• Korean Journal of Mathematics
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• 제26권1호
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• pp.61-74
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• 2018

Let $\mathcal{A}$ and $\mathcal{B}$ be two prime ${\ast}$-algebras. Let ${\Phi}:\mathcal{A}{\rightarrow}\mathcal{B}$ be a bijective and satisfies $${\Phi}(A{\bullet}B{\bullet}A)={\Phi}(A){\bullet}{\Phi}(B){\bullet}{\Phi}(A)$$, for all $A,B{\in}{\mathcal{A}}$ where $A{\bullet}B=A^{\ast}B+BA^{\ast}$. Then, ${\Phi}$ is additive. Moreover, if ${\Phi}(I)$ is idempotent then we show that ${\Phi}$ is ${\mathbb{R}}$-linear ${\ast}$-isomorphism.

• 대한수학회논문집
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• 제9권3호
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• pp.731-737
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• 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}$.

• Communications for Statistical Applications and Methods
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• 제13권1호
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• pp.177-190
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• 2006

The aim of this study is to propose a Bayesian model for fitting mortality rate of colon cancer. For the analysis of mortality rate of a disease, factors such as age classes of population and spatial characteristics of the location are very important. The model proposed in this study allows the age class to be a random effect in addition to its conventional role as the covariate of a linear regression, while the spatial factor being a random effect. The model is fitted using Metropolis-Hastings algorithm. Posterior expected predictive deviances, standardized residuals, and residual plots are used for comparison of models. It is found that the proposed model has smaller residuals and better predictive accuracy. Lastly, we described patterns in disease maps for colon cancer.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.486-491
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• 2003

The paper presents the relationship between the eigenvalue branches and the corresponding flutter modes of cantilevered pipes conveying fluid. The pipes are located on elastic foundations which can be regarded as a soil model. In this paper, elastic foundations are assumed as linear distributed translational springs. Governing equations of motion are derived by extended Hamilton's principle, and the numerical scheme using finite element method is applied to obtain the discretized equations. The critical How velocity and stability maps of the pipe are investigated according to the variation of elastic foundation parameters, mass ratios of the pipe and internal damping Parameter. Also, the vibrational modes associated with flutter are shown.

• Journal of Information Processing Systems
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• 제15권6호
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• pp.1392-1405
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• 2019

The cathode voltage of aluminum electrolytic cell is relatively stable under normal conditions and fluctuates greatly when it has an anomaly. In order to detect the abnormal range of cathode voltage, an anomaly detection algorithm based on sliding window was proposed. The algorithm combines the time series segmentation linear representation method and the k-nearest neighbor local anomaly detection algorithm, which is more efficient than the direct detection of the original sequence. The algorithm first segments the cathode voltage time series, then calculates the length, the slope, and the mean of each line segment pattern, and maps them into a set of spatial objects. And then the local anomaly detection algorithm is used to detect abnormal patterns according to the local anomaly factor and the pattern length. The experimental results showed that the algorithm can effectively detect the abnormal range of cathode voltage.

• 대한산업공학회지
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• 제23권2호
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• pp.371-383
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• 1997

This paper propose a fuzzy regression method using fuzzy neural networks when a membership value is attached to each input-output pair. First, a method of linear fuzzy regression analysis is described by interpreting the reliability of each input-output pair as its membership values. Next, an architecture of fuzzy neural networks with fuzzy weights and fuzzy biases is shown. The fuzzy neural network maps a crisp input vector to a fuzzy output. A cost function is defined using the fuzzy output from the fuzzy neural network and the corresponding target output with a membership value. A learning algorithm is derived from the cost function. The derived learning algorithm trains the fuzzy neural network so that the level set of the fuzzy output includes the target output. Last, the proposed method is illustrated by computer simulations on numerical examples.

• Advances in robotics research
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• 제2권1호
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• pp.1-11
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• 2018

To monitor the environment and determine the source of a pollutant gradient using a multiple robot swarm, we propose a hybrid algorithm that combines two bio-inspired algorithms mimicking chemotaxis and pheromones of bacteria. The algorithm is implemented in virtual robot agents in a simulator to evaluate their feasibility and efficiency in gradient maps with different sizes. Simulation results show that the chemotaxis controller guided robot agents to the locations with higher pollutant concentrations, while the pheromone marked in a virtual field increased the efficiency of the search by reducing the visiting redundancy. The number of steps required to reach the target point did not increase proportionally as the map size increased, but were less than those in the linear whole-map search method. Furthermore, the robot agents could function with simple sensor composition, minimum information about the map, and low calculation capacity.

• 대한수학회지
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• 제42권3호
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• pp.573-597
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• 2005

A continuous linear operator T, on the space of entire functions in d variables, is PDE-preserving for a given set $\mathbb{P}\;\subseteq\;\mathbb{C}|\xi_{1},\ldots,\xi_{d}|$ of polynomials if it maps every kernel-set ker P(D), $P\;{\in}\;\mathbb{P}$, invariantly. It is clear that the set $\mathbb{O}({\mathbb{P}})$ of PDE-preserving operators for $\mathbb{P}$ forms an algebra under composition. We study and link properties and structures on the operator side $\mathbb{O}({\mathbb{P}})$ versus the corresponding family $\mathbb{P}$ of polynomials. For our purposes, we introduce notions such as the PDE-preserving hull and basic sets for a given set $\mathbb{P}$ which, roughly, is the largest, respectively a minimal, collection of polynomials that generate all the PDE-preserving operators for $\mathbb{P}$. We also describe PDE-preserving operators via a kernel theorem. We apply Hilbert's Nullstellensatz.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 1987년도 제29회 수공학연구발표회논문초록집
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• pp.123-137
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• 1987

The groundwater hydrographs due to the recharge of water table aquifer resulting from rainfall are simulated by relating the existing linearized method, which is originally the non-linear equation suggested by Boussinesq, to the basin charcteristics. To thes end, the recharge curve is assumed as the skewed distribution of sine curve, and the parameters contained in the equation are determined from the geomorphologic and soil maps. The whole drainage area is divied in order to consider the spatial variation of parameters. The obtained parameters are tried for several cases with different values given arbitrarily to study the aspects of hydrographs according to their variation. This procedures are applied to the natural basin of Bocheong watershed(area:475.5$\textrm{km}^2$) in Korea. As a result, it is shown that considerable uncertainty is expressed for the results obtained with the given values of parameters. Thus, such uncertainty should be precluded to a certain extent by examining and observing the physical characteristics as much as possible for the determination of groundwater flows.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.427-441
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• 2009

The method of Lattice Dynamical System is used to establish a global model on an infinite chain of many local markets interacting each other through a diffusion of prices between them. This global model extends the Walrasian evolutionary cobweb model in an independent single local market to the global market evolution. We assume that each local market has linear decreasing demands and quadratic supplies with naive predictors, and investigate the stationary behaviors of global price dynamics and show that their dynamics are conjugate to those of $H{\acute{e}}non$ maps and hence can exhibit complicated behaviors such as period-doubling bifurcations, chaos, and homoclic orbits etc.