• Honam Mathematical Journal
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• v.39 no.3
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• pp.401-416
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• 2017

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.67-83
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• 2009

Several common fixed point theorems for a few contractive type mappings in complete metric spaces are established. As applications, the existence and uniqueness of common solutions for certain systems of functional equations arising in dynamic programming are discussed.

• East Asian mathematical journal
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• v.30 no.3
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• pp.327-334
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• 2014

In this paper, we construct extrapolated expanded mixed finite element approximations to approximate the scalar unknown, its gradient and its flux of semilinear Sobolev equations. To avoid the difficulty of solving the system of nonlinear equations, we use an extrapolated technique in our construction of the approximations. Some numerical examples are used to show the efficiency of our schemes.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.1-10
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• 2012

Let ${\Omega}$ be a bounded subset of $\mathbb{R}^n$ with smooth boundary. We investigate the solvability for a class of the system of the nonlinear elliptic equations with Dirichlet boundary condition. Using the mountain pass theorem we prove that the system has at least one nontrivial solution.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.159-180
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• 1999

The present paper shows a new non-tensorial approach to derive basic equations for various structural analyses. It can be used directly in numerical computation procedures. The aim of the paper is, however, to show that the approach serves as an excellent tool for analytical purposes also, working as a link between analytical and numerical techniques. The paper gives a method to derive, at first, expressions for strains in general beam and shell analyses, and secondly, the governing equilibrium equations. The approach is based on the utilization of local fixed Cartesian coordinate systems. Applying these, all the definitions required are the simple basic ones, well-known from the analyses in common global coordinates. In addition, the familiar principle of virtual work has been adopted. The method will be, apparently, most powerful in teaching the theories of curved beam and shell structures for students not familiar with tensor analysis. The final results obtained have no novelty value in themselves, but the procedure developed opens through its systematic and graphic progress a new standpoint to theoretical considerations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.25-32
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• 2011

In this paper, we study the existence and uniqueness of solutions for the impulsive semilinear fuzzy integrodifferential equations with nonlocal conditions and forcing term with memory in n-dimensional fuzzy vector space ($E^n_N$, $d_{\varepsilon}$) by using Banach fixed point theorem. That is an extension of the result of Kwun et al. [9] to impulsive system.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.34-40
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• 2007

Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equations with nonlocal initial condition. Park et al. (2006) found the sufficient condition of this system. Recently, Kwun et al. (2006) proved the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal initial conditions and forcing term with memory in $E_N$. In this paper, we study the controllability for this system by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.1
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• pp.271-276
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• 1995

This paper presents a systematic method for the dynamic analysis of flexible mechanical systems containing closed kinematic loops. Kinematics between pairs of contiguous flexible bodies is described with the joint coordinates and the deformation modal coordinates. The cut-joint constraint equations associated with the closed kinematic loops are derived, simply using the geometric conditions. The equations of motions are initially written in terms of the joint and modal coordinates using the velocity transformation technique. Lagrange multipliers associated with the cut-joint constraints for closed-loop systems are then eliminated systematically using the generalized coordinate partitioning method, resulting to a minimal set of equations of motion.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.79-92
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• 2004

This paper offers an analysis of how students reasoned with the dynamic parameter time to support their mathematical activity and deepen their understandings of mathematical concepts. This mathematical thinking occurred as they participated in a differential equations class before, during, and instruction on solutions to linear systems of differential equations. Students participated in the following identified mathematical practices related to parametric reasoning during this time period: reasoning simultaneously in a qualitative and quantitative manner, reasoning by moving from discrete to continuous imaging of time, and reasoning by imagining the motion. Examples of this reasoning are provided in this report. Implications of this research include the possibility that instructional activities can build on this reasoning to help students learn about the mathematics of change at the middle school, high school, and the university.

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.5
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• pp.207-215
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• 2000

This study theoretically investigated the roll-off cleanliness operation to eliminate the built-in contaminants which are primarily the result of manufacturing and assembly procedures first. A rigorous analytical examination of the cleaning process associated with hydraulic systems was performed by developing the general filtration process equations. The sloughing process by which built-in contaminant is entrained in the system fluid was examined during the development of a general analytical expression for sloughing rate. This sloughing rate expression in conjunction with the filtration process equations have lead to a relationship rate expression in conjunction with the filtration process equations have lead to a relationship which describes the flushing and clean-up operation for the hydraulic systems. The effects of the primary roll-off cleanliness factors was discussed and illustrated on the figures. Then, the analytical results was shown to be usefully applied into the design of roll-off flushing equipment for the hydraulic system of a tractor.