• Communications of Mathematical Education
• /
• v.37 no.4
• /
• pp.569-590
• /
• 2023

The purpose of this case study is to compare and analyze the covariational reasoning levels of two middle school students revealed in the process of solving and generalizing algebra word problems. A class was conducted with two middle school students who had not learned quadratic equations in school mathematics. During the retrospective analysis after the class was over, a noticeable difference between the two students was revealed in solving algebra word problems, including situations where speed changes. Accordingly, this study compared and analyzed the level of covariational reasoning revealed in the process of solving or generalizing algebra word problems including situations where speed is constant or changing, based on the theoretical framework proposed by Thompson & Carlson(2017). As a result, this study confirmed that students' covariational reasoning levels may be different even if the problem-solving methods and results of algebra word problems are similar, and the similarity of problem-solving revealed in the process of solving and generalizing algebra word problems was analyzed from a covariation perspective. This study suggests that in the teaching and learning algebra word problems, rather than focusing on finding solutions by quickly converting problem situations into equations, activities of finding changing quantities and representing the relationships between them in various ways.

• Journal for History of Mathematics
• /
• v.13 no.2
• /
• pp.95-104
• /
• 2000

This paper is a sequel to [24]. It is well known that the order structure plays the important role in the study of various mathematical structures. In 1972, Scott has introduced a concept of continuous lattices and has shown the equivalence between continuous lattices and injective $T_0-spaces$. There have been many efforts made to generalize continuous lattices and extend corresponding properties to them. We introduce another class of frames, namely countably approximating frames, generalizing continuous frames and study its basic properties.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.405-413
• /
• 2005

We consider the connections $\nabla$ on the Rizza manifold (M, J, L) satisfying ${\nabla}G=0\;and\;{\nabla}J=0$. Among them, we derive a Lichnerowicz connection from the Cart an connection and characterize it in terms of torsion. Generalizing Kahler condition in Hermitian geometry, we define a Kahler condition for Rizza manifolds. For such manifolds, we show that the Cartan connection and the Lichnerowicz connection coincide and that the almost complex structure J is integrable.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.1
• /
• pp.105-113
• /
• 2012

Generalizing modular lattices, a concept of modular ordered sets was introduced by Chajda and Rachunek. In this paper, we characterize modular ordered sets as those partially ordered set P satisfying that for $a,\;b,\;c\;{\in}\;P\;with\;b\;{\leq}\;c,\;l(a,\;b)\;=\;l(a,\;c)\;and\;u(a,\;b)\;=\;u(a,\;c)$ imply $b\;=\;c$. Using this, we obtain a sufficient condition for them. We also discuss the modularity of the Dedekind-MacNeille completions of ordered sets.

• Journal of applied mathematics & informatics
• /
• v.41 no.6
• /
• pp.1303-1315
• /
• 2023

In this paper, the degenerate q-Bernoulli polynomials are defined by generalizing it more, and various properties of these polynomials are introduced. To do this, we define generating functions of them and use the definition to introduce some interesting properties. Finally, we observe the structure of the roots for the degenerate q-Bernoulli polynomials.

• Journal for History of Mathematics
• /
• v.20 no.3
• /
• pp.59-72
• /
• 2007

In this paper we find the germ of geometric interpretation of complex number in the Euclid Element and try to show the evolution of geometric interpretation of complex number by through Descarte, Wallis, Vessel. As a result, relations and differences between them are found. They related line with complex number and interpreted complex number geometrically by generalizing the multiplication operation.

• Proceedings of the Korea Inteligent Information System Society Conference
• /
• 2004.11a
• /
• pp.171-178
• /
• 2004

This study suggests a general paradigm enhancing genetic mutability. Mutability among heterogeneous members in a genetic population has been a major problem in application of genetic programming to diverse business problems. This suggested paradigm is implemented to developing new methods from existing methods. Within the evolutionary approach taken to designing new methods, a general representation scheme of the genetic programming framework, called a kernel, is introduced. The kernel is derived from the literature of algorithms and heuristics for combinatorial optimization problems. The commonality and differences among these methods have been identified and again combined by following the genetic inheritance merging them. The kernel was tested for selected methods in combinatorial optimization. It not only duplicates the methods in the literature, it also confirms that each of the possible solutions from the genetic mutation is in a valid form, a running program. This evolutionary method suggests diverse hybrid methods in the form of complete programs through evolutionary processes. It finally summarizes its findings from genetic simulation with insight.

• Asian Oncology Nursing
• /
• v.8 no.1
• /
• pp.40-49
• /
• 2008

Purpose: This descriptive study was to investigate the quality of life in patients with hematopoietic stem cell transplantation (HSCT) from June 1 to October 13, 2007. Method: The survey was conducted in 6 different university hospitals which located in Seoul and Jeollanam-do province using the Functional Assessment of Cancer Therapy-BMT Scale (FACT-BMT) version 4. We collected a total of 155 questionnaires and analyzed 149 among them. Results: The average score of quality of life was 2.53 out of 5. Physical well being score was highest among sub-domains, followed by emotional well-being, additional concerns, social/family well-being, and functional well-being. Study subjects worried that their conditions would get worse. However study subjects didn't regret having been received HSCT. Age, duration from HSCT, age at diagnosis, income, readmission, HSCT type, educational background, marital status, and the level of activities of daily living were related to quality of life. Conclusions: The findings of this study indicates that the HSCT survivor's quality of life issue is still important and have to be investigated repeatedly in the future. That is necessary for generalizing QOL outcomes for clinical use. We also suggest to develop interventions to improve QOL.

• Korean Journal of Mathematics
• /
• v.23 no.3
• /
• pp.337-355
• /
• 2015

We in this note consider a class of rings which is related to both power-Armendariz and central Armendariz rings, in the spirit of Armendariz and Kaplansky. We introduce central power-Armendariz as a generalization of them, and study the structure of central products of coefficients of zero-dividing polynomials. We also observe various sorts of examples to illuminate the relations between central power-Armendariz and related ring properties.

• Journal of the HCI Society of Korea
• /
• v.7 no.2
• /
• pp.1-10
• /
• 2012

Past studies in HCI explained the cultural characteristics of individual users by generalizing them at the country-level. However, since the usage of devices or online services, which are main research subjects for the HCI field, are personal, cultural categorization by countres may have limitations in explaining the personal behavior. This is because cultural characteristics of individuals may vary even within the same country; moreover, in may vary depending on the product of usage. Therefore, this exploratory study aims to suggest that there may be differences in cultural characteristics not only between countries but also between individuals and product of usage.