Filters compatible with isomorphism testing

Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central series, the associated graded Lie ring may share few features with the original group: e.g. the associated Lie ring can be trivial or arbitrarily large. We determine properties of filters such that every isomorphism between groups is induced by an isomorphism between graded Lie rings.     

Alkaline oxygen evolution: exploring synergy between fcc and hcp cobalt nanoparticles entrapped in N-doped graphene

Herein, we report a Mott-Schottky catalyst by entrapping cobalt nanoparticles inside the N-doped graphene shell (Co@NC). The Co@NC delivered excellent oxygen evolution activity with an overpotential of merely 248 mV at a current density of 10 mA cm^–2 with promising long-term stability. The importance of Co encapsulated in NC has further been demonstrated by synthesizing Co nanoparticles without NC shell. The synergy between the hexagonal close-packed (hcp) and face-centered cubic (fcc) Co plays a major role to improve the OER activity, whereas the NC shell optimizes the electronic structure, improves the electron conductivity, and offers a large number of active sites in Co@NC. The density functional theory calculations have revealed that the hcp Co has a dominant role in the surface reaction of electrocatalytic oxygen evolution, whereas the fcc phase induces the built-in electric field at the interfaces with N-doped graphene to accelerate the H⁺ ion transport.     

Functional Binding Surface of a β‐Hairpin VEGF Receptor Targeting Peptide Determined by NMR Spectroscopy in Living Cells

In this study, the functional interaction of HPLW peptide with VEGFR2 (Vascular Endothelial Growth Factor Receptor 2) was determined by using fast ¹⁵N‐edited NMR spectroscopic experiments. To this aim, ¹⁵N uniformly labelled HPLW has been added to Porcine Aortic Endothelial Cells. The acquisition of isotope‐edited NMR spectroscopic experiments, including ¹⁵N relaxation measurements, allowed a precise characterization of the in‐cell HPLW epitope recognized by VEGFR2.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

Numerical methods for finding multiple eigenvalues of matrices depending on parameters

Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods. Received December 19, 1994 / Revised version received January 18, 1996     

A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems

Summary Consider the solution of one-dimensional linear initial-boundary value problems by a finite element method of lines using a piecewiseP ^th -degree polynomial basis. A posteriori estimates of the discretization error are obtained as the solutions of either local parabolic or local elliptic finite element problems using piecewise polynomial corrections of degreep+1 that vanish at element ends. Error estimates computed in this manner are shown to converge in energy under mesh refinement to the exact finite element discretization error. Computational results indicate that the error estimates are robust over a wide range of mesh spacings and polynomial degrees and are, furthermore, applicable in situations that are not supported by the analysis.This research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 90-0194; by the U.S. Army Research Office under Contract Number DAAL03-91-G-0215; and by the National Science Foundation under Institutional Infrastructure Grant Number CDA-8805910     

Absolutely indecomposable symmetric matrices

Let A be a symmetric matrix of size n×n with entries in some (commutative) field K. We study the possibility of decomposing A into two blocks by conjugation by an orthogonal matrix T∈Mat_n(K). We say that A is absolutely indecomposable if it is indecomposable over every extension of the base field. If K is formally real then every symmetric matrix A diagonalizes orthogonally over the real closure of K. Assume that K is a not formally real and of level s. We prove that in Mat_n(K) there exist symmetric, absolutely indecomposable matrices iff n is congruent to 0, 1 or −1 modulo 2s.     

On the realization of Riemannian symmetric spaces in Lie groups

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G.