• 대한수학회논문집
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• 제32권3호
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• pp.661-676
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• 2017

Let T be a bounded linear operator acting on a complex Hilbert space ${\mathfrak{H}}$. In this paper we introduce the class, denoted ${\mathcal{Q}}(A(k),m)$, of operators satisfying $T^{m{\ast}}(T^{\ast}{\mid}T{\mid}^{2k}T)^{1/(k+1)}T^m{\geq}T^{{\ast}m}{\mid}T{\mid}^2T^m$, where m is a positive integer and k is a positive real number and we prove basic structural properties of these operators. Using these results, we prove that if P is the Riesz idempotent for isolated point ${\lambda}$ of the spectrum of $T{\in}{\mathcal{Q}}(A(k),m)$, then P is self-adjoint, and we give a necessary and sufficient condition for $T{\otimes}S$ to be in ${\mathcal{Q}}(A(k),m)$ when T and S are both non-zero operators. Moreover, we characterize the quasinilpotent part $H_0(T-{\lambda})$ of class A(k) operator.

• Advances in nano research
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• 제2권1호
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• pp.15-22
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• 2014

In recent years, spins of confined carriers in quantum dots are promising candidates for the logical units in quantum computers. In many concepts developed so far, the individual spin q-bits are being manipulated by magnetic fields, which is difficult to achieve. In the current research the recent developments of spin based quantum computing has been reviewed. Then, Single-hole spin in a molecular quantum dots with less energy and more speed has been electrically manipulated and the results have been compared with the magnetic manipulating of the spin.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.193-208
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• 2006

A modified BFGS algorithm for solving the unconstrained optimization, whose Hessian matrix at the minimum point of the convex function is of rank defects, is presented in this paper. The main idea of the algorithm is first to add a modified term to the convex function for obtain an equivalent model, then simply the model to get the modified BFGS algorithm. The superlinear convergence property of the algorithm is proved in this paper. To compared with the Tensor algorithms presented by R. B. Schnabel (seing [4],[5]), this method is more efficient for solving singular unconstrained optimization in computing amount and complication.

• 대한수학회지
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• 제49권2호
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• pp.379-394
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• 2012

Given an almost complex structure ($\mathbb^{C}^m$, J), $m\geq2$, that is defined by setting $\theta^{\alpha}=dz^{\alpha}+a_{\beta}^{\alpha}d\bar{z}^{\beta}$, ${\alpha}=1,\ldots$,m, to be (1, 0)-forms, we find conditions on ($a_{\beta}^{\alpha}$) for the existence of holomorphic functions an classify the almost complex structures by type ($\nu$,q). Then we determine types for several examples in $\mathbb{C}^2$ and $\mathbb{C}^3$ including the natural almost complex structure on $S^6$.

• 한국자기학회지
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• 제10권1호
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• pp.22-29
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• 2000

Ca-Zr이 치환된 YIG산화물 자성체의 유효 선폭이 마이코로파 진동수 9.43 GHz에서 공동공진기의 섭동법에 의해 측정되었다. 실험장치는 network analyzer, 전자석, 공동 공진기로 구성되었으며, 시편이 삽입된 공진기에서 정자기장의 변화에 따른 공명진동수와 품질인자의 측정치로부터 계산된 마이크로파 자기감수율 텐서의 대각성분에 의해 분석되었다. 유효 선폭은 균일 모드와 스핀파가 축퇴되는 영역에서 급격한 손실을 보이며, 축퇴영역 밖에서도 비교적 큰 손실을 보이고 있다.

• Journal of the Optical Society of Korea
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• 제9권2호
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• pp.74-78
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• 2005

With the fast Q-tensor method, which can model the defect dynamics in a liquid crystal director field, the nucleation and dynamical behavior of defects is modeled. In order to model the defect, hormeotropic aligned liquid crystal cell with step inhomogeneous electrode which has a height of $1\;{\mu}m$ is used. From the simulation, we can observe the nucleation and line of the defect from surface inhomogeneity and the experiment is performed for confirmation. The experimental result is compared with numerical modeling in order to verify the simulation of the defect nucleation.

• 디지털산업정보학회논문지
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• 제17권3호
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• pp.9-15
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• 2021

In this paper, the Embedded MEMS system to the power apparatus used Edge Impulse machine learning tools and therefore an improved predictive system design is implemented. The proposed MEMS embedded system is developed based on nRF52840 system and the sensor with 3-Axis Digital Magnetometer, I2C interface and magnetic measurable range ±120 uT, BM1422AGMV which incorporates magneto impedance elements to detect magnetic field and the ARM M4 32-bit processor controller circuit in a small package. The MEMS embedded platform is consisted with Edge Impulse Machine Learning and system driver implementation between hardware and software drivers using SensorQ which is special queue including user application temporary sensor data. In this paper by experimenting, TensorFlow machine learning training output is applied to the power apparatus for analyzing the status such as "Normal, Warning, Hazard" and predicting the performance at level of 99.6% accuracy and 0.01 loss.

• 대한수학회지
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• 제60권6호
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• pp.1137-1169
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• 2023

Let C be a curve and V → C an orthogonal vector bundle of rank r. For r ≤ 6, the structure of V can be described using tensor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of exceptional isomorphisms between Spin(r, ℂ) and other groups for these r. We analyze these structures in detail, and in particular use them to describe moduli spaces of orthogonal bundles. Furthermore, the locus of isotropic vectors in V defines a quadric subfibration Q_V ⊂ ℙV . Using familiar results on quadrics of low dimension, we exhibit isomorphisms between isotropic Quot schemes of V and certain ordinary Quot schemes of line subbundles. In particular, for r ≤ 6 this gives a method for enumerating the isotropic subbundles of maximal degree of a general V , when there are finitely many.

• 충청수학회지
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• 제13권1호
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.347-359
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• 2018

A Kenmotsu manifold $M^n({\phi},\;{\xi},\;{\eta},\;g)$, (n = 2m + 1 > 3) is called a generalized ${\phi}-recurrent$ if its curvature tensor R satisfies $${\phi}^2(({\nabla}_wR)(X,Y)Z)=A(W)R(X,Y)Z+B(W)G(X,Y)Z$$ for all $X,\;Y,\;Z,\;W{\in}{\chi}(M)$, where ${\nabla}$ denotes the operator of covariant differentiation with respect to the metric g, i.e. ${\nabla}$ is the Riemannian connection, A, B are non-vanishing 1-forms and G is given by G(X, Y)Z = g(Y, Z)X - g(X, Z)Y. In particular, if A = 0 = B then the manifold is called a ${\phi}-symmetric$. Now, a Kenmotsu manifold $M^n({\phi},\;{\xi},\;{\eta},\;g)$, (n = 2m + 1 > 3) is said to be generalized ${\phi}-Ricci$ recurrent if it satisfies $${\phi}^2(({\nabla}_wQ)(Y))=A(X)QY+B(X)Y$$ for any vector field $X,\;Y{\in}{\chi}(M)$, where Q is the Ricci operator, i.e., g(QX, Y) = S(X, Y) for all X, Y. In this paper, we study generalized ${\phi}-recurrent$ and generalized ${\phi}-Ricci$ recurrent Kenmotsu manifolds with respect to quarter-symmetric metric connection and obtain a necessary and sufficient condition of a generalized ${\phi}-recurrent$ Kenmotsu manifold with respect to quarter symmetric metric connection to be generalized Ricci recurrent Kenmotsu manifold with respect to quarter symmetric metric connection.