• Journal for History of Mathematics
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• v.31 no.5
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• pp.211-222
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• 2018

This paper surveys the theory of symmetry group of differential equations. A proof of the simplest version of the Noether's theorem on conservation laws has been presented with examples in the classical mechanics. As a new approach to the conservation laws the theory of characteristic cohomology due to S. H. Wang and others has been presented.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.445-464
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• 2019

In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51-60] and Benavides et al. [Math. Nachr. 248(2003), 62-71].

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.141-146
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• 2011

Kou et al. presented a class of new variants of Ostrowski's method in their paper (J. of Comput. Appl. Math., 209(2007), pp.153-159) whose title is "Some variants of Ostrowski's method with seventh-order convergence". They proposed an incorrect error equation, although they showed a correct seventh-order of convergence. The main objective of this note is to establish the correct error equation of the method and confirm its validity via concrete numerical examples.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.1
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• pp.179-184
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• 2020

Cellular automata (CA), which is known as a pseudo random number generator due to its excellent randomness, has various applications. Cho et al. designed a CA-based shrinking generator to generate a long period of nonlinear sequence. In addition, chaotic cat maps have been studied by many researchers as the complex nonlinear dynamics systems with sensitivity in initial conditions and unpredictable characteristics. In this paper, we propose a new image encryption method using nonlinear sequence generated by CA-based shrinking generator with maximum period and 3D chaotic cat map for high security.

• East Asian mathematical journal
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• v.34 no.4
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• pp.511-536
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• 2018

There is currently a growing need to nurture creative and convergent talent in the face of the fourth Industrial Revolution. Developing such talent requires interdisciplinary convergent education across the science, engineering, humanities, social studies, and arts disciplines. Such interdisciplinary convergence could cultivate humanities and social knowledge and qualities along with scientific expertise. In Korea, there are currently six science schools for the gifted that aim to discover and nurture science, technology, engineering, and mathematics (STEM) researchers from an early stage, and two science and art schools for the gifted that aim to cultivate new talent combining students' scientific and artistic qualities. These schools establish and follow curriculums that are suited to achieving the education objectives guaranteed by the Gifted Education Promotion Act and its Enforcement Decrees. This study compares the curriculums and curriculum tables of the science schools for the gifted to those of the science and art schools for the gifted to evaluate their methods of operation and performance. Additionally, it determines which curriculums provide an opportunity for students to nurture convergent thinking, and discusses how suitable curriculums could be implemented to develop convergent thinking.

• Wind and Structures
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• v.26 no.2
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• pp.69-74
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• 2018

Nowadays, using math logic in great civil projects is considered by the clients to achieve the goals of project including quality optimization, costs, avoiding individual, emotional and political decision making, long-term and short-term goals and they are the main requirements of each project and should be considered by the decision makers to avoid the illogical decision making applied on the majority of civil projects and this imposes great financial and spiritual costs on our country. The present study attempts to present one of the civil projects (Ghasre Shirin storage dam) whose client was not ministry of energy for the first time and the short-term and long-term goals of the private sector were applied based on the triangle of quality, cost and time. Also, the math logic and model (multi-criteria decision making method and decision making matrix) is used in one of the most important sections of project, sealing element, policies and new materials (Geosynthetics) are considered and this leads to suitable decision making in this regard. It is worth to mention that this method is used for other sections of a dam including body, water diversion system, diaphragm and other sectors or in other civil projects of building, road construction, etc.

• Journal of Mechanical Science and Technology
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• v.19 no.8
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• pp.1582-1596
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• 2005

Groundwater flow and behavior have to be investigated based on heterogeneous subsurface formation since the homogeneity assumption of this formation is not valid. Over the past twenty years, stochastic approach and Monte Carlo technique have been utilized very efficiently to understand the groundwater flow behavior. However, these techniques require lots of computational and numerical efforts according to the various researchers' comments. Therefore, utilizing new techniques with much less computational efforts such as Artificial Neural Network (ANN) in the prediction of the stochastic behavior for the groundwater based on heterogeneous subsurface formation is highly appreciated. The current paper introduces the ANN technique to investigate and predict the stochastic behavior of a well draw down in a confined aquifer based on subsurface heterogeneous hydraulic conductivity. Several ANN models are developed in this research to predict the unsteady two dimensional well draw down and its stochastic characteristics in a confined aquifer. The results of this study showed that ANN method with less computational efforts was very efficiently capable of simulating and predicting the stochastic behavior of the well draw down resulted from the continuous constant pumping in the middle of a confined aquifer with subsurface heterogeneous hydraulic conductivity.

• Journal of Engineering Education Research
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• v.25 no.4
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• pp.35-41
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• 2022

In order to enhance basic competencies for freshmen at engineering college, whose learning ability is gradually declining, a new course was developed to review basic mathematics and physics through a process of collecting opinions from fellow professors. Tests in six fields of math and physics with the same problems showed the correct answer rate rose from 24.8% at the beginning of the semester to 59.0% at the end of the semester after operating the course developed. According to the survey, the students' self-evaluated confidence on the basic competencies in 16 fields of math and physics showed a significant increase. Students with high confidence in basic competencies also received high actual grades. General high school graduates' confidence point in basic competencies improved from 54.7 at the beginning to 75.3 points at the end of the semester, while specialized high school graduates' enhanced from 38.3 to 64.0 which is higher than that of general high school graduates at the beginning of the semester.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.467-482
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• 2023

In this paper, we present our new teaching and learning materials on gradient descent method, which is widely used in artificial intelligence, available for college mathematics. These materials provide a good explanation of gradient descent method at the level of college calculus, and the presented SageMath code can help students to solve minimization problems easily. And we introduce how to solve least squares problem using gradient descent method. This study can be helpful to instructors who teach various college-level mathematics subjects such as calculus, engineering mathematics, numerical analysis, and applied mathematics.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.983-996
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• 2015

In the paper A new parameter for Ramanujan's theta-functions and explicit values, Arab J. Math. Sc., 18 (2012), 105-119, Saikia studied the parameter $A_{k,n}$ involving Ramanujan's theta-functions ${\phi}(q)$ and ${\psi}(q)$ for any positive real numbers k and n and applied it to find explicit values of ${\psi}(q)$. As more application to the parameter $A_{k,n}$, in this paper we prove a new general theorem for explicit evaluation of Ramanujan-$G{\ddot{o}}llnitz$-Gordon continued fraction K(q) in terms of the parameter $A_{k,n}$ and give examples. We also find some new explicit values of the parameter $A_{k,n}$ and offer reciprocity theorems for the continued fraction K(q).