Optimal boundary displacement control of string vibrations with a nonlocal evenness condition of the second kind

We study the behavior of a string with the nonlocal boundary condition u _x (l, t) = u _x ($ x^\circ $ x^\circ , t). A displacement control u(0, t) = μ(t) bringing the string from an arbitrarily given initial state to an arbitrarily given terminal state is applied at the left endpoint of the string. For the initial and terminal functions, we find necessary and sufficient conditions for the controllability of the string. Under these conditions, we carry out optimization; i.e., of all admissible controls, we choose a control minimizing the boundary energy integral.     

Optimal boundary force control at one end of a string for a given displacement mode at the other end

We solve the problem of optimal boundary force control at one end of a string for the case of a given displacement mode at the other end. The problem is studied in the sense of a generalized solution of the corresponding mixed initial-boundary value problem in the Sobolev space. We also solve the problem of choosing an optimal boundary control from infinitely many feasible controls. The generalized solution of the mixed initial-boundary value problem is constructed in closed form, and the uniqueness of the solution is proved.     

Classical solution of a problem with an integral condition for the one-dimensional wave equation

We find a closed-form classical solution of the homogeneous wave equation with Cauchy conditions, a boundary condition on the lateral boundary, and a nonlocal integral condition involving the values of the solution at interior points of the domain. A classical solution is understood as a function that is defined everywhere in the closure of the domain and has all classical derivatives occurring in the equation and conditions of the problem. The derivatives are defined via the limit values of finite-difference ratios of the function and corresponding increments of the arguments.     

Long‐Lived Charge Separation in Novel Axial Donor–Porphyrin–Acceptor Triads Based on Tetrathiafulvalene,Aluminum(III) Porphyrin and Naphthalenediimide

Two self‐assembled supramolecular donor–acceptor triads consisting of Al^III porphyrin (AlPor) with axially bound naphthalenediimide (NDI) as an acceptor and tetrathiafulvalene (TTF) as a secondary donor are reported. In the triads, the NDI and TTF units are attached to Al^III on opposite faces of the porphyrin, through covalent and coordination bonds, respectively. Fluorescence studies show that the lowest excited singlet state of the porphyrin is quenched through electron transfer to NDI and hole transfer to TTF. In dichloromethane hole transfer to TTF dominates, whereas in benzonitrile (BN) electron transfer to NDI is the main quenching pathway. In the nematic phase of the liquid crystalline solvent 4‐(n‐pentyl)‐4′‐cyanobiphenyl (5CB), a spin‐polarized transient EPR spectrum that is readily assigned to the weakly coupled radical pair TTF^.+NDI^.? is obtained. The initial polarization pattern indicates that the charge separation occurs through the singlet channel and that singlet–triplet mixing occurs in the primary radical pair. At later time the polarization pattern inverts as a result of depopulation of the states with singlet character by recombination to the ground state. The singlet lifetime of TTF^.+NDI^.? is estimated to be 200–300 ns, whereas the triplet lifetime in the approximately 350 mT magnetic field of the X‐band EPR spectrometer is about 10 μs. In contrast, in dichloromethane and BN the lifetime of the charge separation is <10 ns.     

Application of vegetable oils for electrocatalytic synthesis of hydrocarbons

Conditions of Kolbe cross-electrosynthesis of 10-undecylenic and acetic acids are studied on different catalyst anodes. It is shown that the key anodic process stages are the stages of formation of vinyl radicals from anions of unsaturated and methyl radicals under electrosynthesis of acetate anions. As dependent on the conditions of the process, the main product formed on the anode of the Pt-10% Ir alloy is either hydrocarbon CH₃CH₂CH(CH₃)(CH₂)7CH₂CH₃ (58 wt %) being the product of addition of three methyl radicals to a vinyl radicals or olefin CH₂=CH(CH₂)₇CH₂CH₃ (57 wt %) being the product of dimerization of vinyl and methyl radicals.     

Complex formation of crown ethers with α-amino acids: Estimation by NMR spectroscopy

Complex formation of 18-crown-6 and dibenzo crowns with glycine, leucine, and norleucine was studied by NMR spectroscopy. The efficiency of non-valence interactions with participation of different active centers of the host and guest molecules is determined by solvation effects, mutual arrangement of benzene rings in dibenzo crowns, and the presence of bulky aliphatic substituents in the α-amino acid. The complexation of dibenzo crowns with α-amino acids in acid medium involves a system of different non-valence interactions, the most efficient of which are NH ₃ ⁺ ... O hydrogen bond between the ammonium group in the guest molecule and ether oxygen atoms in the host molecule and dipole-dipole interaction between the guest ammonium group and host benzene ring (NH ₃ ⁺ ... Ar). The efficiency of NH ₃ ⁺ ... O hydrogen bonding decreases in going from 18-crown-6 to dibenzo crowns due to distortion of symmetry of the macroring cavity and violation of geometric complementarity of some ether oxygen atoms. The integral efficiency of non-valence interactions in the system dibenzo crown-α-amino acid was estimated on a quantitative level by ¹H NMR relaxation technique.     

Plasma Composition by Mass Spectrometry in a Ar-SiH<Subscript>4</Subscript>-H<Subscript>2</Subscript> LEPECVD Process During nc-Si Deposition

Mass spectrometry has been used to assess plasma composition during a low-energy plasma-enhanced chemical vapor deposition (LEPECVD) process using argon-silane-hydrogen (Ar-SiH₄-H₂) gas mixtures with input flows of 50 sccm Ar, 2–20 sccm SiH₄ and 0–50 sccm H₂ at total pressures of 1–4 Pa. Energy-integrated ion densities, residual gas analysis and threshold ionization mass spectrometry have been used to characterize the transition from amorphous (a-Si) to nano-crystalline silicon (nc-Si) deposition at constant LEPECVD operating parameters. While relative ion densities have a marked decrease with H₂ input, the densities of SiH_x (x < 4) radicals show evolution trends depending on the SiH₄ and H₂ input. For conditions leading to nc-Si growth a turning point is reached above which SiH is the main radical. Observed SiH_x density trends with H₂ input are explained based on kinetic reaction rates calculated from previously obtained Langmuir probe data.     

Aquaperoxovanadium(V) complexes: Quantum-chemical study

The addition of a water molecule to mono-, di-, and triperoxovanadium(V) complexes has been studied at the density functional theory (B3LYP/6-31G**) and Møller-Plesset perturbation theory (MP2/6-31G**) levels. It has been demonstrated that the H₂O…V donor-acceptor interaction cannot compete with hydrogen bonds and becomes weaker with an increase in the number of peroxo groups in the complex. In the most stable isomers of aquaperoxo complexes, water is mainly held by intermediate hydrogen bonds. The energy of addition of a water molecule to peroxovanadate is lower than or close to the heat of evaporation of water; i.e., the formation of stable aquaperoxovanadium complexes in aqueous solutions is improbable. This conclusion is consistent with the mass spectra of aqueous solutions of peroxovanadates, which show that the concentration of water-free peroxo complexes considerably exceeds the concentration of complexes with a coordinated water molecule. The coordination of the water molecule through the V…OH₂ donor-acceptor interaction is prevented by the cis effect of the peroxo group, which has the HOMO orbital of symmetry suitable for interaction with the LUMO orbital of the VO group.     

Temperature dependence of the magnetic properties and magnetoimpedance of nanocrystalline Fe<Subscript>73.5</Subscript>Si<Subscript>16.5</Subscript>B<Subscript>6</Subscript>Nb<Subscript>3</Subscript>Cu<Subscript>1</Subscript> ribbons

The temperature dependences of the magnetic properties and the magnetoimpedance effect of soft magnetic nanocrystalline Fe_73.5Si_16.5B₆Nb₃Cu₁ alloy ribbons are studied in the temperature range 24–160°C. A high temperature sensitivity of the impedance and the magnetoimpedance effect of the ribbons are detected in the ac frequency range 0.1–50 MHz. At an ac frequency of 50 MHz, the change in the impedance reaches 0.2 Ω/°C (0.5%/°C) in the temperature range 85–160°C. When the temperature increases, a monotonically decreasing character of the dependence of the magnetoimpedance effect on the applied magnetic field changes into a dependence having an increasing initial segment. The effect of temperature on the magnetoimpedance properties of the soft magnetic nanocrystalline ribbons is shown to result from temperature-induced changes in their electrical conductivity, magnetization, and effective magnetic anisotropy.