Search results for "Trix"
showing 10 items of 3314 documents
Two-dimensional Banach spaces with polynomial numerical index zero
2009
We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
2012
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in $${(\mathbb {C}^d)^{\otimes k}}$$ , where k and p/d k are fixed while d → ∞. When k = 1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ( $${(1+\sqrt{p/d^k})^2}$$ ) but the smallest eigenvalue $${(\min(0,1-\sqrt{p/d^k})^2)}$$ and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately $${(1+\sqrt{p/d^k})^2}$$ and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix…
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method.
2021
Abstract Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is one of the methods that have been used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described, and it is briefly compared with other commonly used frequency extraction methods. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytical…
Multiple low-frequency broad band gaps generated by a phononic crystal of periodic circular cavity sandwich plates
2017
Abstract We propose a new type of phononic crystal (PnC) composed of a periodic alternation of circular cavity sandwich plates. In the low-frequency regime, the crystal can modulate the propagation of flexural waves. Governing equations are deduced basing on the classical theory of coupled extensional and flexural vibrations of plates. The dispersion relation of the infinite PnC is calculated by combining the transfer matrix method with Bloch theory. The dynamic response of the PnC with finite unit cells is further studied with finite element analysis. An experiment is carried out to demonstrate the performance of the PnC in vibration isolation. Numerical results and experimental results bo…
Quasi-static behaviour and damage assessment of flax/epoxy composites
2015
Experimental investigations were conducted on flax and E-glass fibres reinforced epoxy matrix composites subjected to quasi-static loadings. Flax/epoxy samples having [0]12, [90]12, [0/90]3S and [±45]3S stacking sequences, with a fibre volume fraction of 43% have been tested under tension, compression and in-plane shear loadings. Overall, the compression strength of glass/epoxy was 76% greater than for the flax/epoxy composite. The damage evolution of flax/epoxy of [0/90]3S and [±45]3S samples has been evaluated in terms of transverse crack densities with respect to the load increment. The crack density exhibited a classical “S” shaped pattern for [0/90]3S and linearly for [±45]3S specimens…
Diagrammatic Expansion for Positive Spectral Functions in the Steady-State Limit
2019
Recently, a method was presented for constructing self-energies within many-body perturbation theory that are guaranteed to produce a positive spectral function for equilibrium systems, by representing the self-energy as a product of half-diagrams on the forward and backward branches of the Keldysh contour. We derive an alternative half-diagram representation that is based on products of retarded diagrams. Our approach extends the method to systems out of equilibrium. When a steady-state limit exists, we show that our approach yields a positive definite spectral function in the frequency domain.
Matrix isolation and quantum chemical studies on the H2O2–SO2complex
2004
Complexation and photochemical reactions of hydrogen peroxide and sulfur dioxide have been studied in solid Ar, Kr and Xe. Complexes between H2O2 and SO2 are characterized using Fourier transform infrared spectroscopy and ab initio calculations. In solid Ar, the H2O2–SO2 complex absorptions are found at wavenumbers of 3572.8, 3518.7, 3511.2, 3504.3, 1340.3, 1280.2 and 1149.9 cm−1. In Kr and Xe matrices, the bonded OH stretching frequencies deviate from the values in Ar, and we propose that the matrix surrounding influences the structure of the H2O2–SO2 complex. UV photolysis of the H2O2–SO2 was also studied in solid Ar, Kr and Xe. This photolysis produces mainly a complex between sulfur tri…
Isolating reactive metal-based species in Metal-Organic Frameworks - viable strategies and opportunities.
2021
Structural insight into reactive species can be achieved via strategies such as matrix isolation in frozen glasses, whereby species are kinetically trapped, or by confinement within the cavities of host molecules. More recently, Metal–Organic Frameworks (MOFs) have been used as molecular scaffolds to isolate reactive metal-based species within their ordered pore networks. These studies have uncovered new reactivity, allowed observation of novel metal-based complexes and clusters, and elucidated the nature of metal-centred reactions responsible for catalysis. This perspective considers strategies by which metal species can be introduced into MOFs and highlights some of the advantages and lim…
Effect of different concentrations of specific inhibitor of matrix metalloproteinases on the shear bond strength of self-adhesive resin cements to de…
2017
Background Considering the probability of chemical and enzymatic reactions between matrix metalloproteinases (MMPs) in the dentin structure and their specific inhibitors, the aim of the present study was to evaluate the effect of different concentrations of specific inhibitor of MMPs (galardin) on the shear bond strength of self-adhesive resin cements to dentin. Material and Methods Forty-eight sound human premolars were mounted in self-cured acrylic resin after removal of the enamel on the buccal and lingual surfaces. The dentin surfaces achieved were polished and prepared with 600-grit silicon carbide paper. The samples were divided into 3 groups (n=16) based on the concentration of galar…