• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1327-1338
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• 2015

In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a $Pr\ddot{u}fer$ v-multiplication domain if and only if w-w.gl.dim(R) ${\leq}1$. We also show that there is a large class of domains in which Hilbert's syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x]) = w-w.gl.dim(R).

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.12
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• pp.2511-2519
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• 2009

In this paper, we introduce the methodological system design via feature selection using Principal Component Analysis and Particle Swarm Optimization algorithms. The overall methodological system design comes from three kinds of modules such as preprocessing module, feature extraction module, and recognition module. First, Histogram equalization enhance the quality of image by exploiting contrast effect based on the normalized function generated from histogram distribution values of 2D face image. Secondly, PCA extracts feature vectors to be used for face recognition by using eigenvalues and eigenvectors obtained from covariance matrix. Finally the feature selection for face recognition among the entire feature vectors is considered by means of the Particle Swarm Optimization. The optimized Polynomial-based Radial Basis Function Neural Networks are used to evaluate the face recognition performance. This study shows that the proposed methodological system design is effective to the analysis of preferred face recognition.

• Journal of the Korean earth science society
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• v.32 no.6
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• pp.665-673
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• 2011

In order to estimate the hydrocarbon reserves, the porosity of the reservoir must be determined. The porosity of the area without a well is generally calculated by extrapolating the porosity logs measured at wells. However, if not only well logs but also seismic data exist on the same site, the more accurate pseudo porosity log can be obtained through artificial neural network technique by extracting the relations between the seismic data and well logs at the site. In this study, we have developed a module which creates pseudo porosity logs by using the polynomial neural network method. In order to obtain more accurate pseudo porosity logs, we selected the seismic attributes which have high correlation values in the correlation analysis between the seismic attributes and the porosity logs. Through the training procedure between selected seismic attributes and well logs, our module produces the correlation weights which can be used to generate the pseudo porosity log in the well free area. To verify the reliability and the applicability of the developed module, we have applied the module to the field data acquired from F3 Block in the North Sea and compared the results to those from the probabilistic neural network method in a commercial program. We could confirm the reliability of our module because both results showed similar trend. Moreover, since the pseudo porosity logs from polynomial neural network method are closer to the true porosity logs at the wells than those from probabilistic method, we concluded that the polynomial neural network method is effective for the data sets with insufficient wells such as F3 Block in the North Sea.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.1-10
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• 2015

In this paper, we propose a new multiplication algorithm for primitive polynomial with all 1 of coefficient in case that m is odd and even on finite fields $GF(3^m)$, and design the multiplier with parallel input-output module structure using the presented multiplication algorithm. The proposed multiplier is designed $(m+1)^2$ same basic cells. Since the basic cells have no a latch circuit, the multiplicative circuit is very simple and is short the delay time $T_A+T_X$ per cell unit. The proposed multiplier is easy to extend the circuit with large m having regularity and modularity by cell array, and is suitable to the implementation of VLSI circuit.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1627-1638
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• 2018

In this paper, we study an special type of cyclic codes called skew cyclic codes over the ring ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$, where p is a prime number. This set of codes are the result of module (or ring) structure of the skew polynomial ring (${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$)[$x;{\theta}$] where $v^3=1$ and ${\theta}$ is an ${\mathbb{F}}_p$-automorphism such that ${\theta}(v)=v^2$. We show that when n is even, these codes are either principal or generated by two elements. The generator and parity check matrix are proposed. Some examples of linear codes with optimum Hamming distance are also provided.

• Journal of Ship and Ocean Technology
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• v.11 no.4
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• pp.21-28
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• 2007

Recently the importance of the utilization of engineering data is gradually increasing. Engineering data contains the experiences and know-how of experts. Data mining technique is useful to extract knowledge or information from the accumulated existing data. This paper deals with generating optimal polynomials using genetic programming (GP) as the module of Data Mining system. Low order Taylor series are used to approximate the polynomial easily as a nonlinear function to fit the accumulated data. The overfitting problem is unavoidable because in real applications, the size of learning samples is minimal. This problem can be handled with the extended data set and function node stabilization method. The Data Mining system for the ship design based on polynomial genetic programming is presented.

• East Asian mathematical journal
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• v.36 no.3
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• pp.359-364
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• 2020

It is known that a 2-generator knot K has a cyclic Alexander module ℤ[t, t^―1]/(Δ(t)) where Δ(t) is the Alexander polynomial of K. In this paper we explicitly show how to reduce 2-generator Alexander modules to cyclic ones by using Chiswell, Glass and Wilsons presentations of 2-generator knot groups $$<\;x,\;y\;{\mid}\;(x^{{\alpha}_1})^{y^{{\gamma}_1}},\;{\cdots}\;,\;(x^{{\alpha}_k})^{y^{{\gamma}_k}}\;>$$ where a^b = bab^-1.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.719-725
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• 2013

A domain is called an LPI domain if every locally principal ideal is invertible. It is proved in this note that if D is a LPI domain, then D[X] is also an LPI domain. This fact gives a positive answer to an open question put forward by D. D. Anderson and M. Zafrullah.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.247-257
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• 1999

In this article, we give an example of local derivation, that is not derivation, on the algebra F(x1,…, xn) of rational functions in x1, …, xn over an infinite field F, and show that if X is a set of symbols and {x1,…, xn} is a finite subset of X, n$\geq$1, then each local derivation of F[x1,…, xn] into F[X] is a F-derivation and each local derivation of F[X] into itself is also a F-derivation.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.683-694
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• 2023

Let a be an ideal of 𝔞 commutative noetherian ring R. We give some descriptions of the 𝔞-depth of 𝔞-relative Cohen-Macaulay modules by cohomological dimensions, and study how relative Cohen-Macaulayness behaves under flat extensions. As applications, the perseverance of relative Cohen-Macaulayness in a polynomial ring, formal power series ring and completion are given.