• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.157-164
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• 2019

In this article, we study expansiveness of the shift maps on orbital inverse limit spaces which consist of two cross bonding mappings. On orbital inverse limit systems, horizontal directions express inverse limit systems and vertical directions mean orbits based on horizontal axes. We characterize the c-expansiveness of functions on orbital spaces. We also prove that the c-expansiveness of the functions is equivalent to the expansiveness of the shift maps on orbital inverse limit spaces.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.69-76
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• 2022

In this article, we investigate minimality, transitivity and mixing property for a shift map on the orbital inverse limit systems.

• Transactions of Materials Processing
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• v.22 no.6
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• pp.328-333
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• 2013

The current study aims to determine the limit strains more accurately and reasonably when producing a forming limit curve (FLC) from experiments. The international standard ISO 12004-2 in its recent version (2008) states that the limit major strain should be determined by using the best-fit inverse second-order parabola through the experimental strain distribution. However, in cases where fracture does not occur at the center of the specimen, due to insufficient lubrication, the inverse parabola does not give a realistic fit because of its intrinsic symmetry in shape. In this study it is demonstrated that an inverse quartic function can give a much better fit than an inverse parabola in almost all FLC test samples showing asymmetric strain distributions. Using a quartic fit creates more reliable FLCs.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.461-466
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• 2018

$Let\;f:X{\rightarrow}X$ be a continuous surjection of a compact metric space X and let ${\sigma}_f:X_f{\rightarrow}X_f$ be the shift map on the inverse limit space $X_f$ constructed by f. We show that if a continuous surjective map f has some shadowing properties: the asymptotic average shadowing property, the average shadowing property, the two side limit shadowing property, then ${\sigma}_f$ also has the same properties.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.819-833
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• 2021

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history and has been widely applied in insurance, finance, queueing theory, statistics, and many other fields. Seol [27] proposed the inverse Markovian Hawkes processes and studied some asymptotic behaviors. In this paper, we consider an extended inverse Markovian Hawkes process which combines a Markovian Hawkes process and inverse Markovian Hawkes process with features of several existing models of self-exciting processes. We study the limit theorems for an extended inverse Markovian Hawkes process. In particular, we obtain a law of large number and central limit theorems.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.285-297
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• 1997

We will study the generalization of theorems on the pe-riodic locally - solvable FC-groups to the theorems on the periodic locally-solvable CC-groups. The main theorem is the Theorem A. For the proof the inverse limit of inverse system and topological ap-proch developed by Dixon is useful.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.77-82
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• 2000

After considering an equivalence relation on a directed preordered set, we construct an isomorphism between derived limits of inverse systems indexed by the directed (pre)ordered sets.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.657-661
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• 2016

Let $f:X{\rightarrow}X$ be a continuous surjection of a compact metric space and let ($X_f,{\tilde{f}}$) be the inverse limit of a continuous surjection f on X. We show that for a continuous surjective map f, if f has the asymptotic average, the average shadowing, the ergodic shadowing property then ${\tilde{f}}$ is topologically transitive.

• Transactions of Materials Processing
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• v.6 no.4
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• pp.300-310
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• 1997

A finite element inverse method is introduced for direct prediction of blank shapes, strain distributions, and reliable intermediate shapes from desired final shapes in axisymmetric multi-step deep drawing processes. This mothod enables the determination of process disign. The approach deals with the Hencky's deformation theory. Hill's second order yield criterion, simplified boundary conditions, and minimization of plastic work with constraints. The algorithm developed is applied to motor case forming, and cylindrical cup drawing with the large limit drawing ratio so that it confirms its validity by demonstrating resonably accurate numerical results of each problem. Numerical examples reveal the reason of difficulties in motor case forming with corresponding limit diagrams.

• Structural Engineering and Mechanics
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• v.41 no.3
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• pp.339-348
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• 2012

The slope stability analysis is usually done using the methods of calculation to rupture. The problem lies in determining the critical failure surface and the corresponding factor of safety (FOS). To evaluate the slope stability by a method of limit equilibrium, there are linear and nonlinear methods. The linear methods are direct methods of calculation of FOS but nonlinear methods require an iterative process. The nonlinear simplified Bishop method's is popular because it can quickly calculate FOS for different slopes. This paper concerns the use of inverse analysis by genetic algorithm (GA) to find out the factor of safety for the slopes using the Bishop simplified method. The analysis is formulated to solve the nonlinear equilibrium equation and find the critical failure surface and the corresponding safety factor. The results obtained by this approach compared with those available in literature illustrate the effectiveness of this inverse method.