• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1221-1233
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• 2021

In this paper, we introduce and investigate a new class of modules that is closely related to the class of Noetherian modules. Let R be a commutative ring and M be an R-module. We say that M is an r-Noetherian module if every r-submodule of M is finitely generated. Also, we call the ring R to be an r-Noetherian ring if R is an r-Noetherian R-module, or equivalently, every r-ideal of R is finitely generated. We show that many properties of Noetherian modules are also true for r-Noetherian modules. Moreover, we extend the concept of weakly Noetherian rings to the category of modules and we characterize Noetherian modules in terms of r-Noetherian and weakly Noetherian modules. Finally, we use the idealization construction to give non-trivial examples of r-Noetherian rings that are not Noetherian.

• Communications of Mathematical Education
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• v.36 no.3
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• pp.335-353
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• 2022

The purpose of this study is to identify the characteristics and types of errors in the conceptual image of Korean language learners according to the types of terms in mathematics that are the basis for solving mathematical word problems, and to prepare basic data for effective teaching and learning methods in solving the word problems of Korean language learners. To do this, a case study was conducted targeting four Korean language learners to analyze the specific conceptual images of terms registered in curriculum and terms that were not registered in curriculum but used in textbooks. As a result of this study, first, it is necessary to guide Korean language learners by using sufficient visualization material so that they can form appropriate conceptual definitions for terms in school mathematics. Second, it is necessary to understand the specific relationship between the language used in the home of Korean language learners and the conceptual image of terms in school mathematics. Third, it is necessary to pay attention to the passive term, which has difficulty in understanding the meaning rather than the active term. Fourth, even for Korean language learners who do not have difficulties in daily communication, it is necessary to instruct them on everyday language that are not registered in the curriculum but used in math textbooks. Fifth, terms in school mathematics should be taught in consideration of the types of errors that reflect the linguistic characteristics of Korean language learners shown in the explanation of terms. This recognition is expected to be helpful in teaching word problem solving for Korean language learners with different linguistic backgrounds.

• School Mathematics
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• v.16 no.2
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• pp.237-257
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• 2014

The purpose of this study is to investigate the academic achievement characteristics in terms of proficiency levels through the in-depth analysis of mathematics test items and achievement standards of the National Assessment of Educational Achievement(NAEA) from 2010 to 2012, and to provide suggestions for teaching and assessing mathematics in middle schools. The results showed that 'Advanced level' students could fully understand the concept of mathematical terms and symbols as well as various mathematical properties presented in the national curriculum. However, 'Proficient level' students tended to feel difficult to apply linear function, properties of a plane figure, and a solid figure, while 'Basic level' students seemed to have trouble solving mathematical problems in almost all areas. Thus, it is necessary to identify the mathematical misconceptions that students have and to strengthen teaching, particularly, the areas of number and operation.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.2
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• pp.192-201
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• 2008

The design process becomes more difficult due to the increasing complexity of products. Thus, without any proper design experience, designer cannot handle his design problems systematically. Besides, the conventional optimal design method cannot be used effectively at the early design stage, since most design problems must be formulated in terms of objective and constraint functions based on the mathematical concepts of Operation Research. Thus, in this paper, new design concept based on FBS (Function-Behavior-Structure) design model is introduced to help the novice designer formulate the complex design problems systematically into a mathematical form. In this FBS model, function means the designer's new intents designer wants to create for, structure stand for a final product configuration and behaviour is a product's performance. FBS design model is thus rather totally different concept used for formulating design problem, compared with conventional optimal design method. To validate this new FBS model, 330K VLCC design case is performed, and we found, though it is one design example case, that this new design concept could be effectively used for future ship design problems since, during the formulating design problem, the only engineering terminology such as function, structure, and behaviour of design product is used based on the engineering concepts, instead of mathematical terminology such as objective and constraints.

• The Mathematical Education
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• v.61 no.2
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• pp.305-322
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• 2022

Angle has a variety of aspects, such as figure, measurement, and rotation, but is mainly introduced from a figure perspective and a quantitative perspective of the angle is also partially experienced in the elementary mathematics textbooks. The purpose of this study was to examine how the angle concept introduction and development pattern in elementary school mathematics textbooks are linked or changed in middle school mathematics textbooks, and based on this, was to get the direction of writing math textbooks and implications for guidance. To this end, 57 math textbooks for the first grade of middle school were collected from the first to the 2015 revised curriculum. As a result of the study, it was found that middle school textbooks had a greater dynamic aspect of each than elementary school textbooks, and the proportion of quantitative attributes of angle was higher in addition to qualitative and relational attributes. In other words, the concept of angle in middle school textbooks is presented in a more multifaceted and complex form than in elementary school textbooks. Finally, matters that require consensus within elementary, secondary, and secondary schools were also proposed, such as the use of visual expression or symbol, such as the use of arrows and dots, and the use of mathematical terms such as vertex of angle and side of angle.

• Geomechanics and Engineering
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• v.16 no.2
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• pp.141-150
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• 2018

In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

• Journal of Educational Research in Mathematics
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• v.12 no.1
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• pp.125-143
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• 2002

The concept of "set" in school mathematics has undergone many changes according to the revision of curriculum and the transition of the paradigm in mathematics education. In the discipline-centered curriculum, a set was a representative concept which reflected the spirit of New Math. After the Back to Basics period, the significance of a set concept in school mathematics has been diminished. First, this paper elaborated several controversial aspects of the terms related to set, such as a collection and a set, a subset, and an empty set. In addition, the changes of the significance imposed to a set concept in school mathematics were investigated. Finally, this paper provided two alternative approaches to introduce and explain a set concept which emphasized both mathematical rigor and learner's psychology.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.579-594
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• 2014

Let R be a ring and $Nil_*$(R) be the prime radical of R. In this paper, we say that a ring R is left $Nil_*$-coherent if $Nil_*$(R) is coherent as a left R-module. The concept is introduced as the generalization of left J-coherent rings and semiprime rings. Some properties of $Nil_*$-coherent rings are also studied in terms of N-injective modules and N-flat modules.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.609-633
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• 2014

From the ordinary notion of uniformly strong mixing for a sequence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mixing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by conditionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1851-1861
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• 2014

We introduce the concept of w-zero-divisor (w-ZD) rings and study its related rings. In particular it is shown that an integral domain R is an SM domain if and only if R is a w-locally Noetherian w-ZD ring and that a commutative ring R is w-Noetherian if and only if the polynomial ring in one indeterminate R[X] is a w-ZD ring. Finally we characterize universally zero divisor rings in terms of w-ZD modules.