• Honam Mathematical Journal
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• v.38 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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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 $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• Journal of the Korean Society of Clothing and Textiles
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• v.44 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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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).

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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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.

• Proceedings of the Korea Contents Association Conference
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• 2003.11a
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• pp.245-248
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• 2003

We construct a universal derivation module of an R-algebra which is constructed by means of a tensor product of three copies of the algebras.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.39 no.6
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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.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.265-270
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• 1995

Let $K_1, \ldots, K_n$ be fields of transcendence degrees $t_1, \ldots, t_n$ respectively over a common subfield F. O'Carroll and Qureshi [7] conjectured that the tensor product $R = K_1 \otimes K_2 \otimes \ldots \otimes K_n$ is an equidimensional Hilbert ring and proved the conjecture in special cases. Trung proved the conjecture [9] and O'Carroll, Bowman and Howie [3,5] generalized the Trung's result in two directions and obtained two theorems stated below.