• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.823-834
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• 1999

The present paper deals with the problem of nonselective harvesting in a partly infecte prey and predator system in which both the suseptible prey and the predator follow the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of the system has been studied in both the local and global sense. The optimal policy of exploitation has been derived by using Pontraygin's maximal principle. Numerical analysis and computer simulation of the results have been performed to inverstigate the global properties of the system.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1185-1202
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• 2010

In this paper, we have studied the dynamical behaviour such as boundedness, local and global stabilities, bifurcation of a single species population affected by environmental toxicant and population toxicant. We have also studied the effect of discrete delay of the environmental toxicant on the instantaneous growth rates of the population biomass and population toxicant due to incubation period. The length of delay preserving the stability is also estimated. Computer simulations are carried out to illustrate our analytical findings.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1261-1277
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• 2021

An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.

• Smart Structures and Systems
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• v.25 no.1
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• pp.57-64
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• 2020

The nonlinear dynamics of a directly forced clamped-clamped-free-free magneto-rheological elastomer (MRE) sandwich shell has been experimentally investigated. Experiments have been conducted on an aluminium shallow shell (shell A) and an MRE-aluminium sandwich shallow shell with single curvature (shell B). An electrodynamic shaker has been used to directly force shells A and B in the vicinity of their fundamental resonance frequency; a laser displacement sensor has been used to measure the vibration amplitude to construct the frequency-response curves. It was observed that for an aluminium shell (shell A), that at small forcing amplitudes, a weak softening-type nonlinear behaviour was observed, however, at higher forcing amplitudes the nonlinear dynamical behaviour shifted and a strong hardening-type response occurred. For the MRE shell (shell B), the effect of forcing amplitude showed softening at low magnetic fields and hardening for medium magnetic fields; it was also observed the mono-curved MRE sandwich shell changed dynamics to quasiperiodic displacement at some frequencies, from a periodic displacement. The presence of a magnetic field, initial curvature, and forcing amplitude has significant qualitative and quantitative effects on the nonlinear dynamical response of a mono curved MRE sandwich shell.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.107-116
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• 2005

A suspension bridge is an example of a nonlinear dynamical system, especially systems with the so called jumping nonlinearity. The fact that we deal with a serious and topical problem is demonstrated for example by the collapse of the Tacoma Narrow suspension bridge. So it would be very contributive to determine under what conditions a similar situation cannot occur and find out safe parameters of the bridge construction. In this paper, we show various possibilities how to model the behaviour of suspension bridge. Then we introduce our own results concerning existence and uniqueness of time-periodic solutions.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.835-850
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• 1999

The present paper deals with the problem of nonselective harvesting in a partly infected prey and predator system in which both the susceptible prey and the predator follow the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of the system has been studied in both the local and global sense. The optimal policy of exploitation has been derived by using Pontraygin's maximal principle. Numerical analysis and computer simulation of the results have been performed to investigate the golbal properties of the system.

• 한국공간정보시스템학회:학술대회논문집
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• 2004.05a
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• pp.279-286
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• 2004

An accumulated crack damage which propagates progressively with time was frequently observed on several engineering structures, This paper numerically demonstrates this damage process on large cooling tower shells under thermal and wind loads. Damage states under varying loads are investigated and the influence of this progressive damage process on the life-cycle of cooling towers discussed. The paper presents briefly some fundamentals of the geometrically and physically non-linear numerical analysis employed for reinforced concrete, especially concerning the models used for concrete, steel reinforcement and the bond between them. As a numerical example an existing cooling tower with noticeable meridian crack damage is analysed. The existing damage state of the cooling tower is determined by quasi-static analyses for temperature, hygric and cyclic wind leading. The change in the dynamical behaviour of the structure as mirrored in its natural frequencies and mode shapes is presented and discussed. Finally, the example shows that such damage processes develop progressively over the life-time of the structures.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1067-1082
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• 2022

This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.

• Structural Engineering and Mechanics
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• v.28 no.1
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• pp.53-67
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• 2008

Anisotropic materials are increasingly required in modern technological applications. Certainly, civil, mechanical and naval engineers frequently deal with the situation of analyzing the dynamical behaviour of structural elements being composed of such materials. For example, panels of anisotropic materials must sometimes support electromechanical engines, and besides, holes are performed in them for operational reasons e.g., conduits, ducts or electrical connections. This study is concerned with the natural frequencies and normal modes of vibration of rectangular anisotropic plates supported by different combinations of the classical boundary conditions: clamped, simply - supported and free, and with additional complexities such holes of free boundaries and attached concentrated masses. A variational approach (the well known Ritz method) is used, where the displacement amplitude is approximated by a set of beam functions in each coordinate direction corresponding to the sides of the rectangular plate. Consequently each coordinate function satisfies the essential boundary conditions at the outer edge of the plate. The influence of the position and magnitude of both hole and mass, on the natural frequencies and modal shapes of vibration are studied for a generic anisotropic material. The classical Ritz method with beam functions as spatial approximation proved to be a suitable procedure to solve a problem of such analytical complexity.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.747-767
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• 2013

In this paper we have constructed a mathematical model of alcohol abuse which consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined and sensitivity analysis of $R_0$ indicates that ${\beta}1$ (the transmission coefficient from moderate and occasional drinker to heavy drinker) is the most useful parameter for preventing drinking habit. Stability analysis of the model is made using the basic reproduction number. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0<1$. It is found that, when $R_0=1$, a backward bifurcation can occur and when $R_0>1$, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE under some conditions. Our important analytical findings are illustrated through computer simulation. Epidemiological implications of our analytical findings are addressed critically.