• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권4호
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• pp.273-288
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• 2014

In recent years, coding education has been globally emphasized and the Free Semester System will be executed to the public schools in Korea from 2016. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this research aims to design 'learning environment' in which learners can design and construct mathematical objects through computers and print them out through 3D printers. Furthermore, it will design learning mathematics by constructing the figurate number patterns from 'soma cubes' in the playing context and connecting those to algebraic and combinatorial patterns, which will allow students to experience mathematical connectivity. It is expected that the activities of designing figurate number patterns suggested in this research will not only strengthen CT capacity in relation to mathematical thinking but also serve as a meaningful program for the Free Semester System in terms of career experience as 3D printers can be widely used.

• 대한기계학회논문집
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• 제12권2호
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• pp.193-199
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• 1988

본 연구의 목적은 SCPA방법을 이용한 비선형 2자유도 비감쇠계의 해석을 통하여 응답곡선을 구하고, 그 응답곡선의 분기현상을 규명함에 있다. 결과의 비교를 위하여 4차의 Runge-Kutta방법을 이용한 수치실험을 수행하였다.

• 대한수학회보
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• 제39권2호
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• pp.299-307
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• 2002

As a by-product of [5], we produce algebraic integers of certain values of quotients of Eisenstein series. And we consider the relation of $\Theta_3(0,\tau)$ and $\Theta_3(0,\tau^n)$. That is,we show that $$\mid$\Theta_3(0,\tau^n)$\mid$=$\mid$\Theta_3(0,\tau)$\mid$,\bigtriangleup(0,\tau)=\bigtriangleup(0,\tau^n)$ and $J(\tau)=J(\tau^n)$ for some $\tau\in\eta$.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.361-378
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• 2020

The most apparent aspect of the present study is to introduce a new sequence space 𝚽^⋆(𝓛_p) derived by double Euler-Totient matrix operator. We examine its topological and algebraic properties and give an inclusion relation. In addition to those, the α-, β(bp)- and γ-duals of the space 𝚽^⋆(𝓛_p) are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.376-382
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• 1991

In the analysis of constrained holonomic systems, the Lagange multiplier method yields a system of second-order ordinary differential equations of motion and algebraic constraint equations. Conventional holonomic or nonholonomic constraints are defined as geometric constraints in this paper. Previous works concentrate on the geometric constraints. However, if the total energy of a dynamic system can be computed from the initial energy plus the time integral of the energy input rate due to external or internal forces, then the total energy can be artificially treated as a constraint. The violation of the total energy constraint due to numerical errors can be used as information to control these errors. It is a necessary condition for accurate simulation that both geometric and energy constraints be satisfied. When geometric constraint control is combined with energy constraint control, numerical simulation of a constrained dynamic system becomes more accurate. A new convenient and effective method to implement energy constraint control in numerical simulation is developed based on the geometric interpretation of the relation between constraints in the phase space. Several combinations of energy constraint control with either Baumgarte's Constraint Violation Stabilization Method (CVSM) are also addressed.

• 대한수학회논문집
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• 제27권1호
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• pp.7-13
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• 2012

In this paper we consider pseudo-BCK/BCI-algebras. In particular, we consider properties of minimal elements ($x{\leq}a$ implies x = a) in terms of the binary relation $\leq$ which is reflexive and anti-symmetric along with several more complicated conditions. Some of the properties of minimal elements obtained bear resemblance to properties of B-algebras in case the algebraic operations $\ast$ and $\circ$ are identical, including the property $0{\circ}(0{\ast}a)$ = a. The condition $0{\ast}(0{\circ}x)=0{\circ}(0{\ast}x)=x$ all $x{\in}X$ defines the class of p-semisimple pseudo-BCK/BCI-algebras($0{\leq}x$ implies x = 0) as an interesting subclass whose further properties are also investigated below.

• 한국철도학회논문집
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• 제6권4호
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• pp.294-299
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• 2003

Using a conventional railway, a tilting train was applied as a means of improving vehicle speed during curve negotiation without any modification of infrastructure. As a study for the optimum design of the tilting mechanism of a tilting vehicle, the kinematics sensitivity of the tilting mechanism was analyzed. Using the geometric relationship of the linkage-type tilting mechanism, the relationship of the parameters and the performance index was defined using nonlinear algebraic equations. With the defined relation, the effect of change in the parameters on the performance was analyzed. The analysis result can be used in the optimum design of a tilting mechanism that considers the track environment, vehicle and operational condition in which the tilting vehicle is applied.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.1841-1844
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• 2004

'Mixing Index($D_I$)'s generally used to measure the degree of mixing. A new method to calculate $D_I$ was proposed, when insoluble solution flows in micromixer. 'Vortex Index (${\Omega}_I$)'which indicate the degree of chaotic advection, is defined and formulated. A lots of arbitrary shaped microchannels were tested to calculate the $D_I$ and ${\Omega}_I$. And then a simple algebraic equation, $D_I=A{\Omega}_I+B$, was obtained. This equation may be used instead of partial differential equation, concentration equation.

• Wind and Structures
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• 제29권1호
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• pp.33-41
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• 2019

The interaction of head waves with an infinite row of identical, equally spaced, rectangular breakwaters is investigated in the presence of uneven bottom topography. Using linear water wave theory and matched eigenfunction expansion method, the boundary value problem is transformed into a system of linear algebraic equations which are numerically solved to know the velocity potentials completely. Utilizing this method, reflected and transmitted wave energy are computed for different physical parameters along with the wave field in the vicinity of breakwaters. It is observed that the wave field becomes more complicated when the incoming wavelength becomes smaller than the channel width. A critical ratio of the gap width to the channel width, corresponding to the inflection point of the transmitted energy variation, is identified for which 1/3 of the total energy is transmitted. Similarly, depending on the incident wavelength, there is a critical breakwater width for which a minimum energy is transmitted. Further, the accuracy of the computed results is verified by using the derived energy relation.

• Geomechanics and Engineering
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• 제24권3호
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• pp.227-235
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• 2021

A criterion and a method for solving a problem on the prevention of mine working fracture under the action of tectonic and gravitational forces are offered. Based on minimal criterion, theoretical analysis of the definition of the optimal shape of working in the rock mass weakened by arbitrarily located rectilinear cracks was carried out. A closed system of algebraic equations allowing to minimize the stress state and stress intensity factors depending on mechanical and geometrical characteristics of the rock, is constructed. The relation between the shape of the working and the stress intensity factors and also location and sizes of the cracks is obtained. The found optimal shape of working increases load-bearing capacity of the rock.