• The Korean Journal of Applied Statistics
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• v.33 no.4
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• pp.357-364
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• 2020

We review the characteristics of a geometric mean and statistical inferences based on geometric means. We also show that the statistical results obtained by the logarithmic transform and back-transformation are related to geometric means and explain how to interpret the results produced in this process.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.351-358
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• 2014

In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for $$\sum_{k{\leq}N}k^{-1}f(S_k/{\sigma}\sqrt{k})$$, where $S_k$ is the partial sums of strictly stationary mixing random variables with $EX_1=0$ and ${\sigma}^2=EX^2_1+2\sum_{k=1}^{\infty}EX_1X_{1+k}$. We also establish an almost sure limit behaviors of the above sums.

• 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.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.329-342
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• 2016

Motivated essentially by Brychkov's work [1], we evaluate some new integrals involving hypergeometric function and the logarithmic function (including those obtained by Brychkov[1], Choi and Rathie [3]), which are expressed explicitly in terms of Gamma, Psi and Hurwitz zeta functions suitable for numerical computations.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.127-137
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• 1999

An inequality of Ostrowski type for twice differentiable mappings whose derivatives belong to $L_{1}(a,\;b)$ and applications in Numerical Integration and for special means (logarithmic mean, identric mean, p-logarithmic mean etc...) are given.

• Proceedings of the CALSEC Conference
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• 2004.02a
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• pp.89-97
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• 2004

1. Introduction; Fundamental Difference between conventional old commerce and e-commerce？ 2. "Quantity changes into Quality"; Phase transition and Critical phenomena Logarithmic Convergence and Emergence of Quality 3. Networked Small World; Indications from Genomics; Power-Law Ordered Plain Structure of Super-Complex System ⇔ The Structure of e-Biz. 4. Uniquitous Crisis to Ubiquitous Critical Points for the Emergence of Qualified Business with e-strucrure

• KCID journal
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• v.5 no.1
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• pp.20-31
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• 1998

The Power transformation, the modified Power transformation, the logarithmic transformation, the square-root logarithmic transformation, the SMEMAX transformation, the Extreme value type III, the Weibull, the log Pearson type III, the lognormal distributi

• Journal of the Korean Institute of Telematics and Electronics
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• v.6 no.1
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• pp.19-22
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• 1969

Detailed analysis has been developed concerning the transfer function and stability condition of the logarithmic amplifier using a common emitter transistor as a feed-back element. The analysis shows that input current vs output voltage transfer characteristics is accurately ogarithmic through entire operating current, and the time constant depends on input capcitance and collector-emitter equivalent resistance. Also the minimum value of imput capacitance required to stabilize the system is derived.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.65-73
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• 2003

In this work, we use a numerical method to solve the nonlinear integral equation of the second kind when the kernel of the integral equation in the logarithmic function form or in Carleman function form. The solution has a computing time requirement of $0(N^2)$, where (2N +1) is the number of discretization points used. Also, the error estimate is computed.

• East Asian mathematical journal
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• v.35 no.5
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• pp.597-612
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• 2019

In this study, we propose a new logarithmic barrier approach to solve linear programming problem using the projective method of Karmarkar. We are interested in computation of the direction by Newton's method and of the step-size using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. We reinforce our purpose by many interesting numerical simulations proved the effectiveness of the algorithm developed in this work.