• Journal of IKEEE
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• v.5 no.1 s.8
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• pp.1-7
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• 2001

In this paper, we have investigated the CDMA(Code Division Multiple Access) Cellular System with non-linear equalizer in reverse link channel. In general, due to unknown characteristics of channel in the wireless communication, the distribution of the observables cannot be specified by a finite set of parameters; instead, we partitioned the m-dimensional sample space Into a finite number of disjointed regions by using quantiles and a vector quantizer based on training samples. The algorithm proposed is based on a piecewise approximation to regression function based on quantiles and conditional partition moments which are estimated by Robbins Monro Stochastic Approximation (RMSA) algorithm. The resulting equalizers and detectors are robust in the sense that they are insensitive to variations in noise distributions. The main idea is that the robust equalizers and robust partition detectors yield better performance in equiprobably partitioned subspace of observations than the conventional equalizer in unpartitioned observation space under any condition. And also, we apply this idea to the CDMA system and analyze the BER performance.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1231-1240
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• 2020

The asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field has recently been reviewed. We extend quasi-polynomial behavior of graded Betti numbers of powers of homogenous ideals to ℤ-graded algebra over Noetherian local ring. Furthermore our main result treats the Betti table of filtrations which is finite or integral over the Rees algebra.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.9-9
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• 2003

Let $\Omega$ be a bounded, open, and polygonal domain in $R^2$ with re-entrant corners. We consider the following Partial Differential Equations: $$(I-\nabla\nabla\cdot+\nabla^{\bot}\nabla\times)u\;=\;f\;in\;\Omega$$, $$n\cdotu\;0\;0\;on\;{\Gamma}_{N}$$, $${\nabla}{\times}u\;=\;0\;on\;{\Gamma}_{N}$$, $$\tau{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$, $$\nabla{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$ where the symbol $\nabla\cdot$ and $\nabla$ stand for the divergence and gradient operators, respectively; $f{\in}L^2(\Omega)^2$ is a given vector function, $\partial\Omega=\Gamma_{D}\cup\Gamma_{N}$ is the partition of the boundary of $\Omega$; nis the outward unit vector normal to the boundary and $\tau$represents the unit vector tangent to the boundary oriented counterclockwise. For simplicity, assume that both $\Gamma_{D}$ and $\Gamma_{N}$ are nonempty. Denote the curl operator in $R^2$ by $$\nabla\times\;=\;(-{\partial}_2,{\partial}_1$$ and its formal adjoint by $${\nabla}^{\bot}\;=\;({-{\partial}_1}^{{\partial}_2}$$ Consider a weak formulation(WF): Find $u\;\in\;V$ such that $$a(u,v):=(u,v)+(\nabla{\cdot}u,\nabla{\cdot}v)+(\nabla{\times}u,\nabla{\times}V)=(f,v),\;A\;v{\in}V$$. (2) We assume there is only one singular corner. There are many methods to deal with the domain singularities. We introduce them shortly and we suggest a new Finite Element Methods by using Singular representation for the solution.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.4
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• pp.456-462
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• 2008

The classification is that a new data is classified into one of given classes and is one of the most generally used data mining techniques. Memory-Based Reasoning (MBR) is a reasoning method for classification problem. MBR simply keeps many patterns which are represented by original vector form of features in memory without rules for reasoning, and uses a distance function to classify a test pattern. If training patterns grows in MBR, as well as size of memory great the calculation amount for reasoning much have. NGE, FPA, and RPA methods are well-known MBR algorithms, which are proven to show satisfactory performance, but those have serious problems for memory usage and lengthy computation. In this paper, we propose DPA (Dynamic Partition Averaging) algorithm. it chooses partition points by calculating GINI-Index in the entire pattern space, and partitions the entire pattern space dynamically. If classes that are included to a partition are unique, it generates a representative pattern from partition, unless partitions relevant partitions repeatedly by same method. The proposed method has been successfully shown to exhibit comparable performance to k-NN with a lot less number of patterns and better result than EACH system which implements the NGE theory and FPA, and RPA.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.106-109
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• 1998

Wireless communication systems, in particular, must operate in a crowded electro-magnetic environmnet where in-band undesired signals are treated as noise by the receiver. These interfering signals are often random but not Gaussian Due to nongaussian noise, the distribution of the observables cannot be specified by a finite set of parameters; instead r-dimensioal sample space (pure noise samples) is equiprobably partitioned into a finite number of disjointed regions using quantiles and a vector quantizer based on training samples. If we assume that the detected symbols are correct, then we can observe the pure noise samples during the training and transmitting mode. The algorithm proposed is based on a piecewise approximation to a regression function based on quantities and conditional partition moments which are estimated by a RMSA (Robbins-Monro Stochastic Approximation) algorithm. In this paper, we develop a diversity combiner with modified detector, called Non-Linear Detector, and the receiver has a differential phase detector in each diversity branch and at the combiner each detector output is proportional to the second power of the envelope of branches. Monte-Carlo simulations were used as means of generating the system performance.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.593-601
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• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.709-723
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• 2016

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}{\mathbb{R}}^n$ by $Zn(x)=(\int_{0}^{t_1}h(s)dx(s),{\cdots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $t_n$ < t is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. In this paper we will introduce a simple formula for a generalized conditional Wiener integral on C[0, t] with the conditioning function $Z_n$ and then evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function $F(x)=f(\int_{0}^{t}e(s)dx(s))$ for $x{\in}C[0,t]$, where $f{\in}L_p(\mathbb{R})(1{\leq}p{\leq}{\infty})$ and e is a unit element in $L_2[0,t]$. Finally we express the generalized analytic conditional Feynman integral of F as two kinds of limits of non-conditional generalized Wiener integrals of polygonal functions and of cylinder functions using a change of scale transformation for which a normal density is the kernel. The choice of a complete orthonormal subset of $L_2[0,t]$ used in the transformation is independent of e and the conditioning function $Z_n$ does not contain the present positions of the generalized Wiener paths.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.