Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

On incidence structures of nonsingular points and hyperbolic lines of ovoids in finite orthogonal spaces

We study the point-line incidence structures of nonsingular points and hyperbolic secant lines associated with ovoids in finite orthogonal spaces. We show that these incidence structures frequently produce partial linear spaces and the parameters of the bipartite graphs (called ovoidal graphs) associated with these structures produce simple and effective isomorphism invariants to distinguish non-isomorphic ovoids. We prove explicit formulas for these isomorphism invariants for a number of infinite families of 2-transitive ovoids.     

Incidence Structures of Type (p, n)

Every incidence structure (understood as a triple of sets (G, M, I), I G×M) admits for every positive integer p an incidence structure where G ^p (M ^p) consists of all independent p-element subsets in G (M) and I ^p is determined by some bijections. In the paper such incidence structures are investigated the 's of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets G and M.     

Incidence graphs and subdesigns of semisymmetric designs

A semisymmetric design is a connected incidence structure satisfying; two points (blocks) are on 0 or λ blocks (points). Every block (point) is incident with k points (blocks). Properties of the incidence graph of these structures are investigated, leading to bounds on its diameter (d?k if λ = 2, d?[2k/(λ + 1)]+ 1 if λ > 2), and the number of points of these structures (υ?2^k-1 if λ = 2, υ?k2^{[2k/(λ + 1)]} if λ > 2). Bounds are also found for semisymmetric designs containing a subdesign. We give characterizations of semisymmetric designs with λ = 2 (semibiplanes) which contain a subdesign and achieve the bounds. This leads to a construction for a semibiplane with parameters υ = 2^r-1 (q²?1), k = q+q₁+?+q_r, where q_r is aprime power, q_i = q²_i+1 and q=q²₁.     

Automorphisms of (B)-geometries

(B)-Geometries are incidence structures arising from permutation sets. The present paper studies the automorphism groups of (B)-Geometries. In certain cases these automorphisms yield examples of inversive planes and of subplanes which are embedded in Minkowski planes (chapter 2). In chapter 3 we describe the automorphism groups of the (B)-Geometries arising from the groups PL(2, pⁿ) and AL(1, pⁿ) in their natural representations on the points of the projective and affine line.Dedicated to Prof.Dr. Walter Benz on his 60th birthdayWork done within the activity of G.N.S.A.G.A. of C.N.R. and supported by the 40% grants of M.U.R.S.T.     

Exotic analytic structures and Eisenman intrinsic measures

Using Eisenman intrinsic measures we prove a cancellation theorem. This theorem allows to find new examples of exotic analytic structures onC ⁿ under which we understand smooth complex affine algebraic varietiers which are diffeomorphic toR ²ⁿ but not biholomorphic toC ⁿ . We also develop a new method of constructing these structures which enables us to produce exotic analytic structures onC ³ with a given number of hypersurfaces isomorphic toC ² and a family of these structures with a given number of moduli.     

Equivariant Classification of <Emphasis Type="Italic">b</Emphasis><Superscript><Emphasis Type="Italic">m</Emphasis></Superscript>-symplectic Surfaces

Inspired by Arnold’s classification of local Poisson structures [1] in the plane using the hierarchy of singularities of smooth functions, we consider the problem of global classification of Poisson structures on surfaces. Among the wide class of Poisson structures, we consider the class of b^m-Poisson structures which can be also visualized using differential forms with singularities as b^m-symplectic structures. In this paper we extend the classification scheme in [24] for b^m-symplectic surfaces to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this yields the classification of these objects for nonorientable surfaces. The paper also includes recipes to construct b^m-symplectic structures on surfaces. The feasibility of such constructions depends on orientability and on the colorability of an associated graph. The desingularization technique in [10] is revisited for surfaces and the compatibility with this classification scheme is analyzed in detail.     

Ein Axiomatischer Aufbau der Ähnlichkeitsgeometrie

Let Φ?F fields. With respect to the complex number plane we call the elements of Fpoints, the subsets Φm^+b, m≠O,b?F, lines and the bijektions z?F→zm⁺b?F (direct)similitudes. Two noncollinear point-triplets (a₁,a₂,a₃) and (b₁,b₂,b₃) are said to besimilar triangles if there exists a similitude, mapping a₁ onto b₁ for i=1,2,3. Therefore, similarity is an equivalence. relation on the set of all triangles. In this paper, we characterize these geometries axiomatically, starting from incidence structures with an abstract equivalence relation — called similarity — on the set of all triangles by imposing successively similarity-axioms for triangles.     

Infinite Distance Components of the Boundary of Moduli Spaces of Conformal Structures

We continue the investigation of the L ²-geometry of moduli spaces of conformal structures, where the L ²-metric is induced from the canonical metrics for conformal structures that supports a positive scalar curvature metric introduced in previous papers.     

Point-weight designs with design conditions on t points

This paper examines some of the properties of point-weight incidence structures, i.e. incidence structures for which every point is assigned a positive integer weight. In particular it examines point-weight designs with a design condition that stipulates that any two “identical” sets of t points must lie on the same number of blocks. We introduce a new class of designs with this property: row-sum designs, and examine the basic properties of row-sum point-weight designs and their similarities to classical (non-point-weight) designs and the point-weight designs of Horne [On point-weighted designs, Ph.D. Thesis, Royal Holloway, University of London, 1996].     

Forced convective flow and heat transfer past an unconfined blunt headed cylinder at different angles of incidence

In the present paper, a numerical investigation has been carried out to study the forced convective flow and heat transfer characteristics past a blunt-headed cylinder in crossflow. Employing air as an operating fluid, calculations are carried out for a range of Reynolds number (Re) from 40 to 160. The angle of incidence is varied in the range of 0^∘ ≤ α ≤ 180 ^∘. The thermofluid features of flow and heat transport are analysed in detail for different angles of incidence. To analyse the aerodynamic characteristics, several parameters such as drag and lift coefficients, moment coefficient, Strouhal number, recirculation length, and local time-averaged vorticity flux have been calculated. Furthermore, a stability analysis has been undertaken by using the Stuart Landau equation to enumerate the critical Reynolds number at each angle of incidence. Heat transfer characteristics are studied by computing local and time-averaged values of Nusselt numbers. When compared to a rectangular cylinder, a blunt-headed cylinder exhibits an enhanced heat transfer rate. In the end, an entropy generation analysis has been carried out to study the effects of Re and angle of incidence on the efficiency of thermofluid transport characteristics.     

Real Hypersurfaces in Nearly Kaehler 6-Sphere

In this paper we study real hypersurfaces in the nearly Kaehler 6-sphere S ⁶ and show that there are three almost contact metric structures on a real hypersurface. Then we use a conformal vector field on the 6-sphere S ⁶ and study its influence on the almost contact metric structures on the real hypersurface M and use it to characterize the hyperspheres in S ⁶.     

Quasi-Cyclic Codes from a Finite Affine Plane

Finite geometry codes are defined as the null spaces of the incidence matrices of points and flats in finite geometries. In this paper, we investigate the incidence matrix of points other than the origin and lines not passing through the origin in the affine plane AG(2,2^s), and we present two classes of quasi-cyclic codes derived from submatrices of the point-line incidence matrix. We also investigate the 2-ranks of those submatrices. AMS Classification: 94B25, 94B05     

Characterizations of adjacency on the branching polyhedron

Given two distinct branchings of a directed graph G, we present several conditions which are equivalent to the corresponding incidence vectors of the branchings being adjacent on the branching polyhedron of G. The proof of these equivalences uses a “shrinking algorithm” which will determine in O(n²) time and space whether or not the incidence vectors are adjacent.     

Some results on the incidence coloring number of a graph

This paper proves that if G is a cubic graph which has a Hamiltonian path or G is a bridgeless cubic graph of large girth, then its incidence coloring number is at most 5. By relating the incidence coloring number of a graph G to the chromatic number of G², we present simple proofs of some known results, and characterize regular graphs G whose incidence coloring number equals Δ(G)+1.     

Incidence Theorems for Pseudoflats

We prove Pach-Sharir type incidence theorems for a class of curves in Rⁿ and surfaces in R³, which we call pseudoflats}. In particular, our results apply to a wide class of generic irreducible real algebraic sets of bounded degree.     

交换群上Hopf路余代数的结构分类

设G是群, kG是域k上的群代数. 对任意Hopf箭向Q=(G, r), 利用右kZ_u(C) -模的直积范畴∏_C∈K(G) MkZ_u(C)与kG-Hopf双模范畴^kG_kG M^kG_kG之间的同构, 可由^u(C)(kQ₁)¹上的右kZ_u(C) -模结构导出在箭向余模kQ₁上的kG-Hopf双模结构. 该文讨论在群G分别是2阶循环群与克莱茵四元群时的Hopf路余代数kQ^c的同构分类及其子Hopf代数kG[kQ₁]结构.     

Constructions in Sasakian geometry

We first generalize the join construction described previously by the first two authors [4] for quasi-regular Sasakian-Einstein orbifolds to the general quasi-regular Sasakian case. This allows for the further construction of specific types of Sasakian structures that are preserved under the join operation, such as positive, negative, or null Sasakian structures, as well as Sasakian-Einstein structures. In particular, we show that there are families of Sasakian-Einstein structures on certain 7-manifolds homeomorphic to S ² × S ⁵. We next show how the join construction emerges as a special case of Lerman’s contact fibre bundle construction [32]. In particular, when both the base and the fiber of the contact fiber bundle are toric we show that the construction yields a new toric Sasakian manifold. Finally, we study toric Sasakian manifolds in dimension 5 and show that any simply-connected compact oriented 5-manifold with vanishing torsion admits regular toric Sasakian structures. This is accomplished by explicitly constructing circle bundles over the equivariant blow-ups of Hirzebruch surfaces. During the preparation of this work the first two authors were partially supported by NSF grants DMS-0203219 and DMS-0504367.     

Classification of incidence scrolls (I)

The aim of this paper is to obtain a classification of scrolls of genus 0 and 1, which are defined by a one-dimensional family of lines meeting a certain set of linear spaces in p ⁿ . These ruled surfaces will be called incidence scrolls and such a set will be the base of the incidence scroll. Unless otherwise stated, we assume that the base spaces are in general position. Received: 1 December 2000     

Incidence coloring of the squares of some graphs

The incidence chromatic number of G, denoted by χ_i(G), is the least number of colors such that G has an incidence coloring. In this paper, we determine the incidence chromatic number of the powers of paths, trees, which are min{n,2k+1}, and Δ(T²)+1, respectively. For the square of a Halin graph, we give an upper bound of its incidence chromatic number.