• Title/Summary/Keyword: invariant function

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INVARIANT MEAN VALUE PROPERTY AND 𝓜-HARMONICITY ON THE HALF-SPACE

  • Choe, Boo Rim;Nam, Kyesook
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.3
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    • pp.559-572
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    • 2021
  • It is well known that every invariant harmonic function on the unit ball of the multi-dimensional complex space has the volume version of the invariant mean value property. In 1993 Ahern, Flores and Rudin first observed that the validity of the converse depends on the dimension of the underlying complex space. Later Lie and Shi obtained the analogues on the unit ball of multi-dimensional real space. In this paper we obtain the half-space analogues of the results of Liu and Shi.

WARPED PRODUCT SKEW SEMI-INVARIANT SUBMANIFOLDS OF LOCALLY GOLDEN RIEMANNIAN MANIFOLDS

  • Ahmad, Mobin;Qayyoom, Mohammad Aamir
    • Honam Mathematical Journal
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    • v.44 no.1
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    • pp.1-16
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    • 2022
  • In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

Simplification of Linear Time-Invariant Systems by Least Squares Method (최소자승법을 이용한 선형시불변시스템의 간소화)

  • 추연석;문환영
    • Journal of Institute of Control, Robotics and Systems
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    • v.6 no.5
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    • pp.339-344
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    • 2000
  • This paper is concerned with the simplification of complex linear time-invariant systems. A simple technique is suggested using the well-known least squares method in the frequency domain. Given a high-order transfer function in the s- or z-domain, the squared-gain function corresponding to a low-order model is computed by the least squares method. Then, the low-order transfer function is obtained through the factorization. Three examples are given to illustrate the efficiency of the proposed method.

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Yield Functions Based on the Stress Invariants J2 and J3 and its Application to Anisotropic Sheet Materials (J2 와 J3 불변량에 기초한 항복함수의 제안과 이방성 판재에의 적용)

  • Kim, Y.S;Nguyen, P.V.;Kim, J.J.
    • Transactions of Materials Processing
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    • v.31 no.4
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    • pp.214-228
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    • 2022
  • The yield criterion, or called yield function, plays an important role in the study of plastic working of a sheet because it governs the plastic deformation properties of the sheet during plastic forming process. In this paper, we propose a novel anisotropic yield function useful for describing the plastic behavior of various anisotropic sheets. The proposed yield function includes the anisotropic version of the second stress invariant J2 and the third stress invariant J3. The anisotropic yield function newly proposed in this study is as follows. F(J2)+ αG(J3)+ βH (J2 × J3) = km The proposed yield function well explains the anisotropic plastic behavior of various sheets by introducing the parameters α and β, and also exhibits both symmetrical and asymmetrical yield surfaces. The parameters included in the proposed model are determined through an optimization algorithm from uniaxial and biaxial experimental data under proportional loading path. In this study, the validity of the proposed anisotropic yield function was verified by comparing the yield surface shape, normalized uniaxial yield stress value, and Lankford's anisotropic coefficient R-value derived with the experimental results. Application for the proposed anisotropic yield function to aluminum sheet shows symmetrical yielding behavior and to pure titanium sheet shows asymmetric yielding behavior, it was shown that the yield curve and yield behavior of various types of sheet materials can be predicted reasonably by using the proposed new yield anisotropic function.

WEAK SOLUTIONS FOR THE HAMILTONIAN BIFURCATION PROBLEM

  • Choi, Q-Heung;Jung, Tacksun
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.667-680
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    • 2016
  • We get a theorem which shows the multiple weak solutions for the bifurcation problem of the superquadratic nonlinear Hamiltonian system. We obtain this result by using the variational method, the critical point theory in terms of the $S^1$-invariant functions and the $S^1$-invariant linear subspaces.

Digital Filter Design using the Symbol Pulse Invariant Transformation

  • ;Rokuya Ishii
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.19 no.1
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    • pp.1-9
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    • 1994
  • In general, when IIR digital filter are designed from analog filters, the bilinera transformation and the impluse invariant tramsformation are commonly used. It is known, however, that high frequency response of digital filters designed by these transformations can not be well approximated to the sampled analog signals. In this paper, the symbol pulse invariant transformation is analyzed theoretically so that the symbol pulse invariant transformation which was originally application to a rectangular pulse is newly applied to double rate pulse signals and generic shape pulse signals. Also, the relation of spectra between a transfer function of digital filter and one of analog filter is considered. Further, we apply to design the digital high pass filters using the symbol pulse invariant transformation method.

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A NOTE ON THE BOUNDARY BEHAVIOUR OF THE SQUEEZING FUNCTION AND FRIDMAN INVARIANT

  • Kim, Hyeseon;Mai, Anh Duc;Nguyen, Thi Lan Huong;Ninh, Van Thu
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.5
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    • pp.1241-1249
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    • 2020
  • Let Ω be a domain in ℂn. Suppose that ∂Ω is smooth pseudoconvex of D'Angelo finite type near a boundary point ξ0 ∈ ∂Ω and the Levi form has corank at most 1 at ξ0. Our goal is to show that if the squeezing function s(𝜂j) tends to 1 or the Fridman invariant h(𝜂j) tends to 0 for some sequence {𝜂j} ⊂ Ω converging to ξ0, then this point must be strongly pseudoconvex.

A LOGARITHMIC CONJUGATE GRADIENT METHOD INVARIANT TO NONLINEAR SCALING

  • Moghrabi, I.A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.8 no.2
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    • pp.15-21
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    • 2004
  • A Conjugate Gradiant (CG) method is proposed for unconstained optimization which is invariant to a nonlinear scaling of a strictly convex quadratic function. The technique has the same properties as the classical CG-method when applied to a quadratic function. The algorithm derived here is based on a logarithmic model and is compared to the standard CG method of Fletcher and Reeves [3]. Numerical results are encouraging and indicate that nonlinear scaling is promising and deserves further investigation.

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DYNAMICAL PROPERTIES ON THE ITERATION OF CF-FUNCTIONS

  • Yoo, Seung-Jae
    • Journal of the Chungcheong Mathematical Society
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    • v.12 no.1
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    • pp.1-13
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    • 1999
  • The purpose of this paper is to show that if the Fatou set F(f) of a CF-meromorphic function f has two completely invariant components, then they are the only components of F(f) and that the Julia set of the entire transcendental function $E_{\lambda}(z)={\lambda}e^z$ for 0 < ${\lambda}$ < $\frac{1}{e}$ contains a Cantor bouquet by employing the Devaney and Tangerman's theorem[10].

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