• Journal of the Korea Society of Computer and Information
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• v.9 no.3
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• pp.163-169
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• 2004

In this paper, a conventional key exchange method simply performs the key exchange setup step based on discrete algebraic subjects. But the mutual-authentication procedure of wireless PKI for reducing authentication time uses an elliptical curve for a key exchange setup step. Proposed handover method shows reduced handover processing time than conventional method since it can reduce CRL retrieval time. Also, we compared proposed authentication structure and conventional algorithm. and simulation results show that proposed authentication method outperforms conventional algorithm in all environment regardless of call arrival rate. queue service rate. queue size.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.1211-1214
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• 1998

Real-time implementation of Conjugate-Structure Algebraic CELP(CS-ACELP) is presented. ITU-T Study Group(SG) 15 has standardized the CS-ACELP speech coding algorithm as G.729. A real-time implementation of the CS-ACELP is achieved using 16 bit fixed point DSP16210 Digital Signal Processor (DSP) of Lucent Technologies. The speech coder has been implemented in the bit-exact manner using the fixed point CS-ACELP C source which is the part of the G.729 standard. To provide a multi-channel vocoder solution to digital communication system, we try to minimize the complexity(e.g., MIPS, ROM, RAM) of CS-ACELP. Our speech coder shows 15.5 MIPS in performance which enables 4 channel CS-ACELP to be processed with one DSP16210.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.17-24
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• 2002

It will be described the discovery of fundamental algebras such as complex numbers and the quaternions. Cardano(1539) was the first to introduce special types of complex numbers such as 5$\pm$$\sqrt{-15}$. Girald called the number a$\pm$$\sqrt{-b}$ solutions impossible. The term imaginary numbers was introduced by Descartes(1629) in “Discours la methode, La geometrie.” Euler knew the geometrical representation of complex numbers by points in a plane. Geometrical definitions of the addition and multiplication of complex numbers conceiving as directed line segments in a plane were given by Gauss in 1831. The expression “complex numbers” seems to be Gauss. Hamilton(1843) defined the complex numbers as paire of real numbers subject to conventional rules of addition and multiplication. Cauchy(1874) interpreted the complex numbers as residue classes of polynomials in R[x] modulo $x^2$＋1. Sophus Lie(1880) introduced commutators [a, b] by the way expressing infinitesimal transformation as differential operations. In this paper, it will be studied general quaternion algebras to finding of algebraic structure in Algebras.

• School Mathematics
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• v.4 no.3
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• pp.463-481
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• 2002

In this paper, I review the historical background of "the principle of the permanence of equivalent forms" and sum- marize properties of "the principle of the permanence of equivalent forms" as a kind of heuristic. 1 think that "the principle of the permanence of equivalent forms" can be used effectively for student's discovery of the algebraic structure. There are three ways of using "the principle of the permanence of equivalent forms" in extending number system - an extension on the base of set theory(SMSC), the formal or axiomatic extrapolation and the inductive-extrapolatory method. All those three methods are mixed up and being used potentially at various levels in current Korean text books. "The principle of the permanence of equivalent forms" is used most effectively in the subject of the exponent. 1 try to present a situation that makes the students find more general definition and cultivate their desirable attitudes for the mathematics in the process of extending the exponent through summarizing the debate between Goel & Robillard(1997) and Tirosh S, Even(1997).

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.7
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• pp.883-888
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• 2014

The paper describes the parameter tuning of power system stabilizer (PSS) for a power plant based on hybrid system modeling. The existing tuning method based on bode plot and root locus is well applied to keep power system stable. However, due to linearization of power system and an assumption that the parameter ratio of the lead-lag compensator in PSS is fixed, the results cannot guarantee the optimal performances to damp out low-frequency oscillation. Therefore, in this paper, hybrid system modeling, which has a DAIS (differential-algebraic-impusive-switched) structure, is applied to conduct nonlinear modeling for power system and find optimal parameter set of the PSS. The performances of the proposed method are carried out by time domain simulation with a single machine connected to infinite bus (SMIB) system.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.239-246
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• 2015

If for every elements x and y of an associative algebraic structure (S, ${\cdot}$) there exists a positive integer r such that $ab=b^ra$, then S is called quasi-commutative. Evidently, every abelian group or commutative semigroup is quasi-commutative. Also every finite Hamiltonian group that may be considered as a semigroup, is quasi-commutative however, there are quasi-commutative semigroups which are non-group and non commutative. In this paper, we provide three finitely presented non-commutative semigroups which are quasi-commutative. These are the first given concrete examples of finite semigroups of this type.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1313-1327
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• 2007

We review the algebraic structure of $\mathbb{H}{\sharp}$ and show that $\mathbb{H}{\sharp}$ has a scalar product that allows as to identify it with semi Euclidean ${\mathbb{E}}^4_2$. We show that a pair q and p of unit split quaternions in $\mathbb{H}{\sharp}$ determines a rotation $R_{qp}:\mathbb{H}{\sharp}{\rightarrow}\mathbb{H}{\sharp}$. Moreover, we prove that $R_{qp}$ is a product of rotations in a pair of orthogonal planes in ${\mathbb{E}}^4_2$. To do that we call upon one tool from the theory of second ordinary differential equations.

• Proceedings of the Korea Contents Association Conference
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• 2004.11a
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• pp.220-227
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• 2004

In this paper, we made out blocking probability analysis for a new authentication structure for reducing the certificate acquisition time which is one of the factors that should be improved in a conventional wireless PKI. A conventional key exchange method simply performs the key exchange setup step based on discrete algebraic subjects. But the mutual-authentication procedure of wireless PKI for reducing authentication time uses an elliptical curve for a key exchange setup step. Besides, we proposed advanced handover method and blocking probability analysis for wireless PKI.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.7
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• pp.399-406
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• 2000

We propose an nonlinear demodulation algorithm for undersampled multicomponent AM(Amplitude Modulation), FM(Frequency Modulation) and AM-FM signals. First, we derive respectively undersampling frequency of the AM, FM and AM-FM using undersampling scheme, and separate respectively monocomponent signals from multicomponent signals using periodic algebraic separation algorithm. In this case augmented separation matrix is very regular and sparse, it has a special structure. The proposed demodulation algorithm detects respectively message signals of the IA(Instantaneous Amplitude) and IF(Instantaneous Frequency) from descrete monocomponent AM, FM and AM-FM signals with an undersampling frequency to be controllable. Verifying the RMS(Root Mean Squares) errors of the detected signals, we show that the performance is excellent.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.1
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• pp.80-87
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• 1989

Many Traditional Algebraic Analyses of preference and choice for a finite set of alternatives have been based on binary choices. They have assumed that the binary preference information given by a decision maker is transitive. However, there is considerable evidence that many relations that might occur as preference relations cannot be presented as transitive relations. To construct transitive binary comparisons from intransitive ones, we suggest the notion of superior set, which helps us to understand the structure of intransitive binary comparisons. We also provide a heuristic method to construct transitive binary comparisons. And some merits merits of the suggested method over the existing methods are also discussed.