• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.617-626
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• 2000

We study the vectors related tro states on the Cuntz algebra Ο(sub)n and prove hat, for tow states $\omega$ and $\rho$ on Ο(sub)n with $\omega$│UHF(sub)n = $\rho$│UHF(sub)n, if ($\omega$(s$_1$), …, $\omega$(s(sub)n)) and ($\rho$(s$_1$),…, $\rho$(s(sub)n)) are unit vectors, then they and linearly dependent. We also study the linear functional on Ο(sub)n associated to a sequence of unit vectors in C(sup)n which is the generalization of the Cuntz state. We show that if the linear functional associated to a sequence of unit vectors with a certain condition is a state, then it is just the Cuntz state.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.597-606
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• 2009

In this paper, we introduce the notion of the statistically complete fuzzy norm on a linear space. And we consider some relations between the fuzzy statistical completeness and ordinary completeness on a linear space.

• The Transactions of the Korea Information Processing Society
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• v.7 no.5
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• pp.1474-1481
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• 2000

The number of keystream cycle sequences has been proposed as a characteristic of binary sequence generator for cryptographic application, but in general the most of binary sequence generators have a single cycle. On the other hand, S-box has been used to block cipher for a highly nonlinear element and then we apply it to the stream cipher with a high crypto-degree. In this paper, we propose a multiple-cycle binary sequence generator based on S-box which has a high nonlinearity containing SAC property and analyze its period, linear complexity, randomness and the number of keystream cycle sequences.

• Genomics & Informatics
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• v.17 no.4
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• pp.39.1-39.20
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• 2019

Analyzing patterns in data points embedded in linear and non-linear feature spaces is considered as one of the common research problems among different research areas, for example: data mining, machine learning, pattern recognition, and multivariate analysis. In this paper, data points are heterogeneous sets of biosequences (composite data points). A composite data point is a set of ordinary data points (e.g., set of feature vectors). We theoretically extend the derivation of the largest generalized eigenvalue-based distance metric D_ij(γ₁) in any linear and non-linear feature spaces. We prove that D_ij(γ₁) is a metric under any linear and non-linear feature transformation function. We show the sufficiency and efficiency of using the decision rule $\bar{{\delta}}_{{\Xi}i}$(i.e., mean of D_ij(γ₁)) in classification of heterogeneous sets of biosequences compared with the decision rules min_𝚵iand median_𝚵i. We analyze the impact of linear and non-linear transformation functions on classifying/clustering collections of heterogeneous sets of biosequences. The impact of the length of a sequence in a heterogeneous sequence-set generated by simulation on the classification and clustering results in linear and non-linear feature spaces is empirically shown in this paper. We propose a new concept: the limiting dispersion map of the existing clusters in heterogeneous sets of biosequences embedded in linear and nonlinear feature spaces, which is based on the limiting distribution of nucleotide compositions estimated from real data sets. Finally, the empirical conclusions and the scientific evidences are deduced from the experiments to support the theoretical side stated in this paper.

• The KIPS Transactions:PartD
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• v.17D no.5
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• pp.337-346
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• 2010

Timing diagram is popularly utilized for the reason of its advantages; it is convenient for timing diagram to describe behavior of system and it is simple for described behaviors to recognize it. Various techniques are needed to test systems described in timing diagram. One of them is a technique to derive the system into a certain condition under which a test case is effective. This paper proposes a technique to automatically generate the test input sequence to reach the condition for systems described in timing diagram. It requires a proper input set which satisfy transition condition restricted by input waveform and timing constraints to generate a test input sequence automatically. To solve the problem, this paper chooses an approach utilizing the linear programming, and solving procedure is as follows: 1) Get a Timing diagram model as an input, and transforms the timing diagram model into a linear programming problem. 2) Solve the linear programming problem using a linear programming tool. 3) Generate test input sequences of a timing diagram model from the solution of linear programming problem. This paper addresses the formal method to drive the linear programming model from a given timing diagram, shows the feasibility of our approach by prove it, and demonstrates the usability of our paper by showing that our implemented tool solves an example of a timing diagram model.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.841-849
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• 2007

In this paper we discuss the Hyers-Ulam-Rassias stability of a system of first order linear recurrences with variable coefficients in Banach spaces. The concept of the Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. As an application, the Hyers-Ulam-Rassias stability of a p-order linear recurrence with variable coefficients is proved.

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.45-51
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• 2017

In this paper, we propose an accelerating scheme of convergence of numerical solutions of fuzzy non-linear equations. Numerical experiments show that the new method has significant acceleration of convergence of solutions of fuzzy non-linear equation. Three-dimensional graphical representation of fuzzy solutions is also provided as a reference of visual convergence of the solution sequence.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.150-154
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• 1993

A new method is proposed for obtaining Volterra kernals of a nonlinear system by use of a nonlinear systems by use of pseudorandom M-sequences and correlation technique. M-sequence is applied to a nonlinear technique. M-sequence is applied to a nonlinear system and the crosscorrelation function between the input and the output displays not only the linear impulse response of the linear part of the system, but also crosssections of the Volterra kernals of nonlinear system. Simulations are carried out for up to 3rd order Volterra kernal, and the results show a good agreement with the theoretical considerations.

• Journal of Korea Multimedia Society
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• v.17 no.11
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• pp.1279-1285
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• 2014

In this paper, we propose on image encryption method which uses NC(Non-linear Cycle) and 2D CAT(Two-Dimensional Cellular Automata Transform) in sequence to encrypt medical images. In terms of the methodology, we use NC to generate a pseudo noise sequence equal to the size of the original image. We then conduct an XOR operation of the generated sequence with the original image to conduct level 1 NC encryption. Then we set the proper Gateway Values to generate the 2D CAT basis functions. We multiply the generated basis functions by the altered NC encryption image to conduct the 2nd level 2D CAT encryption. Finally, we verify that the proposed method is efficient and extremely safe by conducting an analysis of the key spatial and sensitivity analysis of pixels.

• Journal of Information Processing Systems
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• v.13 no.6
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• pp.1554-1574
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• 2017

This paper introduces a new type of determining factor for Pseudo Random Strings (PRS). This classification depends upon a mathematical property called Finite Induction (FI). FI is similar to a Markov Model in that it presents a model of the sequence under consideration and determines the generating rules for this sequence. If these rules obey certain criteria, then we call the sequence generating these rules FI a PRS. We also consider the relationship of these kinds of PRS's to Good/deBruijn graphs and Linear Feedback Shift Registers (LFSR). We show that binary sequences from these special graphs have the FI property. We also show how such FI PRS's can be generated without consideration of the Hamiltonian cycles of the Good/deBruijn graphs. The FI PRS's also have maximum Shannon entropy, while sequences from LFSR's do not, nor are such sequences FI random.