• Journal of Applied and Pure Mathematics
• /
• v.5 no.1_2
• /
• pp.69-93
• /
• 2023

Here we give multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a parametrized Gudermannian sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.367-376
• /
• 1996

We characterize best simultaneous approximations from a finite-dimensional subspace of a normed linear space. In the characterization we reveal usefulness of a minimax theorem presented in [2,4].

• Journal of the Korean Data and Information Science Society
• /
• v.9 no.2
• /
• pp.255-262
• /
• 1998

In this paper, we study the saddlepoint approximations for the ratio of independent random variables. In Section 2, we derive the saddlepoint approximation to the probability density function. In Section 3, we represent a numerical example which shows that the errors are small even for small sample size.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.377-387
• /
• 2006

In this paper, some characterizations of representation for continuous linear functionals on $2{\kappa}$-inner product spaces in terms of best approximations and orthogonalities are given.

• Journal of the Korean Data and Information Science Society
• /
• v.11 no.1
• /
• pp.103-110
• /
• 2000

Suppose that there is a population of hidden objects of which the total number N is unknown. From such data, we derive second-order approximations to the stopping time with fixed proportional accuracy.

• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.1-14
• /
• 1999

In this paper we shall analyze the fully discrete Galerkin type approximations to solutions of the Rosenau equation. We provide the numerical results of several cases.

• Communications for Statistical Applications and Methods
• /
• v.13 no.1
• /
• pp.141-150
• /
• 2006

Penalized likelihood regression for exponential families have been considered by Kim (2005) through smoothing parameter selection and asymptotically efficient low dimensional approximations. We derive approximate Bayesian confidence intervals based on Bayes model associated with lower dimensional approximations to provide interval estimates in penalized likelihood regression and conduct empirical studies to access their properties.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.20 no.4
• /
• pp.596-601
• /
• 2010

Weinvestigatethevariousoperationsoflowerandupperapproximationsonastscquantalelattice L.

• Nuclear Engineering and Technology
• /
• v.48 no.1
• /
• pp.98-113
• /
• 2016

A reactor vessel level monitoring system measures the water level in a reactor during normal operation and abnormal conditions. A drop in the water level can expose nuclear fuel, which may lead to fuel meltdown and radiation spread in accident conditions. A level monitoring system mainly consists of a sensing line and pressure transmitter. Over a period of time boron sediments or other impurities can clog the line which may degrade the accuracy of the monitoring system. The aim of this study is to determine blockage in a sensing line using the energy of the composite signal. An equivalent Pi circuit model is used to simulate blockages in the sensing line and the system's response is examined under different blockage levels. Composite signals obtained from the model and plant's unblocked and blocked channels are decomposed into six levels of details and approximations using a wavelet filter bank. The percentage of energy is calculated at each level for approximations. It is observed that the percentage of energy reduces as the blockage level in the sensing line increases. The results of the model and operational data are well correlated. Thus, in our opinion variation in the energy levels of approximations can be used as an index to determine the presence and degree of blockage in a sensing line.

• Journal of the Korean Data and Information Science Society
• /
• v.25 no.6
• /
• pp.1171-1180
• /
• 2014

We considered saddlepoint approximations to VaR (value at risk) and ES (expected shortfall) which frequently encountered in finance and insurance as the measures of risk management. In this paper we supposed univariate and multivariate skew-normal distributions, instead of traditional normal class distributions, as underlying distribution of linear portfolios. Simulation results are provided and showed the suggested saddlepoint approximations are very accurate than normal approximations.