Structural features of tricarbonyl(N-methyl-2-pyridinecarboxyamide)chloro-rhenium(I)-potential precursor of radiopharmaceuticals

Structural characteristics of the novel [fac-Re(CO)₃L]Cl complex, where L denotes the N-methyl-2-pyridinecarboxyamide, are presented. Molecular structure of the complex has been established by means of X-ray single crystal diffraction and compared with quantum mechanical calculations. It has been shown that pyridinethioamide is softer base than pyridineamide. As a result of different Re^I–S and Re^I–O bond covalent shortenings (reflecting their diverse ionic/covalent character ratio) difference of the bond lengths decreases from a theoretical value of 0.45 Å to the value of 0.28 Å.     

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.     

Positive-Part Moments via the Fourier–Laplace Transform

Integral expressions for positive-part moments E X₊^p\mathsf{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.     

Interference noise spectrum above a rough sea surface at small glancing angles

The interference noise spectrum due to sea clutter has been investigated using statistical scattering theory. The scattered field was calculated in the tangent-plane approximation. The bearings of a motionless source are taken in the bistatic case. Taking the function of shadows on a spatially inhomogeneous random surface into account, we were able to explain the nonmonotonic dependence of the width of the spectrum of arrival angle fluctuations on the distance as well as the presence of maxima in the spectrum at frequencies substantially higher than that of the maximum of a rough sea surface. The theoretical results are compared with data from a full-scale experiment.Radioastronomical Institute, Ukrainian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, No. 10, pp. 1294–1302, October, 1994.     

High-frequency diffraction corrections to backscattering cross sections from a rough three-dimensional surface

Diffraction corrections to scalar wave fields at perfectly free and rigid rough surfaces were derived by two iterations of the corresponding integral equations. These diffraction corrections to the pressure or normal velocity (which, in the geometrical optics limit, are doubled at perfectly rigid and free surfaces, respectively) were obtained with an accuracy of approximately 1k(2), where k is the wave number of incidence radiation. Based on these corrections to the surface fields, the backscattering cross sections at normal incidence from the statistically rough Gaussian surfaces were derived. It was found that for the gentle roughness, diffraction results in effective "smoothing" of roughness for rigid and free surfaces and increasing of the backscattering cross sections, but for a rigid surface with steep roughness, the "fictitious" surface can be more rough than the real one, and the diffraction corrections become negative.     

Model equations for the Eiffel Tower profile: historical perspective and new results

Model equations for the shape of the Eiffel Tower are investigated. One model purported to be based on Eiffel's writing does not give a tower with the correct curvature. A second popular model not connected with Eiffel's writings provides a fair approximation to the tower's skyline profile of 29 contiguous panels. Reported here is a third model derived from Eiffel's concern about wind loads on the tower, as documented in his communication to the French Civil Engineering Society on 30 March 1885. The result is a nonlinear, integro-differential equation which is solved to yield an exponential tower profile. It is further verified that, as Eiffel wrote, “in reality the curve exterior of the tower reproduces, at a determined scale, the same curve of the moments produced by the wind”. An analysis of the actual tower profile shows that it is composed of two piecewise continuous exponentials with different growth rates. This is explained by specific safety factors for wind loading that Eiffel & Company incorporated in the design of the free-standing tower. To cite this article: P. Weidman, I. Pinelis, C. R. Mecanique 332 (2004).     

Cloused cycle of production of ulltrafine polytetrafluoroethylene and new areas of use of fluoropolymer manufacture waste

The features of processes of ultrafine polytetrafluoroethylene manufacture of waste technological polytetrafluoroethylene by hydrothermal method and thermal degradation with an exhaustive fluorination in the presence of cobalt trifluoride were studied. Compositions and properties of gaseous and solid products of pyrolysis and recycling in ultrafine polytetrafluoroethylene manufacture were determined. Methods of use of ultrafine polytetrafluoroethylene, gaseous products, and spent catalyst were developed. On the basis of the experiments a closed scheme of producing ultrafine polytetrafluoroethylene was proposed in view of its application with recycling of accompanying gas fraction, and separating manufacture waste with recycling of cobalt trifluoride catalyst and using the resulting cobalt difluoride for producing composite coatings and lubricants.