Theory of Submanifolds, Associativity Equations in 2D Topological Quantum Field Theories, and Frobenius Manifolds

We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat torsionless submanifolds in pseudo-Euclidean spaces bear natural structures of Frobenius algebras on their tangent spaces. These Frobenius structures are generated by the corresponding flat first fundamental form and the set of the second fundamental forms of the submanifolds (in fact, the structural constants are given by the set of the Weingarten operators of the submanifolds). We prove in this paper that each N-dimensional Frobenius manifold can locally be represented as a potential flat torsionless submanifold in a 2N-dimensional pseudo-Euclidean space. By our construction this submanifold is uniquely determined up to motions. Moreover, in this paper we consider a nonlinear system, which is a natural generalization of the associativity equations, namely, the system describing all flat torsionless submanifolds in pseudo-Euclidean spaces, and prove that this system is integrable by the inverse scattering method.Comment: 10 pages, Proceedings of the Workshop "Nonlinear Physics. Theory and Experiment. IV. Gallipoli (Lecce), Italy, June 22 - July 1, 200

Banados-Silk-West effect with nongeodesic particles: Nonextremal horizons

When two particles collide near a black hole, the energy in their center of mass frame can, under certain conditions, grow unbounded. This is the Banados-Silk-West effect. We show that this effect retains its validity even if some force acts on a particle, provided some reasonable and weak restrictions are imposed on this force. In the present work we discuss the case of nonextremal horizons. The result under discussion is similar to that for extremal horizons considered in our previous work.Comment: v2 matches the published version; revtex4, 11 page

Effects of Raw Ethanolic Seed Extract of Tetracarpidium conophorum on Heamatological and Histopathological Parameters in Swiss Albino Mice Infected with Plasmodium berghei

Study was carried out to determine the heamatological and histopathological effects of raw ethanolic seed extract of Tetracarpidium conophorum in swiss albino mice infected with Plasmodium berghei (NK65). Standard methods were employed to determine the heamatological, histopathological indices and biochemical assay. The experimental mice were acclimatized for seven days before the commencement of treatment. Mice were grouped into six groups (A, B, C, D, E and F) of four mice each. The mice in group B were treated with a standard antimalarial drug (chloroquine as positive control) at a dose of 5 mg/kg body weight, while mice in groups D, E and F was administered with increasing dosages (200, 400, 600 mg/kg body weight) of seed extracts for four consecutive days respectively. Group C (Normal control) served as mice that was not infected and treated. Heamatological analysis revealed an increase in Packed Cell Volume, Red Blood Cells, Heamoglobin and Platelet values of all mice in groups D, E and F (mice administered different concentrations of the extract). Mice in group B (chloroquine treated group) have the highest value. Mice in group A (negative control) exhibited lowest values of Heamoglobin, Platelet, Red blood cells, and Packed Cell Volume. There was significant increase in the levels of Alanine Transaminase and Aspartate Transaminase in group A (infected and not treated) compared to mice in groups C, D, and E. Restorative effects of seed extract was observed on the liver and kidney of mice at dose levels (400 and 600 mg/kg) used, but the seed extract at the dose of 600 mg/kg was observed to have adverse effects on the liver of the mice. This study therefore shows that Tetracarpidium conophorum was able to boost the formation of heamatological indices and was not toxic to the organs (liver and kidney) in mice

Quantum phase slips in a confined geometry

We consider tunneling of vortices across a superconducting film that is both narrow and short (and connected to bulk superconducting leads at the ends). We find that in the superconducting state the resistance, at low values of the temperature (T) and current, does not follow the power-law dependence on T characteristic of longer samples but is exponential in 1/T. The coefficient of 1/T in the exponent depends on the length or, equivalently, the total normal-state resistance of the sample. These conclusions persist in the one-dimensional limit, which is similar to the problem of quantum phase slips in an ultra-narrow short wire.Comment: 14 pages, 1 figure; published in Phys. Rev.