A technique for determining the permeability of a phospholipid membrane on a single giant unilamellar vesicle (GUV) is described, which complements the existing methods utilizing either a planar black lipid membrane or sub-micrometre-sized liposomes. In this paper, we propose a complementary technique based on an analysis of a sequence of videomicroscopy images and the approximation of circles.
COBISS.SI-ID: 25510361
In the 1960s, Atkinson showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems. In this paper, the above relation is extended to singular two-parameter eigenvalue problems for the first time. In particular, it is shown that the simple finite regular eigenvalues of a two-parameter eigenvalue problem and the associated system of singular generalized eigenvalue problems agree. Based on the above, we obtained the first numerical method for the singular two-parameter eigenvalue problem.
COBISS.SI-ID: 15261017
Stone Duality (ASD) is a direct axiomatisation of general topology, which reconciles mathematical and computational viewpoints, providing an inherently computable calculus. The core of the paper constructs the real line using two-sided Dedekind cuts. We show that the closed interval is compact and overt, where these concepts are defined using quantifiers. The interval domain plays an important foundational role. We make a thorough study of arithmetic, in which operations are more complicated than Moore's, because we work constructively, and we also consider back-to-front (Kaucher) intervals.
COBISS.SI-ID: 15322201
In this paper, geometric Hermite interpolation by planar cubic $G^1$ splines is studied. Three data points and three tangent directions are interpolated per polynomial segment. Sufficient conditions for the existence of such a $G^1$ spline are determined that cover most of the cases encountered in practical applications. The existence requirements are based only upon geometric properties of data and can easily be verified in advance. The optimal approximation order 6 is confirmed, too.
COBISS.SI-ID: 15508569
The dilation coefficient of a graph representation is defined as the quotient of the longest and the shortest edge representation. The minimum of the dilation coefficients over all planar representations of a graph ?$G$? is called the dilation coefficient of the graph ?$G$?. The dilation coefficient of different planar representations of complete graphs is considered and upper and lower bounds for the dilation coefficients of complete graphs are given. Two iterative graph-drawing algorithms that try to minimize the dilation coefficient of a given graph are given.
COBISS.SI-ID: 15390809