• School Mathematics
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• v.12 no.3
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• pp.371-388
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• 2010

The goals of this study are to inquire middle school students' understanding about prime number and to propose pedagogical implications for school mathematics. Written questionnaire were given to 198 Korean seventh graders who had just finished learning about prime number and prime factorization and then 20 students participated in individual interviews for member checks. In defining prime and composite numbers, the students focused on distinguishing one from another by numbering of factors of agiven natural number. However, they hardly recognize the mathematical connection between prime and composite numbers related on the multiplicative structure of natural number. This study suggests that it is needed to emphasize the conceptual relationship between divisibility and prime decomposition and the prime numbers as the multiplicative building blocks of natural numbers based on the Fundamental Theorem of Arithmetic.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.717-734
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• 1996

For a scalar rational function, the spectral data consisting of zeros and poles with their respective multiplicities uniquely determines the function up to a nonzero multiplicative factor. But due to the richness of the spectral structure of a rational matrix function, reconstruction of a rational matrix function from a given spectral data is not that simple.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.5
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• pp.528-535
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• 1988

This paper presents a constructing theory of variable arithmetic operation systems for computing multiplications and multiplicative inverse in GF(2**m) based on a modulo operation of degree on elements in Galois fields. The proposed multiplier is composed of a zero element control part, input element conversion part, inversion circuit, and output element conversion part. These systems can reduce reasonable circuit areas due to the common use of input/output element converison parts, and the PLA and module structure provice a variable property capable of convertible uses as arithmetic operation systems over different finite fields. This type of designs gives simple, regular, expandable, and concurrent properties suitable for VLSI implementation. Expecially, the multiplicative inverse circuit proposed here is expected to offer a characteristics of the high operation speed than conventional method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.4C
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• pp.379-383
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• 2003

A simpler nonparametric detector test statistic based on reference observation in addition to the rank statistics of regular observations is suggested in this letter. Using reference observations instead of sign statistics helps us a simpler detector structure especially for random signals buried in multiplicative noise.

• Proceedings of the KWS Conference
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• 2003.11a
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• pp.156-158
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• 2003

An implicit finite element implementation for Leblond's transformation plasticity constitutive equations, which are widely used in welded steel structure is proposed in the framework of parallel computing. The implementation is based upon the multiplicative decomposition of deformation gradient and hyper elastic formulation. We examine the efficiency of parallel computation for the finite element analysis of a welded structure using domain-wise multi-frontal solver.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.8
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• pp.35-45
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• 1999

In this paper, the addition and the multiplicative algorithm of two polynomials over finite field $GF(p^m)$ are presented. The 4-valued arithmetic processor of the serial input-parallel output modular structure on $GF(4^3)$ to be performed the presented algorithm is implemented by current mode CMOS. This 4-valued arithmetic processor using current mode CMOS is implemented one addition/multiplication selection circuit and three operation circuits; mod(4) multiplicative operation circuit, MOD operation circuit made by two mod(4) addition operation circuits, and primitive irreducible polynomial operation circuit to be performing same operation as mod(4) multiplicative operation circuit. These operation circuits are simulated under $2{\mu}m$ CMOS standard technology, $15{\mu}A$ unit current, and 3.3V VDD voltage using PSpice. The simulation results have shown the satisfying current characteristics. The presented 4-valued arithmetic processor using current mode CMOS is simple and regular for wire routing and possesses the property of modularity. Also, it is expansible for the addition and the multiplication of two polynomials on finite field increasing the degree m and suitable for VLSI implementation.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.30 no.3
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• pp.337-347
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• 2020

In CRYPTO 2019, Gohr presents that Deep-learning can be used for cryptanalysis. In this paper, we verify whether Deep-learning can identify the structures of S-box. To this end, we conducted two experiments. First, we use DDT and LAT of S-boxes as the learning data, whose structure is one of mainly used S-box structures including Feistel, MISTY, SPN, and multiplicative inverse. Surprisingly, our Deep-learning algorithms can identify not only the structures but also the number of used rounds. The second application verifies the pseudo-randomness of and structures by increasing the nuber of rounds in each structure. Our Deep-learning algorithms outperform the theoretical distinguisher in terms of the number of rounds. In general, the design rationale of ciphers used for high level of confidentiality, such as for military purposes, tends to be concealed in order to interfere cryptanalysis. The methods presented in this paper show that Deep-learning can be utilized as a tool for analyzing such undisclosed design rationale.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.53-68
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• 2012

This paper investigated the conceptual schemes four children constructed as they related division number sentences to various types of fraction: Proper fractions, improper fractions, and mixed numbers in both contextual and abstract symbolic forms. Methods followed those of the constructivist teaching experiment. Four fifth-grade students from an inner city school in the southwest United States were interviewed eight times: Pre-test clinical interview, six teaching / semi-structured interviews, and a final post-test clinical interview. Results showed that for equal sharing situations, children conceptualized division in two ways: For mixed numbers, division generated a whole number portion of quotient and a fractional portion of quotient. This provided the conceptual basis to see improper fractions as quotients. For proper fractions, they tended to see the quotient as an instance of the multiplicative structure: $a{\times}b=c$ ; $a{\div}c=\frac{1}{b}$ ; $b{\div}c=\frac{1}{a}$. Results suggest that first, facility in recall of multiplication and division fact families and understanding the multiplicative structure must be emphasized before learning fraction division. Second, to facilitate understanding of the multiplicative structure children must be fluent in representing division in the form of number sentences for equal sharing word problems. If not, their reliance on long division hampers their use of syntax and their understanding of divisor and dividend and their relation to the concepts of numerator and denominator.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.48.1-48
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• 2001

In this paper, we present a global adaptive output feedback control scheme for a class of uncertain nonlinear systems to which adaptive observer backstepping method may not be applicable directly. The allowed output feedback structure includes quadratic and multiplicative dependency of unmeasured states. Our novel design technique employs a change of coordinates and adaptive backstepping. With these proposed tools, we can remove linear and quadratic dependence on the unmeasured states in the state equation. Also, the multiplication of the two unmeasured states can be eliminated ...

• Fisheries and Aquatic Sciences
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• v.6 no.2
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• pp.51-58
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• 2003

The gonadal development and the gametogenic cycle and the fine structure of ripe germ cells of the cultured Pacific oyster, Crassostrea gigas were investigated using oysters monthly collected from the southern coast of Korea from October 2000 to September 2001. Monthly changes in the condition index were similar to that of meat weight rate and the highest value was observed in between April and May, and the lowest value in August. The external colors of the testis and the ovary were milky white and yellowish, respectively. The spawning period of the Pacific oyster was continued from May to September, with a peak in July. The gametogenic cycle could be classified into five successive stages: multiplicative stage (December to March), growing stage (March and April), mature stage (April to June), spawning stage (June to August) and resting stage (August to January). Variety of egg yolk granules, lipid granules, mitochondria, and endoplasmic reticula were observed in cytoplasm of ripe oocyte. The spermatozoon consisted of the head, middle piece and tail; including cap-shaped acrosome with domed structure, elliptical shaped nucleus, four mitochondria, two centrioles and flagellum.