• 대한수학회지
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• 제37권6호
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• pp.915-927
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• 2000

This paper is concerned with degenerate Volterra equations Mu(t) + ∫(sub)0(sup)t k(t-s) Lu(s)ds = f(t) in Banach spaces both in the hyperbolic case, and the parabolic one. The key assumption is played by the representation of the underlying space X as a direct sum X = N(T) + R(T), where T is the bounded linear operator T = ML(sup)-1. Hyperbolicity means that the part T of T in R(T) is an abstract potential operator, i.e., -T(sup)-1 generates a C(sub)0-semigroup, and parabolicity means that -T(sup)-1 generates an analytic semigroup. A maximal regularity result is obtained for parabolic equations. We will also investigate the cases where the kernel k($.$) is degenerated or singular at t=0 using the results of Pruss[8] on analytic resolvents. Finally, we consider the case where $\lambda$ is a pole for ($\lambda$L + M)(sup)-1.

• 대한수학회보
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• 제25권2호
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• pp.179-183
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• 1988

In this paper we study a $C^{*}$-dynamical system (A, G, .alpha.) where A is a UHF-algebra, G is a finite abelian group and .alpha. is a *-automorphic action of product type of G on A. In [2], A. Kishimoto considered the case G= $Z_{n}$, the cyclic group of order n and investigated a condition in order that the fixed point algebra $A^{\alpha}$ of A under the action .alpha. is UHF. In later N.J. Munch studied extremal tracial states on $A^{\alpha}$ by employing the method of A. Kishimoto [3], where G is a finite abelian group. Generally speaking, when G is compact (not necessarily discrete and abelian), $A^{\alpha}$ is an AF-algebra and its ideal structure was well analysed by N. Riedel [4]. Here we obtain some conditions for $A^{\alpha}$ to be UHF, where G is a finite abelian group, which is an extension of the result of A. Kishimoto.oto.

• 대한수학회지
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• 제47권2호
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• pp.425-443
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• 2010

We investigate the Schr$\ddot{o}$dinger type operator $H_2\;=\;(-\Delta_{\mathbb{H}^n})^2+V^2$ on the Heisenberg group $\mathbb{H}^n$, where $\Delta_{\mathbb{H}^n}$ is the sublaplacian and the nonnegative potential V belongs to the reverse H$\ddot{o}$lder class $B_q$ for $q\geq\frac{Q}{2}$, where Q is the homogeneous dimension of $\mathbb{H}^n$. We shall establish the estimates of the fundamental solution for the operator $H_2$ and obtain the $L^p$ estimates for the operator $\nabla^4_{\mathbb{H}^n}H^{-1}_2$, where $\nabla_{\mathbb{H}^n}$ is the gradient operator on $\mathbb{H}^n$.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.363-375
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• 2004

In this paper, We show that the bandpass random signals of the form ∑$_{\alpha}$$\alpha$$_{\alpha}$ a Sin(2$\pi$f$_{\alpha}$t + b$_{\alpha}$) where a$_{\alpha}$ being a random number in [0,1], f$_{\alpha}$ a random integer in a given frequency band, and b$_{\alpha}$ a random number in [0, 2$\pi$], generate Gaussian white noise signals and hence they are adequate for simulating Continuous Markov processes. We apply the result to the fluctuation-dissipation formula for the Johnson noise and show that the probability distribution for the long term average of the power of the Johnson noise is a X$^2$ distribution and that the relative error of the long term average is (equation omitted) where N is the number of blocks used in the average.error of the long term average is (equation omitted) where N is the number of blocks used in the average.

• 대한수학회논문집
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• 제35권4호
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• pp.1159-1170
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• 2020

We consider the weighted spaces ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓) for 1 < p < +∞, where 𝜑 and 𝜓 are weights on 𝕊 (= ℕ or ℤ). We obtain a sufficient condition for ℓ^p(𝕊, 𝜓) to be multiplier weighted-space of ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓). Our condition characterizes the last multiplier weighted-space in the case where 𝕊 = ℤ. As a consequence, in the particular case where 𝜓 = 𝜑, the weighted space ℓ^p(ℤ,𝜓) is a convolutive algebra.

• 한국군사과학기술학회지
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• 제7권2호
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• pp.13-21
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• 2004

GPS is widely used in various applications since GPS receivers are capable of measuring precise position and velocity in any weather condition for a relatively low cost. However, GPS requires more than four simultaneously visible GPS satellites for optimal performance. In high-motion, high-attitude-changing applications, there exist some situations where less than four satellites are visible or where the dilution of precision (DOP) is high. In this paper, we propose a simulation algorithm that predicts the performance of GPS navigation according to changes in vehicle attitude. We have compared simulation results with experimental results, where simulation results of the proposed algorithm are shown to closely match actual experimental data. This algorithm could be used to predict GPS navigational performance and to determine optimal GPS antenna position.

• East Asian mathematical journal
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• 제29권1호
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• pp.39-52
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• 2013

Let (X, S) be an association scheme where X is a finite set and S is a partition of $X{\times}X$. The size of X is called the order of (X, S). We define $\mathcal{C}$ to be the set of positive integers m such that each association scheme of order $m$ is commutative. It is known that each prime is belonged to $\mathcal{C}$ and it is conjectured that each prime square is belonged to $\mathcal{C}$. In this article we give a sufficient condition for a scheme of order pq to be commutative where $p$ and $q$ are primes, and obtain a partial answer for the conjecture in case where $p=q$.

• 호남수학학술지
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• 제41권3호
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• pp.559-568
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• 2019

In this paper we introduce and study the concept of of (${\varphi}$, ${\psi}$)-am-enability of a locally compact group G, where ${\varphi}$ is a continuous homomorphism on G and ${\psi}:G{\rightarrow}{\mathbb{C}}$ multiplicative linear function. We prove that if the group algebra $L^1$ (G) is (${\tilde{\varphi}}$, ${\tilde{\psi}}$)-amenable then G is (${\varphi}$, ${\psi}$)-amenable, where ${\tilde{\varphi}}$ is the extension of ${\varphi}$ to M(G). In the case where ${\varphi}$ is an isomorphism on G it is shown that the converse is also valid.

• 로봇학회논문지
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• 제16권2호
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• pp.122-129
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• 2021

For the Simultaneous Localization and Mapping (SLAM) problem, a different path results in different SLAM results. Usually, SLAM follows a trail of input data. Active SLAM, which determines where to sense for the next step, can suggest a better path for a better SLAM result during the data acquisition step. In this paper, we will use reinforcement learning to find where to perceive. By assigning entire target area coverage to a goal and uncertainty as a negative reward, the reinforcement learning network finds an optimal path to minimize trajectory uncertainty and maximize map coverage. However, most active SLAM researches are performed in indoor or aerial environments where robots can move in every direction. In the urban environment, vehicles only can move following road structure and traffic rules. Graph structure can efficiently express road environment, considering crossroads and streets as nodes and edges, respectively. In this paper, we propose a novel method to find optimal SLAM path using graph structure and reinforcement learning technique.

• 중국학논총
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• 제62호
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• pp.71-84
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• 2019

Brothel in China is another word of origin and a noble expression at the same time. Brothel has long been used as a symbol of prestige and wealth as a synonym for integrity innocence. According to documentary records, brothel was used as a place where people with a lot of power and wealth. This meaning in the literature continued until the Late Tang period. In addition, the brothel was also used to refer to the place where the King resides. Therefore, the meaning of Brothel in the Tang period is generally understood as a place where people with high status symbolize the integrity of innocence. However, the image of the brothel, which is connected to the characteristics of a lot of young and beautiful women is increasingly recognized as a place where young ladies reside. For this reason, entering the Tang period the brothel eventually turned into a dwelling of a young woman in a prestigious and wealthy house. Since the time of Ming-Qing, brothel has already been used to refer to prostitute and brothel. In this article, we will look at the historical process of the change of brothel, and examine the process of brothel culture through the environment of brothel and cultural literacy of residents. We hope that this study will provide new perspectives and data to the study of women's cultural history in China.