The aspherical Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups

The Cavicchioli–Hegenbarth–Repovš generalized Fibonacci groups are defined by the presentations Gn (m, k) = 〈x 1, … , xn | xixi+m = xi+k (1 ⩽ i ⩽ n)〉. These cyclically presented groups generalize Conway's Fibonacci groups and the Sieradski groups. Building on a theorem of Bardakov and Vesnin we classify the aspherical presentations Gn (m, k). We determine when Gn (m, k) has infinite abelianization and provide sufficient conditions for Gn (m, k) to be perfect. We conjecture that these are also necessary conditions. Combined with our asphericity theorem, a proof of this conjecture would imply a classification of the finite Cavicchioli–Hegenbarth–Repovš groups

Vacuum Photon Splitting in Lorentz-Violating Quantum Electrodynamics

Radiative corrections arising from Lorentz violation in the fermion sector induce a nonzero amplitude for vacuum photon splitting. At one loop, the on-shell amplitude acquires both CPT-even and CPT-odd contributions forbidden in conventional electrodynamics.Comment: 4 pages, minor wording changes, references added, accepted in Physical Review Letter

On the action principle for a system of differential equations

We consider the problem of constructing an action functional for physical systems whose classical equations of motion cannot be directly identified with Euler-Lagrange equations for an action principle. Two ways of action principle construction are presented. From simple consideration, we derive necessary and sufficient conditions for the existence of a multiplier matrix which can endow a prescribed set of second-order differential equations with the structure of Euler-Lagrange equations. An explicit form of the action is constructed in case if such a multiplier exists. If a given set of differential equations cannot be derived from an action principle, one can reformulate such a set in an equivalent first-order form which can always be treated as the Euler-Lagrange equations of a certain action. We construct such an action explicitly. There exists an ambiguity (not reduced to a total time derivative) in associating a Lagrange function with a given set of equations. We present a complete description of this ambiguity. The general procedure is illustrated by several examples.Comment: 10 page

Fruit and vegetable juice fermentation with Bifidobacteria

Consumers are becoming more interested in healthy nutrition. To meet consumer requirements, the possibility of the fruit and vegetable juice fermentation by bifidobacteria was investigated. Sour cherry, orange, carrot, and tomato juice was fermented with five Bifidobacterium strains (from human origin and starter culture). The tested strains have grown well in orange, carrot, and tomato juices. The B. longum Bb-46 strain demonstrated the best growth activities. It was found that ratio of the produced acetic and lactic acids are dependent on the Bifidobacterium strain rather than on the fermentation medium. The most intensive inhibition was observed against the Campylobacter jejuni strain. In course of the fermentation the antioxidant capacities slightly decreased, except when the orange juice was fermented with B. lactis Bb-12 and B. longum A4.8. The obtained results may contribute to the design of a novel functional food product