1,721,096 research outputs found
The genus Arvernoceros Heintz, 1970 in Italy: Preliminary report
No full textThe first occurrence of the large-sized deer Arvernoceros in the Early Pleistocene of Italy is reported. This genus was found in the sites of Madonna della Strada and Selvella (Central Italy). The considered remains have morphological and biometrical characters similar to those of the species A. giulii and are quite different from those of the genus Eucladoceros and of the genus Praemegaceros
Realizations of certain odd-degree surface branch data
Full text linkWe consider surface branch data with base surface the sphere, odd degree d, three branching points, and partitions of d of the form with π having length l. This datum satisfies the Riemann-Hurwitz nec-essary condition for realizability if h-lis odd and at least 1. For several small values of h and l(namely, for h + l6 5) we explicitly compute the number π of realizations of the datum up to the equivalence relation given by the action of automorphisms (even unoriented ones) of both the base and the covering surface. The expression of π depends on arithmetic properties of the entries of π. In particular we find that in the only case where π is 0 the entries of π have a common divi-sor, in agreement with a conjecture of Edmonds-Kulkarny-Stong and a stronger one of Zieve
Stephanorhinus hemitoechus (Falconer, 1868) del Pleistocene superiore dell'area di Melpignano-Cursi e S. Sidero (Lecce, Italia)
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Resti di Stephanorhinus hemitoechus (Falconer, 1868) conservati presso la Collezione Mirigliano
No full textOn Roberts' proof of the Turaev-Walker theorem
No full textIn this paper we discuss the beautiful idea of Justin Roberts [7] (see also [8]) to re-obtain the Turaev-Viro invariants [11] via skein theory, and re-prove elementarily the Turaev-Walker theorem [9], [10], [13]. We do this by exploiting the presentation of 3-manifolds introduced in [1], [4]. Our presentation supports in a very natural way a formal implementation of Roberts' idea. More specifically, what we show is how to explicitly extract from an o-graph (the object by which we represent a manifold, see below), one of the framed links in S3 which Roberts uses in the construction of his invariant, and a planar diagrammatic representation of such a link. This implies that the proofs of invariance and equality with the Turaev-Viro invariant can be carried out in a completely "algebraic"way, in terms of a planar diagrammatic calculus which does not require any interpretation of 3-dimensional figures. In particular, when proving the "term-by-term" equality of the expansion of the Roberts invariant with the state sum which gives the Turaev-Viro invariant, we simultaneously apply several times the "fusion rule" (which is formally defined, strictly speaking, only in diagrammatic terms), showing that the "braiding and twisting" which a priori may exist on tetrahedra is globally dispensable. In our point of view the success of this formal "algebraic" approach witnesses a certain efficiency of our presentation of 3-manifolds via o-graphs. In this work we will widely use recoupling theory which was very clearly exposed in [2], and therefore we will avoid recalling notations. Actually, for the purpose of stating and proving our results we will need to slightly extend the class of trivalent ribbon diagrams on which the bracket can be computed. We also address the reader to the references quoted in [2], in particular for the fundamental contributions of Lickorish to this area. In our approach it is more natural to consider invariants of compact 3-manifolds with non-empty boundary. The case of closed 3-manifolds is included by introducing a correction factor corresponding to boundary spheres, as explained in §2. Our main result is actually an extension to manifolds with boundary of the Turaev-Walker theorem: we show that the Turaev-Viro invariant of such a manifold coincides (up to a factor which depends on the Euler characteristic) with the Reshetikhin-Turaev-Witten invariant of the manifold mirrored in its boundary
Solution of the Hurwitz problem with a length-2 partition
Full text linkIn this note, we provide a new partial solution to the Hurwitz existence problemfor surface branched covers. Namely, we consider candidate branch data with base surfacethe sphere and one partition of the degree having length2, and we fully determine whichof them are realizable and which are exceptional. The case where the covering surface isalso the sphere was solved somewhat recently by Pakovich, and we deal here with the caseof positive genus. We show that the only other exceptional candidate data, besides thoseof Pakovich (five infinite families and one sporadic case), are a well-known, very specificinfinite family in degree4(indexed by the genus of the candidate covering surface, whichcan attain any value), five sporadic cases (four in genus1and one in genus2), and anotherinfinite family in genus1also already known. Since the degree is a composite number for allthese exceptional data, our findings provide more evidence for the prime-degree conjecture.Our argument proceeds by induction on the genus and on the number of branching points,so our results logically depend on those of Pakovich, and we do not employ the technologyof constellations on which his proof is base
Resti fossili di rinoceronte dal sito del Pleistocene Superiore di Ingarano (Foggia, Italia meridionale)
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