Search results for "algebraic topology"
showing 10 items of 306 documents
Pearl-necklace structures of molecular brushes with rigid backbone under poor solvent conditions: A simulation study
2010
Bottle-brush polymers, where flexible side chains containing N=20 to 50 effective monomers are grafted to a rigid backbone, are studied by molecular dynamics simulations, varying the grafting density σ and the solvent quality. Whereas for poor solvents and large enough σ the molecular brush is a cylindrical object, homogeneous in axial direction, for intermediate values of σ an axially inhomogeneous structure of "pearl-necklace" type is formed. The "pearls," however, have a strongly nonspherical ellipsoidal shape, due to the fact that several side chains cluster together in one pearl, qualitatively consistent with predictions of Sheiko et al. [Eur. Phys. J. E 13, 125 (2004)] We analyze the …
Alternating Ferro/Antiferromagnetic Copper(II) Chain Containing an Unprecedented Triple Formato/Hydroxido/Sulfato Bridge.
2016
The first example of a triple formato/hydroxido/sulfato (FHS) bridge for any metal is reported in compound [Cu2(bpym)(OH)(HCO2)(SO4)(H2O)2]·3H2O (1). Its structure shows the presence of alternating triple FHS bridges and 2,2'-bipyrimidine (bpym) ones. Although in the initial synthesis the sulfate anions were introduced accidentally, here we report the rational synthesis and the magnetic properties of this compound. The magnetic properties show that 1 is an alternating ferro/antiferromagnetic (F/AF) chain compound with predominant antiferromagnetic interactions and were fit to an alternating F/AF S = (1)/2 chain with g = 2.103, JAF = -139 cm(-1), and JF = 116 cm(-1) (α = JF/|JAF| = 0.83). Th…
Inter-Chain Structure Factors of Flexible Polymers in Solutions: A Monte Carlo Investigation
1997
Off-lattice Monte Carlo simulations of both the single chain structure factor h(q) and the inter-chain structure factor HD(q) of flexible polymers in solutions are presented over a wide range of both wavenumber q and concentration c from the dilute to the concentrated regime, for chain lengths up to N = 256. The single chain properties $\{$gyration radius 〈Rg2〉, $h(q)\}$ are in reasonable agreement with the expected theoretical behavior, showing a crossover from swollen chains $\{\langle R_{\rm g}^2\rangle \propto N^{2\nu} ,~ h(q) \propto q^{-1/\nu}\}$ to Gaussian chains, and the data comply with a scaling description, with a correlation length ξ∝c-ν/(3ν-1). However, the inter-chain structu…
Stable Images and Discriminants
2020
We show that the discriminant/image of a stable perturbation of a germ of finite \(\mathcal {A}\)-codimension is a hypersurface with the homotopy type of a wedge of spheres in middle dimension, provided the target dimension does not exceed the source dimension by more than one. The number of spheres in the wedge is called the discriminant Milnor number/image Milnor number. We prove a lemma showing how to calculate this number, and show that when the target dimension does not exceed the source dimension, the discriminant Milnor number and the \(\mathcal {A}\)-codimension obey the “Milnor–Tjurina relation” familiar in the case of isolated hypersurface singularities. This relation remains conj…
Quantum-state transfer via resonant tunneling through local-field-induced barriers
2013
Efficient quantum-state transfer is achieved in a uniformly coupled spin-1/2 chain, with open boundaries, by application of local magnetic fields on the second and last-but-one spins, respectively. These effective barriers induce the appearance of two eigenstates, bilocalized at the edges of the chain, which allow a high-quality transfer also at relatively long distances. The same mechanism may be used to send an entire e-bit (e.g., an entangled qubit pair) from one to the other end of the chain. DOI: 10.1103/PhysRevA.87.042313
Crystal structure and absolute configuration of (4S,5R,6S)-4,5,6-trihydroxy-3-methylcyclohex-2-enone (gabosine H)
2017
The absolute configuration of the title compound, determined as 4S,5R,6S on the basis of the synthetic pathway, was confirmed by single-crystal X-ray diffraction. The molecule is formed by a substituted six-membered cyclohexene ring adopting an envelope conformation and substituted by carbonyl, methyl and hydroxyl groups. The supramolecular structure is mainly built by a combination of O—H⋯O and weaker C—H⋯O hydrogen bonds.
ChemInform Abstract: Reactions of the Hydrofluoroborate Salts of Open-Chain Analogues of Reissert Compounds with Some α,β-Ethylenic Esters.
2010
The reaction of the hydrofluoroborate salt of an open-chain analogue of a Reissert compound with some α,β-ethylenic esters does not give a [4 + 2] cycloadduct, as previously described in the case of ethyl acrylate. The reaction starts with a 1,3-dipolar cycloaddition of a munchnone imine 5c, d. The [3 + 2] cycloadducts 13 evolve via a rearrangement–condensation sequence to give a substituted 2-pyridone derivative 18 or 19. The proposed mechanism has been verified by the isolation and structural X-ray analysis of some compounds of the reaction sequence.
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…
Cohomology of Lie algebras
1995
This chapter is devoted to studying some concepts that will be extensively used in the last chapters, namely the cohomology of Lie algebras with values in a vector space, the Whitehead lemmas and Lie algebra extensions (which are related to second cohomology groups). The same three different cases of extensions of chapter 5 as well as the ℱ( M )-valued version of cohomology will be considered. In fact, the relation between Lie group and Lie algebra cohomology will be explored here, first with the simple example of central extensions of groups and algebras (governed by twococycles), and then in the higher order case, providing explicit formulae for obtaining Lie algebra cocycles from Lie gro…
On the construction of lusternik-schnirelmann critical values with application to bifurcation problems
1987
An iterative method to construct Lusternik-Schnirelmann critical values is presented. Examples of its use to obtain numerical solutions to nonlinear eigenvalue problems and their bifurcation branches are given