• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.49-55
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• 1995

This paper is the third of a series in which smoothness properties of function in several variables are discussed. The germ of the whole theory was laid in the works by Folland and Stein [4]. On nilpotent Lie groups, they difined analogues of the classical $L^p$ Sobolev or potential spaces in terms of fractional powers of sub-Laplacian, L and extended several basic theorems from the Euclidean theory of differentaiability to these spaces: interpolation properties, boundedness of singular integrals,..., and imbeding theorems. In this paper we study the analogue to the extension theorem for the Folland-Stein spaces. The analogue to Stein's restriction theorem were studied by M. Mekias [5] and Y.M. Kim [6]. First, we have the space of Bessel potentials on the Heisenberg group introduced by Folland [4].

• Bulletin of the Korean Chemical Society
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• v.25 no.7
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• pp.986-990
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• 2004

Condensation of salicylaldehyde $(2-HOC_6H_4C(O)H)$ with allylamine afforded the unsaturated salicylaldimine, $2-HOC_6H_4C(H)=NCH_2CH=CH_2$. Similar reactivity was observed with substituted salicylaldehydes. Further reaction of these Schiff bases with palladium acetate or $Na_2PdCl_4$ afforded complexes of the type $PdL_2$, where L = deprotonated Schiff base. The molecular structure of the parent salicylaldimine palladium complex $[trans-(2-OC_6H_4C(H)=NCH_2CH=CH_2)_2Pd]$ (1) was characterized by an X-ray diffraction study. Crystals of 1 were monoclinic, space group $P2_1/n,\;a\;=\;14.0005(9)\;{\AA},\;b\;=7.2964(5)\;{\AA},\;c\;=\;17.5103(12)\;{\AA},\;{\beta}\;=\;100.189(1)^{\circ}$, Z = 4. Analogous chemistry with 4-vinylaniline also gave novel palladium complexes containing a pendant styryl group. Crystals of $[trans-(2-HOC_6H_4C(H)=N-4-C_6H_4CH=CH_2)_2Pd]$ (4) were monoclinic, space group $P2_1/c$, a = 13.7710(14) ${\AA}$, b = 11.0348(11) ${\AA}$, c = 7.8192(8) ${\AA}$, ${\beta}\;=\;98.817(2)^{\circ}$, Z = 2.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.947-951
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• 1989

A Class of nonlinear distributed parameter control problems is first stated in a partial differential equation form in multi-index notion and then converted into an integral equation form. Necessary conditions for optimality in the form of maximum principle are then derived in Sobolev space W$^{l}$, p/(1 leq. p .leq. .inf.)..

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.701-708
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• 2007

In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), $1.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.399-406
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• 2019

Let n be the spatial dimension. For d, $0<d{\leq}n$, let $H^d$ be the d-dimensional Hausdorff content. The purpose of this paper is to prove the boundedness of the dyadic strong maximal operator on the Choquet space $L^p(H^d,{\mathbb{R}}^n)$ for min(1, d) < p. We also show that our result is sharp.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.87-102
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• 2011

The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of fixed points of a weak relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping by a new hybrid method in a Banach space. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced by Ying Liu[Ying Liu, Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space, Appl. Math. Mech. -Engl. Ed. 30(7)(2009), 925-932] and some others.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.323-342
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions which have the form $${\int}_{L_2[0,t]}{{\exp}\{i(v,x)\}d{\sigma}(v)}{{\int}_{\mathbb{R}^r}}\;{\exp}\{i{\sum_{j=1}^{r}z_j(v_j,x)\}dp(z_1,{\cdots},z_r)$$ for $x{\in}C[0,t]$, where $\{v_1,{\cdots},v_r\}$ is an orthonormal subset of $L_2[0,t]$ and ${\sigma}$ and ${\rho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $\mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.

• Honam Mathematical Journal
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• v.7 no.1
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• pp.7-13
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• 1985

We show that a bounded linear qperator, T, on a Banach space, X, is $C^{n}$-scalar if the sepuence {$\frac{k!}{(k+n)!}{\phi}(T^{k+n}x)$}$_{k=0}^{\infty}$ is positive-definite, for sufficiently many $\phi$ in $X^{\ast}$, x in X. We use this to show that $(T_{n}f)(t){\equiv}tf(t)+nJf(t)$, where $If(t)=\int_{0}^{1}f(s)ds$, is $C^{n}$-scalar on $L^{p}([0,1],v)$, for $1{\leq}p{\leq}\infty$, for a large class of measures, v. Other corollaries include the spectral theorem for bounded symmetric operators on a Hilbert space.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.287-292
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• 2004

The operator $A \; {\in} \; L(H_{i})$, the Banach algebra of bounded linear operators on the complex infinite dimensional Hilbert space $\cal H_{i}$, is said to be p-hyponormal if $(A^\ast A)^P \geq (AA^\ast)^p$ for $p\; \in \; (0,1]$. Let (equation omitted) denote the completion of (equation omitted) with respect to some crossnorm. Let $I_{i}$ be the identity operator on $H_{i}$. Letting (equation omitted), where each $A_{i}$ is p-hyponormal, it is proved that the commuting n-tuple T = ($T_1$,..., $T_{n}$) satisfies Bishop's condition ($\beta$) and that if T is Weyl then there exists a non-singular commuting n-tuple S such that T = S + F for some n-tuple F of compact operators.

• Journal of Veterinary Science
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• v.21 no.2
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• pp.27.1-27.10
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• 2020

The efficacies of a supraglottic airway device (SGAD) and an endotracheal tube (ETT) in cats under general anesthesia with volume-controlled ventilation (VCV) were compared. Thirty healthy cats were randomly allocated for airway control using either an SGAD or an ETT. Five tidal volumes (6, 8, 10, 12, and 14 mL/kg) were randomly tested, and respiratory rates were adjusted to achieve a minute ventilation of 100 mL/kg/min. The dose of propofol necessary to insert the SGAD or ETT, the static respiratory pressure, leakage during VCV, and end tidal CO₂ (ETCO₂) were recorded. Dosages of propofol and static respiratory measurements for the SGAD and ETT groups were compared using a t-test. The distribution of leakages and hypercapnia (ETCO₂ > 45 mmHg) were compared using Fisher's exact test. A significance level of p < 0.05 was established. No significant difference in dose of propofol was observed between the SGAD and ETT groups (7.1 ± 1.0, 7.3 ± 1.7 mg/kg; p = 0.55). Static resistance pressure of the SGAD (22.0 ± 8.1 cmH₂O/L/sec) was significantly lower than that of the ETT (36.6 ± 12.9 cmH₂O/L/sec; p < 0.01). Of the 75 trials, leakage was more frequent when using an SGAD (8 events) than when using an ETT (1 event; p = 0.03). Hypercapnia occurred more frequently with SGAD (18 events) than with ETT (3 events; p < 0.01). Although intubation with an ETT is the gold standard in small animal anesthesia, the use of an SGAD can reduce airway resistance and the work of breathing. Nonetheless, SGAD had more dead space and the tidal volume for VCV needs adjustment.