• Journal for History of Mathematics
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• v.9 no.2
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• pp.30-42
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• 1996

최근 <수학기초론>이란 용어는 Burali-Forti paradox 이후 족(class)과 집합(set) 개념을 이해하려는 시도에서 출발한 20세기적 문제에 적용되고 있다. 이 글에서는 그 해결책으로 제시된 주의ㆍ주장 중 논리적인 모순을 해결하기 위한 Russel의 논리주의적 공리론에 바탕을 두고 살펴보려고 한다. 제 2장에서는 무한의 심연 속에 웅크리고 있는 집합론에서의 역설과 발생 원인에 대하여 살펴보았다. 제 3장에서는 공리론적 집합론 중에서 러셀의 유형론과 그것을 단순화시킨 현대의 유형론을 살펴보고, ZF 집합론과 ZF 집합론의 연장인 처치 집합론의 기본 공리를 살펴보았다.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.175-184
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• 2018

We give several sharp estimates for some initial coefficients problems for the so-called gamma starlike functions f, analytic and univalent in the unit disk ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$, and normalized so that f(0) = 0 = f'(0)-1, and satisfying Re $\left[\left(1+{\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}}\right)^{\gamma}\left({\frac{zf^{\prime}(z)}{f(z)}}\right)^{1-{\gamma}}\right]$ > 0.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.465-481
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• 2021

Let f be the function defined on the open unit disk, with f(0) = 0 = f'(0) - 1, satisfying Re (αf'(z) + (1 - α)zf'(z)/f(z)) > 0 or Re (αf'(z) + (1 - α)(1 + zf"(z)/f'(z)) > 0 respectively, where 0 ≤ α ≤ 1. Estimates for the Toeplitz determinants have been obtained when the elements are the coefficients of the functions belonging to these two subclasses.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.243-258
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• 2023

A normalized analytic function f defined on the unit disk 𝔻 is starlike of reciprocal order α, 0 ≤ α < 1, if Re(f(z)/(zf'(z))) > α for all z ∈ 𝔻. Such functions are starlike and therefore univalent in 𝔻. Using the well-known Miller-Mocanu differential subordination theory, sufficient conditions involving differential inclusions are obtained for a normalized analytic function to be starlike of reciprocal order α. Furthermore, a few conditions are derived for a function f to belong to a subclass of reciprocal starlike functions, satisfying |f(z)/(zf'(z)) - 1| < 1 - α.

• Advances in concrete construction
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• v.9 no.5
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• pp.449-457
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• 2020

The influence of subsequent curing on the performance of fly ash contained mortar under steam curing was studied. Mortar samples incorporated with different content (0%, 20%, 50% and 70%) of Class F fly ash under five typical subsequent curing conditions, including standard curing (ZS), water curing(ZW) under 25℃, oven-dry curing (ZD) under 60℃, frozen curing (ZF) under -10℃, and nature curing (ZN) exposed to outdoor environment were implemented. The unsteady chloride diffusion coefficient was measured by rapid chloride migration test (RCM) to analyze the influence of subsequent curing condition on the resistance to chloride penetration of fly ash contained mortar under steam curing. The compressive strength was measured to analyze the mechanical properties. Furthermore, the open porosity, mercury intrusion porosimetry (MIP), x-ray diffraction (XRD) and thermogravimetric analysis (TGA) were examined to investigate the pore characteristics and phase composition of mortar. The results indicate that the resistance to chloride ingress and compressive strength of steam-cured mortar decline with the increase of fly ash incorporated, regardless of the subsequent curing condition. Compared to ZS, ZD and ZF lead to poor resistance to chloride penetration, while ZW and ZN show better performance. Interestingly, under different fly ash contents, the declining order of compressive strength remains ZS>ZW>ZN>ZD>ZF. When the fly ash content is blow 50%, the open porosity grows with increase of fly ash, regardless of the curing conditions are diverse. However, if the replacement amount of fly ash exceeds a certain high proportion (70%), the value of open porosity tends to decrease. Moreover, the main phase composition of the mortar hydration products is similar under different curing conditions, but the declining order of the C-S-H gels and ettringite content is ZS>ZD>ZF. The addition of fly ash could increase the amount of harmless pores at early age.

• Journal of Microbiology and Biotechnology
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• v.23 no.12
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• pp.1757-1764
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• 2013

Trichoderma harzianum ZF-2 producing laccase was isolated from decaying samples from Shandong, China, and showed dye decolorization activities. The objective of this study was to optimize its culture conditions using a statistical analysis of its laccase production. The interactions between different fermentation parameters for laccase production were characterized using a Plackett-Burman design and the response surface methodology. The different media components were initially optimized using the conventional one-factor-at-a-time method and an orthogonal test design, and a Plackett-Burman experiment was then performed to evaluate the effects on laccase production. Wheat straw powder, soybean meal, and $CuSO_4$ were all found to have a significant influence on laccase production, and the optimal concentrations of these three factors were then sequentially investigated using the response surface methodology with a central composite design. The resulting optimal medium components for laccase production were determined as follows: wheat straw powder 7.63 g/l, soybean meal 23.07 g/l, $(NH_4)_2SO_4$ 1 g/l, $CuSO_4$ 0.51 g/l, Tween-20 1 g/l, $MgSO_4$ 1 g/l, and $KH_2PO_4$ 0.6 g/l. Using this optimized fermentation method, the yield of laccase was increased 59.68 times to 67.258 U/ml compared with the laccase production with an unoptimized medium. This is the first report on the statistical optimization of laccase production by Trichoderma harzianum ZF-2.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.12
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• pp.34-41
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• 2008

In this paper, we present an asymptotical analysis of channel capacity of Bell labs layered space-time (BLAST) architectures based on a zero-forcing (ZF) criterion in the sense of signal-to-noise ratio (SNR). We begin by introducing a new relationship related to multi-input multi-output (MIMO) channel capacity. We prove that Diagonal Bell Labs Space-Time (DBLAST) attains the lower bound for MIMO channels when interference nulling is carried out based on the ZF-criterion. An exact closed-form expression for the probability density function of the channel capacity is analyzed. Based on the asymptotic behavior of the channel capacity of each layer, closed-form expressions for the asymptotic ergodic capacity are derived for BLAST. Based on the analysis presented in this paper, we gain an insight on the channel capacity behavior for a MIMO channel. Computer simulation results have verified the validity and accuracy of the proposed analysis for a wide range of antenna array sizes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.11A
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• pp.1092-1100
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• 2006

In this paper, we propose a full rate quasi-orthogonal space-time-frequency block coded orthogonal frequency division multiplexing(QOSTF-OFDM) that can achieve full symbol rate with four transmit antennas. Sincr: the proposed QOSTF-OFDM can not achieve full diversity, we use diversity advantage collection with zero forcing (DAC-ZF) decoder to compensate the diversity loss at receive side. At the same frequency efficiency, compared with linear orthogonal space-time codes which can not achieve full rate with four transmit antennas over complex constellations, low level modulation can be employed by proposed scheme due to its full rate, i.e., modulation advantage can be achieved. Due to modulation advantage and collected diversify advantage, the proposed scheme exhibits better BER performance than other orthogonal schemes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.3A
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• pp.223-231
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• 2011

It has been shown that the performance of multiple-input multiple-output (MIMO) spatial multiplexing systems is significantly degraded when spatial correlation exists between transmit and receive antenna pairs. In this paper, we investigate designs of a new statistical precoder for spatial multiplexing systems with maximum likelihood (ML) receiver which requires only correlation statistics at the transmitter. Two kinds of closed-form solution precoders based on rotation and power allocation are proposed by means of maximizing the minimum E tlidean distance of joint symbol constellations. In addition, we extend our results to linear receivers for correlated channels. We provide a method which yields the same profits from the proposed precoders based on a simple zero-forcing (ZF) receiver. The simulation shows that 2dB and 8dB gains are achieved for ML and ZF systems with two transmit antennas, respectively, compared to the conventional systems.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.727-749
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• 2015

We obtain the conditions on ${\beta}$ so that $1+{\beta}zp^{\prime}(z){\prec}1+4z/3+2z^2/3$ implies p(z) ${\prec}$ (2+z)/(2-z), $1+(1-{\alpha})z$, $(1+(1-2{\alpha})z)/(1-z)$, ($0{\leq}{\alpha}$<1), exp(z) or ${\sqrt{1+z}}$. Similar results are obtained by considering the expressions $1+{\beta}zp^{\prime}(z)/p(z)$, $1+{\beta}zp^{\prime}(z)/p^2(z)$ and $p(z)+{\beta}zp^{\prime}(z)/p(z)$. These results are applied to obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy the condition ${\mid}log(zf^{\prime}(z)/f(z)){\mid}$ < 1 or ${\mid}(zf^{\prime}(z)/f(z))^2-1{\mid}$ < 1 or zf'(z)/f(z) lying in the region bounded by the cardioid $(9x^2+9y^2-18x+5)^2-16(9x^2+9y^2-6x+1)=0$.