Bodil Branner and John Hubbard produced the first extensive study of iterated complex maps for cubic polynomials in Picard orbit [Acta Math., 160(3-4):1988, 143-206]. Since then few researchers worked on Julia sets for cubic polynomials. In 2004, Rani and Kumar [J. Korea Soc. Math. Educ. Ser. D; Research in Math. Educ., 8(4):2004, 261-277] studied cubic polynomials in superior orbit and gave im...

Bivariate cubic L1 smoothing splines are introduced. The coefficients of a cubic L1 smoothing spline are calculated by minimizing the weighted sum of the L1 norms of second derivatives of the spline and the 1 norm of the residuals of the data-fitting equations. Cubic L1 smoothing splines are compared with conventional cubic smoothing splines based on the L2 and 2 norms. Computational results fo...

Cubic membranes are soft three-dimensional crystals found within cell organelles in a variety of living systems, despite the aphorism of Fedorov: 'crystallization is death'. They consist of multi-bilayer lipid-protein stacks, folded onto anticlastic surfaces that resemble triply periodic minimal surfaces, forming highly swollen crystalline sponges. Although cubic membranes have been observed in...

We investigate univariate and bivariate binary subdivision schemes based on cubic B-splines with double knots. It turns out that double knots change the behaviour of a uniform cubic scheme from primal to dual. We focus on the analysis of new bivariate cubic schemes with double knots at extraordinary points. These cubic schemes produce C surfaces with the original Doo-Sabin weights.

In this paper we define some operations such as P-union, P-intersection, R-union, R-intersection for neutrosophic cubic soft sets (NCSSs). We prove some theorems on neutrosophic cubic soft sets. We also discuss various approaches of Internal Neutrosophic Cubic Soft Sets (INCSSs) and external neutrosophic cubic soft sets (ENCSSs). We also investigate some of their properties.

Colloidal cubic silicon carbide (SiC) nanocrystals with an average diameter of 4.4 nm have been fabricated by anisotropic wet chemical etching of microsized cubic SiC powder. Fourier transform infrared spectra show that these cubic SiC nanocrystals contain carboxylic acid, SiH, CH, and CHx groups. UV/Vis absorption and photoluminescence (PL) spectroscopy clearly indicate that water and ethanol ...

We give a correspondence between non-trivial solutions to a parametric family of cubic Thue equations X − mXY − (m + 3)XY 2 − Y 3 = k where k | m + 3m+ 9 and non-isomorphic simplest cubic fields. By applying R. Okazaki’s result for non-isomorphic simplest cubic fields, we obtain all solutions to the family of cubic Thue equations for k | m + 3m+ 9.

A hydrothermal method for preparation of nano-size zirconia has been studied to optimize the effective parameters (precursor concentration, temperature and time) using response surface methodology (RSM). The synthesized zirconia samples were characterized through X-ray diffraction (XRD), scanning electron microscope (SEM) and transmission electron microscopy (TEM) analyses to identify mean nano...