• Kyungpook Mathematical Journal
• /
• v.50 no.1
• /
• pp.153-164
• /
• 2010

We study the global asymptotic stability, the character of the semicycles, the periodic nature and oscillation of the positive solutions of the difference equation $x_{n+1}=\frac{p+x_{n-k}}{q+x_n}+\frac{x_{n-k}}{x_n}$, n=0, 1, 2, ${\cdots}$. where p, q ${\in}$ (0, ${\infty}$), q ${\neq}$ 2, k ${\in}$ {1, 2, ${\cdots}$} and the initial values $x_{-k}$, ${\cdots}$, $x_0$ are arbitrary positive real numbers.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.287-300
• /
• 2003

In this paper we shall consider the nonlinear delay differential equation (equation omitted) where m is a positive integer, ${\beta}$(t) and $\delta$(t) are positive periodic functions of period $\omega$. In the nondelay case we shall show that (*) has a unique positive periodic solution (equation omitted), and show that (equation omitted) is a global attractor all other positive solutions. In the delay case we shall present sufficient conditions for the oscillation of all positive solutions of (*) about (equation omitted), and establish sufficient conditions for the global attractivity of (equation omitted). Our results extend and improve the well known results in the autonomous case.

• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.281-295
• /
• 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.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.1492-1495
• /
• 2005

This paper presents a new linear-matrix-inequality-based intelligent digital redesign (LMI-based IDR) technique to match the states of the analog and the digital T-S fuzzy control systems at the intersampling instants as well as the sampling ones. The main features of the proposed technique are: 1) the affine control scheme is employed to increase the degree of freedom; 2) the fuzzy-model-based periodic control is employed; and the control input is changed n times during one sampling period; 3) The proposed IDR technique is based on the approximately discretized version of the T-S fuzzy system; but its discretization error vanishes as n approaches the infinity. 4) some sufficient conditions involved in the state matching and the stability of the closed-loop discrete-time system can be formulated in the LMIs format.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2005.04a
• /
• pp.378-381
• /
• 2005

This paper presents a new linear-matrix-inequality-based intelligent digital redesign (LMI-based IDR) technique to match the states of the analog and the digital T-S fuzzy control systems at the intersampling instants as well as the sampling ones. The main features of the proposed technique are: 1) the fuzzy-model-based periodic control is employed, and the control input is changed n times during one sampling period; 2) The proposed IDR technique is based on the approximately discretized version of the T-S fuzzy system, but its discretization error vanishes as n approaches the infinity. 3) some sufficient conditions involved in the state matching and the stability of the closed-loop discrete-time system can be formulated in the LMIs format.

• Bulletin of the Korean Chemical Society
• /
• v.29 no.3
• /
• pp.609-614
• /
• 2008

A periodic mesoporous organosilica material was synthesized by microwave heating (PMO-M) using 1,2-bis(trimethoxysilyl)ethane as a precursor in a cationic surfactant solution, and textural properties were compared with those of the product produced by conventional convection heating (PMO-C). These synthesized materials were characterized using XRD, TEM/SEM, N2 adsorption isotherm, 29Si and 13C NMR, and TGA, which confirmed their good structural orders and clear arrangements of uniform 3D-channels. Synthesis time was reduced from 21 h in PMO-C to 2-4 h in PMO-M. PMO-M was made of spherical particles of 1.5-2.2 m m size, whereas PMO-C was made of decaoctahedron-shaped particles of ca. 8.0 m m size. Effect of synthesis temperature, time, and heating mode on the PMO particle morphology was examined. The particle size of PMO-M could be controlled by changing the heating rate by adjusting microwave power level. PMO-M demonstrated improved separation of selected organic compounds compared to PMO-C in a reversed phase HPLC experiment. Ti-grafted PMO-M also resulted in higher conversion in liquid phase cyclohexene epoxidation than by Ti-PMO-C.

• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.81-108
• /
• 2003

We consider the Korteweg-de Vries-Burgers (KdVB) equation on the domain [0,11]. We derive a control law which guarantees $L^2$-global exponential stability, $H^3$-global asymptotic stability, and $H^3$-semiglobal exponential stability.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.1325-1337
• /
• 2014

In this paper we study the sequences defined by the last and the last non-zero digits of $n^n$ in base b. For the sequence given by the last digits of $n^n$ in base b, we prove its periodicity using different techniques than those used by W. Sierpinski and R. Hampel. In the case of the sequence given by the last non-zero digits of $n^n$ in base b (which had been studied only for b = 10) we show the non-periodicity of the sequence when b is an odd prime power and when it is even and square-free. We also show that if $b=2^2{^s}$ the sequence is periodic and conjecture that this is the only such case.

• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.217-230
• /
• 2017

In this paper we deal with the difference equation $$y_{n+1}=\frac{ay_{n-1}}{by_ny_{n-1}+cy_{n-1}y_{n-2}+d}$$, $$n{\in}\mathbb{N}_0$$, where the coefficients a, b, c, d are positive real numbers and the initial conditions $y_{-2}$, $y_{-1}$, $y_0$ are nonnegative real numbers. Here, we investigate global asymptotic stability, periodicity, boundedness and oscillation of positive solutions of the above equation.

• Bulletin of the Korean Chemical Society
• /
• v.22 no.9
• /
• pp.948-952
• /
• 2001

Periodic mesoporous organosilicas with rope-based morphology from a reaction gel composition of 1 BTME : 0.57 ODTMABr : 2.36 NaOH : 353 H2O were synthesized. While long rope-shaped product dominated in case of static synthesis condition , gyroid type products instead of rope shaped product appeared and rope shaped product disappeared with agitation. PMO with such a long rope shaped morphology is firstly reported. Additionally, various rope-based morphologies depending on the degree of bending, twisting, folding and winding of rope such as spirals, discoids, toroids, and worm-like aggregates were observed. White powdered products were characterized by X-ray diffraction, N2 sorption measurement, SEM and TEM. From XRD pattern and TEM image, ODTMA-PMO with hexagonal symmetry was identified. The pore diameter and BET surface area of ODTMA-PMO are $32.9{\AA}$ and 799 m2g-1 , respectively. Hexagonally arrayed channels run with long axis of rope and rope-based shapes with various degree of curvature, which was elucidated by using TEM images.