• 대한수학회보
• /
• 제47권3호
• /
• pp.467-482
• /
• 2010

For a double array of random elements {$V_{mn};m{\geq}1,\;n{\geq}1$} in a real separable Banach space, some mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under which $k_{mn}^{-\frac{1}{r}}\sum{{u_m}\atop{i=1}}\sum{{u_n}\atop{i=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in $L_r$ (0 < r < 2). The weak law results provide conditions for $k_{mn}^{-\frac{1}{r}}\sum{{T_m}\atop{i=1}}\sum{{\tau}_n\atop{j=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in probability where {$T_m;m\;{\geq}1$} and {${\tau}_n;n\;{\geq}1$} are sequences of positive integer-valued random variables, {$k_{mn};m{{\geq}}1,\;n{\geq}1$} is an array of positive integers. The sharpness of the results is illustrated by examples.

• 대한수학회지
• /
• 제54권5호
• /
• pp.1483-1504
• /
• 2017

We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain ${\Omega}{\subset}{\mathbb{R}}^3$ with initial value $u_0{\in}L^2_{\sigma}({\Omega})$. It is known that a weak solution is a local strong solution in the sense of Serrin if $u_0$ satisfies the optimal initial value condition $u_0{\in}B^{-1+3/q}_{q,s_q}$ with Serrin exponents $s_q$ > 2, q > 3 such that ${\frac{2}{s_q}}+{\frac{3}{q}}=1$. This result has recently been generalized by the authors to weighted Serrin conditions such that u is contained in the weighted Serrin class ${{\int}_0^T}({\tau}^{\alpha}{\parallel}u({\tau}){\parallel}_q)^s$ $d{\tau}$ < ${\infty}$ with ${\frac{2}{s}}+{\frac{3}{q}}=1-2{\alpha}$, 0 < ${\alpha}$ < ${\frac{1}{2}}$. This regularity is guaranteed if and only if $u_0$ is contained in the Besov space $B^{-1+3/q}_{q,s}$. In this article we consider the limit case of initial values in the Besov space $B^{-1+3/q}_{q,{\infty}}$ and in its subspace ${{\circ}\atop{B}}^{-1+3/q}_{q,{\infty}}$ based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.

• Smart Structures and Systems
• /
• 제19권1호
• /
• pp.1-10
• /
• 2017

The operation of subway trains induces secondary structure-borne vibrations in the nearby underground spaces. The vibration, along with the associated noise, can cause annoyance and adverse physical, physiological, and psychological effects on humans in dense urban environments. Traditional tethered instruments restrict the rapid measurement and assessment on such vibration effect. This paper presents a novel approach for Wireless Smart Sensor (WSS)-based autonomous evaluation system for the subway train-induced vibrations. The system was implemented on a MEMSIC's Imote2 platform, using a SHM-H high-sensitivity accelerometer board stacked on top. A new embedded application VibrationLevelCalculation, which determines the International Organization for Standardization defined weighted acceleration level, was added into the Illinois Structural Health Monitoring Project Service Toolsuite. The system was verified in a large underground space, where a nearby subway station is a good source of ground excitation caused by the running subway trains. Using an on-board processor, each sensor calculated the distribution of vibration levels within the testing zone, and sent the distribution of vibration level by radio to display it on the central server. Also, the raw time-histories and frequency spectrum were retrieved from the WSS leaf nodes. Subsequently, spectral vibration levels in the one-third octave band, characterizing the vibrating influence of different frequency components on human bodies, was also calculated from each sensor node. Experimental validation demonstrates that the proposed system is efficient for autonomously evaluating the subway train-induced ambient vibration of underground spaces, and the system holds the potential of greatly reducing the laboring of dynamic field testing.

• International Journal of Control, Automation, and Systems
• /
• 제4권6호
• /
• pp.775-781
• /
• 2006

An intelligent optimization method for designing Fractional Order PID(FOPID) controllers based on Particle Swarm Optimization(PSO) is presented in this paper. Fractional calculus can provide novel and higher performance extension for FOPID controllers. However, the difficulties of designing FOPID controllers increase, because FOPID controllers append derivative order and integral order in comparison with traditional PID controllers. To design the parameters of FOPID controllers, the enhanced PSO algorithms is adopted, which guarantee the particle position inside the defined search spaces with momentum factor. The optimization performance target is the weighted combination of ITAE and control input. The numerical realization of FOPID controllers uses the methods of Tustin operator and continued fraction expansion. Experimental results show the proposed design method can design effectively the parameters of FOPID controllers.

• 대한수학회지
• /
• 제38권6호
• /
• pp.1191-1204
• /
• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• ETRI Journal
• /
• 제40권4호
• /
• pp.531-536
• /
• 2018

The weighted K-nearest neighbor (WKNN) algorithm is used to reduce positioning accuracy, as it uses a fixed number of neighbors to estimate the position. In this paper, we propose a dynamic threshold location algorithm (DH-KNN) to improve positioning accuracy. The proposed algorithm is designed based on a dynamic threshold to determine the number of neighbors and filter out singular reference points (RPs). We compare its performance with the WKNN and Enhanced K-Nearest Neighbor (EKNN) algorithms in test spaces of networks with dimensions of $20m{\times}20m$, $30m{\times}30m$, $40m{\times}40m$ and $50m{\times}50m$. Simulation results show that the maximum position accuracy of DH-KNN improves by 31.1%, and its maximum position error decreases by 23.5%. The results demonstrate that our proposed method achieves better performance than other well-known algorithms.

• Korean Journal of Mathematics
• /
• 제24권4호
• /
• pp.647-662
• /
• 2016

In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.

• 대한수학회보
• /
• 제54권4호
• /
• pp.1443-1455
• /
• 2017

Let $M_{z^N}(N{\in}{\mathbb{Z}}^d_+)$ be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n:n{\in}{\mathbb{Z}}^d_+\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that d = 2, we find all the minimal reducing subspaces of $M_{z^N}$ ($N=(N_1,N_2)$, $N_1{\neq}N_2$) on weighted Bergman space $A^2_{\alpha}({\mathbb{B}}_2)$(${\alpha}$ > -1) and Hardy space $H^2({\mathbb{B}}_2)$, and characterize the structure of ${\mathcal{V}}^{\ast}(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제9권11호
• /
• pp.4534-4555
• /
• 2015

We propose a robust object cataloging method using multiple locally distinct heterogeneous features for aiding image retrieval. Due to challenges such as variations in object size, orientation, illumination etc. object recognition is extraordinarily challenging problem. In these circumstances, we adapt local interest point detection method which locates prototypical local components in object imageries. In each local component, we exploit heterogeneous features such as gradient-weighted orientation histogram, sum of wavelet responses, histograms using different color spaces etc. and combine these features together to describe each component divergently. A global signature is formed by adapting the concept of bag of feature model which counts frequencies of its local components with respect to words in a dictionary. The proposed method demonstrates its excellence in classifying objects in various complex backgrounds. Our proposed local feature shows classification accuracy of 98% while SURF,SIFT, BRISK and FREAK get 81%, 88%, 84% and 87% respectively.

• 대한수학회지
• /
• 제56권1호
• /
• pp.239-263
• /
• 2019

The $Calder{\acute{o}}n$-Zygmund type estimate is proved for elliptic obstacle problems in bounded non-smooth domains. The problems are related to divergence form nonlinear elliptic equation with measurable nonlinearities. Precisely, nonlinearity $a({\xi},x_1,x^{\prime})$ is assumed to be only measurable in one spatial variable $x_1$ and has locally small BMO semi-norm in the other spatial variables x', uniformly in ${\xi}$ variable. Regarding non-smooth domains, we assume that the boundaries are locally flat in the sense of Reifenberg. We also investigate global regularity in the settings of weighted Orlicz spaces for the weak solutions to the problems considered here.