Matrix Lax Polynomials, Geometry of Prym Varieties and Systems of Hess–Appel’rot Type

We consider a four-dimensional generalization of Hess–Appel’rot system and costruct its Lax pair. Both classical and algebro-geometric integration procedure are proceeded. The algebro-geometric integration is based on deep facts from geometry of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. The integration is similar to the integration of Lagrange bitop which has recetly been performed by the authors.     

Rational summation ofp-adic series

The problem of rational summation for a wide class ofp-adic convergent series is considered. Here, rational summation refers to the method of obtaining the rational sum of a power series for a rational value of its variable. A formula suitable for this summation is derived. Conditions for rational summability are obtained. Rational summation is possible only for special forms of the series. It is shown that the inverse problem of rational summation is always solvable. This is illustrated by some characteristic examples. Possible rational (adelic) summation of divergent perturbative expansions in string theory, and quantum field theory, is discussed.Institute of Physics, P.O. Box 57, 11001 Belgrade, Yugoslavia. Published in Toereticheskaya i Matematicheskaya Fizika, Vol. 100, No. 3, pp. 342–353, September, 1994.     

On the p-adic summability of the anharmonic oscillator

Some remarkable arithmetic properties of the anharmonic oscillator are considered. The concept of the p-adic summability is discussed. For the ground-state energy of the anharmonic oscillator the p-adic summability is shown.     

Stereospecific Ligands and Their Complexes. III. Oxalato and Malonato-(ethylenediamine- N , N ′-di- S , S -2-propionato)-Chromate(III) Complexes. Crystal Structure of the Δ-(–)589- s - cis -K[Cr( S , S -eddp)(ox)]?·?0.5H2O

Abstract  The s-cis-[Cr(S,S-eddp)L]⁻ complexes (S,S-eddp = S,S-ethylenediamine-N,N′-di-2-propionate ion; L = oxalate or malonate ions) were prepared. The complexes were purified by ion-exchange chromatography. The geometry of the complexes has been supposed on the basis of the electronic absorption spectra, and the absolute configurations of the isolated s-cis-[Cr(S,S-eddp)L]⁻ complexes have been predicted on the basis of their circular dichroism (CD) spectra and confirmed by X-ray analysis of the crystal structure of the Δ-(–)₅₈₉-s-cis-K[Cr(S,S-eddp)(ox)] 0.5H₂O complex. Index Abstract  The title compound, s-cis-potassium-(ethylenediamine-N,N’-di-S,S-2-propionato) (oxalato)chromate(III) semihydrate was synthesized by passing the corresponding sodium salt through cation exchange-resin Merck I in potassium form and its crystal structure determined. Single crystal X-ray diffraction analysis reveals s-cis geometry of the complex cation. For Part II see Glodjović VV, Trifunović SR (2008) J Serb Chem Soc 73:541.     

Singular Manakov flows and geodesic flows on homogeneous spaces of SO(N)

We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous spaces SO(n)/SO(k₁) ×⋯× SO(k _r ), for any choice of k ₁,…,k _r , k ₁ + ⋯ + k _r ⩽ n. In particular, a new proof of the integrability of a Manakov symmetric rigid body motion around a fixed point is presented. Also, the proof of integrability of the SO(n)-invariant Einstein metrics on SO(k ₁ + k ₂ + k ₃)/SO(k ₁) × SO(k ₂) × SO(k ₃) and on the Stiefel manifolds V (n, k) = SO(n)/SO(k) is given.     

Isolation of Hemoglobin from Bovine Erythrocytes by Controlled Hemolysis in the Membrane Bioreactor

In this work, we describe an optimized procedure based on gradual hemolysis for the isolation of hemoglobin derived from bovine slaughterhouse erythrocytes in a membrane bioreactor. The membrane bioreactor system that provided high yields of hemoglobin (mainly oxyhemoglobin derivate) and its separation from the empty erythrocyte membranes (ghosts) was designed at a pilot scale. Ten different concentrations of hypotonic media were assessed from the aspect of the extent of hemolysis, hematocrit values of the erythrocyte suspensions, cell swelling, and membrane deformations induced by decreased salt concentration. Effective gradual osmotic hemolysis with an extent of hemolysis of 88% was performed using 35 mM Na-phosphate/NaCl buffer of pH 7.2–7.4. Under these conditions most of the cell membranes presented the appearance of the normal ghosts under phase contrast microscope. The hemoglobin purity of >80% was confirmed by SDS-PAGE. Kinetic studies showed that maximal concentration of hemoglobin was reached after 40 min, but the process cycle at which recovery of 83% was achieved lasted for 90 min. The dynamics of both steps, (1) transport through the membrane of erythrocytes during process of hemolysis and (2) transport through the reactor filters, were evaluated.     

Metal complexes with chloramphenicol: Part I. Polarographic investigation of copper-chloramphenicol complexes

Polarographic investigations of copper-chloramphenicol (Hf) complex were performed in 1 M NaCl which was used as the supporting electrolyte, at pH values from 11 to 13. Amperometric titration method was used to determine the composition of the complex compound. The molar ratio Cu to Hf varies with pH value of solution but not with relative KOH to Hf ratio. At pH values 12–12.5 amperometric curves indicate formation of complex compound with Cu to Hf molar ratio equal 1:2. It was found that a two-electron irreversible process takes place on the DME. The value of diffusion coefficient of the reducible species D=9.25×10^?7 cm² s^?2 was found.     

On the cases of Kirchhoff and Chaplygin of the Kirchhoff equations

It is proven that the completely integrable general Kirchhoff case of the Kirchhoff equations for B ?? 0 is not an algebraic complete integrable system. Similar analytic behavior of the general solution of the Chaplygin case is detected. Four-dimensional analogues of the Kirchhoff and the Chaplygin cases are defined on e(4) with the standard Lie-Poisson bracket.