Conformal Mappings of Riemannian Spaces onto Ricci Symmetric Spaces

Mathematical Notes -     

Projective equivalence and manifolds with equiaffine connection

In this paper, we prove that all manifolds with affine or projective connection are globally projectively equivalent to some manifolds with equiaffine connection (equiaffine manifold).     

Development of an automated flow injection chemiluminescence immunoassay for human immunoglobulin G

The development of a competitive solid phase flow-injection immunoassay with on-column chemiluminescence detection is described. The immunoreactor column consists of a transparent teflon tubing packed with immobilized antibodies. It is placed in front of the photomultiplier tube. The entire assay takes place in this immunoreactor cell. The assay is performed by injection of a mixture of sample HIgG and acridinium labeled HIgG followed by hydrogen peroxide to initiate the chemiluminescence reaction. One assay cycle including regeneration takes 7 min. The system is fully automated and controlled by computer to ensure exact timing resulting in a precision of 1 to 3%, dependent on concentration. The detection limit was 7 fmol. The method was applied to serum samples without any sample clean-up. The average recovery from spiked serum samples was 103%.Dedicated to Professor Dr. Dr. h.c. mult. J.F.K. Huber on the occasion of his 70 birthday     

Geodesic mapping onto Kählerian spaces of the first kind

In the present paper a generalized Kählerian space Open image in new window of the first kind is considered as a generalized Riemannian space \(\mathbb{G}\mathbb{R}_N \) with almost complex structure F _i ^h that is covariantly constant with respect to the first kind of covariant derivative.Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings f: Open image in new window with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives with respect to unknown components of the metric tensor and the complex structure of the Kählerian space Open image in new window .     

Infinitesimal F-planar transformations

The theory of F-planar maps of Riemannian spaces and affinely connected spaces developed by J. Mike? and N. S. Sinyukov [1–6] naturally extends the theory of geodesic and holomorphic projective maps. In the present paper we find basic equations of infinitesimal F-planar maps and study these equations. The F-planar maps are maps between spaces endowed with affinor structures. The geometry of Riemannian spaces and affinely connected spaces endowed by affinor structures was investigated by A. P. Shirokov (see, e.g., [7–14]) who also studied maps between spaces of this type ([13, 14]).     

Polynomials associated with a functional product of the Hermite type

We have found the motivation for this paper in the research of a quantized closed Friedmann cosmological model. There, the second‐order linear ordinary differential equation emerges as a wave equation for the physical state functions. Studying the polynomial solutions of this equation, we define a new functional product in the space of real polynomials. This product includes the indexed weight functions which depend on the degrees of participating polynomials. Although it does not have all of the properties of an inner product, a unique sequence of polynomials can be associated with it by an additional condition. In the special case presented here, we consider the Hermite‐type weight functions and prove that the associated polynomial sequence can be expressed in the closed form via the Hermite polynomials. Also, we find their Rodrigues‐type formula and a four‐term recurrence relation. In contrast to the zeros of Hermite polynomials, which are symmetrically located with respect to the origin, the zeros of the new polynomial sequence are all positive. Copyright © 2015 John Wiley & Sons, Ltd.     

Applications of a simultaneous assay of ascorbic acid, dehydroascorbic acid and ascorbic sulphate in biological materials

A modified spectrophotometric assay for ascorbic acid and its derivatives based on their reaction with 2,4-dinitrophenylhydrazine (DNPH) is described. Using standard ascorbic acid or ascorbic sulphate solutions, together with animal tissue or compound diet extracts, the conditions for ascorbic acid degradation were determined. For the differential measurement of reduced ascorbic acid (AA), dehydroascorbic acid (dAA) and ascorbic sulphate (AS), five series of simultaneous determinations were performed. These included the use of (1) KBrO3 for the hydrolysis of AS, (2) 2,6-dichlorophenolindophenol as an oxidant, (3) DNPH to form a hydrazone derivative with dAA and (4 and 5) two blanks (where ascorbate was degraded) to correct for interfering substances. A variety of vertebrate and invertebrate tissues were examined for their ascorbate content, and the advantages of the modified procedure over currently available assays are discussed. The results suggest that the Artemia cyst is a unique material in which ascorbic sulphate is present in large amounts whereas fish tissues do not contain this form of vitamin C.     

Conformal mappings onto Einstein spaces

We study conformal mappings of Riemannian manifolds onto Einstein manifolds under minimal condition on the differentiability class of manifolds in question. We establish under what conditions the linear equations obtained by J. Mike?, M. L. Gavril’chenko and E. I. Gladyscheva that define such mappings.     

Geodesic Maps “in the Large” of Ricci-Flat Spaces with $$n$$ Complete Geodesic Lines

Mathematical Notes -