• East Asian mathematical journal
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• 제19권1호
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• pp.73-80
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• 2003

Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

• 대한수학회보
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• 제43권2호
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• pp.309-318
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• 2006

Let X and Y be real Banach spaces and ${\varepsilon}\;>\;0$, p > 1. Let f : $X\;{\to}\;Y$ be a bijective mapping with f(0) = 0 satisfying $$|\;{\parallel}f(x)-f(y){\parallel}-{\parallel}{x}-y{\parallel}\;|\;{\leq}{\varepsilon}{\parallel}{x}-y{\parallel}^p$$ for all $x\;{\in}\;X$ and, let $f^{-1}\;:\;Y\;{\to}\;X$ be uniformly continuous. Then there exist a constant ${\delta}\;>\;0$ and N(${\varepsilon},p$) such that lim N(${\varepsilon},p$)=0 and a unique surjective isometry I : X ${\to}$ Y satisfying ${\parallel}f(x)-I(x){\parallel}{\leq}N({\varepsilon,p}){\parallel}x{\parallel}^p$ for all $x\;{\in}\;X\;with\;{\parallel}x{\parallel}{\leq}{\delta}$.

• 충청수학회지
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• 제26권2호
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• pp.393-402
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• 2013

For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• 대한수학회보
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• 제60권6호
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• pp.1555-1566
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• 2023

A Hilbert space operator A ∈ B(H) is a generalised n-projection, denoted A ∈ (G-n-P), if A^*n = A. (G-n-P)-operators A are normal operators with finitely countable spectra σ(A), subsets of the set $\{0\}\,{\cup}\,\{\sqrt[n+1]{1}\}.$ The Aluthge transform à of A ∈ B(H) may be (G - n - P) without A being (G - n - P). For doubly commuting operators A, B ∈ B(H) such that σ(AB) = σ(A)σ(B) and ${\parallel}A{\parallel}\,{\parallel}B{\parallel}\;{\leq}\;{\parallel}{\tilde{AB}}{\parallel},$ ${\tilde{AB}}\;{\in}\;(G\,-\,n\,-\,P)$ if and only if $A\;=\;{\parallel}{\tilde{A}}{\parallel}\,(A_{00}\,{\oplus}\,(A_0\,{\oplus}\,A_u))$ and $B\;=\;{\parallel}{\tilde{B}}{\parallel}\,(B_0\,{\oplus}\,B_u),$ where A₀₀ and B₀, and A₀ ⊕ A_u and B_u, doubly commute, A₀₀B₀ and A₀ are 2 nilpotent, A_u and B_u are unitaries, A^*n_u = A_u and B^*n_u = B_u. Furthermore, a necessary and sufficient condition for the operators αA, βB, αà and ${\beta}{\tilde{B}},\;{\alpha}\,=\,\frac{1}{{\parallel}{\tilde{A}}{\parallel}}$ and ${\beta}\,=\,\frac{1}{{\parallel}{\tilde{B}}{\parallel}},$ to be (G - n - P) is that A and B are spectrally normaloid at 0.

• 한국통신학회논문지
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• 제30권6C호
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• pp.442-449
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• 2005

최근 터보 부호에 비해서 구현시 복잡하지 않고, 높은 부호화율에서 거의 샤논 이론에 접근하는 Turbo Product Code(TPC)에 대해 관심이 고조되고 있다. 본 논문에서는 초고속 통신 시스템에 적용하기 위한 고속 TPC 복호를 위한 세가지의 알고리즘을 제안하는 바이다. 첫째로, 기존의 Turbo Product code 복호기에서 row과 column을 직렬로 복호를 하지 않고 복호 구조가 병렬로 동작하는 Turbo Product code 복호기를 제안한다. 둘째로 반복 중지 알고리즘을 제안하고 마지막으로, P-Parallel 알고리즘을 통해 P rows와 P columns을 병렬로 처리하여 복호한다. 모의 실험을 한 결과 기존의 방식에 비해 복호 지연이 줄어들고 성능면에서 직렬 방식과 거의 비슷한 성능이 나타난다. 또한 고속알고리즘을 바탕으로 VHDL모델링을 하였으며, 이를 timing 시뮬레이션 하여 메모리 요구량 및 복호 속도 향상도를 분석하였다.

• 충청수학회지
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• 제26권1호
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• pp.105-110
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• 2013

A logarithmic composition inequality in Besov spaces is derived which generalizes Vishik's inequality: ${\parallel}f{\circ}g{\parallel}_{B^s_{p,1}}{\leq}(1+{\log}({\parallel}{\nabla}g{\parallel}_{L^{\infty}}{\parallel}{\nabla}g^{-1}{\parallel}_{L^{\infty}})){\parallel}f{\parallel}_{B^s_{p,1}}$, where $g$ is a volume-preserving diffeomorphism on ${\mathbb{R}}^n$.

• 한국시뮬레이션학회논문지
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• 제2권1호
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• pp.31-44
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• 1993

Zeigler's DEVS(Discrete Event Systems Specification) formalism supports formal specification of discrete event systems in a hierarchical , modular manner. Associated are hierarchical, distributed simulation algorithms, called abstract simulators, which interpret dynamics of DEVS models. This paper deals with performance evaluation of P-DEVSIM ++, a parallel simulation environment which implements the DEVS formalism and associated simulation algorithms in a parallel environment. Performance simulator has been developed and used to experiment models of parallel simulation executions in different conditions. The experimental result shows that simulation time depends on both the number of processors in the parallel system and the communication overheads among such processors.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.185-220
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• 2016

We study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator defined on the half plane. Next, we establish a principle of maximum for the singular partial differential operator $${\Delta}_{\alpha}={\frac{{\partial}^2}{{\partial}r^2}+{\frac{2{\alpha}+1}{r}{\frac{\partial}{{\partial}r}}+{\frac{{\partial}^2}{{\partial}x^2}}+{\frac{{\partial}^2}{{\partial}t^2}}};\;(r,x,t){\in}]0,+{\infty}[{\times}{\mathbb{R}}{\times}]0,+{\infty}[$$. Later, we define the Littlewood-Paley g-function and using the principle of maximum, we prove that for every $p{\in}]1,+{\infty}[$, there exists a positive constant $C_p$ such that for every $f{\in}L^p(d{\nu}_{\alpha})$, $${\frac{1}{C_p}}{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}{\leqslant}{\parallel}g(f){\parallel}_{p,{\nu}_{\alpha}}{\leqslant}C_p{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}$$.

• 대한수학회지
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• 제44권1호
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• pp.25-34
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• 2007

An operator $T{\in}L(H)$ is said to be p-paranormal if $$\parallel{\mid}T\mid^pU{\mid}T\mid^px{\parallel}x\parallel\geq\parallel{\mid}T\mid^px\parallel^2$$ for all $x{\in}H$ and p > 0, where $T=U{\mid}T\mid$ is the polar decomposition of T. It is easy that every 1-paranormal operator is paranormal, and every p-paranormal operator is paranormal for 0 < p < 1. In this note, we discuss some properties for p-paranormal operators.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.1482-1487
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• 2003

This paper presents a new family of 4-DoF parallel mechanism with two platforms. The new mechanism is composed of front and rear platforms, and three limbs. Two limbs with 6dof joint (P-P-S-P) are attached to the each platform and are perpendicular to baseplate, while the middle limb with 4-Dof joints (R-R-R-P or R-R-P-P) is attached to the revolute joint that connect front and rear platform. The two-DoF-driving mechanism at the middle limb with two base-fixed prismatic actuators can generate the heaving and roll motions or two translational motions. Therefore, Therefore, the new 4-Dof parallel mechanism (1T-3R) can generate pitch motions at each platforms, roll, and heaving motions, while another type of new 4-Dof parallel mechanism (2T-2R) can generate pitch motions at each platforms, x and z translational motions. For 1T-3R mechanism, kinematic analyses including inverse, forward kinematics, and Jacobian are performed.