THEOREM 1. Let G be a permutation group on a finite set S of v points. If a, b are distinct points then the set ab of all points fixed by the stabilizer Gab will be called aline. Assume that (i) G is 2-transitive on the points of S; (ii) the number k of points on the line ab satisfies 2 < k < v; (iii) Gab is transitive on the lines containing a and distinct from ab. Then S provided with the set...

We prove that on a punctured oriented surface with Euler characteristic χ < 0, the maximal cardinality of a set of essential simple arcs that are pairwise nonhomotopic and intersecting at most once is 2|χ|(|χ|+1). This gives a cubic estimate in |χ| for a set of curves pairwise intersecting at most once on a closed surface. We also give polynomial estimates in |χ| for sets of arcs and curves pai...

Frankl, P., On cross-intersecting families, Discrete Mathematics 108 (1992) 291-295. Let n 3 t z 1 be integers. Let 9, YI be families of subsets of the n-element set X. They are called cross t-intersecting if IF n GI 2 t holds for all F E 9 and G E 3. If 9 = CfI then 9 is called t-intersecting. Let m(n, t) denote the maximum possible cardinality of a r-intersecting family. Our main result says ...

The above result motivated the study of intersecting families of permutations which was initiated by Deza and Frankl, see [2]. Let Sn be the symmetric group on [n], that is the group of all permutations of [n]. For a positive integer t, a subset A of Sn is said to be t-intersecting if, for any g, h ∈ A with g 6= h, we have |{x : g(x) = h(x)}| ≥ t. By an intersecting family, we mean an 1-interse...

We formulate $U(1)$ $bda$ Chern-Simons theory, which is also called BF on a lattice, adapting method proposed by Kantor and Susskind for the groups $\mathbb{R}$ $\mathbb{Z}_N$. Our applies to any finite or infinite abelian group. study discrete symmetries use model provide rigorous treatment of composite fermion theory fractional quantum Hall effect (FQHE), with no ambiguities relating intersec...

Real cubic algebraic surfaces may be described by either implicit or parametric equations. Each of these representations has strengths and weaknesses and have been used extensively in computer graphics. Applications involving both representations include the efficient computation of surface intersections, and triangulation of curved surfaces. One particularly useful representation is the ration...

Consider the graphs of n distinct polynomials of a real variable intersecting at some point. In the neighborhood of this point, the qualitative picture is described by some permutation of {1, . . . , n}. We describe the permutations that occur in such a situation. In this note, we shall examine the relative positions of the graphs of several functions in the neighborhood of a point where they i...

BPS configurations of intersecting branes have many applications in string theory. We attempt to provide an introductory and pedagogical review of supergravity solutions corresponding to orthogonal BPS intersections of branes with an emphasis on eleven and ten space-time dimensions. Recent work on BPS solutions corresponding to nonorthogonally intersecting branes is also discussed. These notes ...

This paper describes a new approach to solve the problem of intersecting features extraction. Feature extraction is important from several standpoints—automated process planning, NC machining, automated assembly and virtual prototyping. Feature extraction reported in the literature indicates limited success mostly in extracting a partial list of non-intersecting features. There has not been muc...

In the present paper, applicability of the modified fixed grid finite element method in solution of three dimensional elasticity problems of functionally graded materials is investigated. In the non-boundary-fitted meshes, the elements are not conforming to the domain boundaries and the boundary nodes which are used in the traditional finite element method for the application of boundary condit...