• Research in Mathematical Education
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• v.12 no.3
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• pp.179-191
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• 2008

Although problem solving was a major focus of mathematics education research in many countries throughout the 1990s, not enough is known about how people best acquire problem-solving skills. This paper is an attempt to advance further development of problem-solving skills of talented school students through combination of some methods accessible from curriculum knowledge and more special techniques that are beyond curriculum. Analysis of various problems is provided in detail. Educational aspects of challenging problems in mathematical contests up to IMO level are, also, taken into account and discussed in the paper.

• East Asian mathematical journal
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• v.39 no.4
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• pp.479-492
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• 2023

Although Euclidean plane geometry is implemented in the middle school course, there are three major problems in high school space geometry that can be intuitively taken for granted or misinterpreted as circular arguments. In order to solve this problem, this study proved three major problems using sets, Euclidean plane geometry, and parallel line postulates. This corresponds to a logical sequence and has mathematical and mathematical educational values. Furthermore, it will be possible to configure spatial geometry using sets, and by giving legitimacy to non-Euclidean spatial geometry, it will open the possibility of future research.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.2
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• pp.173-178
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• 2007

This paper is to establish an appropriate model for predicting the temperature decreases in the batch transferred from the refining process to the caster in steel-making companies. Mathematical modeling of the temperature decreases between the processes is difficult, since the reaction mechanism by which the temperature changes in a molten steel batch is dynamic, uncertain and complex. Three soft computing techniques are examined using the same data, namely the multiple regression, fuzzy regression, and neural net (NN) models. To compare the accuracy of these three models, a limited number of input variables are selected from those variables significantly affecting the temperature decrease. The results show that the difference in accuracy between the three models is not statistically significant. Nonetheless, the NN model is recommended because of its adaptive ability and robustness. The method presented in this paper allows the temperature decrease to be predicted without requiring any precise metallurgical knowledge.

• Journal of Information Science Theory and Practice
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• v.2 no.4
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• pp.20-30
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• 2014

This study examines the foremost concerns related to most noted research performance index. The most popular and widely acceptable h-index underestimates the highly visible scientist, the middle order group, due to citation distribution issues. The study addresses this issue and uses 'Corrected Quality Ratio' (CQ) to check the implicit underpinnings as evident in h-index. CQ helps to incorporate the aspects of a good research performance indicator. This simple revision performs more intimately and logically to gauge the broader research impact for all groups and highly visible scientists with less statistical error.

• 한국정보디스플레이학회:학술대회논문집
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• 2009.10a
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• pp.509-509
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• 2009

In this presentation, the speaker draws upon his years of research into volumetric display systems. Key content from several books is used as a basis to discuss current activity and to provide a basis for discussion on the next generation of volumetric technologies.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.12
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• pp.184-197
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• 1995

In this paper, high speed IC package-to-package interconnections are modeled as lossless multiconductor transmission lines operating in the TEM mode. And, three mathematical algorithms for computing electrical parameters of the lossless multiconductor transmission lines are described. A semi-analytic Green's function method is used in computing per unit length capacitance and inductance matrices, a matrix square root algorithm based on the QR algorithm is used in computing a characteristic impedance matrix, and a matrix algorithm based on the theory of M-matrix is used in computing a diagonally matched load impedance matrix. These algorithms are implemented in a computer program DIME (DIagonally Matched Load Impedance Extractor) which computes electrical parameters of the lossless multiconductor transmission lines. Also, to illustrate the concept of design database for high speed IC package-to-package interconnection, a database for the multi conductor strip transmission lines system is constructed. This database is constructed with a sufficiently small number of nodes using the multi-dimensional cubic spline interpolation algorithm. The maximum interpolation error for diagonally matched load impedance matrix extraction from the database is 1.3 %.

• Structural Engineering and Mechanics
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• v.74 no.1
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• pp.91-104
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• 2020

A mathematical analysis has been carried out for understanding the traversal attributes of torsional waves in a Voigt-type viscoelastic porous layer bounded with corrugated surfaces resting over a heterogeneous transversely isotropic gravitating semi-infinite medium. Both the media are assumed to be under the effect of initial stresses acting along horizontal directions. In the presumed geometry, continuous and periodic type of corrugation has been considered. The condensed form of dispersion relation has been obtained analytically with the aid of the Whittaker's function and suitable boundary conditions. The influence of viscoelasticity, porosity, initial stresses, heterogeneity, gravity, undulation and position parameters on the phase and damped velocities has been illustrated graphically. In addition, relative examination investigating the impact of corrugated and planar bounded surfaces on the dispersion and damping characteristics is one of the important highlights of this study.

• Structural Engineering and Mechanics
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• v.77 no.3
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• pp.417-439
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• 2021

The geometric nonlinearity has been successfully integrated with the design of steel structural system. Thus, the tubular lattice girder, one application of steel structural systems have already been optimized to obtain an economic design following the completion of computationally expensive design procedure. In order to decrease its computing cost, this study proposes to employ five multi-objective metaheuristics for the design optimization of geometrically nonlinear tubular lattice girder. Then, the employed multi-objective optimization algorithms (MOAs), NSGAII, PESAII, SPEAII, AbYSS and MoCell are evaluated considering their computing performances. For an unbiased evaluation of their computing performance, a tubular lattice girder with varying size-shape-topology and a benchmark truss design with 17 members are not only optimized considering the geometrically nonlinear behavior, but three benchmark mathematical functions along with the four benchmark linear design problems are also included for the comparison purpose. The proposed experimental study is carried out by use of an intelligent optimization tool named JMetal v5.10. According to the quantitative results of employed quality indicators with respect to a statistical analysis test, MoCell is resulted with an achievement of showing better computing performance compared to other four MOAs. Consequently, MoCell is suggested as an optimization tool for the design of geometrically nonlinear tubular lattice girder than the other employed MOAs.

• International Journal of Computer Science & Network Security
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• v.21 no.12spc
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• pp.570-578
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• 2021

Recently, in the field of engineering and scientific and technical calculations, problems of mathematical modeling, real-time problems, there has been a tendency towards rejection of sequential solutions for single-processor computers. Almost all modern application packages created in the above areas are focused on a parallel or distributed computing environment. This is primarily due to the ever-increasing requirements for the reliability of the results obtained and the accuracy of calculations, and hence the multiply increasing volumes of processed data [2,17,41]. In addition, new methods and algorithms for solving problems appear, the implementation of which on single-processor systems would be simply impossible due to increased requirements for the performance of the computing system. The ubiquity of various types of parallel systems also plays a positive role in this process. Simultaneously with the growing demand for parallel programs and the proliferation of multiprocessor, multicore and cluster technologies, the development of parallel programs is becoming more and more urgent, since program users want to make the most of the capabilities of their modern computing equipment[14,39]. The high complexity of the development of parallel programs, which often does not allow the efficient use of the capabilities of high-performance computers, is a generally accepted fact[23,31].

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.7-17
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• 2017

Let R be a commutative ring with zero-divisors Z(R). The extended zero-divisor graph of R, denoted by $\bar{\Gamma}(R)$, is the (simple) graph with vertices $Z(R)^*=Z(R){\backslash}\{0\}$, the set of nonzero zero-divisors of R, where two distinct nonzero zero-divisors x and y are adjacent whenever there exist two non-negative integers n and m such that $x^ny^m=0$ with $x^n{\neq}0$ and $y^m{\neq}0$. In this paper, we consider the extended zero-divisor graphs of idealizations $R{\ltimes}M$ (where M is an R-module). At first, we distinguish when $\bar{\Gamma}(R{\ltimes}M)$ and the classical zero-divisor graph ${\Gamma}(R{\ltimes}M)$ coincide. Various examples in this context are given. Among other things, the diameter and the girth of $\bar{\Gamma}(R{\ltimes}M)$ are also studied.