Infinite Dimensional Parametric Optimal Control Problems

In this paper we study parametric optimal control problems monitored by nonlinear evolution equations. The parameter appears in all the data, including the nonlinear operator. First we show that for every value of the parameter, the optimal control problem has a solution. Then we study how these solutions as well as the value of the problem respond to changes in the parameter. Finally, we work out in detail two examples of nonlinear parabolic optimal control systems.     

Fractional almost Kähler–Lagrange geometry

The goal of this paper is to encode equivalently the fractional Lagrange dynamics as a nonholonomic almost Kähler geometry. We use the fractional Caputo derivative generalized for nontrivial nonlinear connections (N-connections) originally introduced in Finsler geometry, with further developments in Lagrange and Hamilton geometry. For fundamental geometric objects induced canonically by regular Lagrange functions, we construct compatible almost symplectic forms and linear connections completely determined by a “prime” Lagrange (in particular, Finsler) generating function. We emphasize the importance of such constructions for deformation quantization of fractional Lagrange geometries and applications in modern physics.     

Syntheses, electronic structures, and EPR/UV-vis-NIR spectroelectrochemistry of nickel(II), copper(II), and zinc(II) complexes with a tetradentate ligand based on S-methylisothiosemicarbazide

Template condensation of 3,5-di-tert-butyl-2-hydroxybenzaldehyde S-methylisothiosemicarbazone with pentane-2,4-dione and triethyl orthoformate at elevated temperatures resulted in metal complexes of the type M(II)L, where M = Ni and Cu and H(2)L = a novel tetradentate ligand. These complexes are relevant to the active site of the copper enzymes galactose oxidase and glyoxal oxidase. Demetalation of Ni(II)L with gaseous hydrogen chloride in chloroform afforded the metal-free ligand H(2)L. Then by the reaction of H(2)L with Zn(CH(3)COO)(2)·2H(2)O in a 1:1 molar ratio in 1:2 chloroform/methanol, the complex Zn(II)L(CH(3)OH) was prepared. The three metal complexes and the prepared ligand were characterized by spectroscopic methods (IR, UV-vis, and NMR spectroscopy), X-ray crystallography, and DFT calculations. Electrochemically generated one-electron oxidized metal complexes [NiL](+), [CuL](+), and [ZnL(CH(3)OH)](+) and the metal-free ligand cation radical [H(2)L](+?) were studied by EPR/UV-vis-NIR and DFT calculations. These studies demonstrated the interaction between the metal ion and the phenoxyl radical.     

Structural investigation of xAg2O·(100−x)·[2B2O3·As2O3] glasses doped with manganese ions

Structural analysis of x[(100−y)Ag₂O·yMnO]·(100−x)[2B₂O₃·As₂O₃] glasses, with x=10 mol% and 0≤y≤10 mol%, was performed by means of FT-IR and FT-Raman spectroscopies. The purpose of this work is to investigate the structural changes that appear in the xAg₂O·(100−x)·[2B₂O₃·As₂O₃] glasses with the addition and increase in manganese ions content. FT-IR measurements revealed the presence of pyro-, ortho-, di-, tri-, tetra- and penta-borate groups and structural units characteristic to As₂O₃ in the structure of the studied glasses. FT-IR spectroscopy measurements also show that BO₃ units are the main structural units of the glass system. The presence of structural units characteristic to Ag₂O were not directly evidenced by FT-IR spectroscopy. In addtition, the FT-Raman analysis evidenced the presence of boroxol rings in the structure of the studied glasses.     

Global Solution for Massive Maxwell-Klein-Gordon Equations

We derive the asymptotic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) in the exterior of the domain of influence of a compact set. This complements the previous well-known results, restricted to compactly supported initial conditions, based on the so-called hyperboloidal method. That method takes advantage of the commutation properties of the Maxwell and Klein-Gordon equations with the generators of the Poincaré group to resolve the difficulties caused by the fact that they have, separately, different asymptotic properties. Though the hyperboloidal method is very robust and applies well to other related systems, it has the well-known drawback of requiring compactly supported data. In this paper we remove this limitation based on a further extension of the vector field method adapted to the exterior region. Our method applies, in particular, to nontrivial charges. The full problem can then be treated by patching together the new estimates in the exterior with the hyperboloidal ones in the interior. This purely physical space approach introduced here maintains the robust properties of the old method and can thus be applied to other situations such as the coupled Einstein Klein-Gordon equation. © 2019 Wiley Periodicals, Inc.     

Electron–phonon heat exchange in quasi-two-dimensional nanolayers

We study the heat power P transferred between electrons and phonons in thin metallic films deposited on free-standing dielectric membranes. The temperature range is typically below 1 K, such that the wavelengths of the excited phonon modes in the system is large enough so that the picture of a quasi-two-dimensional phonon gas is applicable. Moreover, due to the quantization of the components of the electron wavevectors perpendicular to the metal film’s surface, the electrons spectrum forms also quasi two-dimensional sub-bands, as in a quantum well (QW). We describe in detail the contribution to the electron–phonon energy exchange of different electron scattering channels, as well as of different types of phonon modes. We find that heat flux oscillates strongly with thickness of the film d while having a much smoother variation with temperature (T _e for the electrons temperature and T _ph for the phonons temperature), so that one obtains a ridge-like landscape in the two coordinates, (d, T _e ) or (d, T _ph ), with crests and valleys aligned roughly parallel to the temperature axis. For the valley regions we find P ∝ T _e ^3.5 – T _ph ^3.5 . From valley to crest, P increases by more than one order of magnitude and on the crests P cannot be represented by a simple power law. The strong dependence of P on d is indicative of the formation of the QW state and can be useful in controlling the heat transfer between electrons and crystal lattice in nano-electronic devices. Nevertheless, due to the small value of the Fermi wavelength in metals, the surface imperfections of the metallic films can reduce the magnitude of the oscillations of P vs. d, so this effect might be easier to observe experimentally in doped semiconductors.     

Curve Flows and Solitonic Hierarchies Generated by Einstein Metrics

We investigate bi-Hamiltonian structures and mKdV hierarchies of solitonic equations generated by (semi) Riemannian metrics and curve flows of non-stretching curves. There are applied methods of the geometry of nonholonomic manifolds enabled with metric-induced nonlinear connection (N-connection) structure. On spacetime manifolds, we consider a nonholonomic splitting of dimensions and define a new class of liner connections which are ‘N-adapted’, metric compatible and uniquely defined by the metric structure. We prove that for such a linear connection, one yields couples of generalized sine-Gordon equations when the corresponding geometric curve flows result in solitonic hierarchies described in explicit form by nonholonomic wave map equations and mKdV analogs of the Schrödinger map equation. All geometric constructions can be re-defined for the Levi-Civita connection but with “noholonomic mixing” of solitonic interactions. Finally, we speculate why certain methods and results from the geometry of nonholonmic manifolds and solitonic equations have general importance in various directions of modern mathematics, geometric mechanics, fundamental theories in physics and applications, and briefly analyze possible nonlinear wave configurations for modeling gravitational interactions by effective continuous media effects.