• The Pure and Applied Mathematics
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• v.11 no.2
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• pp.149-154
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• 2004

We show that the Choquet boundary of the tensor product of two real function algebras is the product of their Choquet boundaries.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.127-139
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• 1997

The spherical non-commutative $\mathbb{S}_{\omega}$ were defined in [2,3]. Assume that no non-trivial matrix algebra can be factored out of the $\mathbb{S}_{\omega}$, and that the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus with a matrix algebra $M_k(\mathbb{C})$. It is shown that the tensor product of the spherical non-commutative torus $\mathbb{S}_{\omega}$ with the even Cuntz algebra $\mathcal{O}_{2d}$ has a trivial bundle structure if and only if k and 2d - 1 are relatively prime, and that the tensor product of the spherical non-commutative torus $S_{\omega}$ with the generalized Cuntz algebra $\mathcal{O}_{\infty}$ has a non-trivial bundle structure when k > 1.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.107-111
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• 2000

We study Einstein warped product spaces. As a result, we prove the following: if M is an Einstein warped product space with base a compact 2-dimensional surface, then M is simply a Riemannian product space.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.269-277
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• 2005

The tensor product $A{\bigotimes}B$ of Hilbert space operators A and B will be shown to be log-hyponormal if and only if A and Bare log-hyponormal. Some general comments about generalized hyponormality are also made.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.751-760
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• 2021

We study in this paper the right Rényi mean for a quantum divergence induced from the α - z Rényi relative entropy. Many properties including homogeneity, invariance under permutation, repetition and unitary congruence transformation, and determinantal inequality have been presented. Moreover, we give the identity of two right Rényi means with respect to tensor product.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.977-1003
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• 2019

Let 𝓐 and 𝓑 be two unital C^⁎-algebras and 𝓐 ⊗ 𝓑 be their algebraic tensor product. For two bilinear maps on 𝓐 and 𝓑 with some specific conditions, we derive a bilinear map on 𝓐 ⊗ 𝓑 and study some characteristics. Considering two 𝓐 ⊗ 𝓑 bimodules, a centralizer is also obtained for 𝓐 ⊗ 𝓑 corresponding to the given bilinear maps on 𝓐 and 𝓑. A relationship between orthogonal complements of subspaces of 𝓐 and 𝓑 and their tensor product is also deduced with suitable example.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.1
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• pp.137-143
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• 2017

In this paper, we investigate static control of Boolean networks described in the framework of semi-tensor product (STP) operation. The control objective is to determine control input nodes and their logical values so as to stabilize the considered Boolean network to a desired fixed point or cycle. Using topology of Boolean networks such as incidence matrix and hub nodes, a set of appropriate control input nodes is selected, and based on STP operations, we assign constant control inputs so that the controlled network can converge to a prescribed fixed point or cycle. To validate applicability of the proposed scheme, we conduct a numerical study on the problem of determining control input nodes for a Boolean network representing hierarchical differentiation of myeloid progenitors.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.545-557
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• 2015

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G₁ and G₂ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

• Proceedings of the KSMRM Conference
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• 2001.11a
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• pp.57-63
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• 2001

Tensor 하면 최근 3D로 white matter내의 섬유질을 멋있게 그려내는 diffusion tensor를 연상합니다. 하지만 여기서 다룰 tensor는 수학적 연산자(operator)입니다. NMR 혹은 MRI에서 스핀을 vector로 표시하고, 이 vector 스핀이 90도 rf pulse에 의해서 z축에서 x-y Plane으로 rotation되는 것을 vector diagram으로 나타냅니다. 그런데 이 vector notation으로는 스핀에 일어나는 여러 현상들을 수식적으로 모델 하는데 한계가 있습니다. 그래서 도입된 모델이 product operator와 tensor operator입니다 (1, 2, 3). 한 예로 우리가 다루는 proton NMR 신호가 single quantum인데 23Na 등에는 multiple quantum 신호가 생기게 되며 이는 vector로는 나타낼 수가 없으며 tensor로 분석이 가능합니다 (4, 5).

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1069-1077
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• 2013

Several authors investigated the properties which are invariant under the passage from a group to its nonabelian tensor square. In the present note we study this problem from the viewpoint of the classes of groups and the methods allow us to prove a result of invariance for some geometric properties of discrete groups.