• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.705-714
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• 2023

Bennis and El Hajoui have defined a (commutative unital) ring R to be S-coherent if each finitely generated ideal of R is a S-finitely presented R-module. Any coherent ring is an S-coherent ring. Several examples of S-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the S-coherent property to trivial ring extensions and amalgamated duplications.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.663-677
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• 2023

The purpose of this paper is to introduce a new class of rings containing the class of SFT-rings and contained in the class of rings with Noetherian prime spectrum. Let A be a commutative ring with unit and I be an ideal of A. We say that I is SFT if there exist an integer k ≥ 1 and a finitely generated ideal F ⊆ I of A such that x^k ∈ F for every x ∈ I. The ring A is said to be nonnil-SFT, if each nonnil-ideal (i.e., not contained in the nilradical of A) is SFT. We investigate the nonnil-SFT variant of some well known theorems on SFT-rings. Also we study the transfer of this property to Nagata's idealization and the amalgamation algebra along an ideal. Many examples are given. In fact, using the amalgamation construction, we give an infinite family of nonnil-SFT rings which are not SFT.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1309-1320
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• 2023

Let f : X → Y be a map between simply connected CW-complexes of finite type with X finite. In this paper, we prove that the rational cohomology of mapping spaces map(X, Y ; f) contains a polynomial algebra over a generator of degree N, where N = max{i, π_i(Y)⊗ℚ ≠ 0} is an even number. Moreover, we are interested in determining the rational homotopy type of map(𝕊ⁿ, ℂP^m; f) and we deduce its rational cohomology as a consequence. The paper ends with a brief discussion about the realization problem of mapping spaces.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.45-58
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• 2024

Let R be a commutative ring with identity. If the nilpotent radical N il(R) of R is a divided prime ideal, then R is called a ϕ-ring. Let R be a ϕ-ring and S be a multiplicative subset of R. In this paper, we introduce and study the class of nonnil-S-coherent rings, i.e., the rings in which all finitely generated nonnil ideals are S-finitely presented. Also, we define the concept of ϕ-S-coherent rings. Among other results, we investigate the S-version of Chase's result and Chase Theorem characterization of nonnil-coherent rings. We next study the possible transfer of the nonnil-S-coherent ring property in the amalgamated algebra along an ideal and the trivial ring extension.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.563-574
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• 2024

Given a sequence of point blow-ups of smooth n-dimensional projective varieties Z_i defined over an algebraically closed field $k,\,Z_s\,{\overset{{\pi}_s}{\longrightarrow}}\,Z_{s-1}\,{\overset{{\pi}_{s-1}}{\longrightarrow}}\,{\cdots}\,{\overset{{\pi}_2}{\longrightarrow}}\,Z_1\,{\overset{{\pi}_1}{\longrightarrow}}\,Z_0$, with Z₀ ≅ ℙⁿ, we give two presentations of the Chow ring A^•(Z_s) of its sky. The first one uses the classes of the total transforms of the exceptional components as generators and the second one uses the classes of the strict transforms ones. We prove that the skies of two sequences of point blow-ups of the same length have isomorphic Chow rings. Finally we give a characterization of the final divisors of a sequence of point blow-ups in terms of some relations defined over the Chow group of zero-cycles A₀(Z_s) of its sky.

• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1155-1170
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• 2024

The concept of orthogonality is widely used in various fields of study, both within and outside the scope of mathematics, especially algebra. The concept of orthogonality gives a picture of the relationship between two vectors that are perpendicular to each other, or the inner product in both of them is zero. However, the concept of orthogonality has undergone significant development. One of the developments is Pythagorean orthogonality. In this paper, it is explored topics related to Pythagorean orthogonality and linear mappings in inner product spaces. It is also examined how linear mappings preserve Pythagorean orthogonality and provides insights into how mathematical transformations affect geometric relationships. The results reveal several properties that apply to linear mappings preserving Pythagorean orthogonality.

• 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.

• 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 $50{\sim}60^{\circ}C$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• 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.