We consider the two-particle Schrodinger operator¨ H(k), (k∈T³ ≡ (−π,π]³ is the total quasimomentum of a system of two particles) corresponding to the Hamiltonian of the two-particle system on the three-dimensional lattice Z³. It is proved that the number N(k) ≡ N(k⁽¹⁾,k⁽²⁾,k⁽³⁾) of eigenvalues below the essential spectrum of the operator H(k) is nondecreasing function in each k⁽ⁱ⁾ ∈ [0,π], i = 1,2,3. Under some additional conditions potential vˆ, the monotonicity of each eigenvalue z_n(k) ≡ z_n(k⁽¹⁾,k⁽²⁾,k⁽³⁾) of the operator H(k) in k⁽ⁱ⁾ ∈ [0,π] with other coordinates k being fixed is proved.

Polyhydroxyalkanoates (PHAs) are biopolymers, which are stored inside cells as energy storage materials by various microorganisms. PHAs are plastic materials that have a positive environmental impact when compared to regular plastics in terms of production methods and recyclabillity. In addition, PHAs are characterized by biocompatibility, biodegradability and thus have a wide range of applications such as biomedicine, surgery, etc. The most common PHAs are Polyhydroxybutyrate, Polyhydroxyvalerate, and copolymer. In this paper, we calculate the domination topological indices of these polymers; also, we discuss the quantitative structure property relationships (QSPR) analysis of these domination topological indices.

Further, we show that the characteristics have a good correlation with the physico-chemical characteristics of polymers

The density functional theory method was used to study new layered carbon nanostructures consisting of sp³- and sp+sp²-hybridized atoms. The nanostructures are theoretically built on the basis of graphene 5 – 7 layers. As a result of calculations, it is found that the structures of two diamondlike bilayers and twenty-one graphyne layers are stable. The diamond-like bilayers have a band gap of ∼ 1.8 eV, so their properties should be semiconducting. For fourteen graphyne layers, the band gap is zero and their properties are metallic. Seven graphyne layers have band gaps ranging from 0.05 to 0.2 eV.

Temperature dependence of the spectral intensity of recombination radiation in a quasi-zero-dimensional structure, containing impurity complexes “A⁺+e” (a hole localized on a neutral acceptor, interacting with an electron localized in the ground state of a quantum dot), has been investigated in an external electric field in the presence of tunneling decay of a quasistationary A⁺-state. Probability of dissipative tunneling of a hole has been calculated in the one-instanton approximation, and the influence of tunneling decay and of an external electric field on the A⁺-state binding energy and on the spectra of recombination radiation, associated with the optical transition of an electron from the ground state of a quantum dot to the A⁺-state of the impurity center, has been investigated in the adiabatic approximation. “Dips” in the temperature dependence of the SIRR have been revealed, which are associated with the presence of resonant tunneling at certain values of temperature and strength of the external electric field, for which the double-well oscillatory potential becomes symmetric.

The article gives an overview of the main theoretical and experimental studies of the phenomena caused by the formation of coherent states – coherent population trapping, electromagnetically induced transparency, and laser generation without inversion.

We investigate environment induced effects of decoherence in discrimination between the Schrödinger cat states transmitted through noisy quantum¨ channels such as optical fibers. We calculate the fidelity and the statistics of photocounts for both even and odd coherent states. The method that uses the beam splitter-like transformation acting in the enlarged Hilbert space to model the quantum channel is compared with the approach based on the Lindblad dynamics of one-mode bosonic systems.

The saturation in increasing the power conversion efficiency (PCE) of silicon-based solar cells made researchers around world to look for the alternatives. An alternative solar cell would possess some basic requirements like cost effectiveness, reproducible, durable (stability), non-toxicity and higher efficiency. Perovskite solar cell (PSC) opened the new realm of hope for this alternative, consisting of perovskite absorber sandwich between the hole transport layer (HTL) and the electron transport layer (ETL). Good performance of PSCs can be achieved by optimizing many parameters of the components of PSC for obtaining the highest PCE. Among them, the HTL also plays a very vital role. Previously, organic poly (3,4-ethylenedioxythiophene):poly (styrene sulfonic acid) PEDOT:PSS was being widely used as the HTL in PSCs, but due to its hygroscopic nature and acidic properties, it lowered the stability and the life time of the PSCs. Later it was replaced mostly by NiO, a p-type transparent conducting oxide (TCO) enhancing the PCE of PSCs. Its excellent stability and electrical/optical properties attracted the interest of many researchers. Different types of PSCs used NiO thin films prepared from different synthesis routes and obtained variation in efficiency of PSCs. Different parameters of NiO thin films like thickness, annealing temperature (AT) and duration, precursor combinations and more in synthesis processes, have a significant role in optimizing the PCE. Though there are many routes for obtaining NiO thin film, here we are trying to focus more on sol-gel method, as this route is very cost effective and employs basic equipment. Its evolution, present status and the future perspectives will also be discussed.

This paper analyzes the available data on phase equilibria in the TiO₂–SiO₂–ZrO₂ system. The advantages of specialized databases and software systems for the analysis of information on phase equilibria are pointed. Phase diagrams are kind of a roadmap for the design of materials. As shown in the review, nanomaterials are no exception to this. Data on phase equilibria, such as eutectic points, solubility limits, binodal and spinodal curves, make it possible to predict the possibility of the formation of nanoscale structures and materials based on them. In its turn during the transition to the nanoscale state, the mutual component solubility, the temperature of phase transformation may change significantly, and other features may become observable. This provides additional variability when choosing compositions and material design based on the phases of a given system. As an example, for design of nuclear fuel assemblies that are tolerant to severe accidents at nuclear power plants, mixed carbides (so-called MAX-phases) are considered as one of the most promising options as nanoscale layers on fuel cladding. It is suggested that the materials of the TiO₂–SiO₂–ZrO₂ system, which are the product of oxidation of some MAX-phases, can serve as an inhibitor of their further corrosion. Ensuring the stability of materials based on MAX-phases expands their prospects in nuclear power. This requires comprehensive information about phase equilibria and formation conditions of nanostructured states in the analyzed system.

Chitosan is a promising environmentally-friendly polymer with a wide range of applications in biological, medical and water treatment fields. Recent research in chitosan-based electro spun nanofibers has led to the very cost-effective and efficient removal of toxic metal ions from solutions that are extremely important in today’s pollution-ridden world. Nanofiber fabrication of chitosan blends can easily be done by the novel electrospinning technique. Because of their high adsorption capability, metal chelation ability, nontoxicity, biocompatibility, biodegradability, hydrophilicity, and cost effectiveness, chitosan-based nanofibers have seen rapid growth in water treatment applications. This review outlines the ability of electrospinning produced chitosan-based nanofibers to remove toxic metals. The primary goal of this review is to provide current information on various chitosan blend nanofibers that may be useful in water purification, as well as to encourage further research in this area.

Formation of a hybrid system by metallic nanoparticle, protein (or peptide), and a semiconductor QD can be a new and alternate material which may be used for biological applications including cancer cell detection and treatment. Herein, we report on the colloidal synthesis of metal-protein-QD hybrid system considering Au NPs, CdSe QDs, BSA and Lysozyme protein. We demonstrate the structural, optical and vibrational properties of Au-CdSe, Au-BSA-CdSe and Au-Lysozyme-CdSe hybrid systems following their use as cancer cell markers. The study of photoluminescence spectra reveals the predominance fluorescence resonance energy transfer (FRET) between CdSe QDs and Au NPs, Au-BSA and Au-Lysozyme complex. The energy transfer efficiency between QDs donor and the Au NPs, Au-BSA, Au-Lysozyme acceptors are estimated to be 46%, 94% and 64%; respectively. Fluorescence imaging results represent high biocompatibility and fluorescent behavior of the QDs and its hybrid system in the MDA-MB-231 breast cancer cells. The calculation of corrected total counts of fluorescence (CTCF) predicts the higher uptake of CdSe QDs as compared to the Au-QDs, Au-BSA-QDs, Au-Lysozyme-QDs by the cells. The significantly varied zeta potential values of the hybrid systems influence the cellular uptake processes. The fabrication of biocompatible (water soluble, biologically stable, having bioconjugation capability, low cytotoxic to the normal cells, fluorescent in biological environment) Au-CdSe, Au-protein-CdSe hybrid systems would open up an alternative strategy in nanobiotechnology, due to their special physical, optical as well as chemical properties.

Cellulose nanofibrils (TOCNF) with a width of 20±6 nm and a length of 809±98 nm were prepared using 2,2,6,6-tetramethylpiperidinyl-1oxyl (TEMPO)-mediated oxidation. Two modifying agents were used to functionalize the TOCNF surface in aqueous media: alkyl ketene dimer (AKD) and 3-aminopropyltriethoxysilane (APS). The hydrophilic aerogel L-TOCNF, hydrophobic aerogels L-TOCNF-AKD and L-TOCNF-APS with water contact angles of 0, 139±2, and 133±2^◦, respectively, were prepared by freeze-drying of the aqueous dispersions. The elemental composition, morphology, sizes and crystal structure were determined by EDX analysis, scanning electron microscopy and X-ray diffraction, respectively. The process of redispersion of lyophilized samples in water and four organic solvents was investigated. The effect of TOCNF modification and solvent polarity on the redispersibility of lyophilized samples was revealed: the dispersibility of hydrophobic L-TOCNF-AKD and L-TOCNF-APS in organic solvents was significantly improved.

Present work summarized efficient synthesis of ZnO by mechanochemical method via zinc oxalate dihydrate precursor for studies of the photocatalytic degradation of Rose Bengal dye. The process of conversion of zinc oxalate dihydrate to ZnO was studied by TGA-DTG analysis and FT-IR Spectroscopy, XRD data obtained clearly revealed the hexagonal wurtzite crystallite structures of ZnO. FE-SEM images confirmed nanocrystalline morphology of ZnO with an approximately uniform particle size distribution. The purity of ZnO was confirmed by EDX study. The optical band gap of ZnO was determined from UV-Visible spectroscopy. The photocatalytic activity of ZnO was investigated with degradation of Rose Bengal dye. The colorimetric absorbance measurement was used to estimate degradation efficiency. The catalytic activity was studied with reference to the condition of dye concentration, photocatalyst loading capacity, pH of dye solution, irradiation time, etc. Photocatalytic degradation of Rose Bengal dye over mechanochemically synthesized ZnO under visible light irradiation was successfully studied.

Application of sol-gel derived titania nanoparticles in memristive thin film devices has been a subject of several studies. The reported data on the functional properties and stability of such devices scatter considerably. Meanwhile, the role of post-fabrication treatment, such as annealing in reducing atmosphere, is still poorly investigated for this class of devices. In this study, the effects of thermal annealing in a reducing atmosphere on the resistive switching behavior and the morphological changes of the top electrode during the electroforming process have been systematically addressed for the samples of Al/TiO₂/FTO thin film memristors prepared using sol-gel derived titania. Manifestations of several phenomena affecting the functional stability of these thin films, such as electrode delamination and collapse due to formation of gas bubbles, appearance of electrochemical patterns at the electrode surface, and morphological changes induced by the electroforming process have been systematically established in relation with the various conditions of thermal treatment in a reducing atmosphere.

Nickel ferrite nanopowders were obtained under conditions of solution combustion with the addition of various types of organic fuels (glycine, ascorbic acid, oxalic acid, and malic acid) and studied as photocatalysts in the photodegradation of methylene blue. Photocatalytic measurements were carried out under the action of visible light in model dye solutions. The highest photocatalytic activity was found in the case of a sample synthesized using malic acid as a fuel and in which the largest specific surface area (128.1 m²/g) and the smallest particle size (18 nm) were observed. The obtained dependences of the photocatalytic activity of the synthesized samples demonstrate its strong dependence on morphological and structural parameters. Thus, with an increase in the particle size and a decrease in the specific surface area, a decrease in the efficiency of a photocatalyst based on nickel ferrite is observed. In addition, the use of various types of fuels made it possible to obtain aggregates of various shapes and sizes up to several tens of micrometers. The resulting rate constants were established to vary from 0.00756 to 0.00867 min⁻¹.

A lanthanum orthophosphate- and yttrium-based monazite structured La_0.9Y_0.1PO₄ nanocrystalline material was synthesized. The influence of the thermal treatment temperature on its thermal and mechanical properties has been determined. It was shown that the hydrothermal treatment of coprecipitated phosphates at 230 ^◦C for 110 minutes yielded monazite structured nanoparticles with the crystallite size of about 16 nm. Nanopowder thermal treatment for 20 min in the annealing-quenching mode at 1000–1400 ^◦C resulted in obtaining compact materials, the porosity of which varied from 52 to 27% with the grain growth from ∼20 to ∼100 nm. Active sintering occurred at temperatures above 1300 ^◦C. Nanocrystalline materials obtained by heat treatment at 1200 ^◦C with a grain size of ∼40 nm have a porosity of 42%, microhardness of H_v(25 ^◦C) = 4±0.5 GPa, thermal conductivity λ(25 ^◦C) = 0.4 W·m⁻¹·K⁻¹, and can be used as thermal insulation material.

This study presents a green process to synthesize biodiesel using biosynthesized nano-catalyst and a novel methodology for analyzing the impact of influencing factors – methanol/oil ratio, the concentration of nano-catalyst, temperature, and time of reactions- on the yield of biodiesel obtained by heterogeneous nano-catalyst-based transesterification reaction. Nano-calcium oxide (nano-CaO) was obtained as a heterogeneous nano-catalyst using waste eggshells. Waste cooking oil was treated with methanol and nano-catalyst at varying methanol: oil ratios (4 – 14:1), nano-catalyst concentration (0.5 – 2 %), time of reaction (3 – 4.5 hrs), and temperature (50 – 65 ^◦C). The superiority and effectiveness of the proposed transesterification indices were accomplished making use of Deluca and Termini fuzzy entropy weighted indexes to obtain optimal reaction conditions with 95.49 % biodiesel yield.