• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.315-331
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• 2015

The purpose of this paper is to obtain Opial-type inequalities that are useful to study various qualitative properties of certain differential equations involving impulses. After we obtain some Opial-type inequalities, we apply our results to certain differential equations involving impulses.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.61-75
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• 2014

The purpose of this paper is to obtain some integral inequalities with impulses by using the method of Stieltjes derivatives, and we use our results in the study of Lyapunov stability of solutions of a certain nonlinear impulsive integro-differential equation.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.243-252
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• 2008

It has been reported that long-term exercise on a treadmill (running machine) may cause injury to the joints in a human's lower extremities. Previous works related to analysis of human walking motion are, however, mostly based on clinical statistics and experimental methodology. This paper proposes an analytical methodology. Specifically, this work deals with a comparison of normal walking on the ground and walking on a treadmill in regard to the external and internal impulses exerted on the joints of a human's lower extremities. First, a modeling procedure of impulses, impulse geometry, and impulse measure for the human lower extremity model will be briefly introduced and a new impulse measure for analysis of internal impulse is developed. Based on these analytical tools, we analyze the external and internal impulses through a planar 7-linked human lower extremity model. It is shown through simulation that the human walking on a treadmill exhibits greater internal impulses on the knee and ankle joints of the supporting leg when compared to that on the ground. In order to corroborate the effectiveness of the proposed methodology, a force platform was developed to measure the external impulses exerted on the ground for the cases of the normal walking and walking on the treadmill. It is shown that the experimental results correspond well to the simulation results.

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.155-169
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• 2017

In this paper we obtain some integral inequalities involving impulses and apply our results to a certain integro-differential equation with impulses. First, we obtain a bound of the equation, and we use the bound to study some qualitative properties of the equation.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.103-117
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• 2011

By using an important lemma, some analysis techniques and Lyapunov functional method, we establish the sufficient conditions of the existence of equilibrium solution of a class of BAM neural network with impulses and distributed delays. Finally, applications and an example are given to illustrate the effectiveness of the main results.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.1-16
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• 2007

Some Kamenev-type oscillation criteria are obtained for a second order quasilinear damped differential equation with impulses. These criteria generalize and improve some well-known results for second order differential equations with land without impulses. In addition, new oscillation criteria are also obtained to generalize and improve known results. Two examples of applications are given to illustrate the theory.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.431-450
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• 2016

In this paper, the existence, uniqueness, stability via continuous dependence and Ulam stabilities of nonlinear integro-differential equations with random impulses are studied under sufficient condition. The results are obtained by using Leray-Schauder alternative fixed point theorem and Banach contraction principle.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.39-47
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• 2003

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7］are generalized and improved.

• Journal of Korean Medicine Rehabilitation
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• v.19 no.1
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• pp.103-112
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• 2009

Objectives : This study was aimed to find out the physiological mechanism of craniosacral therapy, especially in CV4 technique and cranial rhythmic impulses. Methods : Recent studies were reviewed for cranial rhythmic impulses, and the ancient and present text were reviewed for the therapy of sub-occiput and cranial-suture part. Results and Conclusions : 1. Suboccipital muscles releasing may have made CV4 technique to effect. 2. The mechanism of the meridians of acupuncture and craniosacral system can be cooperative together in many parts of the clinical treatments. 3. Arterial vasomotor waves have a frequency similar to reports of cranial rhythmic impulses. The methods which have relation to heart rate variability, will be useful for the study of craniosacral therapy.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.3
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• pp.143-151
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• 1995

The electrochemical impulse oscillations of the cathodic currents at the platinum group (Pt, Pd) electrode/(0.05M KHC$_{8}H_{4}O_{4}$) buffer solution interfaces have been studied using voltammetric, chronoamperometric, and electrochemical impedance methods. The periodic impulses of the cathodic currents are the activation controlled currents due to the hydrogen evolution reaction, and depend on the fractional surface coverage of the adsorbed hydrogen intermediate and potential. The oscillatory mechanism of the cathodic current impulses is connected with the unstable steady state of negative differential resistance. The widths and periods of the cathodic current impulses are 4ms or 5ms and 152.5ms or 305ms, respectively. The H$^{+}$ discharge reaction step is 38 or 61 times faster thatn the recombination reaction steps and the H$^{+}$ mass transport processes. The atom-atom recombination reaction step is twice faster thatn the atom-ion recombination reaction step. The two kinds of active sites corresponding to the atom-atom and atom-ion recombination reaction steps exist on the platinum group electrode surfaces.