It is well known that the bivariate polynomial interpolation problem at domain points of a triangle is correct. Thus the corresponding interpolation matrix $M$ is nonsingular. L.L. Schumaker stated the conjecture, that the determinant of... more
It is well known that the bivariate polynomial interpolation problem at domain points of a triangle is correct. Thus the corresponding interpolation matrix $M$ is nonsingular. L.L. Schumaker stated the conjecture, that the determinant of $M$ is positive. Furthermore, all its principal minors are conjectured to be positive, too. This result would solve the constrained interpolation problem. In this paper,
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Finite hamiltonian groups are counted. The sequence of numbers of all groups of order $n$ all whose subgroups are normal and the sequence of numbers of all groups of order less or equal to $n$ all whose subgroups are normal are presented.
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In this paper a problem of determining the dimension of the bivariate spline space S31(Δ) is studied. Under certain assumptions on the degrees of vertices and on the collinearity of edges, it is shown that the dimension of the spline... more
In this paper a problem of determining the dimension of the bivariate spline space S31(Δ) is studied. Under certain assumptions on the degrees of vertices and on the collinearity of edges, it is shown that the dimension of the spline space is equal to the lower bound, established by Schumaker in [7].
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Research Interests: Applied Mathematics, Finite Element Methods, Energy, Numerical Analysis, Finite element method, and 57 moreConvergence, Finite Element, Computing, Algorithm, Numerical Method, United Kingdom, Diophantine approximation, Elliptic curves, Higher Order Thinking, Linear Model, Singularity, Probability Distribution & Applications, Riemann zeta function, Extreme Value Theory, Newton Method, IEEE, APPROXIMATION ALGORITHM, Continued Fractions, Error Analysis, Arithmetics, Consistency, Convergence Rate, Discretization, Divergence, PARTIAL DIFFERENTIAL EQUATION, Recurrence Relation, VECTOR, Gaussian quadrature, Numerical Integration, Linear System, Harmonic, Second Order, Large classes, Numerical Analysis and Computational Mathematics, Lower Bound, Upper Bound, Multiplication, Chinese Remainder Theorem, Elliptic Curve Cryptography, Galerkin Method, Poisson Equation, Difference equation, Boundary Condition, Floating Point, Asymptotic Behavior, GAUSS, Convection Diffusion Equation, Mixed Method, Linear Equations, Algebraic Variety, Discontinuous Galerkin, Real Number, Condition number, Prime Number, American Mathematical Society, Hybrid Method, and Radius of Convergence
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One direction in exploring similarities among biological sequences (such as DNA, RNA, and proteins), is to associate with such systems ordered sets of sequence invariants. These invariants represent selected properties of mathematical... more
One direction in exploring similarities among biological sequences (such as DNA, RNA, and proteins), is to associate with such systems ordered sets of sequence invariants. These invariants represent selected properties of mathematical objects, such as matrices, that one can associate with biological sequences. In this article, we are exploring properties of recently introduced Line Distance matrices, and in particular we consider properties of their eigenvalues. We prove that Line Distance matrices of size n have one positive and n - 1 negative eigenvalues. Visual representation of Cauchy's interlacing property for Line Distance matrices is considered. Matlab programs for line distance matrices and examples are available on the following website: www.fmf.uni-lj.si/ approximately jaklicg/ldmatrix.html.
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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... more
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. A single GUV is transferred using a micropipette from a solution of a nonpermeable solute into an iso-osmolar solution of a solute with a higher membrane permeability. Osmotical swelling of the vesicle is monitored with a CCD camera mounted on a phase contrast microscope, and a sequence of images is obtained. On each image, the points on the vesicle contour are determined using Sobel filtering with adaptive binarization threshold, and from these, the vesicle radius is calculated with a great accuracy. From the time-dependence of the vesicle radius, the membrane permeability is obtained. Using a test set of data, the method provided a consistent estimate of the POPC membrane permeability for glycerol, P = 1.7 x 10^-8 m/s, with individual samples ranging from 1.61 x 10^-8 m/s to 1.98 x 10^-8 m/s. This value is ~40% lower than the one obtained on similar systems. Possible causes for this discrepancy are discussed.