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...

To each non totally real cubic extension K of Q and to each generator α of the cubic field K, we attach a family of cubic Thue equations, indexed by the units of K, and we prove that this family of cubic Thue equations has only a finite number of integer solutions, by giving an effective upper bound for these solutions.

Given any family of cubic fields defined by local conditions at finitely many primes, we determine the mean number of 2-torsion elements in the class groups and narrow class groups of these cubic fields, when they are ordered by their absolute discriminants. For an order O in a cubic field, we study the three groups: Cl2(O), the group of ideal classes of O of order 2; Cl2 (O), the group of narr...

It was conjectured by Hoffmann-Ostenhof that the edge set of every cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. We prove the conjecture for 3-connected cubic plane graphs and 3-connected cubic graphs on the projective plane. Our proof provides a polynomial time algorithm to find the decomposition for 3-connected cubic plane graphs.

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 isomorphic simplest cubic fields. By applying R. Okazaki’s result for isomorphic simplest cubic fields, we obtain all solutions to the family of cubic Thue equations for k | m + 3m + 9.