Comment on ``Casimir force in compact non-commutative extra dimensions and radius stabilization''

We call attention to a series of mistakes in a paper by S. Nam [JHEP 10 (2000) 044, hep-th/0008083].Comment: 6 pages, LaTeX, uses JHEP.cl

Fluctuating Commutative Geometry

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized geometries where topology and dimension can also fluctuate. The model describes the geometry of spaces with a countable number $n$ of points. The spectral principle of Connes and Chamseddine is used to define dynamics.We show that this simple model has two phases. The expectation value , the average number of points in the universe, is finite in one phase and diverges in the other. Moreover, the dimension $\delta$ is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, $< 2$. We also address another discrete model defined on a fixed $d=1$ dimension, where topology fluctuates. We comment on a possible spontaneous localization of topology.Comment: 7 pages. Talk at the conference "Spacetime and Fundamental Interactions: Quantum Aspects" (Vietri sul Mare, Italy, 26-31 May 2003), in honour of A. P. Balachandran's 65th birthda

Lifshitz-point critical behaviour to O(ϵ2){\boldsymbol{O(\epsilon^2)}}

We comment on a recent letter by L. C. de Albuquerque and M. M. Leite (J. Phys. A: Math. Gen. 34 (2001) L327-L332), in which results to second order in $\epsilon=4-d+\frac{m}{2}$ were presented for the critical exponents $\nu_{{\mathrm{L}}2}$, $\eta_{{\mathrm{L}}2}$ and $\gamma_{{\mathrm{L}}2}$ of d-dimensional systems at m-axial Lifshitz points. We point out that their results are at variance with ours. The discrepancy is due to their incorrect computation of momentum-space integrals. Their speculation that the field-theoretic renormalization group approach, if performed in position space, might give results different from when it is performed in momentum space is refuted.Comment: Latex file, uses the included iop stylefiles; Uses the texdraw package to generate included figure

Anisotropic Lifshitz Point at O(ϵL2)O(\epsilon_L^2)

We present the critical exponents $\nu_{L2}$, $\eta_{L2}$ and $\gamma_{L}$ for an $m$-axial Lifshitz point at second order in an $\epsilon_{L}$ expansion. We introduced a constraint involving the loop momenta along the $m$-dimensional subspace in order to perform two- and three-loop integrals. The results are valid in the range $0 \leq m < d$. The case $m=0$ corresponds to the usual Ising-like critical behavior.Comment: 10 pages, Revte

Influencia do tipo de estaca e de alguns reguladores de crescimento no enraizamento e desenvolvimento de estacas de figueira (Ficus carica L.).

O presente trabalho teve como objetivo estudar as influencias da posicao da estaca no ramo (apical, mediana e basal) e dos acidos naftalenoacetico (ANA) e indolbutirico (IBA), isolados e combinados, sobre o enraizamento e desenvolvimento da parte aerea de estacas de figueira. O delineamento experimental foi de blocos ao acaso com parcelas subdivididas. As estacas tinham 30 cm de comprimento, sendo que 5 cm da base foram imersas nas solucoes correspondentes durante 1 minuto, sendo depois tratadas com fungicida Captan a 25% para posterior plantio. As mudas mais vigorosas originaram-se das estacas de base dos ramos. Todos os tratamentos com auxinas proporcionaram um melhor enraizamento, sendo que a combinacao 250 ppm IBA + 250 ppm ANA foi mais eficiente na formacao das raizes, acarretando tambem um aumento de peso da parte aerea