Abstract:
Six laticiferous system characters were investigated in 22 three-year-old, half-sib rubber tree [Hevea brasiliensis (Willd. ex Adr. de Juss.) Muell.-Arg.] progenies, evaluated at three sites (Votuporanga, Pindorama and Jaú, all in the S o Paulo State, Brazil). The traits examined were: average rubber yield (Pp), average bark thickness (Bt), number of latex vessel rings (Lv), average distance between consecutive latex vessel rings (Dc), density of latex vessels per 5 mm per ring averaged over all rings (Dd) and the diameter of the latex vessels (Di). The joint analysis showed that site effect and progeny x sites interaction were significant for all traits, except Lv. Estimates of individual heritabilities across the three sites were high for Bt; moderate for Lv, Pp and Dc; low for Dd and very low for Di. Genetic correlations in the joint analysis showed high positive correlations between Pp and the other traits. Selecting the best five progenies would result in genetic gains of 24.91% for Pp while selecting best two plants within a progeny would result in a Pp genetic gain of 30.98%.

Abstract:
Este artículo comienza con una breve introducción para, posteriormente, proporcionarnos una perspectiva histórica que, según el autor, es un factor importante para entender la particularidad de un territorio minúsculo que tiene una posición jurídico-política tan preeminente dentro de la "Gigante China". Después analiza y compara la autonomía de Macau como "territorio bajo la administración portuguesa" en contra de las regiones insulares autónomas portuguesas. El autor elige dos características de la autonomía de Macau: el sistema político y el sistema de los derechos fundamentales, y los analiza, antes y después de la transferencia de los poderes totales soberanos de Portugal con China, y concluye que aquellos juegan un papel importante que acentúa la autonomía de Macau como región especial de China.

Abstract:
in a field trial involving 68 rubber tree (hevea spp.) clones calculation of genotypic correlation coefficients revealed significant age-age correlation from age 1 to 6 (immature period) for girth a and for age 7 to 12 (mature period) for girth b and for age 7 to 12 (production of latex) for yield. rank correlation coefficients between all immature ages of girth (girth a), all ages of mature girth (girth b) and all annual rubber production (yield) were significant for the three traits, with the coefficients decreasing with increasing age. selection of the sets of best 30, 15, 10 and 5 clones from the available 68 clones at a given age was generally accompanied by a descending order of percentage success. it was suggested: (a) to have the best 30 clones of age 6, select the set of best 36 clones at age 2, (b) to have the best 15 clones of age 6, select the set of best 20 clones at age 3, (c) to have the best 5 clones of age 6, select the set of best 8 clones at age 4, and (d) to have the best 3 clones of age 6, select the set of best 3 clones at age 5. more than 80% of the targeted clones on girth a or girth b basis and more than 76.7% clones on yield basis were found to get selected at steps (a) through (d). for achieving early multiplication of the most productive clone for deployment, multiplication should be started with the best 36 (i.e. 60%) clones selected at age 2.

Abstract:
six laticiferous system characters were investigated in 22 three-year-old, half-sib rubber tree [hevea brasiliensis (willd. ex adr. de juss.) muell.-arg.] progenies, evaluated at three sites (votuporanga, pindorama and jaú, all in the s？o paulo state, brazil). the traits examined were: average rubber yield (pp), average bark thickness (bt), number of latex vessel rings (lv), average distance between consecutive latex vessel rings (dc), density of latex vessels per 5 mm per ring averaged over all rings (dd) and the diameter of the latex vessels (di). the joint analysis showed that site effect and progeny x sites interaction were significant for all traits, except lv. estimates of individual heritabilities across the three sites were high for bt; moderate for lv, pp and dc; low for dd and very low for di. genetic correlations in the joint analysis showed high positive correlations between pp and the other traits. selecting the best five progenies would result in genetic gains of 24.91% for pp while selecting best two plants within a progeny would result in a pp genetic gain of 30.98%.

Abstract:
One aspect seldom addressed in studies about monasteries is their relationship with other centers of religious life. In the case of Santa María deTrianos, it is possible to analyze the links developed between the canons and the convent with the Apostolic See, with the bishop of León, with other monasteries in the region, and with the churches under the supervision of the former. Some interesting aspects of the activities conducted by the priests come to light, as well as their commitment to apostolic teaching and their strong defense of both rights and their autonomy vis-à-vis other ecclesiastic powers. Un aspecto escasamente abordado en el estudio de los monasterios es su articulación con otros centros de la vida religiosa. En el caso de Santa María de Trianos, es posible analizar los vínculos que tejen los canónigos y el convento con la Sede Apostólica, con el obispo de León, con otros monasterios de la región y con las iglesias que de él dependían. Se comprueban facetas insospechadas de la actividad de los religiosos, de su compromiso respecto a su labor pastoral así como la pertinaz defensa tanto de sus derechos como de la autonomía frente a otros poderes eclesiásticos.

Abstract:
In this paper we explore a family of congruences over $\N^\ast$ from which one builds a sequence of symmetric matrices related to the Mertens function. From the results of numerical experiments, we formulate a conjecture about the growth of the quadratic norm of these matrices, which implies the Riemann hypothesis. This suggests that matrix analysis methods may come to play a more important role in this classical and difficult problem.

Abstract:
In this paper we explore a class of equivalence relations over $\N^\ast$ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of the quadratic norm of these matrices, which implies the Riemann hypothesis. This suggests that matrix analysis methods may play a more important part in this classical and difficult problem.

Abstract:
The inclusion relation between simple objects in the plane may be used to define geometric set systems, or hypergraphs. Properties of various types of colorings of these hypergraphs have been the subject of recent investigations, with applications to wireless networking. We first prove that every set of homothetic copies of a given convex body in the plane can be colored with four colors so that any point covered by at least two copies is covered by two copies with distinct colors. This generalizes a previous result from Smorodinsky [18]. As a corollary, we find improvements to well studied variations of the coloring problem such as conflict-free colorings, k-strong (conflict-free) colorings and choosability. We also show a relation between our proof and Schnyder's characterization of planar graphs. Then we show that for any k >1, every three-dimensional hypergraph can be colored with 6(k - 1) colors so that every hyperedge e contains min{|e|, k} vertices with mutually distinct colors. Furthermore, we also show that at least 2k colors might be necessary. This refines a previous result from Aloupis et al. [2].

Abstract:
Given a collection of planar graphs $G_1,\dots,G_k$ on the same set $V$ of $n$ vertices, the simultaneous geometric embedding (with mapping) problem, or simply $k$-SGE, is to find a set $P$ of $n$ points in the plane and a bijection $\phi: V \to P$ such that the induced straight-line drawings of $G_1,\dots,G_k$ under $\phi$ are all plane. This problem is polynomial-time equivalent to weak rectilinear realizability of abstract topological graphs, which Kyn\v{c}l (doi:10.1007/s00454-010-9320-x) proved to be complete for $\exists\mathbb{R}$, the existential theory of the reals. Hence the problem $k$-SGE is polynomial-time equivalent to several other problems in computational geometry, such as recognizing intersection graphs of line segments or finding the rectilinear crossing number of a graph. We give an elementary reduction from the pseudoline stretchability problem to $k$-SGE, with the property that both numbers $k$ and $n$ are linear in the number of pseudolines. This implies not only the $\exists\mathbb{R}$-hardness result, but also a $2^{2^{\Omega (n)}}$ lower bound on the minimum size of a grid on which any such simultaneous embedding can be drawn. This bound is tight. Hence there exists such collections of graphs that can be simultaneously embedded, but every simultaneous drawing requires an exponential number of bits per coordinates. The best value that can be extracted from Kyn\v{c}l's proof is only $2^{2^{\Omega (\sqrt{n})}}$.

Abstract:
A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of a hypercube in which the graph can be embedded. We consider the problem of covering the vertices of a partial cube with the minimum number of zones. The problem admits several special cases, among which are the problem of covering the cells of a line arrangement with a minimum number of lines, and the problem of finding a minimum-size fibre in a bipartite poset. For several such special cases, we give upper and lower bounds on the minimum size of a covering by zones. We also consider the computational complexity of those problems, and establish some hardness results.