• 대한수학회지
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• 제51권5호
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• pp.1089-1104
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• 2014

An operator $T{\in}L(H)$, is said to belong to k-quasi class $A_n^*$ operator if $$T^{*k}({\mid}T^{n+1}{\mid}^{\frac{2}{n+1}}-{\mid}T^*{\mid}^2)T^k{\geq}O$$ for some positive integer n and some positive integer k. First, we will see some properties of this class of operators and prove Weyl's theorem for algebraically k-quasi class $A_n^*$. Second, we consider the tensor product for k-quasi class $A_n^*$, giving a necessary and sufficient condition for $T{\otimes}S$ to be a k-quasi class $A_n^*$, when T and S are both non-zero operators. Then, the existence of a nontrivial hyperinvariant subspace of k-quasi class $A_n^*$ operator will be shown, and it will also be shown that if X is a Hilbert-Schmidt operator, A and $(B^*)^{-1}$ are k-quasi class $A_n^*$ operators such that AX = XB, then $A^*X=XB^*$. Finally, we will prove the spectrum continuity of this class of operators.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.1-19
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• 2024

In this paper, the notions of strong Connes amenability for certain products of Banach algebras and module extension of dual Banach algebras is investigated. We characterize χ ⊗ η-strong Connes amenability of projective tensor product ${\mathbb{K}}{\hat{\bigotimes}}{\mathbb{H}}$ via χ ⊗ η-σwc virtual diagonals, where χ ∈ 𝕂_* and η ∈ ℍ_* are linear functionals on dual Banach algebras 𝕂 and ℍ, respectively. Also, we present some conditions for the existence of (χ, θ)-σwc virtual diagonals in the θ-Lau product of 𝕂 ×_θ ℍ. Finally, we characterize the notion of (χ, 0)-strong Connes amenability for module extension of dual Banach algebras 𝕂 ⊕ 𝕏, where 𝕏 is a normal Banach 𝕂-bimodule.

• 대한수학회지
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• 제35권2호
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• pp.331-340
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• 1998

We define the spherical non-commutative torus $L_{\omega}$/ as the crossed product obtained by an iteration of l crossed products by actions of, the first action on C( $S^{2n＋l}$). Assume the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus $A_{p}$ with a matrix algebra $M_{m}$ ( ) (m > 1). We prove that $L_{\omega}$/ $M_{p}$ (C) is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{mp}$ (C), and that the tensor product of $L_{\omega}$/ with a UHF-algebra $M_{p{\infty}}$ of type $p^{\infty}$ is isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) $M_{p{\infty}}$ if and only if the set of prime factors of m is a subset of the set of prime factors of p. Furthermore, it is shown that the tensor product of $L_{\omega}$/, with the C＊-algebra K(H) of compact operators on a separable Hilbert space H is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) K(H) if Prim( $L_{\omega}$/) is homeomorphic to $L^{k}$ (n)$\times$ $T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.$T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.e.

• 대한수학회논문집
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• 제31권3호
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• pp.625-635
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• 2016

In this paper, we study certain doubly-warped products which admit gradient Ricci solitons with harmonic Weyl curvature and non-constant soliton function. The metric is of the form $g=dx^2_1+p(x_1)^2dx^2_2+h(x_1)^2\;{\tilde{g}}$ on ${\mathbb{R}}^2{\times}N$, where $x_1$, $x_2$ are the local coordinates on ${\mathbb{R}}^2$ and ${\tilde{g}}$ is an Einstein metric on the manifold N. We obtained a full description of all the possible local gradient Ricci solitons.

• 정보과학회 컴퓨팅의 실제 논문지
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• 제23권7호
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• pp.440-445
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• 2017

전자상거래 발전에 따라 온라인 쇼핑을 이용하는 사람들이 증가하였고 제품 또한 다양해지고 있다. 이러한 추세로 구매자가 만족할 수 있는 정확한 추천시스템의 중요성이 증대되었으며 정확도를 높이기 위한 새로운 방법의 연구가 계속되고 있다. 순환신경망은 시퀀스 학습에 적합한 딥 러닝 방법 중 하나이며 본 연구에서는 추천시스템의 정확도를 높이는 방법으로 구매자의 제품 접근순서를 순환신경망에 적용하여 알고리즘 성능평가를 하였다. 알고리즘 성능평가에는 대표적인 순환신경망 알고리즘과 최적화 알고리즘으로 진행하였다. 순환신경망 알고리즘으로는 RNN, LSTM, GRU 그리고 최적화 알고리즘으로는 Adagrad, RMSProp, Adam optimizer를 사용하였다. 실험 도구로는 구글의 오픈소스 라이브러리인 텐서플로우를 사용하였고 데이터는 RecSys Challenge 2015에서 제공하는 e-commerce session 데이터를 활용하였다. 실험 결과 실험 데이터에 적합한 최적의 하이퍼파라미터를 발굴하고 적용하여 RecSys Challenge 2015 참가자들의 결과와 비교하였다. 상품 접근 순서만을 학습시킨 결과이기 때문에 등수가 높지는 않았지만 기존 추천시스템에 접목한다면 정확도 향상에 기여할 수 있을 것으로 보인다.

• Asian-Australasian Journal of Animal Sciences
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• 제21권1호
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• pp.138-143
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• 2008

A study was conducted to evaluate nutritional value for twenty-one pork muscles. Ten market-weight crossbred pigs (five gilts and five barrows) were used for evaluating proximate chemical composition, cholesterol, total iron, calorie and fatty acid contents. As preliminary analysis revealed no noticeable sex effect, pooled data from both sexes were used for the final analysis. M. rectus femoris had the highest moisture content, while m. latissimus dorsi was lowest in moisture content (p<0.05). Protein content was highest for m. longissimus dorsi and lowest for m. supraspinatus (p<0.05). The tensor fasciae and latissimus dorsi muscles contained the highest intramuscular fat (p<0.05), while rectus femoris, adductor and vastus lateralis were lowest in intramuscular fat content. When simple correlations between chemical values were computed for the pooled dataset from all muscles, intramuscular fat had significant (p<0.05) negative linear relationships with moisture (r = -0.85) and protein (r = -0.51) contents. Calorie levels were not significantly affected by fat content, while rectus femoris and latissimus dorsi muscles showed lowest and highest calorie contents, respectively (p<0.05). Polyunsaturated fatty acid content was highest (p<0.05) for both m. adductor and m. rectus femoris, while it was lowest for m. longissimus dorsi. Collectively, the current study identified a large amount of variation in nutritional characteristics between pork muscles, and the data can be used for the development of muscle-specific strategies to improve eating quality of meats and meat products.

• 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 $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• 대한수학회보
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• 제54권2호
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• pp.443-454
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• 2017

We study a notion of q-frequent hypercyclicity of linear maps between the Banach algebras consisting of operators on a separable infinite dimensional Banach space. We derive a sufficient condition for a linear map to be q-frequently hypercyclic in the strong operator topology. Some properties are investigated regarding q-frequently hypercyclic subspaces as shown in [5], [6] and [7]. Finally, we study q-frequent hypercyclicity of tensor products and direct sums of operators.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권4호
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• pp.287-292
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• 2004

The operator $A \; {\in} \; L(H_{i})$, the Banach algebra of bounded linear operators on the complex infinite dimensional Hilbert space $\cal H_{i}$, is said to be p-hyponormal if $(A^\ast A)^P \geq (AA^\ast)^p$ for $p\; \in \; (0,1]$. Let (equation omitted) denote the completion of (equation omitted) with respect to some crossnorm. Let $I_{i}$ be the identity operator on $H_{i}$. Letting (equation omitted), where each $A_{i}$ is p-hyponormal, it is proved that the commuting n-tuple T = ($T_1$,..., $T_{n}$) satisfies Bishop's condition ($\beta$) and that if T is Weyl then there exists a non-singular commuting n-tuple S such that T = S + F for some n-tuple F of compact operators.

• Structural Engineering and Mechanics
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• 제54권2호
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• pp.239-256
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• 2015

An adaptive-scale damage detection strategy based on a wavelet finite element model (WFEM) for thin plate structures is established in this study. Equations of motion and corresponding lifting schemes for thin plate structures are derived with the tensor products of cubic Hermite multi-wavelets as the elemental interpolation functions. Sub-element damages are localized by using of the change ratio of modal strain energy. Subsequently, such damages are adaptively quantified by a damage quantification equation deduced from differential equations of plate structure motion. WFEM scales vary spatially and change dynamically according to actual needs. Numerical examples clearly demonstrate that the proposed strategy can progressively locate and quantify plate damages. The strategy can operate efficiently in terms of the degrees-of-freedom in WFEM and sensors in the vibration test.