In this present paper, unique solvability is proved for the boundary value problems for the loaded differential equations associated with non-local boundary value problems, for the classical partial differential equations.

   A quantum graph, consisting of a ring and segment is considered. We deal with the free Schr¨odinger ooperator at the edges and Kirchhoff conditions at the internal vertex. The lengths of the graph edges varies in time. Time evolution of wave packet is studied for different parameters of length varying law.

   In this work, we propose a simple theoretical method for predicting the rate and localization of magnetic field guided particle deposition from aqueous colloids. This method accounts for the colloidal electric double layer interactions between particles and vessel walls. The obtained results suggest that the colloidal interactions can be used to increase the rate of particle deposition and improve its localization.

   Theoretical investigation of the dynamics of three-dimensional few-cycle optical pulses (light bullets) in an inhomogeneous medium of carbon nanotubes with metallic conduction was performed. The stable propagation of pulses under research in accordance with inhomogeneous medium parameters was determined.

   Quantum random number generation allows one to obtain the absolutely random sequences by using nondeterministic physical processes. Fluctuations of the vacuum, recorded by homodyne detection, can be one of the entropy sources in those generators. In this paper, a system of quantum random numbers generation, based on vacuum fluctuations and using a fiber Y-splitter is presented.

   We describe and theoretically study a process of photon distribution statistics measurement for intra-cavity mode of EM field monitored by indirect photo-detection scheme. In particular, we investigate photon number distribution and Mandel’s parameter (normalized dispersion) of the mode using statistics of atomic state detector clicks. In our model, a two-level atom-pointer which passes through the cavity interacts with the mode and environment, distorting the measured statistical properties of the mode. To account for this, phase distortion (decoherece) and population relaxation are introduced in the model. In this paper, we use the super-operators approach to intra-cavity mode evolution conditioned by atomic state detector clicks.

   Transitions between magnetic states of a system coupled to a heat bath can occur by exceeding the energy barrier, but as temperature is lowered quantum mechanical tunneling through the barrier becomes the dominant transition mechanism. A method is presented for estimating the onset temperature for tunneling in a system with an arbitrary number of spins using the second derivatives of the energy with respect to the orientation of the magnetic vectors at the first order saddle point on the energy surface characterizing the over-the-barrier mechanism. An application to a monomer and a dimer of molecular magnets containing a Mn4 group is presented and the result found to be in excellent agreement with reported experimental measurements.

   Study of the CaF₂–YF₃ system by co-precipitation from aqueous nitrate solutions revealed the formation of Ca_1−xYxF_2+x solid solution precipitate containing up to 20 mol. % yttrium fluoride (x ≤ 0.2). A higher yttrium to calcium ratio in the starting solutions caused additional precipitation of orthorhombic β-YF₃ nanophase elongated along the ⟨b⟩ axis. Cubic (H₃O)Y₃F₁₀ phase was also formed (SSG Fm3m, a = 11.60 ˚A, KY₃F₁₀ structural type).

   In this work, microtubes with walls, containing Fe₃O₄ nanoparticles, obtained by “rolling up” of the interfacial films, were synthesized by the gas-solution interface technique (GSIT), using a mixture of aqueous solutions of FeCl₂ and FeCl₃ and gaseous ammonia. The synthesized microtubes were characterized by Scanning Electronic Microscopy (SEM), Energy-Dispersive X-ray spectroscopy (EDX), X-Ray Diffraction analysis (XRD) and magnetization measurements. It was established that under optimal synthetic conditions the microtube diameter ranged from 5 to 10 µm, the length was up to 120 µm and the thickness of walls was about 0.6 µm, the walls themselves being formed by nanoparticles with a size of about 10 nm. The reversible hysteresis behavior, the low coercive force, the low remanence magnetization and the approaching of Mr/Ms to zero, confirmed the superparamagnetic nature of the synthesized microtubes. A hypothesis on the formation of microtubes by the gas-solution interface technique was proposed.

   This review analyzes and summarizes the research results for oxide material synthesis by combustion of organic-inorganic mixtures. We have outlined the range of physical and chemical factors influencing the precursor processes and the oxide material synthesis itself, as well as have shown the ways and options to control these processes and nanoscale materials’ properties. We have highlighted several issues concerning the analysis methods for the resulting materials and processes. We have exemplified the practical implementation of the methods under discussion.

   Thin film solar cells are having the problem of low absorption of light, particularly at longer wavelengths and hence, efficient light trapping engineering is demanded. Here, we propose a design of ultra thin GaAs solar cell with enhanced light absorption with the use of dual (dielectric and metal) gratings. In this way, light trapping can be enhanced at longer wavelengths for both TE and TM polarization modes.

   This paper presents the results of a study of surface morphology of pyrolytic films of solid solutions of ZnS–CdS. We discovered that the change of roughness parameters and microstructure of the surface of the coating film depended on the quantitative composition of the solid solution.

   Comparative size and structure characterization of silver and selenium nanoparticles obtained and stabilized in different polymer solutions was performed by transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS). Effects of instrumental properties, nature of the samples, data collecting and data processing on accuracy of measurements are highlighted and summarized. Numerical differences in the mode diameter values derived from the TEM and SAXS data were found to have different sources. The SAXS results can be misleading in case of small particles (2–4 nm), for instance, Ag nanoparticles formed and stabilized in some aqueous polymer solutions due to instrumental limits, while TEM can provide sufficient statistics on such nanoparticles. SAXS is efficient in characterization of size distributions for soft Se-polymer composite particles of 20 to 100 nm in diameter. TEM is mandatory for investigating the chemical and phase composition of particles in mixtures, and their formation mechanism.

   The dependence of oxide films surface layers’ compositions on the method of depositing of V2O5 on InP and regimes of thermal oxidation of the formed heterostructures was established by the XPS method. Lower indium content near the surface for all samples in comparison with the standard indicates a partial blocking of its diffusion into films during the chemostimulated thermal oxidation of the semiconductor. The presence of vanadium oxides in certain oxidation states and their ratio depends on the method of deposition for the chemostimulator, and on the regime of thermal oxidation. In the case of the electric arc synthesis method, at shorter reaction times, vanadium compounds in the +4 and +5 oxidation states were present in the near-surface layer, which gives evidence for the catalytic mechanism.

   Detonation nanodiamonds (NDs) with chlorinated (ND–Cl) and carboxylated (ND–COOH) surfaces were obtained. The broad-spectrum antibiotic Amikacin (Amik) was covalently grafted to the chlorinated surface (ND–Amik) and immobilized by adsorption to carboxylated surface (Amik/ND–COOH). Biological testing in vitro showed the presence of antibacterial activity of the obtained samples against Staphylococcus aureus FDA P209 and Escherichia coli ATCC 25922, close to activity of free amikacin. It was revealed that to maintain antibacterial activity of the samples after their preliminary treatment, important factors such as the use of antioxidants (hydrosulfite and sodium citrate) and lyophilization were necessary.

   Effect of ammonium dihydrogen phosphate admixture on phase transitions in nanostructured solid solutions (1 − x)KH₂PO4–(x)(NH₄)H₂PO₄ at x = 0, 0.05 and 0.15 has been studied by dielectric spectroscopy. The samples have been prepared by embedding of aqueous solutions into porous borosilicate glasses. The X-ray diffraction have shown that the crystal structure at room temperature corresponds to the bulk KDP and the average nanoparticle diameters are 49 (2) nm for the sample with 5 % of (NH₄)H₂PO₄ (ADP) and 46 (2) nm for the nanocomposites with 15 % of ADP. Dielectric response data analysis have revealed the shifts of the ferroelectric phase transition temperature as a function of (NH₄)H₂PO₄ concentration: at x = 0 ∆TC is equal to ∼6 K, at x = 0.05 ∆TC ∼3 K and at x = 0.15 ∆TC ∼2 K.

   Nb-doped TiO₂ nanoparticles with different doping concentrations, varied from 0 to 2.7 mol. %, were prepared by the sol-gel method followed by thermal treatment. The obtained nanoparticles were used to fabricate a series of electron transport layers for constructing perovskite solar cells (PSCs). The prepared layers were characterized using X-ray diffraction and optical transmission measurements. The effects of Nb doping concentration in TiO₂ layers on the optical absorption behavior, the morphology and charge carrier dynamics were studied. A series of PSCs, based on the developed electron transport layers was fabricated and examined. It was found that PSC fabricated with 2.7 mol. % Nb content TiO₂ electron transport layer have shown up to 19 % improvement of a power conversion efficiency compared to that, based on an undoped TiO₂ layer.