• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.541-545
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• 2007

In this paper, we study the infinitesimal transformation on the fibred Riemannian space. The conharmonic curvature tensor is invariant under the conharmonic transformation. We have proved that the conharmonically flat fibred Riemannian space with totally geodesic fibre is locally the Riemannian product of the base space and a fibre.

• 호남수학학술지
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• 제38권1호
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• pp.39-45
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• 2016

In this paper, we investigate several properties on a weakly symmetric structure on a Riemannian manifold.

• 대한수학회보
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• 제32권2호
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• pp.221-231
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• 1995

Let $Z_1, Z_2, \ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = \smallint gdZ_i$ are well defined. If $g_i = \in g_i (i = 1, 2, \ldots, l) and g_1 \otimes \cdots \otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) \cdots g_l(s_l) for s = (s_1, s_2, \ldots, s_l) and s_i \in S_i$, then we can defined $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• 한국의류학회지
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• 제44권3호
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• pp.556-571
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• 2020

This study predicts consumer preference for social clothing at work, excluding uniforms using the self-product congruence theory that also establishes a model to predict the preference for recommended products that match the consumer's own image. A total of 490 Korean male office workers participated in this study. Participants' self-image and the product images of 20 apparel items were measured using nine adjective semantic scales (namely elegant, stable, sincere, refined, intense, luxury, bold, conspicuous, and polite). A model was then constructed to predict the consumer preferences using a neural network with Python and TensorFlow. The resulting Predict Preference Model using Product Image (PPMPI) was trained using product image and the preference of each product. Current research confirms that product preference can be predicted by the self-image instead of by entering the product image. The prediction accuracy rate of the PPMPI was over 80%. We used 490 items of test data consisting of self-images to predict the consumer preferences for using the PPMPI. The test of the PPMPI showed that the prediction rate differed depending on product attributes. The prediction rate of work apparel with normative images was over 70% and higher than for other forms of apparel.

• 대한수학회논문집
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• 제25권4호
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• pp.615-621
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• 2010

We study pseudo symmetric (briefly $(PS)_n$) and pseudo Ricci symmetric (briefly $(PRS)_n$) warped product manifolds $M{\times}_FN$. If M is $(PS)_n$, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is $(PRS)_n$, then we show that (i) N is Ricci symmetric and (ii) M is $(PRS)_n$ if and only if the tensor T defined by (2.6) satisfies a certain condition.

• 대한수학회논문집
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• 제13권4호
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• pp.759-764
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• 1998

We define the rational lens algebra (equation omitted)(n) as the crossed product by an action of Z on C( $S^{2n＋l}$). Assume the fibres are $M_{ k}$/(C). We prove that (equation omitted)(n) $M_{p}$ (C) is not isomorphic to C(Prim((equation omitted)(n))) $M_{kp}$ /(C) if k > 1, and that (equation omitted)(n) $M_{p{\infty}}$ is isomorphic to C(Prim((equation omitted)(n))) $M_{k}$ /(C) $M_{p{\infty}}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p. It is moreover shown that if k > 1 then (equation omitted)(n) is not stably isomorphic to C(Prim(equation omitted)(n))) $M_{k}$ (c).

• 대한수학회보
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• 제52권1호
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• pp.137-147
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• 2015

We derive in the paper the tensor product functor -${\otimes}_R$- by using proper $\mathcal{GP}_C$-resolutions, where C is a semidualizing module. After giving several cases in which different relative homologies agree, we use the Pontryagin duals of $\mathcal{G}_C$-projective modules to establish a balance result for such relative homology over a Cohen-Macaulay ring with a dualizing module D.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2003년도 추계종합학술대회 논문집
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• pp.245-248
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• 2003

본 논문은 미분가군이 가환대수에서 정의된 미분가군과 임의의 다원환에 대하여 정의된 Bergman 의 관점에서 본 미분가군으로서 보편적 미분가군과 다른 구조를 갖는 미분가군 동형사상에 의하여 유일하게 결정될 수 있다는 것을 밝히는 것이다.

• 대한수학회보
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• 제35권4호
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• pp.757-767
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• 1998

For a Riemannian manifold $(M^n, g)$ we consider the space $V(M^n, g)$ of all smooth functions on $M^n$ whose Hessian is proportional to the metric tensor $g$. It is well-known that if $M^n$ is a space form then $V(M^n)$ is of dimension n+2. In this paper, conversely, we prove that if $V(M^n)$ is of dimension $\ge{n+1}$, then $M^n$ is a Riemannian space form.

• 대한수학회지
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• 제39권6호
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• pp.821-879
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• 2002

Let U, V and W be complex vector spaces of dimensions 3, 3 and 4 respectively. The reductive algebraic group G = PGL(U) $\times$ PGL(W) $\times$ PGL(W) acts linearly on the projective tensor product space (equation omitted). In this paper, we show that the G-equivalence classes of the projective tensors are in one-to-one correspondence with the PGL(3)-equivalence classes of unordered configurations of six points on the projective plane.