Supersymmetric methods in the traveling variable: inside neurons and at the brain scale

We apply the mathematical technique of factorization of differential operators to two different problems. First we review our results related to the supersymmetry of the Montroll kinks moving onto the microtubule walls as well as mentioning the sine-Gordon model for the microtubule nonlinear excitations. Second, we find analytic expressions for a class of one-parameter solutions of a sort of diffusion equation of Bessel type that is obtained by supersymmetry from the homogeneous form of a simple damped wave equations derived in the works of P.A. Robinson and collaborators for the corticothalamic system. We also present a possible interpretation of the diffusion equation in the brain contextComment: 14 pages, 1 figur

THE ROLE OF TRADE IN U.S. HORTICULTURE

International Relations/Trade,

Quantization of strings and branes coupled to BF theory

BF theory is a topological theory that can be seen as a natural generalization of 3-dimensional gravity to arbitrary dimensions. Here we show that the coupling to point particles that is natural in three dimensions generalizes in a direct way to BF theory in d dimensions coupled to (d-3)-branes. In the resulting model, the connection is flat except along the membrane world-sheet, where it has a conical singularity whose strength is proportional to the membrane tension. As a step towards canonically quantizing these models, we show that a basis of kinematical states is given by `membrane spin networks', which are spin networks equipped with extra data where their edges end on a brane

Solutions of the Perturbed KDV Equation for Convecting Fluids by Factorizations

In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential and Weierstrass functionsComment: 4 pages, some changes in the text according to referees' suggestions, added one reference, accepted at Central Europ. J. Phy

Majorana neutrino oscillations in vacuum

In the context of a type I seesaw scenario which leads to get light left-handed and heavy right-handed Majorana neutrinos, we obtain expressions for the transition probability densities between two flavor neutrinos in the cases of left-handed and right-handed neutrinos. We obtain these expressions in the context of an approach developed in the canonical formalism of Quantum Field Theory for neutrinos which are considered as superpositions of mass-eigenstate plane waves with specific momenta. The expressions obtained for the left-handed neutrino case after the ultra-relativistic limit is taking lead to the standard probability densities which describe light neutrino oscillations. For the right-handed neutrino case, the expressions describing heavy neutrino oscillations in the non-relativistic limit are different respect to the ones of the standard neutrino oscillations. However, the right-handed neutrino oscillations are phenomenologically restricted as is shown when the propagation of heavy neutrinos is considered as superpositions of mass-eigenstate wave packets.Comment: 25 pages, abstract changed, two sections added, some references adde

Nonlinear second order ODE's: Factorizations and particular solutions

We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions are obtained in the travelling frame. All these particular solutions are the result of extending a simple and efficient factorization method that we developed in Phys. Rev. E 71 (2005) 046607Comment: 6 pages, v3=published versio