• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.459-468
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• 1997

The purpose of this paper is to give some characterizations of homogeneous real hypersurfaces of type A in complex space forms $M_n(c), c \neq 0$, in terms of Lie derivatives.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.936-938
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• 1999

In this Paper, the design of a feedback linearization controller using multilayer neural network is proposed. The Proposed feedback linearization control scheme is designed by finding Lie derivatives from an identified neural networks. Lie derivatives are expressed as a combination of weights and neuron outputs. The proposed method is applied to an antenna arm problem and the simulation results show performance comparisons between the ordinary feedback linearization and the Proposed method.

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.277-283
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• 1978

The first part of this paper is devoted to the study of F-structure satisfying: $F^K+(-)^{K+1}F=0$ and $F^W+(-)^{W+1}F{\neq}0$, for 1$${\geq_-}3$$) has been considered. In the later part some structures involving Lie-derivatives. exterior and co-derivatives have been studied.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.525-535
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• 2017

In this paper, we consider two kinds of derivatives for the shape operator of a real hypersurface in a $K{\ddot{a}}hler$ manifold which are named the Lie derivative and the covariant derivative with respect to the k-th generalized Tanaka-Webster connection ${\hat{\nabla}}^{(k)}$. The purpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of rank two, whose Lie derivative of the shape operator coincides with the covariant derivative of it with respect to ${\hat{\nabla}}^{(k)}$ either in direction of any vector field or in direction of Reeb vector field.

• Journal of Korean Society of Steel Construction
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• v.8 no.3 s.28
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• pp.21-34
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• 1996

A numerical method is presented for computation of eigenvector derivatives used an iterative procedure with guaranteed convergence. An approach for treating the singularity in calculating the eigenvector derivatives is presented, in which a shift in each eigenvalue is introduced to avoid the singularity. If the shift is selected properly, the proposed method can give very satisfactory results after only one iteration. A criterion for choosing an adequate shift, dependent on computer hardware is suggested ; it is directly dependent on the eigenvalue magnitudes and the number of bits per numeral of the computer. Another merit of this method is that eigenvector derivatives with repeated eigenvalues can be easily obtained if the new eigenvectors are calculated. These new eigenvectors lie "adjacent" to the m (number of repeated eigenvalues) distinct eigenvectors, which appear when the design parameter varies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The results are compared with those of Nelson's method which can find the exact eigenvector derivatives. For the case of repeated eigenvalues, a cantilever beam is considered. The results are compared with those of Dailey's method which also can find the exact eigenvector derivatives. The design parameter of the cantilever plate is its thickness, and that of the cantilever beam its height.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.471-482
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• 1995

A complex n-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a comples space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form consists of a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. The induced almost contact metric structure of a real hypersurface M of $M_n(c)$ is denoted by $(\phi, \zeta, \eta, g)$.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.225-233
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• 1995

This paper presents an efficient numerical method for computation of eigenpair derivatives for the real symmetric eigenvalue problem with distinct and multiple eigenvalues. The method has very simple algorithm and gives an exact solution. Furthermore, it saves computer storage and CPU time. The algorithm preserves the symmetry and band of the matrices, allowing efficient computer storage and solution techniques. Thus, the algorithm of the proposed method will be inserted easily in the commercial FEM codes. Results of the proposed method for calculating the eigenpair derivatives are compared with those of Rudisill and Chu's method and Nelson's method which is efficient one in the case of distinct natural frequencies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The design parameter of the cantilever plate is its thickness. For the eigenvalue problem with multiple natural frequencies, the adjacent eigenvectors are used in the algebraic equation as side conditions, they lie adjacent to the m (multiplicity of multiple natural frequency) distinct eigenvalues, which appear when design parameter varies. As an example to demonstrate the efficiency of the proposed method in the case of multiple natural frequencies, a cantilever beam is considered. Results of the proposed method fDr calculating the eigenpair derivatives are compared with those of Bailey's method (an amendation of Ojalvo's work) which finds the exact eigenvector derivatives. The design parameter of the cantilever beam is its height. Data is persented showing the amount of CPU time used to compute the first ten eigenpair derivatives by each method. It is important to note that the numerical stability of the proposed method is proved.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.825-831
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• 2021

The derivative of a polynomial p(z) of degree n, with respect to point α is defined by D_αp(z) = np(z) + (α - z)p'(z). Let p(z) be a polynomial having all its zeros in the unit disk |z| ≤ 1. The Sendov conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a zero of p'(z) within unit distance of each zero. In this paper, we obtain certain results concerning the location of the zeros of D_αp(z) with respect to a specific zero of p(z) and a stronger result than Sendov conjecture is obtained. Further, a result is obtained for zeros of higher derivatives of polynomials having multiple roots.

• Journal of Microbiology
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• v.45 no.5
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• pp.431-440
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• 2007

A silkworm (Bombyx mori L.) extract known to contain naturally occurring iminosugars, including 1-deoxynojirimycin (1-DNJ) derived from the mulberry tree (Morus alba L.), was evaluated in surrogate HCV and HBV in vitro assays. Antiviral activity of the silkworm extract and one of its purified constituents, 1-DNJ, was demonstrated against bovine viral diarrhea virus (BVDV) and GB virus-B (GBV-B), both members of the Flaviviridae family, and against woodchuck hepatitis virus (WHV) and hepatitis B virus (HBV), both members of the Hepadnaviridae family of viruses. The silkworm extract exhibited a 1,300 fold greater antiviral effect against BVDV in comparison to purified 1-DNJ. Glycoprotein processing of BVDV envelope proteins was disrupted upon treatment with the naturally derived components. The glycosylation of the WHV envelope proteins was affected largely by treatment with the silkworm extract than with purified 1-DNJ as well. The mechanism of action for this therapy may lie in the generation of defective particles that are unable to initiate the next cycle of infection as demonstrated by inhibition of GBV-B in vitro. We postulate that the five constituent iminosugars present in the silkworm extract contribute, in a synergistic manner, toward the antiviral effects observed for the inhibition of intact maturation of hepatitis viral particles and may complement conventional therapies. These results indicate that pre-clinical testing of the natural silkworm extract with regards to the efficacy of treatment against viral hepatitis infections can be evaluated in the respective animal models, in preparation for clinical trials in humans.