Single-Crystal Synthesis and Structures of Rb-Boroleucite Rb(BSi2)O6 and Boropollucite Cs(BSi2)O6 at 293 and 120 K

Crystallography Reports - The structures of Rb-boroleucite Rb1.0(B0.333Si0.667)3O6 and boropollucite Cs0.87(B0.290Si0.710)3O6 were studied using single crystals, which were prepared under...     

Specific Features of Distribution and Relaxation of Elastic Stresses in Homoepitaxial CVD Films of Germanium and Diamond

Crystallography Reports - The real structures of epitaxial CVD films of germanium and diamond have been comparatively analyzed. The influence of the specific features of elastic-stress distribution...     

Validation of quartz crystal rheometry in the megahertz frequency regime

The utility of the quartz crystal microbalance (QCM) as a high‐frequency rheometer operating at 15 MHz was demonstrated. High‐frequency data obtained from a series of rubbery materials were compared with results obtained from traditional dynamic mechanical analysis (DMA) at much lower frequencies. The high‐frequency data enable meaningful shift factors to be obtained at temperatures much further above glass‐transition temperature (T _g) than would otherwise be possible, giving a more complete picture of the temperature dependence of the viscoelastic properties. The QCM can also be used to quantify mass uptake and changes in viscoelastic properties during sample oxidation. The viscoelastic response spanning the full range of behaviors from the rubber to glassy regimes was found to fit well with a six‐element model consisting of three power‐law springpot elements. One of these elements is particularly sensitive to the behavior in the transition regime where the phase angle is maximized. The value of this quantity is obtained from the maximum phase angle, which can be obtained from a temperature sweep at fixed frequency, proving a means for more detailed frequency‐dependent rheometric information to be obtained from a fixed‐frequency measurement at a range of temperatures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1246–1254     

The 6j-Symbols for the SL(2, ℂ) Group

Theoretical and Mathematical Physics - We study 6j-symbols or Racah coefficients for the tensor products of infinite-dimensional unitary principal series representations of the group SL(2,...     

Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.     

Aircraft selection modeling: a multi-step heuristic to enumerate airlift alternatives

Annals of Operations Research - We consider the use of the new C-130J-30 aircraft for long distance (strategic) cargo movement. Currently, only large aircraft, the C-5 and the C-17, are identified...     

The use of hypercrosslinked polymer sorbents and composites based on them in the sorption of toxic and bad-smelling substances

Russian Chemical Bulletin - The sorption of cadaverine from the air on hypercrosslinked polystyrene sorbents was investigated. An available technique for the introduction of iron oxide into the...     

Optical Stereoisomers of Geometric Isomers of the Octahedral Complex TiF4[Ph2P(O)CH2CH(OH)Me)]2 in CH2Cl2

Russian Journal of Coordination Chemistry - Some peculiarities of the effect of enantiomers of the monodentate ligand on the stereoisomerism of the mixed octahedral tetrafluoride complexes of...     

Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in ${\mathbb{R}}^d$ and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.