New Examples of Systems of the Kowalevski Type

A new examples of integrable dynamical systems are constructed. An integration procedure leading to genus two theta-functions is presented. It is based on a recent notion of discriminantly separable polynomials. They have appeared in a recent reconsideration of the celebrated Kowalevski top, and their role here is analogue to the situation with the classical Kowalevski integration procedure.Comment: 17 page

Billiard algebra, integrable line congruences, and double reflection nets

The billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the operational consistency for the billiard algebra, is equivalent to an integrabilty condition of a line congruence. A new notion of the double-reflection nets as a subclass of dual Darboux nets associated with pencils of quadrics is introduced, basic properies and several examples are presented. Corresponding Yang-Baxter maps, associated with pencils of quadrics are defined and discussed.Comment: 18 pages, 8 figure

Systems of Hess-Appel'rot Type and Zhukovskii Property

We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination of both integrable and non-integrable properties. Further, following integrable line, we study partial reductions and systems having what we call the {\it Zhukovskii property}: these are Hamiltonian systems with invariant relations, such that partially reduced systems are completely integrable. We prove that the Zhukovskii property is a quite general characteristic of systems of Hess-Appel'rote type. The partial reduction neglects the most interesting and challenging part of the dynamics of the systems of Hess-Appel'rot type - the non-integrable part, some analysis of which may be seen as a reconstruction problem. We show that an integrable system, the magnetic pendulum on the oriented Grassmannian $Gr^+(4,2)$ has natural interpretation within Zhukovskii property and it is equivalent to a partial reduction of certain system of Hess-Appel'rot type. We perform a classical and an algebro-geometric integration of the system, as an example of an isoholomorphic system. The paper presents a lot of examples of systems of Hess-Appel'rot type, giving an additional argument in favor of further study of this class of systems.Comment: 42 page

On p-Adic Sector of Adelic String

We consider construction of Lagrangians which are candidates for p-adic sector of an adelic open scalar string. Such Lagrangians have their origin in Lagrangian for a single p-adic string and contain the Riemann zeta function with the d'Alembertian in its argument. In particular, we present a new Lagrangian obtained by an additive approach which takes into account all p-adic Lagrangians. The very attractive feature of this new Lagrangian is that it is an analytic function of the d'Alembertian. Investigation of the field theory with Riemann zeta function is interesting in itself as well.Comment: 10 pages. Presented at the 2nd Conf. on SFT and Related Topics, Moscow, April 2009. Submitted to Theor. Math. Phy

Closed geodesics and billiards on quadrics related to elliptic KdV solutions

We consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards. Namely, generic complex invariant manifolds are not Abelian varieties, and the billiard map is no more algebraic. A Poncelet-like theorem for such system is known. We give explicit sufficient conditions both for closed geodesics and periodic billiard orbits on Q and discuss their relation with the elliptic KdV solutions and elliptic Calogero systemComment: 23 pages, Latex, 1 figure Postscrip

On integrability of Hirota-Kimura type discretizations

We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.Comment: 47 pages, some minor change

"It All Ended in an Unsporting Way": Serbian Football and the Disintegration of Yugoslavia, 1989-2006

Part of a wider examination into football during the collapse of Eastern European Communism between 1989 and 1991, this article studies the interplay between Serbian football and politics during the period of Yugoslavia's demise. Research utilizing interviews with individuals directly involved in the Serbian game, in conjunction with contemporary Yugoslav media sources, indicates that football played an important proactive role in the revival of Serbian nationalism. At the same time the Yugoslav conflict, twinned with a complex transition to a market economy, had disastrous consequences for football throughout the territories of the former Yugoslavia. In the years following the hostilities the Serbian game has suffered decline, major financial hardship and continuing terrace violence, resulting in widespread nostalgia for the pre-conflict era

Microencapsulation of Olive Leaf Extract by Spray Drying

The aim of this research was to obtain a high value powder of olive leaf extract (OLE) rich in polyphenols by spray drying. Since carrier, polyphenols/carrier ratio, and inlet temperature could have an impact on process yield and polyphenol retention, to define the most promising drying conditions for OLE experiment with gallic acid model solutions (GAS) was conducted. Influence of carrier type (maltodextrin, inulin, gum arabic, and their two-component blends), polyphenols/carrier ratio, and temperature on process yield of spray dried GAS was examined, and for each carrier the most promising temperature and ratio were selected. Optimal temperature for all GAS samples was 150°C, and optimal gallic acid/carrier ratio for samples with inulin or gum arabic was 3:1, while for all other combinations it was 5:1. In OLE powder produced under these conditions, polyphenol content and physical properties (rehydration, bulk density) were determined. Mixture of maltodextrin and gum arabic resulted in the highest OLE product yield (54.48%) and the highest polyphenol retention (56.50%) obtaining good physical properties (bulk density =0.31 g ml–1, rehydration time=98 s), while use of inulin resulted in the lowest yield (32.71%), polyphenol retention (28.24%), bulk density (0.25 g ml–1), and the highest rehydration time (140 s)

Geodesic flows on Riemannian g.o. spaces

We prove the integrability of geodesic flows on the Riemannian g.o. spaces of compact Lie groups, as well as on a related class of Riemannian homogeneous spaces having an additional principal bundle structure.Comment: 12 pages, minor corrections, final versio

p-Adic View of the Genetic Code

p-Adic View of the Genetic Code. Fifth International Conference in Code Biolog