• 대한수학회지
• /
• 제45권4호
• /
• pp.1007-1025
• /
• 2008

We will describe a way to construct Ford domains of cusped hyperbolic 3-manifolds on maximal cusp diagrams and compute fundamental groups using face pairing maps as generators and Cannon-Floyd-Parry's edge cycles as relations. We also describe explicitly a cutting and pasting alteration to reduce the number of faces on the bottom region of Ford domains. We expect that our analysis of Ford domains will be useful on other future research.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 1999년도 추계종합학술대회 논문집
• /
• pp.767-770
• /
• 1999

This paper investigates the performance of the hyperbolic position location(PL) technique in CDMA system. Hyperbolic PL systems are such technology that can provide accurate PL information using the existing cellualr/PCS infrastructure and without requiring additional hardware/software implementation within the mobile unit. The channel simulation is obtained by applying AWGN and multipath fading. The effect of the mobile position within the cell and the number of base stations on the accuracy of the hyperbolic PL technique is investigated.

• 충청수학회지
• /
• 제28권2호
• /
• pp.243-249
• /
• 2015

Let X be a closed surface for which the Euler characteristic $_{\mathcal{X}}(X)$ is negative, and let $f:X{\rightarrow}X$ be a self-map that is not surjective. In this short paper, we prove that we can compute the Nielsen number of f, N(f), under some algebraic conditions.

• Steel and Composite Structures
• /
• 제25권3호
• /
• pp.337-346
• /
• 2017

Sandwich shells made of composite materials are the main focus on recent literature parallel to the requirements of industry. They are commonly chosen for the modern engineering applications which require moderate strength to weight ratio without dependence on conventional manufacturing techniques. The investigations on hyperbolic paraboloidal formed sandwich composite shells are limited in the literature contrary to shells that have a number of studies, consisting of doubly curved surfaces, arbitrary boundaries and laminations. Because of the lack of contributive data in the literature, the aim of this study is to present the effects of curvature on hyperbolic paraboloidal formed, layered sandwich composite surfaces that have arbitrary boundary conditions. Analytical solution methodology for the analyses of stresses and deformations is based on Third Order Shear Deformation Theory (TSDT). Double Fourier series, which are specialized for boundary discontinuity, are used to solve highly coupled linear partial differential equations. Numerical solutions showing the effects of shell geometry are presented to provide benchmark results.

• 대한수학회보
• /
• 제25권2호
• /
• pp.185-194
• /
• 1988

In [2], we have shown that the optimal boundary controls for hyperbolic systems in L$^{2}$-spaces can be attained in a feedback form via Riccati operators. A number of authors [1, 5, 7 and 10] have investigated approximations of Riccati operators arising in distributed parameter systems. They assumed bounded controls for parabolic systems. However, we in this paper study Galerkin approximations of Riccati operators and feedback controls for hyperbolic systems with unbounded control actions. Let us briefly introduce some results of [2]. Let .ohm. be an open bounded region in R$^{n}$ with smooth boundary .GAMMA. where n is a fixed positive integer. We consider a strictly hyperbolic differential operator H(x) of order 1 on .ohm. with noncharacteristic boundary on .GAMMA.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제20권4호
• /
• pp.269-276
• /
• 2013

We find an explicit $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on the 4-d hyperbolic space $\mathbb{H}^4$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the hyperbolic metric on $\mathbb{H}^4$, the scalar curvatures of $g_t$ are strictly decreasing in t in an open ball and $g_t$ is isometric to the hyperbolic metric in the complement of the ball.

• 대한수학회보
• /
• 제47권2호
• /
• pp.231-249
• /
• 2010

Asymptotic behavior of three-dimensional mixed, periodic and rotating magnetohydrodynamic system is investigated as the Rossby number goes to zero. The system presents the difficulty to be singular and mixed, that is hyperbolic in the vertical direction and parabolic in the horizontal one. The divergence free condition and the spectral properties of the penalization operator are crucial in the proofs. The main tools are the energy method, the Schochet's method and products laws in anisotropic Sobolev spaces.

• 대한수학회보
• /
• 제50권4호
• /
• pp.1243-1259
• /
• 2013

In this paper, we study the root system of rank 2 hyperbolic Kac-Moody algebras. We give some sufficient conditions for the existence of imaginary roots of square length $-2k(k{\in}\mathbb{Z}_{>0}$. We also give several relations between the integral points on the hyperbola $\mathfrak{h}$ to show that the value of the symmetric bilinear form of any two integral points depends only on the number of integral points between them. We also give some generalizations of Binet formula and Catalan's identity.

• 대한수학회보
• /
• 제55권2호
• /
• pp.359-366
• /
• 2018

We extend Jung's result about the relations among bi-closing, open and constant-to-one codes between general shift spaces to closing codes. We also show that any closing factor code ${\varphi}:X{\rightarrow}Y$ has a degree d, and it is proved that d is the minimal number of preimages of points in Y. Some other properties of closing codes are provided. Then, we show that any closing factor code is hyperbolic. This enables us to determine some shift spaces which preserved by closing codes.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제17권4호
• /
• pp.279-294
• /
• 2013

We are interested in an adaptive grid method for hyperbolic equations. A multiresolution analysis, based on a biorthogonal family of interpolating scaling functions and lifted interpolating wavelets, is used to dynamically adapt grid points according to the physical field profile in each time step. Traditional finite-difference schemes with fixed stencils produce high oscillations around sharp discontinuities. In this paper, we hybridize high-resolution schemes, which are suitable for capturing singularities, and apply a finite-difference approach to the scaling functions at non-singular points. We use a total variation diminishing Runge-Kutta method for the time integration. The computational cost is proportional to the number of points present after compression. We provide several numerical examples to verify our approach.