• Korean Journal of Mathematics
• /
• v.19 no.4
• /
• pp.351-365
• /
• 2011

In the present paper we introduce a new subclass of analytic functions in the unit disc defined by convolution $(f_{\mu})^{(-1)}*f(z)$; where $$f_{\mu}=(1-{\mu})z_2F_1(a,b;c;z)+{\mu}z(z_2F_1(a,b;c;z))^{\prime}$$. Several interesting properties of the class and integral preserving properties of the subclasses are also considered.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.425-441
• /
• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Journal of Korean Society on Water Environment
• /
• v.39 no.1
• /
• pp.1-8
• /
• 2023

Monitoring and prediction of water quality are essential for effective river pollution prevention and water quality management. In this study, a multi-classification model was developed to predict chlorophyll-a (Chl-a) level in rivers. A model was developed using CatBoost, a novel ensemble machine learning algorithm. The model was developed using hourly field monitoring data collected from January 1 to December 31, 2015. For model development, chl-a was classified into class 1 (Chl-a≤10 ㎍/L), class 2 (10<Chl-a≤50 ㎍/L), and class 3 (Chl-a>50 ㎍/L), where the number of data used for the model training were 27,192, 11,031, and 511, respectively. The macro averages of precision, recall, and F1-score for the three classes were 0.58, 0.58, and 0.58, respectively, while the weighted averages were 0.89, 0.90, and 0.89, for precision, recall, and F1-score, respectively. The model showed relatively poor performance for class 3 where the number of observations was much smaller compared to the other two classes. The imbalance of data distribution among the three classes was resolved by using the synthetic minority over-sampling technique (SMOTE) algorithm, where the number of data used for model training was evenly distributed as 26,868 for each class. The model performance was improved with the macro averages of precision, rcall, and F1-score of the three classes as 0.58, 0.70, and 0.59, respectively, while the weighted averages were 0.88, 0.84, and 0.86 after SMOTE application.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.999-1006
• /
• 2018

In this article we consider the class ${\mathcal{A}}(p)$ which consists of functions that are meromorphic in the unit disc $\mathbb{D}$ having a simple pole at $z=p{\in}(0,1)$ with the normalization $f(0)=0=f^{\prime}(0)-1$. First we prove some sufficient conditions for univalence of such functions in $\mathbb{D}$. One of these conditions enable us to consider the class ${\mathcal{A}}_p({\lambda})$ that consists of functions satisfying certain differential inequality which forces univalence of such functions. Next we establish that ${\mathcal{U}}_p({\lambda}){\subsetneq}{\mathcal{A}}_p({\lambda})$, where ${\mathcal{U}}_p({\lambda})$ was introduced and studied in [2]. Finally, we discuss some coefficient problems for ${\mathcal{A}}_p({\lambda})$ and end the article with a coefficient conjecture.

• Journal of the Korean Mathematical Society
• /
• v.41 no.4
• /
• pp.617-627
• /
• 2004

Let (equation omitted) denote the class of bounded linear Hilbert space operators with the property that $\midA^2\mid\geq\midA\mid^2$. In this paper we show that (equation omitted)-operators are finitely ascensive and that, for non-zero operators A and B, A (equation omitted) B is in (equation omitted) if and only if A and B are in (equation omitted). Also, it is shown that if A is an operator such that p(A) is in (equation omitted) for a non-trivial polynomial p, then Weyl's theorem holds for f(A), where f is a function analytic on an open neighborhood of the spectrum of A.

• Communications of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.117-133
• /
• 2006

Cameron and Storvick discovered change of scale formulas for Wiener integrals of bounded functions in a Banach algebra S of analytic Feynman integrable functions on classical Wiener space. Yoo and Skoug extended these results to abstract Wiener space for a generalized Fresnel class $F_{A1,A2}$ containing the Fresnel class F(B) which corresponds to the Banach algebra S on classical Wiener space. In this paper, we present a change of scale formula for Wiener integrals of various functions on $B^2$ which need not be bounded or continuous.

• Proceedings of the Korea Concrete Institute Conference
• /
• 1998.04a
• /
• pp.3-8
• /
• 1998

This research is to examine the relationships between viscosity and fluidity according to binders in the super flowing concrete. And this research is described with respect to rheology concept, confined water ratio($\beta_p$) of binders in paste and mortar, also investigated experimentally the relationships between the relative flowing ratio ($\Gamma_m$) and the funneling velocity ratio($R_m$) on the mortar state according to the water binder ratio(W/B) and the dosage of the superplasticizer. From the confined water ratio tests, it is found that $\beta_p$ of the class C fly ash is higher than that of the class F fly and limestone in paste and mortar, therefore class F fly ash and limestone and super flowing concrete. The result of test, the optimum mix condition to the compactibility if satisfied when the replacement ratio is 30% and $K_p$ is 0.8 for the case of fly ash and limestone.

• Communications of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.685-704
• /
• 2021

The purpose of this paper is to establish a very general Cameron-Storvick theorem involving the generalized analytic Feynman integral of functionals on the product function space C²_a,b[0, T]. The function space C_a,b[0, T] can be induced by the generalized Brownian motion process associated with continuous functions a and b. To do this we first introduce the class ${\mathcal{F}}^{a,b}_{A_1,A_2}$ of functionals on C²_a,b[0, T] which is a generalization of the Kallianpur and Bromley Fresnel class ${\mathcal{F}}_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick theorem on the product function space C²_a,b[0, T]. Finally we use our Cameron-Storvick theorem to obtain several meaningful results and examples.

• Communications of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.663-677
• /
• 2023

The purpose of this paper is to introduce a new class of rings containing the class of SFT-rings and contained in the class of rings with Noetherian prime spectrum. Let A be a commutative ring with unit and I be an ideal of A. We say that I is SFT if there exist an integer k ≥ 1 and a finitely generated ideal F ⊆ I of A such that x^k ∈ F for every x ∈ I. The ring A is said to be nonnil-SFT, if each nonnil-ideal (i.e., not contained in the nilradical of A) is SFT. We investigate the nonnil-SFT variant of some well known theorems on SFT-rings. Also we study the transfer of this property to Nagata's idealization and the amalgamation algebra along an ideal. Many examples are given. In fact, using the amalgamation construction, we give an infinite family of nonnil-SFT rings which are not SFT.

• Proceedings of the Korean Institute of Building Construction Conference
• /
• 2022.11a
• /
• pp.63-64
• /
• 2022

In this study, the quality of mineral admixture, Comparison of blast-furnace slag(BS) and fly ash(FA)in Korea and China. In the case of BS, Korea is mainly classified into 1 type to 4 types according to the specific surface area, whereas China is classified into S105, 95, and 75 according to the activity index of 28 days of age. In the case of FA, Korea is like BS, is mainly classified into types 1 to 4 according to specific surface area, whereas China is classified into F, C (class F, class C) by ingredients and class I, II, and III according to powder and ignition loss.