• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.73-82
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• 2019

In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

• 대한수학회지
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• 제48권6호
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• pp.1143-1152
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• 2011

The existence of periodic solutions for the planar Hamiltonian systems with positively homogeneous Hamiltonian is discussed. The asymptotic expansion of the Poincar$\acute{e}$ map is calculated up to higher order and some sufficient conditions for the existence of periodic solutions are given in the case when the first order term of the Poincar$\acute{e}$ map is identically zero.

• Steel and Composite Structures
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• 제23권3호
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• pp.339-350
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• 2017

In this paper, various nonlocal higher-order shear deformation beam theories that consider the size dependent effects in Functionally Graded Material (FGM) beam are examined. The presented theories fulfill the zero traction boundary conditions on the top and bottom surface of the beam and a shear correction factor is not required. Hamilton's principle is used to derive equation of motion as well as related boundary condition. The Navier solution is applied to solve the simply supported boundary conditions and exact formulas are proposed for the bending and static buckling. A parametric study is also included to investigate the effect of gradient index, length scale parameter and length-to-thickness ratio (aspect ratio) on the bending and the static buckling characteristics of FG nanobeams.

• 대한수학회보
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• 제61권1호
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• 대한기계학회논문집
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• 제14권1호
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• pp.241-250
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• 1990

본 연구에서는 낙구식 점도계를 이용하여 낮은 농도의 용액을 실험할 때 종말 속도측정의 어려움을 해결하기 위하여 레이저와 특수 타이머를 설치하였으며 정확한 특성시간을 결정하기 위하여 실린더 내부의 시험유체를 교란시키지 않고, 떨어뜨린 구 를 회수하는 장치를 제작하였다. 또한 주로 rheogoniometer에 의존하던 영 전단률 점성계수를 측정하기 위하여 속이 빈 알루미늄 구(hollow aluminium ball)의 밀도를 시험 유체와 거의 같은 정도까지 변화시켜가며 종말 속도를 측정하였으며 점탄성 유체 로써 Separan AP-273의 낮은 농도인 300에서 2000wppm까지의 저농도 용액에 대한 특성 시간을 여러모델에 의하여 실험적으로 결정하고 저농도 폴리머 용액에서 퇴화로 인한 점탄성유체의 특성 변화를 분석하였다.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2000년도 추계학술대회 논문집
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• pp.184-188
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• 2000

The improved Green integral equation of overdetermined type applied to the radiation problem for an oscillating cylinder in the presence of weak current is presented. A two-dimensional Green function for the weak current is also presented. The present numerical solution of the Improved Green integral equation by the B-spline higher order Kelvin panel method is shown to be free of irregular frequencies which are present in the usual Green integral equation.

• 한국통신학회논문지
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• 제32권9C호
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• pp.888-894
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• 2007

The computational complexity of a sphere decoder (SD) is conventionally reduced by decoding order scheme which sorts candidate symbols in the ascending order of the Euclidean distance from the output of a zero-forcing (ZF) receiver. However, since the ZF output may not be a reliable sorting reference, we propose two types of sorting schemes to allow faster decoding. The first is to use the newly found lattice points in the previous search round instead of the ZF output (Type I). Since these lattice points are closer to the received signal than the ZF output, they can serve as a more reliable sorting reference for finding the maximum likelihood (ML) solution. The second sorting scheme is to sort candidate symbols in descending order according to the number of candidate symbols in the following layer, which are called child symbols (Type II). These two proposed sorting schemes can be combined with layer sorting for more complexity reduction. Through simulation, the Type I and Type II sorting schemes were found to provide 12% and 20% complexity reduction respectively over conventional sorting schemes. When they are combined with layer sorting, Type I and Type II provide an additional 10-15% complexity reduction while maintaining detection performance.

• 한국정밀공학회지
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• 제23권1호
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• pp.174-184
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• 2006

In order to fill the holes with complex shapes in the large polygon model, a new approach which is based on the implicit surface interpolation method combined with domain decomposition method is presented. In the present study, a surface is constructed by creating smooth implicit surface from the incomplete polygon model through which the surface should pass. In the method an implicit surface is defined by a radial basis function, a continuous scalar-valued function over the domain $R^3$ The generated surface is the set of all points at which this scalar function takes on the value zero and is created by placing zero-valued constraints at the vertices of the polygon model. In this paper the well-known domain decomposition method is used in order to treat the large polygon model. The global domain of interest is divided into smaller domains where the problem can be solved locally. LU decomposition method is used to solve a set of small local problems and their local solutions are combined together using the weighting coefficients to obtain a global solution. In order to show the validity of the present study, various hole fillings are carried out fur the large and complex polygon model of arbitrary topology.

• 한국수소및신에너지학회논문집
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• 제18권1호
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• pp.40-45
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• 2007

Methylene blue(MB) was photocatalytically degraded with one-body photoanode and solar simulator to investigate the possible application to both environmental purification and photoelectrochemical cell for hydrogen production. Photoactive titanium dioxide was formed on both sides of Ti plate following steps such as rinsing-annealing-calcination or anodizing(20 V, 30 V)-annealing($350^{\circ}C$, $450^{\circ}C)$ after etching. The prepared titania plate($2cm{\times}2\;cm$, ca 1.6 mg $TiO_2$ on the basis of $1\;{\mu}m$ thickness) was used to degrade MB(10 ppm in 200 mL solution). The reaction tended to follow the Langmuir-Hinshelwood kinetics with zero order. Comparative experiments with Degussa P25 showed the same zero order kinetics when 2 mg of P25 had been used, while the first order kinetics when 200 mg used. This concludes the feasibility of the prepared titania plate as a material for the purification of low-level harmful organics and an electrode or a membrane for photoelectrochemical system for hydrogen production.