Dry matter production and nutrient exportation by pruned leaves and branches of apple trees

A trial was conducted on Latossol Vermelho Escuro Orto (Orthox) at Buri, State of São Paulo, Brazil. The material was collected from 'Ohio Beauty¹ and 'Brasil¹ apples trees grafted on 'Doucin'; the trees were 3-4, 4-5 and 6-7 years old. The authors concluded that at the dormant period differen ces were observed on the dry matter production as well on the nutrients exported by the leaves and branches of the two varieties. Branches exported higher amounts of P, Ca, B, Cu and Zn. Larger quantities of N, P and Mn were exported by the 1 eaves.

Image registration techniques with multiresolution analysis in satellite oceanography

En aquest article es fa una descripció dels procediments realitzats per enregistrar dues imatges geomètricament, de forma automàtica, si es pren la primera com a imatge de referència. Es comparen els resultats obtinguts mitjançant tres mètodes. El primer mètode és el d’enregistrament clàssic en domini espacial maximitzant la correlació creuada (MCC)[1]. El segon mètode es basa en aplicar l’enregistrament MCC conjuntament amb un anàlisi multiescala a partir de transformades wavelet [2]. El tercer mètode és una variant de l’anterior que es situa a mig camí dels dos. Per cada un dels mètodes s’obté una estimació dels coeficients de la transformació que relaciona les dues imatges. A continuació es transforma per cada cas la segona imatge i es georeferencia respecte la primera. I per acabar es proposen unes mesures quantitatives que permeten discutir i comparar els resultats obtinguts amb cada mètode.

Restricted walks in regular trees

Let T be the Cayley graph of a finitely generated free group F. Given two vertices in T consider all the walks of a given length between these vertices that at a certain time must follow a number of predetermined steps. We give formulas for the number of such walks by expressing the problem in terms of equations in F and solving the corresponding equations.

Generating trees for permutations avoiding generalized patterns

We construct generating trees with with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation, which allows us to incorporate the adjacency condition about some entries in an occurrence of a generalized pattern. We use these trees to find functional equations for the generating functions enumerating these classes of permutations with respect to different parameters. In several cases we solve them using the kernel method and some ideas of Bousquet-Mélou [2]. We obtain refinements of known enumerative results and find new ones.

The equation xpyq=zr and groups that act freely on Λ-trees

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Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space H is L2(Rn), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.

Polynomial functors and trees

We explore the relationship between polynomial functors and trees. In the first part we characterise trees as certain polynomial functors and obtain a completely formal but at the same time conceptual and explicit construction of two categories of rooted trees, whose main properties we describe in terms of some factorisation systems. The second category is the category Ω of Moerdijk and Weiss. Although the constructions are motivated and explained in terms of polynomial functors, they all amount to elementary manipulations with finite sets. Included in Part 1 is also an explicit construction of the free monad on a polynomial endofunctor, given in terms of trees. In the second part we describe polynomial endofunctors and monads as structures built from trees, characterising the images of several nerve functors from polynomial endofunctors and monads into presheaves on categories of trees. Polynomial endofunctors and monads over a base are characterised by a sheaf condition on categories of decorated trees. In the absolute case, one further condition is needed, a projectivity condition, which serves also to characterise polynomial endofunctors and monads among (coloured) collections and operads.

Level-wise node size distribution of randomly generated regular trees

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