mid$\gamma(s)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E,F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$.

• 대한수학회논문집
• /
• 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}$.

• Bulletin of the Korean Chemical Society
• /
• 제30권11호
• /
• pp.2749-2753
• /
• 2009

Structural characteristics that influence on the insecticidal activity ($pI_{50}$) of 2-(n-octyl)isothiourea analogues (1-45) against the diamondback moth (Plutella xylostella, L.) based on three dimensional quantitative structure activity relationships (3D-QSARs) were discussed quantitatively using a comparative molecular field analysis (CoMFA) and a comparative molecular similarity indeces analysis (CoMSIA) methods. The statistical values of the CoMFA 2 model were better than those of the CoMSIA 1 model. The CoMFA 2 model was the optimized model with the correlativity (the training set: Ave. = 0.104 & PRESS = 0.613) and the predictability (the test set: Ave. = 0.086 & PRESS = 0.096). Insecticidal activities with the optimized CoMFA 2 model were dependent upon steric factors (79.4%) of $R_1-R_3$ substituents. From the analytical results of CoMFA contour maps, it is predicted that the R1 substituent of 1-45 which has a steric favor in a broad space, $R_2\;and\;R_3$ groups with a steric favor in a narrow space and a H-bond donor favor would have better the insecticidal activity.

• 대한수학회지
• /
• 제59권2호
• /
• pp.353-365
• /
• 2022

Let 𝓐 be the collection of analytic functions f defined in 𝔻 := {ξ ∈ ℂ : |ξ| < 1} such that f(0) = f'(0) - 1 = 0. Using the concept of subordination (≺), we define $$S^*_{\ell}\;:=\;\{f{\in}A:\;\frac{{\xi}f^{\prime}({\xi})}{f({\xi})}{\prec}{\Phi}_{\ell}(\xi)=1+{\sqrt{2}{\xi}}+{\frac{{\xi}^2}{2}},\;{\xi}{\in}{\mathbb{D}}\}$$, where the function 𝚽_ℓ(ξ) maps 𝔻 univalently onto the region Ω_ℓ bounded by the limacon curve (9u² + 9v² - 18u + 5)² - 16(9u² + 9v² - 6u + 1) = 0. For 0 < r < 1, let 𝔻_r := {ξ ∈ ℂ : |ξ| < r} and 𝒢 be some geometrically defined subfamily of 𝓐. In this paper, we find the largest number 𝜌 ∈ (0, 1) and some function f₀ ∈ 𝒢 such that for each f ∈ 𝒢 𝓛_f (𝔻_r) ⊂ Ω_ℓ for every 0 < r ≤ 𝜌, and $${\mathcal{L} _{f_0}}({\partial}{\mathbb{D}_{\rho})\;{\cap}\;{\partial}{\Omega}_{\ell}\;{\not=}\;{\emptyset}$$, where the function 𝓛_f : 𝔻 → ℂ is given by $${\mathcal{L}}_f({\xi})\;:=\;{\frac{{\xi}f^{\prime}(\xi)}{f(\xi)}},\;f{\in}{\mathcal{A}}$$. Moreover, certain graphical illustrations are provided in support of the results discussed in this paper.

• International Journal of Air-Conditioning and Refrigeration
• /
• 제14권4호
• /
• pp.156-165
• /
• 2006

Convective boiling heat transfer coefficients were measured in a horizontal minichannel with R-l34a. The test section was made of stainless steel tube with an inner diameter of 3.0 mm and a length of 2m. It was uniformly heated by applying electric current directly to the tube. Local heat transfer coefficients were obtained for heat fluxes from 10 to $40kW/m^2$, mass fluxes from 200 to $600kgT/m^2s$, qualities up to 1.0, and the inlet saturation temperature of $10^{\circ}C$. The experimental results were mapped on Wojtan et $al.'s^(7)$ and Wang et $al.'s^(8)$ flow pattern maps. The nucleate boiling was predominant at low vapor quality whereas the convective boiling was predominant at high vapor quality. Laminar flow appeared in the flow with minichannel. The experimental results were compared with six existing two-phase heat transfer coefficient correlations. A new boiling heat transfer coefficient correlation based on the superposition model for refrigerants was developed with mean and average deviations of 10.39% and -3.66%, respectively.

• 한국자기공명학회논문지
• /
• 제6권1호
• /
• pp.45-53
• /
• 2002

Objectives: This study investigated alterations in regional cerebral blood flow (rCBF) in patients with transient global amnesia (TGA) using statistical parametric mapping 99 (SPM99). Methods: Noninvasive rCBF measurements using 99mTc-ethyl cysteinate dimer (ECD) SPECT were performed on 8 patients with TGA who have ongoing symptoms and 17 age matched controls. The relative rCBF maps in patients with TGA and controls were compared. Results: In patients with TGA, significant decreased rCBF was found along the L superior temporal extending to L parietal region of the brain and L thalamus. There were areas of increased rCBF in the R temporal, R frontal region and R thalamus. Conclusion: We could demonstrate decreased perfusion in left cerebral hemisphere and increased perfusion in right cerebral hemisphere in patients with TGA using SPM99. The imbalanced change of rCBF between bilateral cerebral hemisphere in patients with TGA might suggest that imbalanced neuronal activity between the bilateral hemispheres may have strong relationship to the pathogenesis of the TGA. For quantitative SPECT analysis in TGA patients, we recommend SPM99 rather than the ROI method because of its definitive advantages.

• 대한수학회보
• /
• 제36권4호
• /
• pp.671-682
• /
• 1999

Using a base-point free version of the infinite symmetric product we define a fibrewise infinite symmetric product for any fibration $E\;\longrightarrow\;B$. The construction works for any commutative ring R with unit and is denoted by $R_f(E)\;l\ongrightarrow\;B$. For any pointed space B let $G_I(B)\;\longrightarrow\;B$ be the i-th Ganea fibration. Defining $M_R-cat(B):= inf{i\midR_f(G_i(B))\longrihghtarrow\;B$ admits a section} we obtain an approximation to the Lusternik-Schnirelmann category of B which satisfies .g.a product formula. In particular, if B is a 1-connected rational space of finite rational type, then $M_Q$-cat(B) coincides with the well-known (purely algebraically defined) M-category of B which in fact is equal to cat (B) by a result of K.Hess. All the constructions more generally apply to the Ganea category of maps.

• 전자공학회논문지B
• /
• 제32B권11호
• /
• pp.153-162
• /
• 1995

When vector quantization is used in low rate image coding (e.g., R<0.5), the primary problem is the tremendous computational complexity which is required to search the whole codebook to find the closest codevector to an input vector. Since the number of code vectors in a vector quantizer is given by an exponential function of the dimension. i.e., L=2$^{nR}$ where Rn. To alleviate this problem, a multiple shell structure of hypercube feature maps (MSSHFM) is proposed. A binary HFM of k-dimension is composed of nodes at hypercube vertices and a multiple shell architecture is constructed by surrounding the k-dimensional hfm with a (k+1)-dimensional HFM. Such a multiple shell construction of nodes inherently has a complete tree structure in it and an efficient partial search scheme can be applied with drastically reduced computational complexity, computer simulations of still image coding were conducted and the validity of the proposed method has been verified.

• 한국농공학회논문집
• /
• 제62권1호
• /
• pp.39-50
• /
• 2020

The objective of this study was to assess the livestock nonpoint source pollutant impact on water quality in Namgang dam watershed using the HSPF (Hydrological Simulation Program-Fortran) model. The input data for the HSPF model was established using the landcover, digital elevation, and watershed and river maps. In order to apply the pollutant load to the HSPF model, the delivery load of the livestock nonpoint source in the Namgang dam watershed was calculated and used as a point pollutant input data for the HSPF model. The hydrologic and water quality parameters of HSPF model were calibrated and validated using the observed runoff data from 2007 to 2015 at Sancheong station. The R² (Determination Coefficient), RMSE (Root Mean Square Error), NSE (Nash-Sutcliffe efficiency coefficient), and RMAE (Relative Mean Absolute Error) were used to evaluate the model performance. The simulation results for annual mean runoff showed that R² ranged 0.79~0.81, RMSE 1.91~2.73 mm/day, NSE 0.7~0.71 and RMAE 0.37~0.49 mm/day for daily runoff. The simulation results for annual mean BOD for RMSE ranged 0.99~1.13 mg/L and RMAE 0.49~0.55 mg/L, annual mean TN for RMSE ranged 1.65~1.72 mg/L and RMAE 0.55 mg/L, and annual mean TP for RMSE ranged 0.043~0.055 mg/L and RMAE 0.552~0.570 mg/L. As a result of livestock nonpoint pollutant loading simulation for each sub-watersehd using the HSPF model, the BOD ranged 16.6~163 kg/day, TN ranged 27.5~337 kg/day, TP ranged 1.22~14.1 kg/day.