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 Our results develop and extend the unpublished thesis of A. Karnaukh [Ka].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.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Positive-Part Moments via the Fourier–Laplace Transform

Integral expressions for positive-part moments E X₊^pmathsf{E},X_{+}^{p} (p>0) of random variables X are presented, in terms of the Fourier–Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such an expression is given. This study was motivated by extremal problems in probability and statistics, where one needs to evaluate such positive-part moments.     

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.     

Carbon nanocones/discs – a new type of filler to improve the thermal and mechanical properties of polymer films

The mechanical characteristics and thermal properties of composite films based on the thermally stable aromatic polyimide (PI) (PMDA‐ODA) and carbon nanocones/discs (CNC) were studied. The introduction of CNC to PMDA‐ODA leads to the substantial increase of film stiffness. The Young's modulus values of the composite films are somewhat higher than those of the previously characterized composite films of this PI filled with nanoclay, carbon nanofibers, and asbestos‐like hydrosilicate nanotubes. The introduction of CNC into PMDA‐ODA (concentrations of CNC were up to 15 vol%) does not cause any marked aggregation of nanoparticles. The presence of CNC in the PI matrix does not affect the glass transition temperature of the polymer but hinders chain mobility at temperatures above T_g. This behavior makes it possible to increase the working temperature range of the composite films containing more than 5 vol% of CNCs, up to the temperature of thermal decomposition. The introduction of CNC into PMDA‐ODA leads to dramatic (～12 orders of magnitude) increase of active electrical conductivity of the material. Copyright © 2011 John Wiley & Sons, Ltd.     

Parameterization of electrostatic interactions for molecular dynamics simulations of heterocyclic polymers

The paper focuses on the problem of electrostatic interactions in molecular dynamics simulations of thermal properties of heterocyclic polymers. The study focuses on three thermoplastic polyimides synthesized on the basis of 1,3‐bis‐(3′,4‐dicarboxyphenoxy)benzene (dianhydride R) and three diamines: 4,4′‐bis‐(4″‐aminophenoxy) diphenylsulfone (diamine BAPS), 4,4′‐bis‐(4″‐aminophenoxy) biphenyl (diamine BAPB), and 4,4′‐bis‐(4''‐aminophenoxy) diphenyloxide (diamine BAPO). In the molecular dynamics simulations these polyimides were described by the Gromos53a5 force field. To parameterize the electrostatic interactions four methods of calculating the partial atomic charges were chosen: B3LYP/6–31G*(Mulliken), AM1(Mulliken), HF/6–31G*(Mulliken), and HF/6–31G*(ChelpG). As our parameterization is targeted to reproduce thermal properties of the thermoplastic polyimides, the choice of proper partial charges was finalized on a basis of the closest match between computational and experimental data for the thermal expansion coefficients of the polyimides below glass transition temperatures. Our finding clearly show that the best agreement with experimental data is achieved with the Mulliken partial atomic charges calculated by the Hartree‐Fock method with 6–31G* basis set. Furthermore, in addition to the thermal expansion coefficients this set of partial atomic charges predicts an experimentally observed relationship between glass transition temperatures of the three polyimides under study: . A mechanism behind the change in thermal properties upon the change in the chemical structure in considered polyimides may be related to an additional spatial ordering of sulfone groups due to dipole‐dipole interactions. Overall, the modified force‐field is proved to be suitable for accurate prediction of thermal properties of thermoplastic polyimides and can serve as a basis for building up atomistic theoretical models for describing other heterocyclic polymers in bulk. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 912–923