Search results for "algebraic topology"

Dual attachment pairs in categorically-algebraic topology

2011

[EN] The paper is a continuation of our study on developing a new approach to (lattice-valued) topological structures, which relies on category theory and universal algebra, and which is called categorically-algebraic (catalg) topology. The new framework is used to build a topological setting, based in a catalg extension of the set-theoretic membership relation "e" called dual attachment, thereby dualizing the notion of attachment introduced by the authors earlier. Following the recent interest of the fuzzy community in topological systems of S. Vickers, we clarify completely relationships between these structures and (dual) attachment, showing that unlike the former, the latter have no inh…

A rare polymeric azido-bridged copper(II) chain with a pentameric repeating unit: Synthesis, structure and magnetic properties

2013

International audience; The novel polymeric chain copper(II) complex [Cu4(μ-Mesalpn)2(μ1,1,1-N3)2(μ1,1-N3)2Cu]n (1) was prepared by the reaction of Cu(NO3)2·3H2O with Mesalpn in the presence of an excess of NaN3. A single-crystal X-ray diffraction study showed an unusual 1D polymeric chain based on pentanuclear Cu5 units with both μ1,1,1-N3 and μ1,1-N3 bridges, and with three independent Cu(II) ions presenting three different coordination numbers (4, 5 and 6). The magnetic susceptibility data show the presence of dominant anti-ferromagnetic interactions.

A Selenium-Nitrogen Chain with Selenium in Different Oxidation States

2017

Synthesis, crystal structure and magnetic properties of a cyanide-bridged heterometallic {CoIIMnIII} chain

2017

The assembly reaction between the low-spin [CoII(dmphen)(CN)3]- metalloligand and the [MnIII(salen)(H2O)]+ complex cation yielded the one-dimensional compound {[MnIII(salen)(μ-NC)2CoII(dmphen)(CN)]·2H2O}n (1), which behaves as a ferrimagnetic chain, the intrachain magnetic coupling being J = -1.71(1) cm-1.

Analysis of Possible Concept Solutions of Chain Drives

2019

Possible concept solutions of chain drives are analysed in this paper in order to point out the benefits of chain drive application and, in particular, the possibility of application of multi-level chain drive. The paper also analyses the possibility of replacing the gear drives with chain drives, which, in the case of short-term drive and using the same direction of rotation, enables a slightly simpler drive solution. The paper doesn’t consider difference between the roller and gear chains application because these two types of chains can be used very successfully. Also, the possibility of using timing belt drive is not considered, but it can be also used very successfully in this type of …

KnotGenome: a server to analyze entanglements of chromosomes.

2018

Abstract The KnotGenome server enables the topological analysis of chromosome model data using three-dimensional coordinate files of chromosomes as input. In particular, it detects prime and composite knots in single chromosomes, and links between chromosomes. The knotting complexity of the chromosome is presented in the form of a matrix diagram that reveals the knot type of the entire polynucleotide chain and of each of its subchains. Links are determined by means of the Gaussian linking integral and the HOMFLY-PT polynomial. Entangled chromosomes are presented graphically in an intuitive way. It is also possible to relax structure with short molecular dynamics runs before the analysis. Kn…

OPERADS AND JET MODULES

2005

Let $A$ be an algebra over an operad in a cocomplete closed symmetric monoidal category. We study the category of $A$-modules. We define certain symmetric product functors of such modules generalising the tensor product of modules over commutative algebras, which we use to define the notion of a jet module. This in turn generalises the notion of a jet module over a module over a classical commutative algebra. We are able to define Atiyah classes (i.e. obstructions to the existence of connections) in this generalised context. We use certain model structures on the category of $A$-modules to study the properties of these Atiyah classes. The purpose of the paper is not to present any really de…

1985

Etude de polyesters avec du triphenylene ou du benzene comme cœur du discogene et des espaces flexibles alkylene

An improvement of a bound of Green

2012

A p-group G of order pn (p prime, n ≥ 1) satisfies a classic Green's bound log p |M(G)| ≤ ½n(n - 1) on the order of the Schur multiplier M(G) of G. Ellis and Wiegold sharpened this restriction, proving that log p |M(G)| ≤ ½(d - 1)(n + m), where |G′| = pm(m ≥ 1) and d is the minimal number of generators of G. The first author has recently shown that log p |M(G)| ≤ ½(n + m - 2)(n - m - 1) + 1, improving not only Green's bound, but several other inequalities on |M(G)| in literature. Our main results deal with estimations with respect to the bound of Ellis and Wiegold.

Obstruction theory in action accessible categories

2013

Abstract We show that, in semi-abelian action accessible categories (such as the categories of groups, Lie algebras, rings, associative algebras and Poisson algebras), the obstruction to the existence of extensions is classified by the second cohomology group in the sense of Bourn. Moreover, we describe explicitly the obstruction to the existence of extensions in the case of Leibniz algebras, comparing Bourn cohomology with Loday–Pirashvili cohomology of Leibniz algebras.