• 충청수학회지
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• 제8권1호
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• pp.29-36
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• 1995

• 대한수학회보
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• 제60권5호
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• pp.1391-1408
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• 2023

Let M and M^# be Hardy-Littlewood maximal operator and sharp maximal operator, respectively. In this article, we present necessary and sufficient conditions for the boundedness properties for commutator operators [M, b] and [M^#, b] in a general context of Banach function spaces when b belongs to BMO(?ⁿ) spaces. Some applications of the results on weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces and Musielak-Orlicz spaces are also given.

• 대한수학회논문집
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• 제10권1호
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• pp.155-162
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• 1995

Let $\mu$ be a positive Borel measure on $R^n$ which is positive on cubes. For any cube $Q \subset R^n$, a Borel measurable nonnegative function $\varphi_Q$, supported and positive a.e. with respect to $\mu$ in Q, is given. We consider a maximal function $$ M_{\mu}f(x) = sup \int \varphi Q$\mid$f$\mid$d_{\mu} $$ where the supremum is taken over all $\varphi Q$ such that $x \in Q$.

• 대한수학회지
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• 제60권5호
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• pp.1057-1072
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• 2023

Let 𝜑 : ℝⁿ × [0, ∞) → [0, ∞) be a growth function and H^𝜑(ℝⁿ) the Musielak-Orlicz Hardy space defined via the non-tangential grand maximal function. A general summability method, the so-called 𝜃-summability is considered for multi-dimensional Fourier transforms in H^𝜑(ℝⁿ). Precisely, with some assumptions on 𝜃, the authors first prove that the maximal operator of the 𝜃-means is bounded from H^𝜑(ℝⁿ) to L^𝜑(ℝⁿ). As consequences, some norm and almost everywhere convergence results of the 𝜃-means, which generalizes the well-known Lebesgue's theorem, are then obtained. Finally, the corresponding conclusions of some specific summability methods, such as Bochner-Riesz, Weierstrass and Picard-Bessel summations, are also presented.

• 대한수학회지
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• 제35권3호
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• pp.713-725
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• 1998

Let X and Y be Ito processes with dX$_{s}$ = $\phi$$_{s}$dB$_{s}$ ＋ $\psi$$_{s}$ds and dY$_{s}$ = (equation omitted)dB$_{s}$ ＋ ξ$_{s}$ds. Burkholder obtained a sharp bound on the distribution of the maximal function of Y under the assumption that │Y$_{0}$│$\leq$│X$_{0}$│,│ζ│$\leq$│$\phi$│, │ξ│$\leq$│$\psi$│ and that X is a nonnegative local submartingale. In this paper we consider a wider class of Ito processes, replace the assumption │ξ│$\leq$│$\psi$│ by a more general one │ξ│$\leq$$\alpha$ │$\psi$│ , where a $\geq$ 0 is a constant, and get a weak-type inequality between X and the maximal function of Y. This inequality, being sharp for all a $\geq$ 0, extends the work by Burkholder.der.urkholder.der.

• 한국통신학회논문지
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• 제30권8C호
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• pp.754-761
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• 2005

본 논문에서는 나카가미-n(라이시안) 페이딩 채널 상에서 그레이 부호화된 직사각 QAM(Rectangular-QAM) 신호를 최대비 합성(maximal ratio combining) 다이버시티로 수신하는 경우 비트노율(Bit Error Rate, BER)을 계산하는 수식을 다양한 채널에 적용할 수 있도록 일반적 형태로 유도하고 그 성능 분석을 실시한다. 유도된 BER 수식은 휘태커 함수)Whittaker function)와 초기하 함수(confluent hypergeometric)로 표현된다. 또한 M-PSK와의 성능 비교를 통하여 나카가미-n 페이딩 채널의 특성을 확인한다. BER 수식이 일반적인 형태로 유도되었기 때문에 가시 경로(line-of-sight)를 가지는 통신채널이나 위성통신 채널의 성능분석에 본 논문에서 유도한 BER 수식을 쉽게 적용할 수 있다.

• 한국통신학회논문지
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• 제33권11A호
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• pp.1053-1062
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• 2008

본 논문은 레일리 페이딩 채널에서 확률밀도함수와 최대비 결합기 출력의 최대모멘트 생성 함수를 일반적이고 간결한 수식적 접근을 통해 보여주었다. 또한, 이를 이용하여 M-PSK, M-PAM, M-QAM의 closed form BER을 증명하였다. 마지막으로 다양한 모의 실험을 통해 증명한 수식이 모의 실험 결과와 정확하게 일치함을 알 수 있다.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2008년도 하계종합학술대회
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• pp.155-156
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• 2008

This paper provides a general and compact expression for the probability density function (pdf) and the moment-generating function (MGF) of the maximal ratio combiner output over Rayleigh fading channels. It is then used to derive closed form expression outage probability for repetition code problem. A variety of simulations is performed and shows that they match exactly with analytic ones.

• 대한수학회논문집
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• 제38권2호
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• pp.401-430
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• 2023

In this paper, we prove L^p estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)² (𝕊^n-1 × 𝕊^m-1). Furthermore, we prove L^p estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

• 한국군사과학기술학회지
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• 제14권3호
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• pp.458-466
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• 2011

In war time, minimizing the logistics response time for supporting military operations is strongly needed. In this paper, i propose the mathematical formulation for minimizing the maximal acquisition completion time in wartime or during a state of emergency. The main structure of this formulation is based on the traveling purchaser problem (TPP), which is a generalized form of the well-known traveling salesman problem (TSP). In the case of the general TPP, an objective function is to minimize the sum of the traveling cost and the purchase cost. However, in this study, the objective function is to minimize the traveling cost only. That's why it's more important to minimize the traveling cost (time or distance) than the purchase cost in wartime or in a state of emergency. I generate a specific instance and find out the optimal solution of this instance by using ILOG OPL STUDIO (CPLEX version 11.1).