• Journal of the Korean Statistical Society
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• v.10
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• pp.97-104
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• 1981

It is shown that a lattice distribution defined on a set of n lattice points $L(n,\delta) = {\delta,\delta+1,...,\delta+n-1}$ is a distribution induced from the distribution of convolution of independently and identically distributed (i.i.d.) uniform [0,1] random variables. Also the m-th moment of the lattice distribution is obtained in a quite different approach from Park and Chung (1978). It is verified that the distribution of the sum of n i.i.d. uniform [0,1] random variables is completely determined by the lattice distribution on $L(n,\delta)$ and the uniform distribution on [0,1]. The factorial mement generating function, factorial moments, and moments are also obtained.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.65-70
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• 2009

In this paper, we introduced the notion of (L,$\bigodot$)-quasi-uniform spaces and (L,$\bigodot$)-neighborhood systems on a strictly two-sided, commutative quantale lattice L. We investigate their properties and give the examples. In particular, we study the relations between (L,$\bigodot$)-quasi-uniform spaces and (L,$\bigodot$)-neighborhood systems.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.621-631
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• 1999

In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.

• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.59-61
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• 1978

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.7
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• pp.1515-1522
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• 1997

Several image coding algorithms have been developed for the telecommunication and multimedia systems with high image quality and high compression ratio. In order to achieve low entropy and distortion, the system should pay great cost of computation time and memory. In this paper, the uniform cubic lattice is chosen for Lattice Vector Quantization (LVQ) because of its generic simplicity. As a transform coding, the Discrete Wavelet Transform (DWT) is applied to the images because of its multiresolution property. The proposed algorithm is basically composed of the biorthogonal DWT and the uniform cubic LVQ. The multiresolution property of the DWT is actively used to optimize the entropy and the distortion on the basis of the distortion-rate function. The vector codebooks are also designed to be optimal at each subimage which is analyzed by the biorthogonal DWT. For compression efficiency, the vector codebook has different dimension depending on the variance of subimage. The simulation results show that the performance of the proposed coding mdthod is superior to the others in terms of the computation complexity and the PSNR in the range of entropy below 0.25 bpp.

• Composites Research
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• v.36 no.2
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• pp.80-85
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• 2023

A cylindrical composite lattice structure is manufactured by filament winding. The distribution of nonuniform fiber volume fraction induced by the manufacturing process can be observed. The stiffness and buckling characteristics can be influenced by non-uniform fiber volume fraction. In this paper, the effect of non-uniform fiber volume fraction through thickness direction on the torsional buckling load of the cylindrical composite lattice structure was examined. The stiffness variation induced by the non-uniform fiber volume fraction was applied to the finite element model, and buckling analysis was performed. The variations of buckling load with variations of fiber volume fraction were compared. The non-uniform fiber volume fraction reduced the torsional buckling load of the composite lattice structure.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1827-1832
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• 2003

In this research, the simulation method for acoustic sounds by a uniform flow around a two-dimensional circular cylinder by using the finite difference lattice Boltzmann model is explained. To begin with, we examine the boundary condition which determined with the distribution function $f_i^{(0)}$ concerning with density, velocity and internal energy at boundary node. Very small acoustic pressure fluctuation, with same frequency as that of Karman vortex street, is compared with the pressure fluctuation around a circular cylinder. The acoustic sound' propagation velocity shows that acoustic approa ching the upstream, due to the Doppler effect in the uniform flow, slowly propagated. For the do wnstream, on the other hand, it quickly propagates. It is also apparently the size of sound pressure was proportional to the central distance $r^{-1/2}$ of the circular cylinder. The lattice BGK model for compressible fluids is shown to be one of powerful tool for simulation of gas flows.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.10
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• pp.2634-2644
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• 1996

Two different low rate speech coders using one of four types of lattice vector quantizers(LVQ's) with fairly low complexity were investigated for an application to mobile communications. More specifically, two-stage vector quantizer-lattic vector quantizer(VQ-LVQ) systems and vector differenctial pulse code modulation(VDPCM)systems with lattice vector quantizers simulated to encode the line spectrum frequencies of various sentences at the rate 22 to 39 bits per 20 msec frame. The simulation results showed that the VDPCM system with the lattice VQ can save up to 10 bits/fram compared to the quantization scheme used in QCELP system. For the VQ-LVQ system, the spherical quasi-uniform LVQ below 36 bits/frame outperformed the other 3 types of LVQ's and the pyramidal quasi-uniform LVQ at 37 bits/frame outperformed the other 3 types of LVQ's with the spectral distortion 0.97.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.2
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• pp.117-121
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• 2005

This paper presents a 3D last design system utilizing an uniform foot pressure FFD method. The proposed uniform foot pressure FFD(UFPFFD) is operated on the rule of foot pressure unbalance analysis and FFD. The deformation factor of the UFPFFD is constructed on the FFD lattice with the foot pressure unbalance analysis on the measured 3D foot bottom shape. In addition, the control points of FFD lattice are decided on the anatomical point and the foot pressure distribution. The 3D last design result obtained from the proposed UFPFFD is saved as a 3D dxf data format. The experimental results demonstrate that the proposed last design guarantees the balanced foot pressure distribution against on the conventional last design method.

• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.315-318
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• 2000

In this note we use the Poisson Summation Formula to generalize a result of Harris and Park (1994) on lattice distributions induced by uniform (0,1) random variables to those generated by random variables with step functions as their probability functions.