• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.551-563
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• 2017

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $$u^{{\Delta}{\nabla}}(t)+a(t)f(t,u(t))=0,\;t{\in}(0,T),\;{\beta}u(0)-{\gamma}u^{\Delta}(0)=0,\;u(T)={\sum_{i=1}^{m-2}}\;a_iu({\xi}_i),\;m{\geq}3$$, where $a(t){\in}C_{ld}((0,T),\;[0,+{\infty}))$, $f{\in}C([0,T]{\times}[0,+{\infty}),\;(-{\infty},+{\infty}))$, the nonlinear term f is allowed to change sign. We obtain several existence theorems of positive solutions for the above boundary value problems. In particular, our criteria generalize and improve some known results [15] and the obtained conditions are different from related literature [14]. As an application, an example to demonstrate our results is given.

• 전기학회논문지
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• 제61권12호
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• pp.1864-1871
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• 2012

This paper proposes the hybrid proportional integral(HBPI) controller for maximum power point tracking(MPPT) control of photovoltaic system. The output characteristics of the solar cell are a nonlinear and affected by a temperature, the solar radiation and influence of a shadow. The MPPT control is a very important technique in order to increase an output and efficiency of the photovoltaic system. The conventional constant voltage(CV), perturbation and observation(PO) and incremental conductance(IC) are the method which finding maximum power point(MPP) by the continued self-excitation vibration, and uses the fixed step size. If the fixed step size is a large, the tracking speed of maximum power point is faster, but the tracking accuracy in the steady state is decreased. On the contrary, when the fixed step size is a small, the tracking accuracy is increased and the tracking speed is slower. Therefore, in order to solve these problems, this paper proposes HBPI controller that is adjusted gain of conventional PI control using fuzzy control, and the maximum power point tracks using this controller. The validity of the controller proposed in this paper proves through the results of the comparisons.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2003년도 춘계학술대회 논문집
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• pp.78-81
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• 2003

Polishing Processes are widely used in the glass, optical, die and semiconductor industry and are conventionally carried out using abrasive slurry and a polishing pad. But abrasive slurry process has a weak point that is high cost of handling of used slurry and hard controllability of slurry. Recently, some researches have attempted to solve these problems and one method is the development of a fixed abrasive pad. FAP has a couple of advantages including clean environment, lower CoC, easy controllability and higher form accuracy. But FAP also has a weak point that is need of dressing because of glazing and loading. The paper introduces the basic concept and fabrication technique of FAP using hydrophilic polymers with swelling characteristics in water and explains the self-conditioning phenomenon. Experimental results demonstrate to achieve nano surface roughness of soda lime glass for optical application

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.205-215
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• 2009

Sufficient conditions for the existence of at least one solution of the boundary value problems for higher order nonlinear difference equations $\{{{{{\Delta^n}x(i-1)=f(i,x(i),{\Delta}x(i),{\cdots},\Delta^{n-2}x(i)),i{\in}[1,T+1],\atop%20{\Delta^m}x(0)=0,m{\in}[0,n-3],}\atop%20\Delta^{n-2}x(0)=\phi(\Delta^{n-1}(0)),}\atop%20\Delta^{n-1}x(T+1)=-\psi(\Delta^{n-2}x(T+1))}\$. are established.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.193-206
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• 2016

In this paper, we study boundary value problems for fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.1-12
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• 2015

This paper is concerned with boundary value problems for systems of n-th order dynamic equations on time scales. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.305-320
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• 2012

In this paper, we study a class of integral boundary value problems for fractional differential equations. By using some fixed point theorems, the results of existence of at least three positive solutions for the boundary value problems are obtained.

• 충청수학회지
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• 제20권1호
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• pp.59-64
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• 2007

In this paper, we will introduce the generalized operator equlibrium problem and generalized operator quasi-equlibrium problem which generalize operator equlibrium problem due to Kazmi and Raouf into multi-valued and quasi-equlibrium problems. Using a Park's fixed point theorem, we will prove a new existence theorem on generalized operator equlibrium problem which serves as a basic existence theorem for various kinds of nonlinear problems.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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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.

• Korean Journal of Mathematics
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• 제16권1호
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• pp.91-101
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• 2008

Let H be a Hilbert space. Assume that $0{\leq}{\alpha}$, ${\beta}{\leq}1$ and r(t) > 0 in I = [0, T]. By means of the fixed point theorem of Leray-Schauder type the existence principles of solutions for two point boundary value problems of the form $\array{(r(t)x^{\prime}(t))^{\prime}+f(t,x(t),r(t)x^{\prime}(t))=0,\;t{\in}I\\x(0)=x(T)=0}$ are established where f satisfies for positive constants a, b and c ${\mid}{f(t,x,y){\mid}{\leq}a{\mid}x{\mid}^{\alpha}+b{\mid}y{\mid}^{\beta}+c\;\;for\;all(t,x,y){\in}I{\times}H{\times}H$.