We provide a construction of free factorization algebras in algebraic geometry and link factorization homology of a scheme with coefficients in a free factorization algebra to the homology of its (unordered) configuration spaces. As an application, this construction allows for a purely algebro-geometric proof of homological stability of configuration spaces. CONTENTS

An (nk) configuration is a set of n points and n lines such that each point lies on k lines while each line contains k points. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. The existence and enumeration of (nk) configurations for a given k has been subject to active research...

The matching of point sets that are characterized only by their geometric configuration is a challenging problem. In this paper, we present a novel point registration algorithm for robustly identifying objects represented by two dimensional point clouds under affine distortions. We make no assumptions about the initial orientation of the point clouds and only incorporate the geometric configura...

We describe a new way to construct finite geometric objects. For every k we obtain a symmetric configuration E(k−1) with k points on a line. In particular, we have a constructive existence proof for such configurations. The method is purely geometric. It also produces interesting periodic matrices. Mathematisches Institut, Universität Tübigen, Deutschland E-mail address: christoph.hering@uni-tu...

In this research DFT/B3LYP method has been employed to investigate the geometrical structures,relative stabilities, and electronic properties of Cun (n=3–10) clusters for clarifying the effect of sizeon the properties. Through a careful analysis of the successive binding energies, second-orderdifference of energy and the highest occupied-lowest unoccupied molecular orbital energy gaps as afunct...

Spaceborne-airborne multistatic synthetic aperture radar (SA-MuSAR) has the ability to provide high-resolution forward-looking imagery for receivers, but it relies on careful design of geometric configuration (GC). In this article, a GC optimization method is proposed obtain high-quality fused image with limited observation time. First, relationship between spatial resolution and illustrated by...

The absolutely abstract and accurate geometric elements defined in Euclidean geometry always have lengths or sizes in reality. While the figures in the real world should be viewed as the approximate descriptions of traditional geometric elements at the rougher granular level. How can we generate and recognize the geometric features of the configurations in the novel space? Motivated by this que...

Exploratory activity was examined in 4 young baboons with the aim of investigating the type of spatial coding (purely geometric and/or by taking into account the identity of the object) used for the configuration of objects. Animals were individually tested in an outdoor enclosure for their exploratory reactions (contact time and order of spontaneous visits) to changes brought about to a config...