• Kyungpook Mathematical Journal
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• 제63권2호
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• pp.235-250
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• 2023

Let 1 ≤ p, q < ∞ be fixed, and let R = [r_jk] be an infinite scalar matrix such that 1 ≤ r_jk < ∞ and sup_j,k r_jk < ∞. Let 𝓑(𝑙_p, 𝑙_q) be the set of all bounded linear operator from 𝑙_p into 𝑙_q. For a fixed Banach algebra 𝐁 with identity, we define a new vector space S^R_p,q(𝐁) of infinite matrices over 𝐁 and a paranorm G on S^R_p,q(𝐁) as follows: let $$S^R_{p,q}({\mathbf{B}})=\{A:A^{[R]}{\in}{\mathcal{B}}(l_p,l_q)\}$$ and $G(A)={\parallel}A^{[R]}{\parallel}^{\frac{1}{M}}_{p,q}$, where $A^{[R]}=[{\parallel}a_{jk}{\parallel}^{r_{jk}}]$ and M = max{1, sup_j,k r_jk}. The existance of S^R_p,q(𝐁) equipped with the paranorm G(·) including its completeness are studied. We also provide characterizations of β -dual of the paranormed space.

• 한국산업융합학회 논문집
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• 제6권3호
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• pp.171-176
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• 2003

The poly(triazine bissulfide) 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, the maximum algebra viscosity (0.57 dL/g) is stable at reaction temperature of $60^{\circ}C$ overall. We could not acquire the good result about solubility, thermal property, and molecular weight to make cast film, we made base for the synthesis of functionalization polymer material.

• 대한수학회논문집
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• 제37권1호
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• pp.259-267
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• 2022

We use L_∞ models to compute the rational homotopy type of the mapping space of the component of the natural inclusion i_n,k : ℂPⁿ ↪ ℂP^n+k between complex projective spaces and show that it has the rational homotopy type of a product of odd dimensional spheres and a complex projective space. We also characterize the mapping aut₁ ℂPⁿ → map(ℂPⁿ, ℂP^n+k; i_n,k) and the resulting G-sequence.

• 대한수학회보
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• 제57권1호
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• 대한수학교육학회지:수학교육학연구
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• 제18권2호
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• pp.239-261
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• 2008

본 연구는 TIMSS 2003 결과를 토대로 우리나라 중학생들의 수학 성취도를 내용 영역별로 싱가포르, 대만, 홍콩, 일본과 비교한 것이다. 우리나라는 구성형과 선다형 문항 모두에서 싱가포르에 비해 정답률이 낮았으며 일본에 비해서는 선다형 문항의 정답률이 더 높은 것으로 나타났다. 내용 영역별 평균 정답률을 보면, 우리나라는 수 영역에서 싱가포르보다 낮았는데, 특히 '비 비율 백분율'의 차이가 컸다. 대수 영역의 하위 주제 정답률은 높았지만 측정 영역, 특히 '속성과 단위'에서는 정답률이 5개국 중 가장 낮았다. 기하 영역에서는 평균 정답률이 가장 높았으나, '평면도형과 입체도형', '대칭과 변환'에서는 높지 않았다. 자료 영역에서도 정답률이 높지 않았는데 우리나라 학생들이 중앙값, 범위, 분포 상태, 자료를 통해 미지의 값 추정하기, 자료 해석에 대하여 평가하기 등의 내용에 대한 학습 경험이 부족한 것에 그 원인이 있을 수 있다. 문항 분석 결과, 우리나라 정답률이 국제 평균보다 35% 이상 높은 문항은 194개 중 42개로서 수 10개, 대수 9개, 측정 10개, 기하 7개, 자료 6개였고, 국제 평균보다 낮은 문항은 측정, 기하, 자료 영역에 각각 하나씩 있었다. 또한 우리나라보다 전체 성취도 순위가 높았던 싱가포르에 비해 정답률이 20% 이상 낮았던 문항은 10개가 있었다.

• 대한수학회보
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• 제54권4호
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• pp.1373-1386
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• 2017

In this paper, we introduce and explore suggested notions of 'above', 'below' and 'between' in general groupoids, Bin(X), as well as in more detail in several well-known classes of groupoids, including groups, semigroups, selective groupoids (digraphs), d/BCK-algebras, linear groupoids over fields and special cases, in order to illustrate the usefulness of these ideas. Additionally, for groupoid-classes (e.g., BCK-algebras) where these notions have already been accepted in a standard form, we look at connections between the several definitions which result from our introduction of these ideas as presented in this paper.

• Steel and Composite Structures
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• 제3권5호
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• pp.307-320
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• 2003

This paper presents an efficient approach to the determination of the buckling loads of down-aisle, spliced, unbraced, pallet rack structures subjected to vertical and horizontal loads. A pallet rack structures is analysed by considering the stability equations of an equivalent free-sway column. The effects of semi-rigid beam-to-upright, splice-to-upright and base-plate-to-upright connections are fully incorporated into the analysis. Each section of upright between successive beam levels in the pallet rack is considered to be a single column element with two rotational degrees of freedom. A computer algebra package was used to determine modified stability equations for column elements containing splices. The influence of the position of splices in a pallet rack is clearly demonstrated.

• 대한수학회논문집
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• 제24권1호
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• pp.5-16
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• 2009

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $$\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)$$ for a fixed positive integer m with $m\;{\geq}\;2$. This is applied to investigate derivations and their stability on proper Lie $CQ^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• 대한수학회지
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• 제44권4호
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• Journal of Information Technology Applications and Management
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• 제12권1호
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• pp.35-48
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• 2005

An architectural framework is developed for integrating geospatial and temporal data with relational information from which a spatio-temporal data warehouse (STDW) system is built. In order to implement the STDW, a generic conceptual model was designed that accommodated six dimensions: spatial (map object), temporal (time), agent (contractor), management (e.g. planting) and tree species (specific species) that addressed the 'where', 'when', 'who', 'what', 'why' and 'how' (5W1H) of the STDW information, respectively. A formal algebraic notation was developed based on a triplet schema that corresponded with spatial, temporal, and relational data type objects. Spatial object structures and spatial operators (spatial selection, spatial projection, and spatial join) were defined and incorporated along with other database operators having interfaces via the generic model.