Richards's curve induced Banach space valued multivariate neural network approximation.

Here, we present multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or by the multivariate normalized, quasi-interpolation, Kantorovich-type and quadrature-type neural network operators. We examine also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high-order Fréchet derivatives.

Richards's curve induced Banach space valued ordinary and fractional neural network approximation.

Here we perform the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative or fractional derivatives. Our operators are defined by using a density function generated by the Richards curve, which is generalized logistic function.

[Hearing Disorders with Glaucoma].

One of the most common sensory impairments of elderly people is hearing loss. Glaucoma is one of the leading causes of blindness worldwide. Hearing and vision loss typically increase with older age.

Optical coherence tomography, scanning laser polarimetry and confocal scanning laser ophthalmoscopy in retinal nerve fiber layer measurements of glaucoma patients.

Purpose: To determine the correlations and strength of association between different imaging systems in analyzing the retinal nerve fiber layer (RNFL) of glaucoma patients: optical coherence tomography (OCT), scanning laser polarimetry (SLP) and confocal scanning laser ophthalmoscopy (CSLO).

Materials And Methodology: 114 eyes of patients with moderate open angle glaucoma underwent spectral domain OCT (Topcon SD-OCT 2000 and Zeiss Cirrus HD-OCT), SLP (GDx VCC and GDx Pro) and CSLO (Heidelberg Retina Tomograph, HRT 3). Correlation coefficients were calculated between the structural parameters yielded by these examinations.