The Schrödinger operators with constant magnetic field in a bent chain and Y-type chain of coupled balls are considered. Coupling exists due to point-like openings at the touching points of neighbor spheres. The mathematical background of the model is the theory of self-adjoint extensions of symmetric operators. The spectral equations for the model operators in each case were derived and analyzed.

In this paper, we consider a linear parabolic type partial differential equation in the space of generalized functions as the equation of neutron diffusion in the presence of neutron absorption by the atomic nucleus with nonlinear impulsive effects. Spectral equation is obtained from the Dirichlet boundary value conditions and this spectral problem is studied. The Fourier method of variables separation is used. Countable system of nonlinear functional integral equations is obtained with respect to the Fourier coefficients of unknown function. Theorem on a unique solvability of the countable system of functional integral equations is proved. The method of successive approximations is used in combination with the method of contracting mapping. Criteria of uniqueness and existence of generalized solution of the impulsive mixed problem is obtained. Solution of the mixed problem is derived in the form of the Fourier series. It is shown that the Fourier series converges uniformly.

We studied photon antibunching in the pump and the harmonic modes of the sixth harmonic generation process. The generalized interaction Hamiltonian is solved for several particular cases in the Heisenberg picture, and the possibility of observing photon antibunching is investigated using the short-time approximation technique. It is shown that the photon antibunching in the pump field depends on the number of pump photons, the interaction time, and the coupling of the field between the modes. With the same amount of pump photons, we deduced that third-order photon antibunching is more nonclassical than second- and first-order photon antibunching. In this process, the effect of photon antibunching is not seen in the harmonic mode over pump mode. It is shown that photon antibunching is more noticeable with shorter interaction times as the depth of nonclassicality increases and the second-order correlation function decreases. The first-order Hamiltonian interaction, which stimulates both pump and harmonic fields, is demonstrated to be more nonclassical than the second-order Hamiltonian interaction. It is clear that the coherent state, or vacuum state, of a pump field with a nonzero harmonic field creates photon clusters because the pump field causes interaction, which leads to bunching effects. It is interpreted that the degree of photon antibunching is maximum in the regions where the second correlation function is minimum. Photon antibunching has been shown to be one of the quantum properties of light.

Exploring advanced saturable absorber (SA) materials that exhibit exceptional performance for achieving Q-switching and mode-locking operations remains a vibrant area of research in the field of fiber lasers. The remarkable optical nonlinearity, coupled with high thermal and chemical stability of MAX phase materials, positions them as promising candidates for high-performance SAs. In this study, we demonstrated the potential of Ti₃AlC₂ MAX phase as an effective material for Q-switched and mode-locked fiber laser applications. The Ti₃AlC₂ film was synthesized through a straightforward and cost-effective casting method employing polyvinyl alcohol (PVA) as a host material. The SA was cleverly constructed from the film, utilizing a sandwich-structured fiber-ferrule platform, and seamlessly integrated into an Erbium-doped fiber laser (EDFL) ring cavity. Initially, a stable Q-switched laser was realized at a center wavelength of 1531 nm. The repetition rate exhibited a commendable increase from 35.0 to 50.8 kHz, and the pulse width reduced from 6.58 to 3.40 µs as the pump power was adjusted within the range of 25.98 to 58.29 mW. Notably, the maximum output power of 2.49 mW and a pulse energy of 49.02 nJ were recorded at a pump power of 58.29 mW. Subsequently, an additional 200 m long single-mode fiber was added into a similar laser cavity, leading to the generation of a stable mode-locked laser at a threshold pump power of 81.37 mW, operating at a central wavelength of 1558.96 nm. The observed stable repetition rate of 969.3 kHz, coupled with a pulse duration of 300 ns, demonstrated robust performance as the pump power increased from 81.37 to 113.68 mW. These findings highlight the exceptional performance of Ti₃AlC₂ SA for both Q-switching and mode-locking applications. The versatility of these lasers makes them valuable for diverse applications, including micromachining of materials, frequency comb generation, and remote sensing.

Magnetic skyrmions are considered promising candidates for coding bits of information in racetrack memory devices. Information recording in such devices is assumed to occur by creating skyrmions. This work is devoted to finding solutions to make this process as energy-efficient as possible. One of the factors influencing the creation of skyrmions is the geometry of the track on which recording takes place. We study the influence of the shape and size of track boundary notches on the energy barriers of skyrmion nucleation. We show that skyrmions generation is facilitated by the presence of irregularities at the track boundary and the best solution is a deep narrow notch. On the other hand the skyrmion nucleation rate is smaller for smooth boundaries and skyrmions generation can be suppressed by their interaction with the track boundary, if notch size is smaller than the skyrmion radius. These results can be used in development of future memory devices based on skyrmions.

Carbon films were obtained by magnetron sputtering of graphite in an argon atmosphere on various metal substrates. As a result, a “metal-semiconductor” junction is formed due to the fact that the temperature dependence of the film resistance is of a semiconductor nature. The current-voltage characteristics of the junction were studied at various ambient temperatures, and the degradation of its electrical properties over time was discovered.

The paper proposes an analytical model of tunneling-recombination processes with forward and reverse displacements in InGaN/GaN-based structures containing a quantum well, assuming that the processes of generation and recombination are complex, while one of the stages of the transition of the charge carrier to the center is tunneling. Comparing the model with the experiment allowed us to determine the energies of the recombination centers of 0.22 and 0.45 eV. These energies may correspond to centers formed by defect complexes along filamentous dislocations, such as divacansions (V_Ga V_N ), and a point isolated defect observed in n-type GaN layers grown by various methods, respectively.

The combination of ultrasonic exposure on ceric phosphate gels with subsequent hydrothermal-microwave treatment resulted in the formation of nanoscale NH₄Ce₂(PO₄)₃ or KCe₂(PO₄)₃ phases. The sun protection factor (SPF) and protection factor against UV-A radiation (UVAPF) values for double ceric phosphates with the smallest crystallite sizes exceeded 4 and 3.5, respectively, which is much higher than the values for samples consisting of larger particles. These results are superior to previously published values for similar ceric compounds, and thus show promise for their application in sunscreens.

In this study, the influence of initial reagents on the phase composition and morphology of magnesium ferrite obtained by combustion of glycine-nitrate gel was investigated. The local environment of iron ions in the gel-precursor was studied in detail using FT-IR, XANES- and EXAFS-spectroscopy. It has been established that in the gel-precursor obtained by dissolving metals (Mg, Fe) in dilute nitric acid, binuclear Fe(III) complexes are formed, while in a similar gel-precursor obtained from crystalline hydrates of nitrates of the corresponding metals, trinuclear Fe(III) complexes predominate. Combustion of a gel consisting of binuclear Fe(III) complexes leads to the formation of nanocrystalline magnesium ferrite powder, characterized by a unimodal particle size distribution.

Zinc-manganese ferrite nanoparticles, denoted as Zn_xMg_1−xFe₂O₄ where x ranges from 0 to 1, were synthesized via solution combustion employing glycine as the organic fuel at a stoichiometric redox ratio. The resultant compositions underwent comprehensive characterization utilizing scanning electron microscopy, energy-dispersive spectroscopy, and powder X-ray diffractometry. Magnetic and electrochemical properties were meticulously examined using a vibrating magnetometer and cyclic voltmeter, respectively. Analysis revealed an average particle size ranging from 24.9 to 30.8 nm across all synthesized samples, with degrees of crystallinity reaching 93–96%. Notably, variations in the magnetic behavior were observed depending on the magnesium content within the samples. The highest magnetic parameters were recorded for Zn_0.4Mg_0.6Fe₂O₄ (Ms = 27.78 emu/g, Mr = 3.77 emu/g, and Hc = 21.4 Oe). Furthermore, the electrochemical capacity of the synthesized powders exhibited dependency on the incorporation of magnesium cations into the crystal lattice. These findings underscore the significance of magnesium content in modulating the magnetic and electrochemical properties of Zn_xMg_1−xFe₂O₄ nanoparticles synthesized via solution combustion.

The concentration stability field localization of the pyrochlore-structured compounds of variable composition formed in the Bi₂O₃–Fe₂O₃–WO₃ system under hydrothermal conditions at a temperature of T = 200◦C and a pressure of P = 7 MPa was determined. It was found that the pyrochlore-structured compounds stability field is longitudinally limited within the atomic ratios 0.47 < Bi/W < 1.25, and in the transverse direction within 1.14 < Bi/Fe < 1.87. It was shown that the pyrochlore phase cubic unit cell parameter a depends on the compound chemical composition as follows: it increases linearly from ∼ 10.3319 A˚ to ∼ 10.4199 A˚ with an increase in the Bi/W atomic ratio from ∼ 0.47 to ∼ 1.25. It was established that from the Bi₂O₃–WO₃ system side, there is a region of two-phase equilibrium, in which a pyrochlore phase of variable composition coexists with the Bi2WO6 compound, which is formed in the form of plate-like (thickness h ∼ 50–100 nm) nanoparticles. It was shown that from the Bi₂O₃–Fe₂O₃ system side, there is a region of compositions, in which the pyrochlore phase of the most enriched in bismuth oxide composition coexists with the Bi₂WO₆ compound, which is formed in the form of rod-shaped (h ∼ 10–30 nm) nanoparticles, and with the X-ray amorphous phase composition, formed in the form of nanocrystalline particles about 10 nm in size. It was found that the higher temperature point of the pyrochlore-structured compounds stability field does not exceed 725◦C, which allows them to be synthesized only by “soft chemistry” methods.

We propose a mathematical model to fit the temperature-dependent thermal conductivity of M_1−xR_xF_2+x heterovalent solid solutions where M stands for alkaline-earth metals and R for rare-earth metals. These solid solutions experience composition-driven transition from the crystal-like to glass-like behavior of thermal conductivity. When tested on Ca_1−xYb_xF_2+x solid solutions, the model showed a potential for use with an option for further improvements.

Cerium fluoride (CeF₃) nanoparticles (NPs), being a unique nanozyme and redox-active nanomaterial, show high promise for advanced biomedical applications. Doping of CeF₃ NPs with the other chemical elements allow one to increase their catalytic activity, impart them new functional properties, and also to increase the efficiency of their interaction with ionizing radiation, which is important in the development of novel nanoradiosensitizers. In this article, we synthesized citrate-stabilized Ce_0.75Bi_0.15Tb_0.1F₃ nanoparticles, which demonstrate high colloidal stability, have good luminescent properties and radiation-induced redox activity. Cytotoxicity analysis of Ce_0.75Bi_0.15Tb_0.1F₃ NPs using normal and tumor cells in vitro showed the sensitivity of B16/F10 and EMTP6 tumor cell lines to the nanoparticles at high concentrations (0.5 – 1 mM). Obtained experimental results allow us to consider Ce_0.75Bi_0.15Tb_0.1F₃ nanoparticles as a possible platform for the development of a new class of nanoradiosensitizers for radiation therapy purposes.

Composite films based on aromatic polyamide imide with carboxyl-containing fragments in repeating units (PAI-Ac) containing hydrosilicate nanotubes (Mg,Fe)₃Si₂O₅(OH)₄ are structurally sensitive to the molecular weight of the polymer used. According to Mössbauer spectroscopy data, nanotubes introduced into a polymer matrix generally retain their original structure. When using a polymer with a relatively low molecular weight, composite films are formed that are not stable during the pervaporation of cyclohexane and ethanol. In the case of a high-molecular polymer, the resulting MMM-type membranes are stable during pervaporation. They are more permeable to polar liquids compared to the base polymer and MMMs containing Mg₃Si₂O₅(OH)₄ nanotubes. Analysis of the found differences in the properties of the studied nanocomposites with iron-containing nanotubes in the PAI-Ac matrix from similar nanocomposites with magnesium-containing nanotubes leads to the conclusion about the need to study MMMs with iron-containing nanoparticles of a different structure.

A green and energy-efficient technique for production of porous carbon-mineral chars from agricultural wastes (rice husk, wheat bran) and sedimentary carbonaceous feedstocks (high-ash peat, coal) was developed. It is based on partial combustion in fluidized bed of a deep oxidation catalyst at low temperatures (465 – 600 ◦C). This technique yields porous chars with an elevated mineral content that depends on a feed-stock used, and gaseous products of complete oxidation. It was found that the obtained chars have developed porosity with BET specific surface area of ca. 50 – 170 m²g⁻¹, pore volume of 0.05 – 0.17 ml·g⁻¹, and ash content of 16 – 79 wt. %. They were additionally characterized by TGA and FTIR. Their testing as adsorbents for heavy metal ions (by the example of Cu²⁺) and organic dyes (by the example of methyl green) revealed that their adsorption capacities are comparable to those of chars produced by the conventional pyrolytic approaches.

We present a plasmonic turn-on biosensing assay for insulin detection via aptamer DNA based on the plasmonic interaction of centimeter scale gold/silver double-layer nanodisk arrays and gold nanoparticles. The large-scale nanostructures were fabricated by laser interference lithography technique. The detecting optical signal-extinction spectra of the system were monitored by UV-visible spectrophotometry. The 3D finite-difference time-domain simulation was used to observe the plasmonic interaction of the sensing system. The platform exhibits an exceptionally large turn-on signal by a 120 nm red shift of the localized surface plasmonic resonance peak, results in the limit detection of 140 pM. The centimeter-scale localized surface plasmon resonance nanostructures combined with turn-on design scheme would offer a promising sensor-on-chip biosensing platform.