• Communications of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.943-966
• /
• 2023

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan-Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with g satisfying some general growth at infinity.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.4
• /
• pp.747-752
• /
• 2012

When the service time distribution has a finite exponential moment, we present a large deviations result for the busy period distribution in the M/G/1 queue without the assumption of Abate and Whitt (1997) and Kyprianou (1971).

• Communications for Statistical Applications and Methods
• /
• v.14 no.1
• /
• pp.141-146
• /
• 2007

In this paper, we consider a Box-Cox transformed threshold GARCH(1,1) process and find a sufficient condition under which the process is geometrically ergodic and has the ${\beta}$-mixing property with an exponential decay rate.

• Journal of the Korean Statistical Society
• /
• v.35 no.1
• /
• pp.79-90
• /
• 2006

We consider the subdiagonal bilinear model and ARMA model with subdiagonal bilinear errors. Sufficient conditions for geometric ergodicity of associated Markov chains are derived by using results on generalized random coefficient autoregressive models and then strict stationarity and ,a-mixing property with exponential decay rates for given processes are obtained.

• Korean Journal of Fisheries and Aquatic Sciences
• /
• v.25 no.3
• /
• pp.219-228
• /
• 1992

The steady state and decay characteristics of primary fluorescence of twelve clones of phytoplankton were investigated in vivo. At 380-435nm region, intense fluorescence emission spectra were obtained from the all phytoplankton, examined', The primary fluorescence of phytoplankton in different growth states was examined In order to find out fluorophores for the observed fluorescence, eight different pteridine derivatives in phosphate buffer solution were examined for their fluorescence characteristics and compared with those of phytoplankton. Fluorescence lifetimes $(\tau)$ and decay curves were compared with standard solution of candidate organic compounds. Decay kinetics of observed fluorescence were shown as hi- and tri-exponential decay curves with 430nm cut-off filter for phytoplankton. Comparison between fluorescence characteristics of bacteria and phytoplankton showed distinct differences for their steady state fluorecence spectra and decay kinetics.

• Journal of Environmental Health Sciences
• /
• v.32 no.2 s.89
• /
• pp.132-139
• /
• 2006

Number of aerosol, CO, $CO_2$ and TVOC after one-, two-, three-cigarettes smoking were monitored with time every 10 minute for 180 minutes in the seminar room (volume $51.1m^3$) when poorly-ventilated. IAQ monitor (IAQRAE, model PGM-5210) and PortCount (TSI, model 8020) were used for monitoring. Aerosol was decreased with exponential decay equation and it was estimated that number of aerosol would be long suspended (one cigarette 75/cc. two cigarettes 66/cc, three cigarettes 141/cc by 8hrs after smoking). While CO was also decreased with exponential or linear decay equation and correlated with number of aerosol strongly, TVOC and $CO_2$ were increased with linear equation in accordance with time lag. Most of TVOC and $CO_2$ were above standard levels of Korean Indoor Air Quality (Ministry of Environment) without regarding number of cigarettes. When naturally ventilated, all of CO, $CO_2$ and TVOC concentrations were dramatically decreased below standard levels of Korean Indoor Air Quality.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
• /
• v.20 no.2
• /
• pp.171-183
• /
• 2022

The parent and daughter nuclides in a radioactive decay chain arrive at secular equilibrium once they have a large half-life difference. The characteristics of this equilibrium state can be used to estimate the production time of nuclear materials. In this study, a mathematical model and algorithm that can be applied to radio-chronometry using the radioactive equilibrium relationship were investigated, reviewed, and implemented. A Bateman equation that can analyze the decay of radioactive materials over time was used for the mathematical model. To obtain a differential-based solution of the Bateman equation, an algebraic numerical solution approach and two different matrix exponential functions (Moral and Levy) were implemented. The obtained result was compared with those of commonly used algorithms, such as the Chebyshev rational approximation method and WISE Uranium. The experimental analysis confirmed the similarity of the results. However, the Moral method led to an increasing calculation uncertainty once there was a branching decay, so this aspect must be improved. The time period corresponding to the production of nuclear materials or nuclear activity can be estimated using the proposed algorithm when uranium or its daughter nuclides are included in the target materials for nuclear forensics.

• Journal of Environmental Health Sciences
• /
• v.28 no.5
• /
• pp.59-64
• /
• 2002

The photocatalytic decolorization of the Rhodamine B (RhB) was studied using a UV/TiO$_2$ reactor. Yakuri titanium dioxide(anatase) was used as the suspended photocatalyst and proved to be effective for decolorization irradiated with UV light (254 mm). The photocatalyzed dioxide concentrations, light intensity and air flow rates. In 0.01 mM RhB, color could be completely photodegraded after 3 hours. Absorption spectrum of an aqueous solution containing RhB showed a continued diminution of the RhB concentration in the solution bulk : concomitantly, no new absorption peaks appeared. This confirmed the decolorization of RhB, i.e., the break up of the chromopore. The optimum loaded titanium dioxide for the decolorization was 0.75 g/(equation omitted). The light intensity showed exponential decay with distance. The decay of light intensity of RhB solution showed different tendency from TiO$_2$. These results suggested that the photocatalytic decolorization of dyes may be available method for decolorizing in wastewater.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
• /
• 2001.06a
• /
• pp.1128-1128
• /
• 2001

We have developed a probe for measuring the light levels inside illuminated fruit. The probe has minimal effect on the light levels being measured and enables the sampling of the light flux at any point within the fruit. We present experimental light extinction rates within apple, nashi, kiwifruit, and mandarin fruit. Moving from the illuminated side to the far side of the fruit, the extinction level follows an initial power law decay as the light diffuses into the fruit then reduces to an exponential decay through the rest of the fruit. Significant variations in the rates of light extinction are found in the core, skin and differing flesh regions. Monte Carlo simulations of the light distribution in fruit, which use scattering and absorption coefficients for the diffusely scattering tissue, and boundary conditions for the skin effects, produce results that follow the experimental results closely.

• East Asian mathematical journal
• /
• v.32 no.5
• /
• pp.659-675
• /
• 2016

In this paper, we study the generalized Kirchhoff type equation in the presence of past and finite history $$\large u_{tt}-M(x,t,{\tau},\;{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\\hspace{25}-{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{-{\infty}}}^t}\;k(t-{\tau}){\Delta}u(x,t)d{\tau}+{\mid}u{\mid}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the expoential decay rate of the Kirchhoff type energy.