• Progress in Superconductivity
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• v.3 no.2
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• pp.183-187
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• 2002

In this paper we analyzed the electromagnetic behavior of high $-T_{c}$ superconductor under the quench state using finite element method. Poisson equation was used in finite element analysis as a governing equation and was solved using algebra equation using Gallerkin method. We first investigate d the electromagnetic behavior of U-type superconductor. Finally we applied our analysis techniques to 5.5 kVA meander-line superconducting fault current limiters (SFCL) which are currently developed by many power-system researcher in the world. Meshes of 14,600 elements were used in analysis of this SFCL. Analysis results show that the distribution of current density was concentrated to inner curvature in meander-line type-superconductors and maximum current density 14.61 $A/\m^2$ and also maximum Joule heat was 6,420 W/㎥. We concluded that this meander line-type SFCL was not pertinet fur uniform electromagnetic field distribution.n.

• Nuclear Engineering and Technology
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• v.44 no.4
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• pp.405-414
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• 2012

In this paper, we propose a reliability estimation method for DI&C systems. At the system level, a fault tree model is suggested and Boolean algebra is used to obtain the minimal cut sets. At the component level, an exponential distribution is used to model hardware failures, and Bayesian estimation is suggested to estimate the failure rate. Additionally, a binomial distribution is used to model software failures, and a recently developed software reliability estimation method is suggested to estimate the software failure rate. The overall system reliability is then estimated based on minimal cut sets, hardware failure rates and software failure rates.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.43-46
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• 1989

In this paper, we are concerned with the pointwise-hypoellipticity (see Definition 2.1) of an m-dimensional Frobenious Lie algebra L of analytic complex vector fields in somel open subset .ohm. of $R^{m+1}$. That is, L is a set of complex vector fields in .ohm. with (real-) analytic coefficients satisfying: (A) each point of .ohm. has an open neighborhood in which L is generated by m linearly independent elements of L; (B) L is closed under the commutation bracket [A, B]. The pointwise-analytic hypoellipticity of L is completely characterized by M.S. Baouendi and F. Treves in [1]. Here, we shall prove that if L is hypoelliptic at a point then it must be analytic hypoelliptic in a full neighborhood of the same point. When the coefficients are $C^{\infty}$, hypoellipticity of L was discussed in [2].2].

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.451-459
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• 2019

Let ${\mathcal{A}}$ and ${\mathcal{B}}$ be two operator ${\ast}$-rings such that ${\mathcal{A}}$ is prime. In this paper, we show that if the map ${\Phi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves Jordan or ${\ast}$-Jordan triple product, then it is additive. Moreover, if ${\Phi}$ preserves Jordan triple product, we prove the multiplicativity or anti-multiplicativity of ${\Phi}$. Finally, we show that if ${\mathcal{A}}$ and ${\mathcal{B}}$ are two prime operator ${\ast}$-algebras, ${\Psi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves ${\ast}$-Jordan triple product, then ${\Psi}$ is a ${\mathbb{C}}$-linear or conjugate ${\mathbb{C}}$-linear ${\ast}$-isomorphism.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.431-436
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i\;:\;y_i,\;for\;i\;=\;1,\;2,\;{\cdots},\;n$. In this article, we obtained the following : $Let\;x\;=\;\{x_i\}\;and\;y=\{y_\}$ be two vectors in a separable complex Hilbert space H such that $x_i\;\neq\;0$ for all $i\;=\;1,\;2;\cdots$. Let L be a commutative subspace lattice on H. Then the following statements are equivalent. (1) $sup\;\{\frac{\$\mid${\sum_{k=1}}^l\;\alpha_{\kappa}E_{\kappa}y\$\mid$}{\$\mid${\sum_{k=1}}^l\;\alpha_{\kappa}E_{\kappa}x\$\mid$}\;:\;l\;\in\;\mathbb{N},\;\alpha_{\kappa}\;\in\;\mathbb{C}\;and\;E_{\kappa}\;\in\;L\}\;<\;\infty\;and\;$\mid$y_n\$\mid$x_n$\mid$^{-1}\;=\;1\;for\;all\;n\;=\;1,\;2,\;\cdots$. (2) There exists an operator A in AlgL such that Ax = y, A is a unitary operator and every E in L reduces, A, where AlgL is a tridiagonal algebra.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.449-472
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• 2013

Instructional materials including problem situations or problems or tasks on real-life situations are considered as an important and significant factor to lead a successful math instruction. MiC Textbook is a representative one showing good examples and tasks including fluent realistic situations on the basis of the background of the Freudenthal's theory. This study explores concretely and in detail the type of level of mathematical tasks, by the subject of MiC Textbook. To accomplish this, this study reconstructs and establishes an elaborated analysis framework using 'the cognitive demand level' suggested by Stein, et, al. The cognitive demand level is comprized of four elements such as Memorization Tasks, Procedures Without Connections Tasks, Procedures With Connections Tasks, and Doing Mathematics Tasks. Memorization Tasks and Procedures Without Connections Tasks are considered as low level tasks, and Procedures With Connections Tasks and Doing Mathematics Tasks are as high level tasks. MiC Textbook is comprized of the four areas of 'number', 'algebra', 'geometry and measurement', and 'data analysis and statistics'. This study deals with the tasks relevant to Function content dealt with in MiC 3 level Textbook, and explore the level of cognitive demands on each task.

• Journal of Korean Ophthalmic Optics Society
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• v.9 no.2
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• pp.481-489
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• 2004

Poly(triazine bissulfide)s were synthesized from 6-dibutylamino-1,3,5-triazine-2,4-dithiol with bis(4-chloro-3-nitrophenyl)sulfone in the presence of the phase transfer catalyst, and from m-dibromide xylene and p-dibromide xylene with 6-dibutylamino-1,3,5-triazine-2,4-dithiol in the presence of cetyltrimethyl ammonium bromide at $70^{\circ}C$ for 24h. We could acquire the good results about solubility, thermal property, and molecular weight to make cast film. These results are important as base for the synthesis of functionalization polymer material being optical plastic material. The maximum algebra viscosity was 0.57~1.40dl/g at the temperature more than $50{\sim}60^{\circ}C$.

• Electronics and Telecommunications Trends
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• v.36 no.2
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• pp.32-42
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• 2021

The rapid growth of deep-learning applications has invoked the R&D of artificial intelligence (AI) processors. A dedicated software framework such as a compiler and runtime APIs is required to achieve maximum processor performance. There are various compilers and frameworks for AI training and inference. In this study, we present the features and characteristics of AI compilers, training frameworks, and inference engines. In addition, we focus on the internals of compiler frameworks, which are based on either basic linear algebra subprograms or intermediate representation. For an in-depth insight, we present the compiler infrastructure, internal components, and operation flow of ETRI's "AI-Ware." The software framework's significant role is evidenced from the optimized neural processing unit code produced by the compiler after various optimization passes, such as scheduling, architecture-considering optimization, schedule selection, and power optimization. We conclude the study with thoughts about the future of state-of-the-art AI compilers.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.401-408
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• 2014

If A is a unital Banach algebra, then the spectrum can be viewed as a function ${\sigma}$ : 𝕬 ${\rightarrow}$ 𝕾, mapping each T ${\in}$ 𝕬 to its spectrum ${\sigma}(T)$, where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of $\mathbb{C}$. This paper is concerned with the continuity of the spectrum ${\sigma}$ via Browder's theorem. It is shown that ${\sigma}$ is continuous when ${\sigma}$ is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.