• Korean Journal of Mathematics
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• 제31권1호
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• pp.25-33
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• 2023

This paper's objectives are to present the $\mathcal{H}$ class of analytical functions and explore the many characteristics of the functions that belong to this class. Some inequalities regarding the angular derivative have been discovered for the functions in this class. In addition, the symmetry points on the unit disc are used for the obtained inequalities.

• 한국농공학회지
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• 제18권1호
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• pp.4071-4078
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• 1976

The authors analyzed the seepage by means of the following mathmatical solutions of the Laplace Equations on the given boundary conditions. The boundaries of the flow region are of two types i) impervious boundaries (${\Phi}$=constant), and ii) reservoir boundaries (${\Phi}$=constant). The corresponding w plane, bounding the flow region, is the rectangle in Fig. 8-a. As the z plane and w plane are both polygons, by means of the Schwarz-Christoffel transformation the flow region in each of these planes can be mapped con for mally onto the same half of an auxiliary t plane, there by yielding, say, the functions z=f1(t) and w=f2(t). Then, either by eliminating the variable t or by using t as a parameter, the function w=f(z) can be established.

• Korean Journal of Mathematics
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• 제26권2호
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• pp.191-214
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• 2018

The aim of this paper is to investigate the Fekete $Szeg{\ddot{o}}$ inequality for subclass of analytic functions defined by convolution between generalized Al-Oboudi differential operator and Srivastava-Attiya integral operator. Further, application to fractional derivatives are also given.

• 대한수학회논문집
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• 제36권4호
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• pp.715-727
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• 2021

In this paper, we give some results an upper bound of Hankel determinant of H₂(1) for the classes of 𝓝 (𝜶). We get a sharp upper bound for H₂(1) = c₃ - c²₂ for 𝓝 (𝜶) by adding z₁, z₂, …, z_n zeros of f(z) which are different than zero. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained. Finally, the sharpness of the inequalities obtained in the presented theorems are proved.

• 대한수학회논문집
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• 제25권4호
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• pp.557-569
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• 2010

Suppose that n is a positive integer. For any real number $\alpha$($\beta$ resp.) with $\alpha$ < 1 ($\beta$ > 1 resp.), let $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) be the class of analytic functions in the unit disk $\mathbb{D}$ with f(0) = f'(0) = $\cdots$ = $f^{(n-1)}(0)$ = $f^{(n)}(0)-1\;=\;0$, Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) > $\alpha$ (Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) < $\beta$ resp.) in $\mathbb{D}$, and for any ${\lambda}\;{\in}\;\bar{\mathbb{D}}$, let $K^{(n)}({\alpha},\;{\lambda})$ $K^{(n)}({\beta},\;{\lambda})$ resp.) denote a subclass of $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) whose elements satisfy some condition about derivatives. For any fixed $z_0\;{\in}\;\mathbb{D}$, we shall determine the two regions of variability $V^{(n)}(z_0,\;{\alpha})$, ($V^{(n)}(z_0,\;{\beta})$ resp.) and $V^{(n)}(z_0,\;{\alpha},\;{\lambda})$ ($V^{(n)}(z_0,\;{\beta},\;{\lambda})$ resp.). Also we shall determine the extreme points of the families of analytic functions which satisfy $f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\alpha})$ ($f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\beta})$ resp.) when f ranges over the classes $K^{(n)}(\alpha)$ ($K^{(n)(\beta)$ resp.) and $K^{(n)}({\alpha},\;{\lambda})$ ($K^{(n)}({\beta},\;{\lambda})$ resp.), respectively.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제36권1호
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• pp.39-57
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• 2022

본 연구는 맥락에서 출발하여 추상화로 나아가는 방식으로 수학 학습을 설명하는 AiC(Abstraction in Context) 이론에 따른 수업이 부정적분과 정적분의 관계에 대한 이해를 촉진하는 지를 파악하는 데 목표를 둔다. 이를 위해 과학고등학교 2학년 학생 8명을 대상으로 설계한 적분 지도 방안에 따라 수업을 실시했으며, 전 수업 과정을 녹화, 녹음한 자료와 활동지 등의 자료를 수집하고 분석하였다. 분석 결과, 연구에 참여한 학생들은 누적 개념이 내재된 맥락에서 출발하여 동료 학생들과 상호 소통하면서 부정적분과 정적분의 관계에 연결되는 세 가지 지식 요소인 '누적함수의 순간 변화율', '부정적분을 이용한 정적분의 계산', '누적함수를 이용한 부정적분의 결정'을 구성하였다. 연구결과를 바탕으로, AiC 관점은 부정적분과 정적분 관계의 학습을 지원하는 잠재력을 가지고 있으며, 이를 다른 학습영역으로 확장하여 고등학교 수학수업을 개선하는 데에도 활용할 수 있음을 논의하였다.

• 한국항만경제학회지
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• 제23권4호
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• pp.216-227
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• 2007

건화물선 발틱운임인 케이프사이즈 운임지수(BCI), 파나막스사이즈 운임지수(BPI), 핸디막스사이즈 운임지수(BSI와 BHSI)들의 인과성과 효율성을 살펴본다. 인과성 분석을 위해 그란저 인과성 방법을 도입하여 BCI는 BPI, BSI, BHSI에 일방 그란저-cause하며, BSI는 BPI, BHSI에 일방 그란저-cause하고, BPI는 BHSI에 일방 그란저-cause함을 보인다. 이에 근거하여 모형을 구성하여 발틱 운임시장은 비효율적임을 보이고 예측능력 비교를 통해 BCI에 의한 발틱 핸디막스 운임의 예측력이 우수하며, 발틱 수퍼막스 운임과 발틱 케이프 사이즈 운임에 의한 발틱 파나막스 운임의 예측이 가장 정확하지 못함을 보인다.

• 한국전자파학회논문지
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• 제23권2호
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• pp.169-176
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• 2012

본 논문에서는 전계 적분 방정식 (Electric Field Integral Equation: EFIE)을 사용하는 모멘트 법의 저주파 오차(low frequency breakdown) 문제를 해결하기 위한 방법으로 루프-스타(loop-star) 기저 함수를 사용하였다. 또한, 모멘트 법의 해를 계산하기 위하여 conjugate gradient method(CGM)과 같은 반복법을 적용할 경우 반복 횟수를 줄이기 위한 기법으로 p-Type Multiplicative Schwarz preconditioner(pMUS)를 이용하였다. 헬름홀쯔 정리(Helmholtz theorem)에 기반한 루프-스타(loop-star) 기저 함수와 주파수 정규화 기법을 이용하여 전계 적분 방정식에서 Rao-Wilton-Glisson(RWG) 기저 함수를 사용하였을 때 발생하는 저주파 오차(low frequency instability) 문제를 해결할 수 있다. 하지만, RWG 기저 함수를 비발산(solenoidal) 성분과 비회전성(irroatational) 성분으로 분해함으로써 발생하는 행렬 방정식의 높은 조건 수(condition number)로 인하여 CGM과 같은 반복법을 사용할 경우 해를 계산하기 위하여 많은 반복 횟수가 요구된다. 본 논문에서는 이러한 문제점을 해결하기 위한 방안으로 pMUS 전제 조건 기법을 이용하여 CGM의 반복 횟수를 줄였다. 수치 해석 결과, pMUS와 같은 희소성(sparsity)을 가진 블럭 대각 전제 조건(Block Diagonal Precondtioner: BDP)과 비교하였을 때 pMUS는 BDP보다 빠르게 해를 계산할 수 있다.

• Asian-Australasian Journal of Animal Sciences
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• 제16권3호
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• pp.435-444
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• 2003

In 1957, Schwarz and Foltz discovered that selenium (Se) was an essential trace mineral and nutritionists then started extensive studies to figure out the metabolic function of this element which has been called as toxic mineral. The discovery that glutathione peroxidase (GSH-Px) contained Se demonstrated a biochemical role for Se as an essential trace element. The major physiological function of Se containing GSH-Px is thought to maintain low levels of $H_2O_2$ and other hydroperoxides in the cell to prevent tissues from peroxidation damages. It is known that the GSH-Px activity is increased when animals were fed high dietary levels of Se. Chemical properties of Se have much in common with sulfur (S) therefore Se would follow the sulfur pathways in its metabolism in animal body. Two sources of Se are available for supplementation of Se in animal feed. Inorganic Se can also exist in selenide (-2), elemental (0), selenite (+4) and selenate (+6) oxidation state with other minerals. When sulfur in S containing amino acids is replaced by Se, organic Se can be made and named "eleno"prior to the name of S containing amino acid, i.e. selenomethionine. Selenium deficiency affects humans as well as animals and dysfunctions such as exudative diathesis, retained placenta, mastitis, liver necrosis, Keshan disease, numerous diseases and cancer. From several centuries ago, Se toxicity was recognized in various animal species and much of the current toxic Se levels has been established largely based upon the controlled toxicity studies used inorganic Se. Toxic effects of Se in animal result in reduced feed intake, growth retardation, ataxia, diarrhea, alopecia and sloughing of hooves. However, several experiments demonstrated that Se deficiencies or toxicities were varied by dietary Se levels and sources. Recent studies demonstrated that the incidence of colorectal and prostate cancer was reduced by approximately 50% when humans consumed 200 ${\mu}g$ of Se daily.

• Journal of Microbiology and Biotechnology
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• 제19권7호
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• pp.718-726
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• 2009

The objective of this study was to develop and validate secondary models that can predict growth parameters of L. monocytogenes Scott A as a function of concentrations (0-3%) of a commercial potassium lactate (PL) and sodium diacetate (SDA) mixture, pH (5.5-7.0), and temperature (4-37DC). A total of 120 growth curves were fitted to the Baranyi primary model that directly estimates lag time (LT) and specific growth rate (SGR). The effects of the variables on L. monocytogenes Scott A growth kinetics were modeled by response surface analysis using quadratic and cubic polynomial models of the natural logarithm transformation of both LT and SGR. Model performance was evaluated with dependent data and independent data using the prediction bias ($B_f$) and accuracy factors ($A_f$) as well as the acceptable prediction zone method [percentage of relative errors (%RE)]. Comparison of predicted versus observed values of SGR indicated that the cubic model fits better than the quadratic model, particularly at 4 and $10^{\circ}C$. The $B_f$and $A_f$for independent SGR were 1.00 and 1.08 for the cubic model and 1.08 and 1.16 for the quadratic model, respectively. For cubic and quadratic models, the %REs for the independent SGR data were 92.6 and 85.7, respectively. Both quadratic and cubic polynomial models for SGR and LT provided acceptable predictions of L. monocytogenes Scott A growth in the matrix of conditions described in the present study. Model performance can be more accurately evaluated with $B_f$and $A_f$and % RE together.