• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• East Asian mathematical journal
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• 제32권3호
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• pp.355-364
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• 2016

In this paper, we study exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the internal material damping in the model as like Kang [3]. Energy decay rate are obtained by the exponential stability of solutions by using multiplier technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권2호
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• pp.85-91
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• 2012

In this paper, we study uniform exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the internal material damping in the model as like Gannesh C. Gorain [1]. Energy decay rates are obtained by the exponential stability of solutions by using multiplier technique.

• East Asian mathematical journal
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• 제28권3호
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• pp.339-345
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• 2012

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchho type wave equation with acoustic boundary in a bounded domain in $R^n$. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.

• East Asian mathematical journal
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• 제30권3호
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• pp.249-258
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• 2014

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the passive viscous damping in the model as like Kang[14]. Energy decay rates are obtained by the uniform exponential stability of solutions by using multiplier technique.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• Steel and Composite Structures
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• 제26권5호
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• pp.649-662
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• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.281-295
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• 2005

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

• Korean Journal of Mathematics
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• 제24권1호
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• pp.81-106
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• 2016

In this paper, we study the fractional iterates of the exponential function. This is an unresolved problem, not due to a lack of a known solution, but because there are an innite number of solutions, and there is no agreement as to which solution is "best." We will approach the problem by rst solving Abel's functional equation ${\alpha}(e^x)={\alpha}(x)+1$ by perturbing the exponential function so as to produce a real xed point, allowing a unique holomorphic solution. We then use this solution to nd a solution to the unperturbed problem. However, this solution will depend on the way we rst perturbed the exponential function. Thus, we then strive to remove the dependence of the perturbed function. Finally, we produce a solution that is in a sense more natural than other solutions.

• 한국토양비료학회지
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• 제43권3호
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• pp.356-362
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• 2010

본 연구는 안성시 관내에서 발생하는 폐기물계 바이오매스 중 가축분뇨, 하수, 음식물 슬러지와 도축장에서 발생하는 소 반추위 잔재물을 실험에 공시하고 각 폐자원별 메탄생산퍼텐셜을 측정하였다. 또한 기존 연구자들이 메탄생산퍼텐셜을 측정 자료로부터 최대메탄생산량을 추정하는데 이용한 Modified Gompertz model과 Exponential model을 이용하여 최대메탄생산량을 추정에 있어 모델별 적용성을 비교 검토하고자 하였다. 하수, 가축분뇨, 음식물 슬러지 및 반추위 잔재물에서 TS 함량은 각각 18.1, 23.7, 13.6, 14.8%이었으며, VS 함량은 14.3, 18.9, 11.9, 12.5%이었다. 유기성 폐자원별로 혐기배양 전후 pH는 7.93~8.32의 범위에서 7.09~7.25로 약간 낮아졌으며, 배양기간 중 VS 분해율은 37.8, 8.3, 12.5, 56.4%이었다. Modified Gompertz model을 이용하여 구한 단위메탄생산량은 하수, 가축분뇨, 음식물, 반추위 잔재물에서 각각 0.086, 0.147, 0.146, 0.121 L $CH_{4}\;g^{-1}\;VS_{added}$이었으며, Exponential model을 이용하여 구한 단위메탄생산량은 하수, 가축분뇨, 반추위 잔재물에서 0.109, 0.246, 0.174 L $CH_{4}\;g^{-1}\;VS_{added}$로 Modified Gompertz model을 이용하여 추정한 단위메탄생산량과 비교하여 26.7 ~67.3% 정도 높게 추산되었다.