• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.491-504
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• 2018

In this article, we consider a fourth order nonlinear difference system. By making use of the critical point theory, we obtain some new existence theorems of at least one periodic solution with minimal period. Our main approach used in this article is the variational technique and the Saddle Point Theorem.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.39-48
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• 2011

Some existence theorems are obtained for periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian by the minimax methods in critical point theory.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.749-759
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• 2005

We apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive periodic solutions of the system of functional differential equations $$x'(t)\;=\;A(t)x(t)+{\lambda}f(t,\;x(t-\tau(t))$$.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.8
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• pp.918-929
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• 1999

동기식 스트림 암호통신 방식을 사용하는 암호통신에서는 암/복호화 과정 수행시 암호통신 과정에서 발생하는 사이클슬립으로 인해 키수열의 동기이탈 현상이 발생되고 이로 인해 오복호된 데이타를 얻게된다. 이러한 위험성을 감소하기 위한 방안으로 현재까지 암호문에 동기신호와 세션키를 주기적으로 삽입하여 동기를 이루는 주기적인 동기암호 통신방식을 사용하여 왔다. 본 논문에서는 CDMA(Cellular Division Multiple Access) 이동망에서 데이타서비스를 제공할 때 사용되는 점대점 프로토콜의 주소영역의 특성을 이용하여 단위 측정시간 동안 측정된 주소비트 정보와 플래그 패턴의 수신률을 이용하여 문턱 값보다 작은경우 동기신호와 세션키를 전송하는 비주기적인 동기방식을 사용하므로써 종래의 주기적인 동기방식으로 인한 전송효율성 저하와 주기적인 상이한 세션키 발생 및 다음 주기까지의 동기이탈 상태의 지속으로 인한 오류확산 등의 단점을 해결하였다. 제안된 알고리즘을 링크계층의 점대점 프로토콜(Point to Point Protocol)을 사용하는 CDMA 이동망에서 동기식 스트림 암호 통신방식에 적용시 동기이탈율 10-7의 환경에서 주기가 1sec인 주기적인 동기방식에서 요구되는 6.45x107비트에 비해 3.84x105비트가 소요됨으로써 전송율측면에서의 성능향상과 오복호율과 오복호 데이타 비트측면에서 성능향상을 얻었다. Abstract In the cipher system using the synchronous stream cipher system, encryption / decryption cause the synchronization loss (of key arrangement) by cycle slip, then it makes incorrect decrypted data. To lessen the risk, we have used a periodic synchronous cipher system which achieve synchronization at fixed timesteps by inserting synchronization signal and session key. In this paper, we solved the problem(fault) like the transfer efficiency drops by a periodic synchronous method, the periodic generations of different session key, and the incorrectness increases by continuing synchronization loss in next time step. They are achieved by the transfer of a non-periodic synchronous signal which carries synchronous signal and session key when it is less than the threshold value, analyzing the address field of point-to-point protocol, using the receiving rate of address bits information and flag patterns in the decision duration, in providing data services by CDMA mobile network. When the proposed algorithm is applied to the synchronous stream cipher system using point-to-point protocol, which is used data link level in CDMA mobile network, it has advanced the result in Rerror and Derror and in transmission rate, by the use of 3.84$\times$105bits, not 6.45$\times$107bits required in periodic synchronous method, having lsec time step, in slip rate 10-7.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.255-268
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• 2005

We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.261-280
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• 2005

We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.3 no.1
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• pp.113-120
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• 1999

In this paper, chaotic signals of a Chua's oscillator are effectively controlled to low periodic signal(1-periodic signal, 2-periodic signal, etc) or equilibrium point using the linear state feedback technique. The proposed linear state feedback technique has characteristics, that any solution of the Chua's oscillator can be a goal of the control(fixed point, periodic orbit, etc). The controller has a very simple structure, which does not require adjusting system parameters.

• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.199-212
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• 2009

We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.75-82
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• 2014

In this paper, we consider the periodic boundary value problem with sign changing nonlinearity $$u^{{\prime}{\prime}{\prime}}+{\rho}^3u=f(t,u),\;t{\in}[0,2{\pi}]$$, subject to the boundary value conditions: $$u^{(i)}(0)=u^{(i)}(2{\pi}),\;i=0,1,2$$, where ${\rho}{\in}(o,{\frac{1}{\sqrt{3}}})$ is a positive constant and f(t, u) is a continuous function. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is the nonlinear term f may change sign.

• Nuclear Engineering and Technology
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• v.50 no.7
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• pp.1051-1059
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• 2018

Fast periodic pulsed reactor is a type of reactor in which the fission bursts are formed entirely with external reactivity modulation with a specified time periodicity. This type of reactors could generate much larger intensity of neutron beams for experimental use, compared with the steady state reactors. In the design of fast periodic pulsed reactors, the time dependent simulation of the power pulse is majorly based on a point kinetic model, which is known to have limitations. A more accurate calculation method is desired for the design analyses of fast periodic pulsed reactors. Monte Carlo computer code MCNP6 is used for this task due to its three dimensional transport capability with a continuous energy library. Some new routines were added to simulate the rotation of the movable reflector parts in the time dependent calculation. Fast periodic pulsed reactor IBR-2M was utilized to validate the new routines. This reactor is periodically in prompt supercritical state, which lasts for ${\sim}400{\mu}s$, during the equilibrium state. This generates long neutron fission chains, which requires tremendously large amount of computation time during Monte Carlo simulations. Russian Roulette was applied for these very long neutron chains in MCNP6 calculation, combined with other approaches to improve the efficiency of the simulations. In the power pulse of the IBR-2M at equilibrium state, there is some discrepancy between the experimental measurements and the calculated results using the point kinetics model. MCNP6 results matches better the experimental measurements, which shows the merit of using MCNP6 calculation relative to the point kinetics model.