Fine Structure of the Photoluminescence Spectrum of Diamond under the Multiple Emission of an Optical Phonon during the Autolocalization of Photoexcited Electrons

JETP Letters - The autolocalization of electrons photoexcited by laser pulses with a wavelength of 525 nm in the visible range and with a duration of 150 fs in an electron-hole plasma (density...     

Novel Highly Energetic Pyrazoles: N‐Trinitromethyl‐Substituted Nitropyrazoles

A new family of energetic compounds, nitropyrazoles bearing a trinitromethyl moiety at the nitrogen atom of the heterocycle, was designed. The desirable high‐energy dense oxidizers 3,4‐dinitro‐ and 3,5‐dinitro‐1‐(trinitromethyl)pyrazoles were synthesized in good yields by destructive nitration of the corresponding 1‐acetonylpyrazoles. All of the prepared compounds were fully characterized by multinuclear NMR and IR spectroscopy, as well as by elemental analysis. Single‐crystal X‐ray diffraction studies show remarkably high density. Impact sensitivity tests and thermal stability measurements were also performed. All of the pyrazoles possess positive calculated heats of formation and exhibit promising energetic performance that is the range of 1,3,5‐trinitroperhydro‐1,3,5‐triazine and pentaerythritol tetranitrate. The new pyrazoles exhibit positive oxygen balance and are promising candidates for new environmentally benign energetic materials.     

Gas-filled electron diode based on a glow discharge

Stable ignition and sustention of a pulsed discharge with a current of up to 180 A and duration of 12 μs at a pressure of 10⁻¹–10⁻² Pa are achieved in a glow-discharge plasma cathode with the help of an auxiliary initiating discharge. An electron emission current density of up to 100 A/cm² and accelerating voltageof 15 kV are obtained in a gas-filled diode based on this type of a plasma cathode. An electron beam witha neutralized space charge can be transported almost without losses in a weak axial magnetic field alonga plasma channel formed due to the gas ionization by the accelerated electrons over a distance of up to 30 cm.     

Optical characterization and composition of abdominal wall muscle from rat

Complete optical characterization of biological tissue is desirable to develop clinical methods using optical technologies. Particularly, to develop optical clearing methods in biological tissues, it is necessary to know the composition of the tissue, the percentage of each constituent and corresponding refractive indexes. To obtain such information for rat muscle, we used a simple method to characterize tissue constituents for both content percentage and refractive index. The study consisted on measuring mass with a precision weighting scale and the refractive index with an Abbe refractometer during tissue dehydration. With the collected data, we used a theoretical model to calculate the refractive index and percentage for both interstitial fluid and solid part of the rat muscle. The results obtained are in good agreement with data published by other authors, and were considered of vital information for the optical clearing studies that we planned to perform.     

Open Sets Avoiding Integral Distances

We study open point sets in Euclidean spaces $\mathbb{R }^d$ R d without a pair of points an integral distance apart. By a result of Furstenberg, Katznelson, and Weiss such sets must be of Lebesgue upper density $0$ 0 . We are interested in how large such sets can be in $d$ d -dimensional volume. We determine the exact values for the maximum volumes of the sets in terms of the number of their connected components and dimension. Here techniques from diophantine approximation, algebra and the theory of convex bodies come into play. Our problem can be viewed as a counterpart to known problems on sets with pairwise rational or integral distances. It possibly opens a new research direction with strong links to topology and measure theory.     

Coercivity of Combined Boundary Integral Equations in High‐Frequency Scattering

We prove that the standard second‐kind integral equation formulation of the exterior Dirichlet problem for the Helmholtz equation is coercive (i.e., sign‐definite) for all smooth convex domains when the wavenumber k is sufficiently large. (This integral equation involves the so‐called combined potential, or combined field, operator.) This coercivity result yields k‐explicit error estimates when the integral equation is solved using the Galerkin method, regardless of the particular approximation space used (and thus these error estimates apply to several hybrid numerical‐asymptotic methods developed recently). Coercivity also gives k‐explicit bounds on the number of GMRES iterations needed to achieve a prescribed accuracy when the integral equation is solved using the Galerkin method with standard piecewise‐polynomial subspaces. The coercivity result is obtained by using identities for the Helmholtz equation originally introduced by Morawetz in her work on the local energy decay of solutions to the wave equation. © 2015 Wiley Periodicals, Inc.     

Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation

Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem.