• Journal of the Optical Society of Korea
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• v.9 no.3
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• pp.111-118
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• 2005

In this paper, a new optical parallel binary arithmetic processor (OPBAP) capable of computing arbitrary n-bit look-ahead carry full-addition is proposed and implemented. The conventional Boolean algebra is considered to implement OPBAP by using two schemes of optical logic processor. One is space-variant optical logic gate processor (SVOLGP), the other is shadow-casting optical logic array processor (SCOLAP). SVOLGP can process logical AND and OR operations different in space simultaneously by using free-space interconnection logic filters, while SCOLAP can perform any possible 16 Boolean logic function by using spatial instruction-control filter. A dual-rail encoding method is adopted because the complement of an input is needed in arithmetic process. Experiment on OPBAP for an 8-bit look-ahead carry full addition is performed. The experimental results have shown that the proposed OPBAP has a capability of optical look-ahead carry full-addition with high computing speed regardless of the data length.

• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.81-93
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• 2008

In [3, 9], using the theory of noncommutative Dirichlet forms in the sense of Cipriani [6] and the symmetric embedding map, authors constructed the KMS-symmetric Markovian semigroup $\{S_t\}_{t{\geq}0}$ on a von Neumann algebra $\cal{M}$ with an admissible function f and an operator $x\;{\in}\;{\cal{M}}$. We give a sufficient and necessary condition for x so that the semigroup $\{S_t\}_{t{\geq}0}$ acts separately on diagonal and off-diagonal operators with respect to a basis and study some results.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.973-981
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• 2021

Let R be a commutative ring with identity 1, n ≥ 3, and let 𝒯_n(R) be the linear Lie algebra of all upper triangular n × n matrices over R. A linear map 𝜑 on 𝒯_n(R) is called to be strong commutativity preserving if [𝜑(x), 𝜑(y)] = [x, y] for any x, y ∈ 𝒯_n(R). We show that an invertible linear map 𝜑 preserves strong commutativity on 𝒯_n(R) if and only if it is a composition of an idempotent scalar multiplication, an extremal inner automorphism and a linear map induced by a linear function on 𝒯_n(R).

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.387-398
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• 2021

In this paper, we will find solutions and investigate the superstability bounded by constant for the p-radical functional equations as follows: $f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=\;\{(i)\;f(x)f(y),\\(ii)\;g(x)f(y),\\(iii)\;f(x)g(y),\\(iv)\;g(x)g(y).$ with respect to the sine functional equation, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebra.

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1015-1027
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• 2009

Many problems of confounding and identifiability for polynomial models in an experimental design can be solved using methods of algebraic geometry. The theory of $Gr\ddot{o}bner$ basis is used to characterize the design. In addition, a fractional factorial design can be uniquely represented by a polynomial indicator function. $Gr\ddot{o}bner$ bases and indicator functions are powerful computational tools to deal with ideals of fractions based on each different theoretical aspects. The problem posed here is to give how to move from one representation to the other. For a given fractional factorial design, the indicator function can be computed from the generating equations in the $Gr\ddot{o}bner$ basis. The theory is tested using some fractional factorial designs aided by a modern computational algebra package CoCoA.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.505-522
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• 2005

In this article we studied the role of spreadsheet in teaching function and modeling activity by some examples and students' activity performed by the six 10th graders. We especially focused the role of spreadsheet in understanding of various kinds of functions and the families of functions, and in the explanation of the given modeling problem situations. The functions of automatic copy, graphic and the cell reference of spreadsheet can be used to make students observe the causes and effects of changes of the various kind of mathematical representations of functions such as algebraic formulas, tables and graphs. Especially those functions give students a chance to identify family of functions by changing the parameters and this may lead them to the discovery of mathematical facts. In modeling activities they play a key role in the stages of the analysis of the model, explanation of the results of model and conjecture of the real world situations. As well as they make students find the rules underlying in the real world by making spreadsheet as simulation environments, which are almost impossible to make in paper and pencil environments, and give them a chance to justify their findings using mathematics.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.363-384
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• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.

• Journal of the Korean Association of Geographic Information Studies
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• v.12 no.1
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• pp.64-72
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• 2009

The method to generate a digital elevation model(DEM) from contour lines causes a problem in which the low relief landform cannot be clearly presented due to the fact that it is significantly influenced by the expression of micro landform elements according to the interval of contours. Thus, this study attempts to develop a landcover burning method that recovers the micro relief landform of the DEM, which applies buffering and map algebra methods by inputting the elevation information to the landcover. In the recovering process of the micro landform, the DEM was recovered using the buffering method and elevation information through the map algebra for the landcover element for the micro landform among the primary DEM generation, making landcover map, and landcover elements. The recovering of the micro landform was applied based on stream landforms. The recovering of landforms using the buffering method was performed for the bar, which is a polygonal element, and wetland according to the properties of concave/convex through generating contours with a uniform interval in which the elevation information applied to the recovered landform. In the case of the linear elements, such as bank, road, waterway, and tributary, the landform can be recovered by using the elevation information through applying a map algebra function. Because the polygonal elements, such as stream channel, river terrace, and artificial objects (farmlands) are determined as a flat property, these are recovered by inputting constant elevation values. The results of this study were compared and analyzed for the degree of landform expression between the original DEM and the recovered DEM. In the results of the analysis, the DEM produced by using the conventional method showed few expressions in micro landform elements. The method developed in this study well described wetland, bar, landform around rivers, farmland, bank, river terrace, and artificial objects. It can be expected that the results of this study contribute to the classification and analysis of micro landforms, plain and the ecology and environment study that requires the recovering of micro landforms around streams and rivers.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.2
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• pp.27-38
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• 2002

A new self-consistent mathematical model for semiconductor quantum well device was developed. The model was based on the direct solution of the Boltzmann transport equation, coupled to the Schrodinger and Poisson equations. The solution yielded the distribution function for a two-dimensional electron gas(2DEG) in quantum well devices. To solve the Boltzmann equation, it was transformed into a tractable form using a Legendre polynomial expansion. The Legendre expansion facilitated analytical evaluation of the collision integral, and allowed for a reduction of the dimensionality of the problem. The transformed Boltzmann equation was then discretized and solved using sparce matrix algebra. The overall system was solved by iteration between Poisson, Schrodinger and Boltzmann equations until convergence was attained.

• School Mathematics
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• v.9 no.2
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• pp.313-326
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• 2007

Recently in algebra curriculum, to recognizes and explains general nile expressing patterns is presented as the one alternative and is emphasized. In the seventh School Mathematic Curriculum regarding 'regularity and function' area, in elementary school curriculum, is guiding pattern activity of various form. But difficulty and problem of students are pointing in study for learning through pattern activity. In this article, emphasizes generalization process through research activity of pictorial/geometric pattern that is introduced much on elementary school mathematic curriculum and investigates various approach and strategy of student's thinking, state of symbolization in generalization process of pictorial/geometric pattern. And discusses generalization of pictorial/geometric pattern, difficulty of symbolization and suggested several proposals for research activity of pictorial/geometric pattern.