• Honam Mathematical Journal
• /
• v.24 no.1
• /
• pp.35-41
• /
• 2002

The solutions of a homogeneous system in state space form $\dot{x}=Ax$ are to the form $x=e^{At}x_0$ and the solutions of an inhomogeneous system $\dot{x}=Ax(t)+f(t)$ are to the form $x=e^{At}x_0+{{\int}_0^t}\;e^{A(t-{\tau})}f({\tau})d{\tau}$. In this note we show that the solution of descriptor systems under some conditions exists, and is unique, moreover it is interesting to know the solutions of descriptor system are schematically like the solutions as in the state space form. Also we will give some algorithms to compute these solutions.

• The Pure and Applied Mathematics
• /
• v.12 no.3 s.29
• /
• pp.179-191
• /
• 2005

In this paper we consider a Dirichlet problem in the unit disk. We show that the equation has a unique or multiple solutions according to the range of the parameter. Moreover, we prove that the equation admits a nonradial bifurcation at each branch of radial solutions.

• The Korean Journal of Ceramics
• /
• v.6 no.4
• /
• pp.390-395
• /
• 2000

Silicon, titanium, zirconium phosphates were synthesized by starting with appropriate chemical precursors in a solution. The synthetic procedure, chemical and physical structures were examined by FT-IR, liquid and solid state NMR, TGA, SEM, XRD, etc. The phosphates were examined for thermal and electrical properties. Advantages of the synthesis technique and the data on unique structures and thermal properties are reported.

• Journal of the Korean Ceramic Society
• /
• v.27 no.5
• /
• pp.693-697
• /
• 1990

TIACA has two different side groups(ligands) as iso-propoxy groups and acetylacetonate groups. These two side groups have different hydrolysis rates. The two different rates of hydrolysis confer unique properties on TIACA, which are stability in aqueous solution and easy preparation of TiO2 and its multi components gels without precipitation. Their hydrolysis rates were monitored with I.R. and U.V. spectrophotometer.

• Proceedings of the KSRS Conference
• /
• 2003.11a
• /
• pp.1353-1355
• /
• 2003

Genetic algorithms (GA) is a well known technique that is capable of handling multiobjective functions and discrete constraints in the process of numerical optimization. Together with the Pareto ranking scheme, more than one possible solution can be obtained despite the imposed constraints and multi-criteria design functions. In view of this unique capability, the design of the log-periodic dipole antenna array (LPDA) using this special feature is proposed in this paper. This method also provides gain, front-back level and S parameter design tradeoff for the LPDA design in broadband application at no extra computational cost.

• Kyungpook Mathematical Journal
• /
• v.49 no.2
• /
• pp.299-312
• /
• 2009

In the present paper we investigate the existence of almost periodic processes of ecological systems which are presented with nonautonomous N-dimensional impulsive Lotka Volterra competitive systems with dispersions and fixed moments of impulsive perturbations. By using the techniques of piecewise continuous Lyapunov's functions new sufficient conditions for the global exponential stability of the unique almost periodic solutions of these systems are given.

• Communications of the Korean Mathematical Society
• /
• v.15 no.2
• /
• pp.309-323
• /
• 2000

The purposes of this paper are to revise the definitions of Ishikawa and Mann type iterative processes with errors, to study the unique solution of the m-accretive operator equation x+Tx=f and the convergence problem of Ishikawa and Mann type iterative processes with errors for m-accretive mappings without the Lipschitz condition. The results presented in this paper improve, extend, and unify the corresponding results in [4, 7, 8, 12, 16] in more general setting.

• Journal of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.191-205
• /
• 1998

In this paper, we prove that the Mann and Ishikawa iteration sequences with errors converge strongly to the unique solution of the equation x + Tx = f, where T is an m-accretive operator in uniformly smooth Banach spaces. Our results extend and improve those of Chidume, Ding, Zhu and others.

• Bulletin of the Korean Chemical Society
• /
• v.18 no.9
• /
• pp.1006-1010
• /
• 1997

The nature and analysis methods of complicated decay profiles found in forced Rayleigh scattering (FRS) have been investigated for the probe diffusion of methyl yellow in 2-propanol. The complementary shifted and ground state grating effect, which is known to be the origin of non-single exponential decays, was analyzed by non-linear regression fitting to a double exponential model function. We confirmed that the parameters were highly correlated so that it was difficult to extract a unique set of parameters in the presence of experimental noise. Nevertheless, a reasonable range of decay time constants could be estimated from the grating spacing dependence.

• Korean Journal of Mathematics
• /
• v.30 no.2
• /
• pp.375-389
• /
• 2022

In this paper, we prove some fixed-point theorems in partially ordered fuzzy metric spaces for (𝜙, 𝜓, 𝛽)-Geraghty contraction type mappings which are generalization of mappings with Geraghty contraction type condition. Application of the derived results are shown in proving the existence of unique solution to some boundary value problems.