• Bulletin of the Korean Mathematical Society
• /
• v.30 no.2
• /
• pp.179-185
• /
• 1993

In this article S is a topologically complete subspace of $R^{1}$i.e., the relativized topology on S may be metrized so as to make S complete. B(S) is the Borel .sigma.-field of S. For .GAMMA. one takes a set of measurable monotone (increasing or dereasing) functions on S into itself. Make the assumption of pp. There exists $x_{0}$ and a positive integer $n_{0}$ such that (Fig.) It is then shown that there exists a unique inveriant probability to which $p^{(n)}$ (x,dy) converges exponentially fast in a metric (stronger than the Kolmogorov distance); this convergence is uniform for all x .mem. S. This generalizes an earlier result of Bhattacharya and Lee (1988) who considered monotone nondecreasing maps on S.

• 한국연소학회:학술대회논문집
• /
• 2004.11a
• /
• pp.97-106
• /
• 2004

Stability of laminar premixed planar flames inclined in gravitational field which generate vorticity is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it becomes more unstable due to not only the decrease of stabilizing effect of gravity but also the increase of destabilizing effect of rotational flow. The obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable flame wave depends on not only the flame angle but also the Lewis number. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.

• 한국연소학회:학술대회논문집
• /
• 2014.11a
• /
• pp.135-137
• /
• 2014

Excess enthalpy flame propagating an porous inert medium, which recirculate exhaust heat to the upstream cold mixture, is theoretically analyzed. Using the activation-energy asymptotics, the flame structure is divided into the thin reaction and the gas-phase preheat zone, as is traditionally done. Ahead and behind of the two, there exist an outer preheat zone, where heat is convectively transferred from solid to gas, and a downstream re-equilibrium zone, where thermal equilibrium between phases is established. Asymptotic solutions of species and energy equations in each zone are obtained and then matched to each other, and finally the mass burning rate is obtained as a function of the flame propagation velocity with respect to the solid phase and physical properties of gas and solid.

• The Pure and Applied Mathematics
• /
• v.9 no.1
• /
• pp.81-90
• /
• 2002

The least informative (favorable) distributions, minimizing Fisher information for a multivariate location parameter, are derived in the parametric class of the exponential-power spherically symmetric distributions under the following characterizing restrictions; (i) a bounded variance, (ii) a bounded value of a density at the center of symmetry, and (iii) the intersection of these restrictions. In the first two cases, (i) and (ii) respectively, the least informative distributions are the Gaussian and Laplace, respectively. In the latter case (iii) the optimal solution has three branches, with relatively small variances it is the Gaussian, them with intermediate variances. The corresponding robust minimax M-estimators of location are given by the $L_2$-norm, the $L_1$-norm and the $L_{p}$ -norm methods. The properties of the proposed estimators and their adaptive versions ar studied in asymptotics and on finite samples by Monte Carlo.

• Communications for Statistical Applications and Methods
• /
• v.14 no.2
• /
• pp.287-299
• /
• 2007

We consider a multiclass queue where queued customers are served in their order of arrival at a rate which depends on the customer type. By using the asymptotic results obtained by Dabrowski et al. (2006) we calculate the sharp asymptotics of the stationary distribution of the number of customers of each class in the system and the distribution of the number of customers of each class when the total number of customers reaches a high level before emptying. We also obtain a fast simulation algorithm to estimate the overflow probability and compare it with the general simulation and asymptotic results.

• Communications for Statistical Applications and Methods
• /
• v.21 no.3
• /
• pp.213-224
• /
• 2014

In this paper, we study the problem of transforming to normality. We propose to estimate the transformation parameter by minimizing a weighted squared distance between the empirical characteristic function of transformed data and the characteristic function of the normal distribution. Our approach also allows for other symmetric target characteristic functions. Asymptotics are established for a random sample selected from an unknown distribution. The proofs show that the weight function $t^{-2}$ needs to be modified to have thinner tails. We also propose the method to compute the influence function for M-equation taking the form of U-statistics. The influence function calculations and a small Monte Carlo simulation show that our estimates are less sensitive to a few outliers than the maximum likelihood estimates.

• Journal of the Korean Society of Combustion
• /
• v.9 no.4
• /
• pp.9-21
• /
• 2004

Stability of laminar premixed planar flames inclined in the gravitational field is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it becomes more unstable due to not only the decrease of stabilizing effect of gravity but also the increase of destabilizing effect of rotational flow. The obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable flame wave depends on not only the flame angle but also the Lewis number. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.

• Journal of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.225-239
• /
• 2006

In [5], Csorgo and Zitikis exposed the strong $uniform-over-[0,\;{\infty}]$ consistency, and weak $uniform-over-[0,\;{\infty}]$ approximation of the empirical mean residual life process by employing weight functions. We carry on the uniform asymptotic behaviors of the empirical mean residual life process over the whole positive half line by representing the process as an integral form. We compare our results with those of Yang [15], Hall and Wellner [8], and Csorgo and Zitikis [5].

• The Korean Journal of Applied Statistics
• /
• v.13 no.2
• /
• pp.371-381
• /
• 2000

In this paper, we describes smoothing spline in nonparametric regression and some asymptotic results for estimates of the regression cofficients in the parametric part were biased on semi parametric regression estimator.

• Journal of the Korean Statistical Society
• /
• v.27 no.4
• /
• pp.421-433
• /
• 1998

In this paper, matching priors for P(X < Y) are investigated when both distributions are exponential distributions. Two recent approaches for finding noninformative priors are introduced. The first one is the verger and Bernardo's forward and backward reference priors that maximizes the expected Kullback-Liebler Divergence between posterior and prior density. The second one is the matching prior identified by matching the one sided posterior credible interval with the frequentist's desired confidence level. The general forms of the second- order matching prior are presented so that the one sided posterior credible intervals agree with the frequentist's desired confidence levels up to O(n$^{-1}$ ). The frequentist coverage probabilities of confidence sets based on several noninformative priors are compared for small sample sizes via the Monte-Carlo simulation.