• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.383-399
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• 2020

Following Matsumoto's definition of continuous orbit equivalence for one-sided subshifts of finite type, we introduce the notion of orbit equivalence to canonically associated dynamical systems, called the limit dynamical systems, of self-similar groups. We show that the limit dynamical systems of two self-similar groups are orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids. We also show that the equivalence class of Cuntz-Pimsner groupoids and the stably isomorphism class of Cuntz-Pimsner algebras of self-similar groups are invariants for orbit equivalence of limit dynamical systems.

• Proceedings of the Korea Information Processing Society Conference
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• 2009.11a
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• pp.583-584
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• 2009

This paper provides a method to analyze the dynamical system. It considers the fact of realistic delay in dynamical system analysis for the first time. The method uses timeline and state space to emulate the inhibitive coupling nodes evolving procedure in transmission delayed environment. The resultant finite state machine shows the system predictability and hardware implementation feasibility.

• Bulletin of the Society of Naval Architects of Korea
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• v.2 no.1
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• pp.15-19
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• 1965

The stability curves are very important data to decide the seaworthiness of all kinds of ships among waves. Both statical and dynamical stability curves on a rectangular coordinate system have broadly been handled at ship yards or at the government concerned, up to data. As concerns a method of obtaining a statical stability curve on polar coordinate system, the papers were presented once. Also, it is of use to research the dynamical stability curve on polar coordinate system. Author treated of the dynamical stability curve by four different methods, and tried to set the stability indicator inboard, adopted those proposals, in order to give some aids for good navigation on the sea. Fig. 1. shows a drawing method in case of the position of centre of buoyancy can be previously pointed out on the line corresponding to its inclination. Fig. 2. shows a method used a statical stability curve on polar coordinate. Fig. 3. shows a method obtained by the most simplified means. Fig. 4. shows dynamical stability curve made by geometrical expression method, instead of dynamical lever. A simple stability indicator which was mechanized above characteristics is attempted by author as shown Fig. 5 and Fig.6. It is demanded at hand, for more advanced improvement of such indicator.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.231-242
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• 2004

The effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view. Here we have studied dynamical model of a single-species population-toxicant system. Two cases are studied: constant exogeneous input of toxicant and rapidly fluctuating random exogeneous input of toxicant into the environment. The dynamical behaviour of the system is analyzed by using deterministic linearized technique, Lyapunov method and stochastic linearization on the assumption that exogeneous input of toxicant into the environment behaves like ‘Coloured noise’.

• Interaction and multiscale mechanics
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• v.3 no.1
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• pp.1-22
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• 2010

In this paper one introduces a method of multiscale modelling called collection of dynamical systems with dimensional reduction. The method is suggested to be an appropriate approach to theoretical modelling of phenomena in mechanics of materials having in mind especially dynamics of processes. Within this method one formalizes scale of averaging of processes during modelling. To this end a collection of dynamical systems is distinguished within an elementary dynamical system. One introduces a dimensional reduction procedure which is designed to be a method of transition between various scales. In order to consider continuum models as obtained by means of the dimensional reduction one introduces continuum with finite-dimensional fields. Owing to geometrical elements associated with the elementary dynamical system we can formalize scale of averaging within continuum mechanics approach. In general presented here approach is viewed as a continuation of the rational mechanics.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.307-317
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• 2012

We say (W, {${\phi}_1,\;{\ldots}\;,{\phi}_t$}) is a polarizable dynamical system of several morphisms if ${\phi}_i$ are endomorphisms on a projective variety W such that ${\otimes}{\phi}_i^*L$ is linearly equivalent to $L^{{\otimes}q}$ for some ample line bundle L on W and for some q > t. If q is a rational number, then we have the equidistribution of small points of given dynamical system because of Yuan's work [13]. As its application, we can build a polarizable dynamical system of an automorphism and its inverse on a K3 surface and can show that its periodic points are equidistributed.

• International Journal of Safety
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• v.10 no.2
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• pp.10-15
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• 2011

The reconfigurable control systems based on feedback controls are utilized to compensate for damages of actuators in control systems. Such systems have multiple feedback controls and switch them in accordance with the degrees of the failures of the actuators. In order to be able to assess those systems, this paper develops a method to obtain reliabilities of reconfigurable dynamical systems which are interconnected in parallel / series configuration. By calculating reliabilities of interconnected dynamical systems, it is possible to assess many dynamical systems by comparing their reliabilities. Firstly, reliabilities of subsystems are obtained according to the definitions of the failures in terms of robust reliability for each subsystem. Then, the reliability of overall system is calculated from reliabilities of subsystems, using the methodology employed for probabilistic safety assessment. Failure rates of subsystems with feedbacks for reconfiguration change in certain time periods because of the switching of feedback controls. In order to deal with this, combinations of subsystems which compose overall system for each time period are derived by the methodology mentioned above and then integrated to calculate the reliability of overall system for a specific time. An illustrative example shows the validity and details of the proposed method.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.397-406
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• 1997

In this paper we introduce GESS method and show that dynamics of the system ｙ＇=A(s,t,y) ｙ is more faithfully approxi-mated by GESS method that by Euler method. Numerical experiments are given for the comparison of GESS method with Euler method.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.575-591
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• 2018

Anosov families were introduced by A. Fisher and P. Arnoux motivated by generalizing the notion of Anosov diffeomorphism defined on a compact Riemannian manifold. Roughly, an Anosov family is a two-sided sequence of diffeomorphisms (or non-stationary dynamical system) with similar behavior to an Anosov diffeomorphisms. We show that the set consisting of Anosov families is an open subset of the set consisting of two-sided sequences of diffeomorphisms, which is equipped with the strong topology (or Whitney topology).

• Smart Structures and Systems
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• v.15 no.6
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• pp.1521-1542
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• 2015

The use of shape memory alloys (SMAs) in dynamical systems has an increasing importance in engineering especially due to their capacity to provide vibration reductions. In this regard, experimental tests are essential in order to show all potentialities of this kind of systems. In this work, SMA springs are incorporated in a dynamical system that consists of a one degree of freedom oscillator connected to a linear spring and a mass, which is also connected to the SMA spring. Two types of springs are investigated defining two distinct systems: a pseudoelastic and a shape memory system. The characterisation of the springs is evaluated by considering differential calorimetry scanning tests and also force-displacement tests at different temperatures. Free and forced vibration experiments are made in order to investigate the dynamical behaviour of the systems. For both systems, it is observed the capability of changing the equilibrium position due to phase transformations leading to hysteretic behaviour, or due to temperature changes which also induce phase transformations and therefore, change in stiffness. Both situations are investigated by promoting temperature changes and also pre-tension of the springs. This article shows several experimental tests that allow one to obtain a general comprehension of the dynamical behaviour of SMA systems. Results show the general thermo-mechanical behaviour of SMA dynamical systems and the obtained conclusions can be applied in distinct situations as in rotor-bearing systems.