• East Asian mathematical journal
• /
• v.28 no.1
• /
• pp.25-36
• /
• 2012

We introduced a Finsler space $F^n$ with an approximate infinite series (${\alpha},{\beta}$-metric $L({\alpha},{\beta})={\beta}\sum\limits_{k=0}^r\(\frac{\alpha}{\beta}\)^k$, where ${\alpha}<{\beta}$ and investigated it with respect to Berwald space ([12]) and Douglas space ([13]). The present paper is devoted to finding the condition that is projectively at on a Finsler space $F^n$ with an approximate infinite series (${\alpha},{\beta}$)-metric above.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.127-133
• /
• 2012

It is well known that if the ${\beta}$-expansion of any nonnegative integer is finite, then ${\beta}$ is a Pisot or Salem number. We prove here that $\mathbb{F}_q((x^{-1}))$, the ${\beta}$-expansion of the polynomial part of ${\beta}$ is finite if and only if ${\beta}$ is a Pisot series. Consequently we give an other proof of Scheiche theorem about finiteness property in $\mathbb{F}_q((x^{-1}))$. Finally we show that if the base ${\beta}$ is a Pisot series, then there is a bound of the length of the fractional part of ${\beta}$-expansion of any polynomial P in $\mathbb{F}_q[x]$.

• Structural Engineering and Mechanics
• /
• v.31 no.6
• /
• pp.663-678
• /
• 2009

An exact solution is obtained for forced torsional vibration of a finite class 622 piezoelectric hollow cylinder with free-free ends subjected to dynamic shearing stress and time dependent electric potential at both internal and external surfaces. The solution is first expanded in axial direction with trigonometric series and the governing equations for the new variables about radial coordinate r and time t are derived with the aid of Fourier series expansion technique. By means of the superposition method and the separation of variables technique, the solution for torsional vibration is finally obtained. Natural frequencies and the transient torsional responses for finite class 622 piezoelectric hollow cylinder with free-free ends are computed and illustrated.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.4
• /
• pp.641-646
• /
• 2004

A convex combination of two products with same degree of finitely many finite geometric series with each having even degree does not always have all its zeros on the unit circle. However, in this paper, we show that a polynomial obtained by just adding a finite geometric series multiplied by a large constant to such a convex combination has all its zeros on the unit circle.

• Kyungpook Mathematical Journal
• /
• v.50 no.1
• /
• pp.49-58
• /
• 2010

We show that the Links-Gould polynomial of a link has finite type coefficients in a multivariate series expansion, and express the leading coefficients in terms of the linking numbers of a link.

• Journal of applied mathematics & informatics
• /
• v.8 no.3
• /
• pp.693-703
• /
• 2001

In this paper we consider non-deterministic finite Rabin-Scott’s automata. We use a special structure to descibe all the possible edges of non-determinstic finite automaton defining the given regular language. Such structure can be used for solving various problems of finite automata theory. One of these problems is edge-minimization of non-deterministic automata. As we have not touched this problem before, we obtain here two versions of the algorithm for solving this problem to continue previous series of articles.

• East Asian mathematical journal
• /
• v.26 no.1
• /
• pp.105-113
• /
• 2010

In the spectral analysis, Fourier coeffcients are very important to give informations for the original signal f on a finite domain, because they recover f. Also Fourier analysis has extension to wavelet analysis for the whole space R. Various kinds of reconstruction theorems are main subject to analyze signal function f in the field of wavelet analysis. In this paper, we will present a new reconstruction theorem of functions in $L^1(R)$ using a nonharmonic Fourier series. When we construct this series, we have used dyadic subdivision schemes.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.27 no.4
• /
• pp.585-592
• /
• 2003

Among various sensitivity evaluation techniques, semi-analytical method(SAM) is quite popular since this method is more advantageous than analytical method(AM) and global finite difference method(FDM). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified fur individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, an iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives.

• Journal for History of Mathematics
• /
• v.28 no.4
• /
• pp.167-179
• /
• 2015

We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.908-913
• /
• 2002

An analytical study is presented on the hydroelastic vibration of two rectangular identical plates coupled with a bounded fluid by using the finite Fourier series expansion method. It is observed that the two contrastive modes, the so called the out-of-phase and in-phase modes appear. The proposed analytical method is verified by observing a good agreement to three dimensional finite element analysis results. All natural frequency of the in-phase modes can be predicted well by the combination of the dry beam modes. The theoretical prediction for the out-of-phase mode can be improved by using the polynomial functions satisfying the plate boundary conditions and fluid volume conservation instead of using dry beam modes.