Comment on ``Validity of Feynman's prescription of disregarding the Pauli principle in intermediate states''

In a recent paper Coutinho, Nogami and Tomio [Phys. Rev. A 59, 2624 (1999); quant-ph/9812073] presented an example in which, they claim, Feynman's prescription of disregarding the Pauli principle in intermediate states of perturbation theory fails. We show that, contrary to their claim, Feynman's prescription is consistent with the exact solution of their example.Comment: 1 pag

Qualitative aspects for the cubic nonlinear Schrödinger equations with localized damping: Exponential and polynomial stabilization

AbstractResults of exponential/polynomial decay rates of the energy in L2-level, related to the cubic nonlinear Schrödinger equation with localized damping posed on the whole real line, will be established in this paper. We use Kato's theory and a priori estimates to obtain the result of global well-posedness and we determine exponential/polynomial stabilization combining the ideas of unique continuation due to Zhang, semigroup property and Komornik's approach

A computational model of gene expression in an inducible synthetic circuit

Synthetic biology aims to the rational design of gene circuits with predictable behaviours. Great efforts have been done so far to introduce in the field mathematical models that could facilitate the design of synthetic networks. Here we present a mathematical model of a synthetic gene-circuit with a negative feedback. The closed loop configuration allows the control of transcription by an inducer molecule (IPTG). Escherichia coli bacterial cells were transformed and expression of a fluorescent reporter (GFP) was measured for different inducer levels. Computer model simulations well reproduced the experimental induction data, using a single fitting parameter. Independent genetic components were used to assemble the synthetic circuit. The mathematical model here presented could be useful to predict how changes in these genetic components affect the behaviour of the synthetic circuit

Anomalous electron trapping by localized magnetic fields

We consider an electron with an anomalous magnetic moment g>2 confined to a plane and interacting with a nonzero magnetic field B perpendicular to the plane. We show that if B has compact support and the magnetic flux in the natural units is F\ge 0, the corresponding Pauli Hamiltonian has at least 1+[F] bound states, without making any assumptions about the field profile. Furthermore, in the zero-flux case there is a pair of bound states with opposite spin orientations. Using a Birman-Schwinger technique, we extend the last claim to a weak rotationally symmetric field with B(r) = O(r^{-2-\delta}) correcting thus a recent result. Finally, we show that under mild regularity assumptions the existence can be proved for non-symmetric fields with tails as well.Comment: A LaTeX file, 12 pages; to appear in J. Phys. A: Math. Ge

Efeito de agentes de controle biológico na indução de resistência em videira.

O objetivo deste trabalho foi avaliar o efeito de agentes comerciais de controle biológico como indutores de resistência em videira para o controle do míldio