Effect of spacing on volume, form factor and taper for Pinus taeda trees in Paraná, Brazil

Several forestry procedures affect tree volume and shape, such as spacing, pruning, and thinning. Studying and understanding the effect of these operations on stand attributes are very important for forest management. This study aimed to evaluate volume, form factor, and taper for Pinus taeda trees stratified into diameter classes within two planting spacings. In addition, we aimed to evaluate the time spent to scale each tree, measured with a chronometer. Indirect scaling was performed using a Criterion RD 1000. Thirty trees were scaled on each planting spacing (3 m x 2 m and 4 m x 2 m), totaling 60 trees encompassing all diameter classes. Tree volume was calculated using the Smalian equation. Tree volume, form factor, and taper were calculated to each tree and evaluated by stand (independent t-test) and diameter class (variance analysis and Tukey test). The average scaling time was 4 minutes and 35 seconds, which decreased with practice (-24%). Form factor and taper differed with spacing and diameter class. Volume did not differ with spacing, but it did in the diameter classes. We concluded that indirect scaling is a practical method for tree volume assessment; higher planting density leads to more cylindrical stems with lower taper ratios in comparison with denser stands; and the fact that tree volume, form factor and taper differed among the diameter classes should be incorporated into studies of taper modeling.

On a class of projective Ricci curvature of Finsler metrics

In Finsler geometry, the projective Ricci curvature is an important projective invariant. In this paper, we investigate the projective Ricci curvature of a class of general [Formula: see text]-metrics satisfying a certain condition, which is invariant under the change of volume form. Moreover, we construct a class of new nontrivial examples on such Finsler metrics.

Bergman kernel on Riemann surfaces and Kähler metric on symmetric products

Let [Formula: see text] be a compact hyperbolic Riemann surface equipped with the Poincaré metric. For any integer [Formula: see text], we investigate the Bergman kernel associated to the holomorphic Hermitian line bundle [Formula: see text], where [Formula: see text] is the holomorphic cotangent bundle of [Formula: see text]. Our first main result estimates the corresponding Bergman metric on [Formula: see text] in terms of the Poincaré metric. We then consider a certain natural embedding of the symmetric product of [Formula: see text] into a Grassmannian parametrizing subspaces of fixed dimension of the space of all global holomorphic sections of [Formula: see text]. The Fubini–Study metric on the Grassmannian restricts to a Kähler metric on the symmetric product of [Formula: see text]. The volume form for this restricted metric on the symmetric product is estimated in terms of the Bergman kernel of [Formula: see text] and the volume form for the orbifold Kähler form on the symmetric product given by the Poincaré metric on [Formula: see text].

The Serial Style and Beyond

This chapter argues that the specific text of Ulysses as published in the Little Review is of critical interest. It looks at the style and nature of Ulysses as a serial and gives an initial account of the ways in which Joyce changed the serial text for the volume version of February 1922. Digital resources have transformed the possibility of studying textual variation, and an early section in the chapter looks at those transformations and focuses, in particular, on the significance of word counts as a key for understanding how Joyce’s text changed. Dushan Popovich, printer of the Little Review, and the first typographer to face the challenge of typesetting Joyce’s challenging text, is discussed in some detail. Pound disliked Joyce’s candour, and the various revisions which he imposed on the serial text are reviewed here. So too are the various ways in which Joyce subsequently revised his text for publication in volume form.

Trial and Error

This chapter looks at the compositional genesis of Ulysses, its early production history, and the circumstances by which the editors of the Little Review became embroiled in a trial in New York in February 1921. The composition of Joyce’s text is discussed in detail, from the moments of conception through to April 1921, when Joyce realized that the Little Review serialization would not continue, and made arrangements for the publication of his work in volume form with Sylvia Beach’s Parisian bookshop, Shakespeare and Company. The trial of the Little Review editors—on the grounds of the putative obscenity of the last instalment of chapter 13 (‘Nausicaa’)—is also discussed in detail. In particular the chapter looks at the sexual politics of the trial, including the homophobia of John Quinn, the lawyer who gave significant financial support to both Joyce and the Little Review.

Principal fibrations over noncommutative spheres

We present examples of noncommutative four-spheres that are base spaces of SU(2)-principal bundles with noncommutative seven-spheres as total spaces. The noncommutative coordinate algebras of the four-spheres are generated by the entries of a projection which is invariant under the action of SU(2). We give conditions for the components of the Connes–Chern character of the projection to vanish but the second (the top) one. The latter is then a non-zero Hochschild cycle that plays the role of the volume form for the noncommutative four-spheres.

On the Sobolev–Poincaré Inequality of CR-manifolds

The purpose is to study the CR-manifold with a contact structure conformal to the Heisenberg group. In our previous work [22], we have proved that if the $Q^{\prime }$-curvature is nonnegative and the integral of $Q^{\prime }$-curvature is below the dimensional bound $c_1^{\prime }$, then we have the isoperimetric inequality. In this paper, we manage to deal with general contact structure conformal to the Heisenberg group, removing the condition that $Q^{\prime }$-curvature is nonnegative. We prove that the volume form $e^{4u}$ is a strong $A_{\infty }$ weight. As a corollary, we prove the Sobolev–Poincaré inequality on a class of CR-manifolds with integrable $Q^{\prime }$-curvature.