• East Asian mathematical journal
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• v.31 no.1
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• pp.127-134
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• 2015

We give a rth conic regular functions with conic quaternion variables in $\mathbb{C}^2$ and obtain a hyper-conjugate harmonic function of conic regular function in conic quaternions in the sense of Clifford analysis.

• The Journal of the Acoustical Society of Korea
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• v.20 no.3
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• pp.8-14
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• 2001

In this paper, we present a new cost function for subband block adaptive algorithm and block conjugate gradient algorithm for noise cancellation of acoustic signal. For the cost function, we process the subband signals with data blocks for each subbands and recombine it a whole data block. After these process, the cost function has a quadratic form in adaptive filter coefficients, it guarantees the convergence of the suggested block conjugate gradient algorithm. And the block conjugate gradient algorithm which minimizes the suggested cost function has better performance than the case of full-band block conjugate gradient algorithm, the computer simulation results of noise cancellation show the efficiency of the suggested algorithm.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.469-477
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• 2024

For a knot in the 3-sphere, the Upsilon invariant is a piecewise linear function defined on the interval [0, 2]. It is known that this invariant of an L-space knot is the Legendre-Fenchel transform (or, convex conjugate) of a certain gap function derived from the Alexander polynomial. To recover an information lost in the Upsilon invariant, Kim and Livingston introduced the secondary Upsilon invariant. In this note, we prove that the secondary Upsilon invariant of an L-space knot is a concave conjugate of a restricted gap function. Also, a similar argument gives an alternative proof of the above fact that the Upsilon invariant of an L-space knot is a convex conjugate of a gap function.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1025-1039
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• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• Proceedings of the Safety Management and Science Conference
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• 2010.11a
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• pp.27-33
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• 2010

The paper proposes the guidelines of application and interpretation for quality and reliability methodologies using deductive or inductive reasoning. The research also reviews Bayesian quality and reliability tools by deductive prior function and inductive posterior function.

• 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.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.461-466
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• 2006

In this paper, an algorithm with a new Armijo-type line search is proposed that ensure global convergence of a correlative Polak-Ribiere conjugate method for the unconstrained minimization of non-convex differentiable function.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.415-422
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• 2018

The Conjugate Finite-Step Length" (CFSL) algorithm is proposed to improve the efficiency and robustness of first order reliability method (FORM) for reliability analysis of highly nonlinear problems. The conjugate FORM-based CFSL is formulated using the adaptive conjugate search direction based on the finite-step size with simple adjusting condition, gradient vector of performance function and previous iterative results including the conjugate gradient vector and converged point. The efficiency and robustness of the CFSL algorithm are compared through several nonlinear mathematical and structural/mechanical examples with the HL-RF and "Finite-Step-Length" (FSL) algorithms. Numerical results illustrated that the CFSL algorithm performs better than the HL-RF for both robust and efficient results while the CFLS is as robust as the FSL for structural reliability analysis but is more efficient.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.17 no.4
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• pp.303-311
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• 2005

The problem of conjugate laminar film condensation of the pure saturated vapor in forced flow over a flat plate has been investigated as boundary layer solutions. A simple and efficient numerical method is proposed for its solution. The interfacial temperature is obtained as a root of 3rd order polynomial for laminar film condensation, and it is presented as a function of the conjugate parameter. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Jacob number, $Ja^{\ast}$, defined by an overall temperature difference, a property ratio R and the conjugate parameter ${\zeta}$. The approximate solutions thus obtained reveal the effects of the conjugate parameter.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.17 no.2
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• pp.191-199
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• 2005

Double pane window system, in which an air layer with a finite width is filled between glasses, is used in order to increase the insulation efficiency. In the present study, a conjugate heat transfer problem of a double pane window system has been studied numerically in order to investigate the effect of an air layer on the heat transmittance of the double pane window system using a finite element method based on P2P1 basis function. In this study on the conjugate heat transfer of a double pane window system, numerically predicted Nusselt numbers with or without conjugate heat transfer effect have been compared with an available existing empirical formula. It has been found that a Nusselt number from an existing formula for an enclosed space is different from that obtained from the present conjugate heat transfer analysis mainly due to the effects of a very high aspect ratio and conjugate heat transfer mechanism. Furthermore, it has been shown that the numerically estimated optimal air thickness of the double pane window system with conjugate heat transfer effect is a little bit longer than that obtained without considering conjugate heat transfer effect.