The HQET/NRQCD Lagrangian to order alpha/m^3

The HQET/NRQCD Lagrangian is computed to order alpha/m^3. The computation is performed using dimensional regularization to regulate the ultraviolet and infrared divergences. The results are consistent with reparametrization invariance to order 1/m^3. Some subtleties in the matching conditions for NRQCD are discussed.Comment: Two terms added to Lagrangian. Explicit value of G^3 coefficient given. Some references added, and TeX problems fixed. (18 pages, uses revtex

Symplectic Lefschetz fibrations on S^1 x M^3

In this paper we classify symplectic Lefschetz fibrations (with empty base locus) on a four-manifold which is the product of a three-manifold with a circle. This result provides further evidence in support of the following conjecture regarding symplectic structures on such a four-manifold: if the product of a three-manifold with a circle admits a symplectic structure, then the three-manifold must fiber over a circle, and up to a self-diffeomorphism of the four-manifold, the symplectic structure is deformation equivalent to the canonical symplectic structure determined by the fibration of the three-manifold over the circle.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper18.abs.htm

A criterion for homeomorphism between closed Haken manifolds

In this paper we consider two connected closed Haken manifolds denoted by M^3 and N^3, with the same Gromov simplicial volume. We give a simple homological criterion to decide when a given map f: M^3-->N^3 between M^3 and N^3 can be changed by a homotopy to a homeomorphism. We then give a convenient process for constructing maps between M^3 and N^3 satisfying the homological hypothesis of the map f.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-12.abs.htm

A quasi-particle description of the M(3,p) models

The M(3,p) minimal models are reconsidered from the point of view of the extended algebra whose generators are the energy-momentum tensor and the primary field \phi_{2,1} of dimension $(p-2)/4$. Within this framework, we provide a quasi-particle description of these models, in which all states are expressed solely in terms of the \phi_{2,1}-modes. More precisely, we show that all the states can be written in terms of \phi_{2,1}-type highest-weight states and their phi_{2,1}-descendants. We further demonstrate that the conformal dimension of these highest-weight states can be calculated from the \phi_{2,1} commutation relations, the highest-weight conditions and associativity. For the simplest models (p=5,7), the full spectrum is explicitly reconstructed along these lines. For $p$ odd, the commutation relations between the \phi_{2,1} modes take the form of infinite sums, i.e., of generalized commutation relations akin to parafermionic models. In that case, an unexpected operator, generalizing the Witten index, is unravelled in the OPE of \phi_{2,1} with itself. A quasi-particle basis formulated in terms of the sole \phi_{1,2} modes is studied for all allowed values of p. We argue that it is governed by jagged-type partitions further subject a difference 2 condition at distance 2. We demonstrate the correctness of this basis by constructing its generating function, from which the proper fermionic expression of the combination of the Virasoro irreducible characters \chi_{1,s} and \chi_{1,p-s} (for 1\leq s\leq [p/3]+1) are recovered. As an aside, a practical technique for implementing associativity at the level of mode computations is presented, together with a general discussion of the relation between associativity and the Jacobi identities.Comment: 29 pages; revised version with two appendices adde

Influence of the slope of terrain on the spatial variability of the wood density within Eucalyptus trees

The aim of this study was to understand how contrasting environments influence the wood formation in Eucalyptus clones and the effect on wood density and spatial variability. Wood density was assessed in clonal tests represented by 150 Eucalyptus urophylla x grandis hybrids with 6-year-old growing under different conditions. The main difference among the sites was the slope of the terrain: the clonal tests were replicated at plan site (0° of inclination), at site with 20°, and 40° of inclination. In order to provide experimental data to perform this study, gravimetric (reference) method and near infrared (NIR) spectroscopy were combined for assessing the wood density in a large sampling of Eucalyptus wood. Hence, regression model based on NIR spectra was developed for estimating such wood traits from NIR spectra recorded at different radial and longitudinal positions along the height of the tree. This approach allows the examination of the patterns of spatial variation of wood density within Eucalyptus trees. Variations in wood density along the stem are less consistent than those in the radial direction, especially close the base of the tree. Overall, the wood density strongly varied from pith (460 kg m-3) to bark (600 kg m-3) at the base. The radial variation in wood density at the base was about 140 kg m-3 while the radial variation at 25% of stem height was slightly low (~130 kg m-3). At 50% of height the trait also increased radially (~104 kg m-3), but in relative low magnitude. The density slightly increased from pith to bark at 75% of height (~50 kg m-3) and at the top of the tree the variation was of lower magnitude (~20 kg m-3). The radial variation at the base take into account the wood formed from the first to the sixty year of growth while the variation in the top of the tree refers to the wood developed with few months of difference. The pith to bark variations in wood density were higher in the trees from the site presenting 40° of inclination. At 25% of the tree height, the radial variation was 104 kg m-3 in the site plan (0°), 133 kg m-3 in the site presenting inclination of 20°, and 157 kg m-3 in the site with 40° of inclination. In conclusion, the higher the inclination of the terrain, the greater the magnitude of wood density variation. Sloped terrains induce formation of reaction wood influencing the radial variation in wood traits. (Résumé d'auteur

On Isosystolic Inequalities for T^n, RP^n, and M^3

If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal cup-length, then for any riemannian metric g on M, we show that the systole Sys(M,g) and the volume Vol(M,g) of the riemannian manifold (M,g) are related by the following isosystolic inequality: Sys(M,g)^n \leq n! Vol(M,g). The inequality can be regarded as a generalization of Burago and Hebda's inequality for closed essential surfaces and as a refinement of Guth's inequality for closed n-manifolds whose Z/2Z-cohomology has the maximal cup-length. We also establish the same inequality in the context of possibly non-compact manifolds under a similar cohomological condition. The inequality applies to (i) T^n and all other compact euclidean space forms, (ii) RP^n and many other spherical space forms including the Poincar\'e dodecahedral space, and (iii) most closed essential 3-manifolds including all closed aspherical 3-manifolds.Comment: 34 pages, 0 figures. v2 contains expository revisions and some additional reference

Counting essential surfaces in a closed hyperbolic three-manifold

Let M^3 be a closed hyperbolic three-manifold. We show that the number of genus g surface subgroups of π_1(M^3) grows like g^(2g)