Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

The effect of carbon nanotubes on epoxy matrix nanocomposites

The paper concerns thermal properties of epoxy/nanotubes composites for aircraft application. In this work, influence of carbon nanotubes on thermal stability, thermal conductivity, and crosslinking density of epoxy matrix was determined. Three kinds of nanotubes were used: non-modified with 1- and 1.5-μm length, and 1-μm length modified with amino groups. Scanning electron microscopy observations were done for examining dispersion of nanotubes in the epoxy matrix. Glass transition temperature (T _g) was readout from differential scanning calorimetry. From dynamic mechanical analysis, crosslinking density was calculated for epoxy and its composites. Also, thermogravimetric analysis was done to determine influence of nanotubes addition on thermal stability and decomposition process of composites. Activation energy was calculated from TGA curves by Flynn–Wall–Ozawa method. Thermal diffusivity was also measured. SEM images proved the uniform dispersion of carbon nanotubes without any agglomerates. It was found that nanotubes modified with amino groups lead to the increase of epoxy matrix crosslinking density. The significant increase in T _g was also observed. On the other hand, addition of carbon nanotubes leads to the decrease of thermal stability of polymer due to the increase of thermal diffusivity.     

Regioselective synthesis of 2-unsubstituted 1-aryl-4- and 1-aryl-5-acylimidazoles

An efficient and simple method for the synthesis of 2-unsubstituted 1-aryl-4- and 1-aryl-5-acylimidazoles has been developed. It consists in the condensation of α-diketone monooximes with aromatic amines and formaldehyde on the presence of boron trifluoride etherate, leading to the formation of stable boron trifluoride complexes of N-oxides. Further reduction of these complexes led to the corresponding imidazoles. This method permits broad variations of substituents in the aryl part of these compounds.     

Prevalence of Antimicrobial Resistant Bacteria from Conjunctival Flora in an Eye Infection Prone Breed (Saint Bernard)

The conjunctival bacterial resident and opportunistic flora of dogs may represent a major source of dissemination of pathogens throughout the environment or to other animals and humans. Nevertheless, contamination with bacteria from external sources is common. In this context, the study of the antimicrobial resistance (AMR) pattern may represent an indicator of multidrug resistant (MDR) strains exchange. The present study was focused on a single predisposed breed—Saint Bernard. The evaluated animals were healthy, but about half had a history of ocular disease/treatment. The swabs collected from conjunctival sacs were evaluated by conventional microbiological cultivation and antimicrobial susceptibility testing (AST). The most prevalent Gram-positive was Staphylococcus spp.; regardless of the history, while Gram-negative was Pseudomonas spp.; exclusively from dogs with a history of ocular disease/treatment. Other identified genera were represented by Bacillus, Streptococcus, Trueperella, Aeromonas and Neisseria. The obtained results suggest a possible association between the presence of mixed flora and a history of ocular disease/treatment. A high AMR was generally observed (90%) in all isolates, especially for kanamycin, doxycycline, chloramphenicol and penicillin. MDR was recorded in Staphylococcus spp. and Pseudomonas spp. This result together with a well-known zoonotic potential may suggest an exchange of these strains within animal human populations and the environment.     

Explicit Constructions of Universal R-Trees and Asymptotic Geometry of Hyperbolic Spaces

This paper presents explicit constructions of universal R-treesas certain spaces of functions, and also proves that a -universal R-tree can be isometricallyembedded at infinity into a complete simply connected manifoldof negative curvature, or into a non-abelian free group. Incontrast to asymptotic cone constructions, asymptotic spacesare built without using the axiom of choice. 2000 MathematicsSubject Classification L53C23, 20F67.     

ML-Based Analysis of Particle Distributions in High-Intensity Laser Experiments: Role of Binning Strategy

When entering the phase of big data processing and statistical inferences in experimental physics, the efficient use of machine learning methods may require optimal data preprocessing methods and, in particular, optimal balance between details and noise. In experimental studies of strong-field quantum electrodynamics with intense lasers, this balance concerns data binning for the observed distributions of particles and photons. Here we analyze the aspect of binning with respect to different machine learning methods (Support Vector Machine (SVM), Gradient Boosting Trees (GBT), Fully-Connected Neural Network (FCNN), Convolutional Neural Network (CNN)) using numerical simulations that mimic expected properties of upcoming experiments. We see that binning can crucially affect the performance of SVM and GBT, and, to a less extent, FCNN and CNN. This can be interpreted as the latter methods being able to effectively learn the optimal binning, discarding unnecessary information. Nevertheless, given limited training sets, the results indicate that the efficiency can be increased by optimizing the binning scale along with other hyperparameters. We present specific measurements of accuracy that can be useful for planning of experiments in the specified research area.     

Eigenvalues of a One-Dimensional Dirac Operator Pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a non-trivial square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.