• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.75-88
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• 2012

A new algorithm is proposed for the construction of Brezing-Weng-like elliptic curves such that polynomials defining the CM discriminant are linear. Using this construction, new families of curves with variable discriminants and embedding degrees of $k{\in}\{8,16,20,24\}$, which were not covered by Freeman, Scott, and Teske [9], are presented. Our result is useful for constructing elliptic curves with larger and more flexible discriminants.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.745-763
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• 2012

We use Kazhdan-Lusztig bases of representations of the symmetric group to express Pfaffians with entries $(a_i-a_j)h_{i+j}$. In the case where the parameters $a_i$ are specialized to successive powers of $q$, and the $h_i$ are complete functions, we obtain the $q$-discriminant.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.201-204
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• 1992

After this discovery of lower bounds by Stark and Odlyzko, some people searched for number fields with relatively small discriminants. Also some others studied algorithms which will produce number fields with the smallest absolute value of the discriminant for a fixed degree n. However, this algorithmic approach does not work well if the extension degree n is greater than seven or eight. And it is not clear whether current computers can finish those algorithms in a reasonable amount of time for large n. So we are justified in our approach for this subject. In this paper we will report the results of our computations. Some number fields we found are better than previously known examples. Others are rediscoveries of known examples. However, there is theoretically nothing new in our approach to this subject.

• Proceedings of the KOSOMBE Conference
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• v.1996 no.05
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• pp.27-30
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• 1996

PR interval variability has been proposed as a noninvasive tool for in-vestigating the autonomic nervous system as welt as heart rate variability. The goal of this paper is to determine whether PR interval variability is generated from deterministic nonlinear dynamics. The data used in this study is a 24-hour bolter ECGs of 20 healthy adults. We developed an automatic PR interval measurement algorithm, and tested it using MIT ECG Databases. The general discriminants of nonlinear dynamics, such as, correlation dimension and phase space reconstruction are used. Surrogate data is generated from simpler linear models to have similar statistical characteristics with the original data. Nonlinear discriminants are applied to both data, and compared for any significant results. It was concluded that PR interval variability shows non-linear characteristics.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.621-630
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• 2008

In this paper, we provide a complete list of 177 equivalence classes of primitive even 2-regular quaternary positive definite quadratic forms and their discriminants. All of them have class number 1.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.563-568
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• 1996

In this paper we study the ramification of prime ideals in the dihedral octic extension N over Q and estimate the possible discriminants of the octic number field N.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.5 s.305
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• pp.55-62
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• 2005

In this paper, we propose the face recognition system using HNMA(Hippocampal Neuron Modeling Algorithm) which can remodel the cerebral cortex and hippocampal neuron as a principle of a man's brain in engineering, then it can learn the feature-vector of the face images very fast and construct the optimized feature each image. The system is composed of two parts. One is feature-extraction and the other is teaming and recognition. In the feature extraction part, it can construct good-classified features applying PCA(Principal Component Analysis) and LDA(Linear Discriminants Analysis) in order. In the learning part, it cm table the features of the image data which are inputted according to the order of hippocampal neuron structure to reaction-pattern according to the adjustment of a good impression in the dentate gyrus region and remove the noise through the associate memory in the CA3 region. In the CA1 region receiving the information of the CA3, it can make long-term memory learned by neuron. Experiments confirm the each recognition rate, that are face changes, pose changes and low quality image. The experimental results show that we can compare a feature extraction and learning method proposed in this paper of any other methods, and we can confirm that the proposed method is superior to existing methods.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.4 s.304
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• pp.79-86
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• 2005

In this paper, we propose a new LINF(Linear Independent Non-negative Factorization) algorithm for real-time face recognition systea This system greatly consists of the two parts: 1) face extraction part; 2) face recognition part. In the face extraction Part we applied subtraction image, the detection of eye and mouth region , and normalization method, and then in the face recognition Part we used LINF in extracted face candidate region images. The existing recognition system using only PCA(Principal Component Analysis) showed low recognition rates, and it was hard in the recognition system using only LDA(Linear Discriminants Analysis) to apply LDA directly when the training set is small. To overcome these shortcomings, we reduced dimension as the matrix that had non-negative value to be different from former eigenfaces and then applied LDA to the matrix in the proposed system We have experimented using self-organized DAIJFace database and ORL database offered by AT(')T laboratory in Cambridge, U.K. to evaluate the performance of the proposed system. The experimental results showed that the proposed method outperformed PCA, LDA, ICA(Independent Component Analysis) and PLMA(PCA-based LDA mixture algorithm) method within the framework of recognition accuracy.

• Journal of Integrative Natural Science
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• v.5 no.2
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• pp.131-134
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• 2012

Bae and Kim displayed a sequence of 4th degree self-reciprocal polynomials whose maximal zeros are related in a very nice and far from obvious way. Kim showed that the auxiliary polynomials in their results are related to Chebyshev polynomials. In this paper, we study two sequences of polynomials satisfying the recurrence of the auxiliary polynomials with generalized initial conditions. We obtain same results with the auxiliary polynomials from a sequence, and some interesting conjectural properties about resultants and discriminants from another sequence.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.153-157
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• 1998

It is wisely stated that the most valuable knowledge that a person cam acquire is the knowledge of how to learn. The human's learning is characterized by the ability to extract relationships between the different characters of a given situation. The ellipse is a first approach of comparison. We assimilate each character to a half axis of the ellipse and the result is a geometrical figure that varies according to values of the two characters. Thus, we take into account the two characters as an alone entity.