Search results for "combinatoric"

An algebraic representation of Steiner triple systems of order 13

2021

Abstract In this paper we construct an incidence structure isomorphic to a Steiner triple system of order 13 by defining a set B of twentysix vectors in the 13-dimensional vector space V = GF ( 5 ) 13 , with the property that there exist precisely thirteen 6-subsets of B whose elements sum up to zero in V , which can also be characterized as the intersections of B with thirteen linear hyperplanes of V .

Effective target arrangement in a deterministic scale-free graph

2010

We study the random walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a measure of transport efficiency, is expected to depend sensitively on the position of targets. We consider several spatial arrangements for targets and we calculate, mainly rigorously, the related MFPT, where the average is taken over all possible starting points and over all possible paths. For all the cases studied, the MFPT asymptotically scales like N^{theta}, being N the volume of the substrate and theta ranging from (1 - log 2/log3), for central target(s)…

Repetitiveness Measures based on String Attractors and Burrows-Wheeler Transform: Properties and Applications

2023

The relationship between interdisciplinarity and distinct modes of university-industry interaction

2019

Abstract Interdisciplinary research (IDR) has raised increasing expectations among scholars and policymakers about its potential to produce ground-breaking scientific contributions and satisfy societal demands. While existing research highlights that novel connections across fields is beneficial for scientific contributions with high academic impact, comparatively less is known about whether IDR is positively associated to scientists’ engagement with non-academic actors. To investigate this, we examine whether there is a systematic relationship between scientists’ IDR-orientation and their interactions with industry. We conceptually distinguish four stylized modes of interaction (firm creat…

Topological classification of 4-dimensional complete intersections

1996

Let X,,(d) C C P "+r denote a complete intersection, the transversal intersection of r hypersurfaces in C P ~+r defined by r homogeneous polynomials of degrees (d l , . . . ,dr) =: d, with dld2...d,. =: d the total degree. It is well-known that the diffeomorphism type of X,,(d) is determined by n and d. In [7] and [8], Libgober and Wood showed that in dimension n -~ 2, there exist k distinct multidegrees ibr any integer k 6 N such that the corresponding complete intersections are all diffeomorphic. For n = 1,3, the diffeomorphism classification of Xn(d) is well-known by surface theory and the classification of 1-connected six-manifolds [12] respectively. For 7z = 2, at least the topological…

Isolated roundings and flattenings of submanifolds in Euclidean spaces

2005

We introduce the concepts of rounding and flattening of a smooth map $g$ of an $m$-dimensional manifold $M$ to the euclidean space $\R^n$ with $m<n$, as those points in $M$ such that the image $g(M)$ has contact of type $\Sigma^{m,\dots,m}$ with a hypersphere or a hyperplane of $\R^n$, respectively. This includes several known special points such as vertices or flattenings of a curve in $\R^n$, umbilics of a surface in $\R^3$, or inflections of a surface in $\R^4$.

Vassiliev invariants for braids on surfaces

2000

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit an universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the considered surface.

On the gonality and the slope of a fibered surface

2018

Abstract Let f : X → B be a locally non-trivial relatively minimal fibration of curves of genus g ≥ 2 . We obtain a lower bound of the slope λ ( f ) increasing with the gonality of the general fiber of f. In particular, we show that λ ( f ) ≥ 4 provided that f is non-hyperelliptic and g ≥ 16 .

INITIAL PARAMETRIC REPRESENTATION OF BLOBS

2009

Blobs, developed by J.F. Blinn in 1982, are the implicit surfaces obtained by composition of a real numerical function and a distance function. Since, many authors (C. Murakami, H. Nishimura, G. Wyvill…) defined their own function of density, from these implicit surfaces are interesting from several points of view. In particular, their fusion makes it possible to easily obtain an implicit equation of resulting surface. However, these surfaces do not admit a parametric equation yet. In this article, we will establish the parametric equation of two blobs in fusion, defined by the function of density of C. Murakami, by using an algebraic method. Then, we will develop another method, based on …

2021

Abstract We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y, dY ). We say that a metric space (Y, dY ) is a quasiconformal Jordan domain if the completion ̄Y of (Y, dY ) has finite Hausdorff 2-measure, the boundary ∂Y = ̄Y \ Y is homeomorphic to 𝕊1, and there exists a homeomorphism ϕ: 𝔻 →(Y, dY ) that is quasiconformal in the geometric sense. We show that ϕ has a continuous, monotone, and surjective extension Φ: 𝔻 ̄ → Y ̄. This result is best possible in this generality. In addition, we find a necessary and sufficient condition for Φ to be a quasiconformal homeomorphism. We provide sufficient conditions for the restriction of Φ to 𝕊1 being a quasi…