56 research outputs found

    Dense near octagons with four points on each line, III

    Get PDF
    This is the third paper dealing with the classification of the dense near octagons of order (3, t). Using the partial classification of the valuations of the possible hexes obtained in [12], we are able to show that almost all such near octagons admit a big hex. Combining this with the results in [11], where we classified the dense near octagons of order (3, t) with a big hex, we get an incomplete classification for the dense near octagons of order (3, t): There are 28 known examples and a few open cases. For each open case, we have a rather detailed description of the structure of the near octagons involved

    Localization of the 17q breakpoint of a constitutional 1;17 translocation in a patient with neuroblastoma within a 25-kb segment located between the ACCN1 and TLK2 genes and near the distal breakpoints of two microdeletions in neurofibromatosis type I patients.

    Get PDF
    We have constructed a 1.4-Mb P1 artificial chromosome/bacterial artificial chromosome (PAC/BAC) contig spanning the 17q breakpoint of a constitutional translocation t(1;17)(p36.2;q11.2) in a patient with neuroblastoma. Three 17q breakpoint-overlapping cosmids were identified and sequenced. No coding sequences were found in the immediate proximity of the 17q breakpoint. The PAC/BAC contig covers the region between the proximally located ACCN1 gene and the distally located TLK2 gene and SCYA chemokine gene cluster. The observation that the 17q breakpoint region could not be detected in any of the screened yeast artificial chromosome libraries and the localization of the 17q breakpoint in the vicinity of the distal breakpoints of two microdeletions in patients with neurofibromatosis type 1 suggest that this chromosomal region is genetically unstable and prone to rearrangement

    Zoology of Atlas-groups: dessins d'enfants, finite geometries and quantum commutation

    Full text link
    Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not neccessarily minimal) permutation representations P. It is unusual but significant to recognize that a P is a Grothendieck's dessin d'enfant D and that most standard graphs and finite geometries G-such as near polygons and their generalizations-are stabilized by a D. In our paper, tripods P -- D -- G of rank larger than two, corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurations defined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G' s have a contextuality parameter close to its maximal value 1.Comment: 19 page

    On semi-finite hexagons of order (2,t)(2, t) containing a subhexagon

    Get PDF
    The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi-finite thick generalized polygons. We show here that no semi-finite generalized hexagon of order (2,t)(2,t) can have a subhexagon HH of order 22. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2)H(2) or its point-line dual HD(2)H^D(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon S\mathcal{S} of order (2,t)(2,t) which contains a generalized hexagon HH of order 22 as an isometrically embedded subgeometry must be finite. Moreover, if HHD(2)H \cong H^D(2) then S\mathcal{S} must also be a generalized hexagon, and consequently isomorphic to either HD(2)H^D(2) or the dual twisted triality hexagon T(2,8)T(2,8).Comment: 21 pages; new corrected proofs of Lemmas 4.6 and 4.7; earlier proofs worked for generalized hexagons but not near hexagon

    Some contributions to incidence geometry and the polynomial method

    Get PDF

    The Romano-African Domus: studies in space, decoration, and function

    Get PDF
    The introduction (chapter I) will present the topic of the present research in two paragraphs. The one will discuss the problems relating to the study of domestic art in Roman Africa and the approach of scholars to them in order to highlight the new aspect of this research. The second one will describe the methodology that will be used in the study of the relationship between architectural forms and mosaic decoration of African domestic architecture during the high and late Empire (Maps 1-2). The following chapters will describe eight room-types in term of architectural layout and mosaic decoration. By following the imaginary route of an ancient guest visiting the Romano-African house, the analysis will begin with the description of the spaces of higher accessibility: the vestibulum as the point of transition from outside and inside and its annexed spaces such as audience-chamber, cella ianitoris, and room for storing sportulae (chapter 2); and the peristyle as a passageway to rooms arranged around it (chapter 3). The analysis of the peristyle as an open space will be followed by the study of the secondary courtyard in chapter 4. The discussion will continue with the description of the reception rooms as public spaces where the house-owner received his selected guests: main triclinium (chapter 5), secondary triclinium (chapter 6), and assembly-rooms (chapter 7). The analysis will end with the description of the most private parts of the house: the cubiculum as the room of a more selective admission (chapter 8) and the private apartments as the spaces reserved for the members of the master's family (chapter 9). Conclusions will follow in chapter 10. The whole analysis will be carried out with the support of the catalogue listing the main Romano-African houses
    corecore