Abstract There is a strange duality between the quadrangle isolated complete intersection singularities discovered by first author and Wall. We derive this from variation of Berglund–Hübsch transposition invertible polynomials introduced in our previous work about hypersurface using matrix factorizations size two.

We tell the history ofMoufang generalized quadrangles.We review someMoufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent linesU,V of theGQ, and for someW ∈ {U,V }⊥, the group of generalized homologies with axes U and V acts transitively on the points ofW incident with neither U nor V. As a by-...

We provide a geometrical construction of the unique slim dense near hexagon with parameters (s, t, t2) = (2, 5, {1, 2}). Using this construction, we construct the rank 3 symplectic dual polar space DSp(6, 2) which is the unique slim dense near hexagon with parameters (s, t, t2) = (2, 6, 2). Both near hexagons are constructed from two copies of the unique generalized quadrangle with parameters (...

In this paper, we classify all generalized quadrangles weakly embedded of degree 2 in projective space. More exactly, given a (possibly infinite) generalized quadrangle Γ = (P,L, I ) and a map π from P (respectively L) to the set of points (respectively lines) of a projective space PG(V ), V a vector space over some skew field (not necessarily finite-dimensional), such that: (i) π is injective ...

there are many techniques for reconstruction after total pharyngolaryngoesophagectomy. the use of a transposed stomach to restore gastrointestinal continuity, and this combined cervical and abdominal approach for pharyngolaryngoesophagectomy and gastric pull up has become one of the most popular. this retrospective study is a review of 50 consecutive iranian patients who underwent pharyngolaryn...

1 Department of Plastic Surgery and Reconstructive Microsurgery, County Emergency Hospital, Ploiesti, Romania 2 „Carol Davila” Universiy of Medicine and Pharmacy, Bucharest, Romania 3 Department of Dermatovenerology, Elias Emergency Clinical Hospital, Bucharest, Romania 4 Department of Plastic Surgery and Reconstructive Microsurgery, Emergency County Hospital Constanta, Romania 5 Department of ...

In this paper, we construct the first known infinite family of primitive Qpolynomial schemes which are not generated by distance-regular graphs. To construct these examples, we introduce the notion of a relative hemisystem of a generalized quadrangle with respect to a subquadrangle.

BATir Building, Architecture and Town Planning, Brussels School of Engineering, Université Libre de Bruxelles, 50 avenue Fr. D. Roosevelt CP 194/02, 1050 Brussels, Belgium. Tel.: +32-26502169. Email: [email protected] Department of Civil and Environmental Engineering, Engineering Quadrangle E332, Princeton University, Princeton NJ, USA MEMC Mechanics of Materials and Construction, Faculty of E...

The M-degree of an edge xy in a graph is the maximum of the degrees of x and y. The M-degree of a graph G is the minimum over M-degrees of its edges. In order to get upper bounds on the game chromatic number, He et al showed that every planar graph G without leaves and 4cycles has M-degree at most 8 and gave an example of such a graph with M-degree 3. This yields upper bounds on the game chroma...