On Laser-Induced High-Order Wave Mixing and Harmonic Generation in a Graphene Quantum Dot

JETP Letters - We present results of numerical investigations of high-order wave mixing/harmonic generation (HWM/HHG) with many-body interaction processes derived by a strong two-frequency circular...     

Electronic states in the valence band of a cylindrical ZnSe quantum dot

Electronic states in the valence band of a cylindrical ZnSe quantum dot are studied with allowance for the valence band mixing. Dependences of the wave functions and energy levels on the quantum dot radius are calculated. The influence of a magnetic field parallel to the quantum dot radius on the energy levels is also considered.     

Interfacial effects for shear waves in one dimensional periodic piezoelectric structure

Within the full system of Maxwell's equations this paper investigates the effects of three kinds of transmission conditions at the interfaces between the laminae of a periodic piezoelectric structure on band gaps of Bloch-Floquet waves propagating oblique to the interfaces. The results that are obtained show that under both electrically shorted and magnetically closed transmission conditions Bloch-Floquet waves exist only at acoustic frequencies. The effects of piezoelectricity on Bloch-Floquet wave band structures are studied at such frequencies. It is shown that for periodic crystal structures with laminae made of identical materials the propagation of Bloch-Floquet waves can occur under electrically shorted interface conditions but not under magnetically closed interface conditions.For electrically open interfaces with mechanically smooth contacts the dynamic setting of the problem provides solutions only for photonic crystals. In this case the piezoelectricity has no effect on band gaps.     

On the problem of axial tension of a circular inhomogeneous transversally isotropic shell

We consider the problem of axial tension of a circular inhomogeneous cylindrical shell by longitudinal forces. The determination of the stress-strain state of the shell is performed on the basis of a refined theory. The possibility of losing local stability under axial tension is discussed.     

Stability of Gasless Combustion Fronts in One-Dimensional Solids

For gasless combustion in a one-dimensional solid, we show a type of nonlinear stability of the physical combustion front: if a perturbation of the front is small in both a spatially uniform norm and an exponentially weighted norm, then the perturbation stays small in the spatially uniform norm and decays in the exponentially weighted norm, provided the linearized operator has no eigenvalues in the right half-plane other than zero. Using the Evans function, we show that the zero eigenvalue must be simple. Factors that complicate the analysis are: (1) the linearized operator is not sectorial, and (2) the linearized operator has good spectral properties only when the weighted norm is used, but then the nonlinear term is not Lipschitz. The result is nevertheless physically natural. To prove it, we first show that when the weighted norm is used, the semigroup generated by the linearized operator decays on a subspace complementary to the operator’s kernel, by showing that it is a compact perturbation of the semigroup generated by a more easily analyzed triangular operator. We then use this result to help establish that solutions stay small in the spatially uniform norm, which in turn helps establish nonlinear convergence in the weighted norm.     

Synthesis of 3,4‐Dialkyl‐5‐(1‐oxo‐ethyl)‐3H‐thiazole‐2‐thiones Derivatives and Their Pesticidal Activity

By interaction of N‐methyl(ethyl)‐dithiocarbamate sodium salt with 3‐chloro‐pentane‐2,4‐dion the 1‐(3‐alkyl‐4‐methyl‐2‐thioxo‐2,3‐dihydro‐thiazol‐5‐yl)‐ethanones 1 , 2 and corresponding oximes 7 , 8 were synthesized. On the basis of the mentioned compounds hydrazono ( 3 , 4 ), ureayl and thioureayl ( 5 , 6 ) derivatives, substituted oximes ( 9 , 10 ) and azinyl oximes ( 11 , 12 ) were obtained. The structures of synthesized compounds were confirmed by proton nuclear magnetic resonance spectroscopy and elemental analysis. The pesticidal activities of synthesized compounds were studied. Some of the synthesized compounds simultaneously have shown growth stimulant and fungicidal activity.     

Smoothness of solutions of almost hypoelliptic equations

A two-dimensional linear differential operator P(D) = P(D ₁, D ₂) is called almost hypoelliptic if all derivatives D ^α P of the characteristic polynomial P(ζ) = P(ζ ₁, ζ ₂) are estimated by P(ζ). Assuming that {Ω _κ = (x ₁, x ₂) ∈ E ² : |x ₁| < κ, x ₂ ∈ R ¹}, the paper proves that if the width κ of the strip Ω _κ exceeds some C = C(P) > 0, then all solutions {u} of the almost hypoelliptic equation P(D)u = 0 in a Sobolev space are infinitely smooth functions with respect to x ₁.     

Erratum to: Several Articles in JETP Letters Published Online First

JETP Letters - An Erratum to this paper has been published: https://doi.org/10.1134/S0021364022330013     

On the infrared spectrum of L-lysinium(2+) sulfate

It is argued that the infrared spectrum of L-lysine sulfate (L-Lys2+·SO4(2-)) published by Krishnakumar et al. [V. Krishnakumar, S. Manohar, R. Nagalakshmi, Spectrochim. Acta A75 (2010) 1394-1397] cannot belong to this crystal species. To confirm this, crystals (L-Lys2+·SO4(2-)) were synthesized and identified by XRD, and ATR FTIR and Raman spectra of L-Lys2+·SO4(2-) were registered and are discussed.     

A New Method for Continuous Solid-State Biaxial Orientation of Polymeric Films

A new laboratory-scale method for continuous solid-state biaxial deformation of polymer materials is introduced. The tabletop biaxial drawing tool utilizes a heated metal disc-like triangular mandrel, which allows for continuous solid-state biaxial deformation of a precursor polymer tube with a controlled drawing speed. The new biaxial drawing tool features two independent heating zones. The main mandrel sets the biaxial drawing temperature. In addition, directly after the mandrel, an annealing unit with a separate heating zone is added for better control of important process parameters, such as post-relaxation and strain-induced crystallization. As such, the new biaxial drawing tool is a tabletop analogue of the industrial triple-bubble process. Finally, a detailed theoretical model describing the deformation field and the forces needed to perform biaxial drawing as a function of the biaxial drawing ratio is presented and compared to experimental values, using isotactic polypropylene as model material. © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 352-362