This paper aims to reduce Lax pairs of AKNS matrix spectral problems using pairs of group reductions or similarity transformations. The corresponding modified Korteweg-de Vries matrix integrable hierarchies are obtained from the reduced Lax pairs, amending the standard AKNS integrable hierarchies. A few exemplary cases are analyzed and computed to demonstrate the diversity of modified Korteweg-de Vries matrix integrable equations.

We report here a series of detailed statistical analyses on a novel largescale multi-domain Romanian corpus that we use to train a small-language model. We identify the core vocabularies pertaining to six different domain-specific subcorpora and show that they follow the so-called Zipf's law independent on how we count words. Moreover, we introduce two novel frequency-word maps for a domain-specific subcorpus, one showcasing word ranks and one measuring the deviation of the word structure from a perfect vowel-consonant or consonant-vowel repeating pattern. Finally, we show a few examples of prompt/response instances.

We study the spatiotemporal dynamics of Bose-Einstein condensates (BECs) with spatiotemporally varying two- and three-body interactions and without an external trapping potential. The cubic and quintic terms in the Gross-Pitaevskii (GP) equation play the roles of external trapping potentials. Spatiotemporal modulation of the two- and three-body interactions can be of great importance in BEC field. But it is the subject of relatively fewer studies. Through theoretical analyses we obtain the equilibrium points (centers and saddles in phase space) of the unperturbed repulsive and attractive cases. With the heteroclinic solution of the unperturbed repulsive system, we theoretically construct the general solution of the 1st-order perturbed equation of the system. By using the boundedness conditions of the general solution we obtain the Melnikov chaos criterion predicting the existence of Smale-horseshoe chaos in the system. With a set of system parameters satisfied the Melnikov chaos criterion, numerical simulations show that the system is in a chaotic state. For BECs that do not satisfy the Melnikov chaos criterion, numerical simulations demonstrate that the modulating frequency can be an effective controlling parameter for the spatiotemporal dynamics of the BECs.

The exact analytical solution of the one-dimensional stationary Schrödinger equation with a spatially distributed hyperbolic potential profile ~1/x in the presence of a Dirac delta function (point) potential is found and analyzed. Localization features are described analytically in dependence on the parameters of a hyperbolic potential profile and point potential. It is found that the localization energy of the ground state monotonically decreases with an increase in defect intensity. The localized states exist near the both attractive and repulsive defects. Excited states are characterized by the formation of oscillations in the region of action of the hyperbolic field. The height of the maximum of the wave function decreases with decreasing intensity of the repulsive defect and with increasing absolute value of the defect intensity in the case of attractive defect. Localization length in the hyperbolic well is greater than in a halfspace with a constant potential.

This paper presents the application of the variable phase approach (VPA) to calculate phase shifts for various states: ³S₁ − np, ¹S₀ − nn, ¹S₀ − np, and ¹S₀ − pp using the effective range approximation potential. No free fitting parameters are used in the calculations, and a reasonably good match with the experimental phase shifts is observed for E ≤ 20 MeV, making the effective range approximation potential a strong candidate for obtaining low-energy scattering phase shifts. VPA employed is a powerful technique that bypasses the well known Schrödinger equation and does not require the wave function for SPS calculations, unlike the R-Matrix, S-Matrix, or Jost method. Interaction potentials are obtained for n-n, n-p, and p-p scattering that are exponential well-shaped.

In this study, the magnetic, magnetocaloric, and hysteresis properties of the anti-perovskite compound ZnFe₃C were investigated using a mean-field approximation. The results demonstrate that the magnetization gradually decreases with increasing temperature. Conversely, the application of an external magnetic field enhances the alignment of magnetic moments, leading to an increase in the critical temperature ($T_c$). The magnetic entropy change ($−\Delta S_m$) exhibits a distinct peak at $T_c$, while the relative cooling power (RCP) shows a linear increase. Additionally, hysteresis analysis reveals that both coercivity and remanence progressively diminish as the temperature rises, with the hysteresis loop disappearing above $T_c$, indicating a transition to the paramagnetic phase. These findings highlight the potential of ZnFe₃C as a promising material for sustainable, high-performance magnetic refrigeration applications.

Certain magnetic characteristics and the hysteresis behavior of double perovskite Sr₂FeMoO₆ were analysed through Monte Carlo simulation. Our investigation shows this ferrimagnetic compound exhibits a second-order phase transition at a Curie temperature $T_C = 490$ K. The effect of the crystal field on magnetization was examined, and a phase diagram was plotted in the (crystal field, temperature) plane. Furthermore, in the presence of an external magnetic field, the influence of temperature on the hysteresis loop’s behaviour was explored.

The mixture of 20.0 wt% Fe and 80.0 wt% BaTiO₃ powders was found to consist of a BaTiO₃ matrix and composite particles comprising Fe cores and BaTiO₃ shells. During the grinding of this mixture, several processes occur, such as pulverization of the particles of both powders; changes in the size, morphology and composition of aggregates, crushing of crystal grains, increase in the density of chaotically distributed dislocations; growth of internal microstrains; rise in the residual stress; decrease in the amount of crystalline and increase in the amount of amorphous phases, as well as oxidation of Fe into its oxides FeO, Fe₃O₄ and Fe₂O₃. These changes in chemical composition, morphology and microstructure substantially affect the magnetization of the pressed powder mixture. With increasing the grinding time from 0 to 90 min, the increase in magnetization is dominantly affected by crushing of Fe crystal grains. The decrease in magnetization during grinding from 90 to 120 min is caused by the decrease in the amount of metallic Fe by oxidation to FeO and increase in both the density of chaotically distributed dislocations and internal microstrains. Formation of Fe₃O₄ and Fe₂O₃ oxides has a prevailing effect on the increase in magnetization when grinding for longer than 130 min. Chemical and microstructural changes in the mixture of powders of 20.0 wt% Fe and 80.0 wt% BaTiO₃ during heating affect the magnetization of cooled samples at 22°C. The powder is thermally stable up to 330°C. The magnetization of samples cooled to 22°C declines with increasing annealing temperature above 330°C. This decrease is caused by both the oxidation of Fe to FeO and formation of larger crystalline grains of Fe. The magnetization of samples heated up to 250°C remains unchanged. At higher temperatures, with increasing the temperature of the sample, its magnetization declines as a result of the transition of directed domains to a chaotic state caused by the effect of thermal energy, formation of larger crystal grains and oxidation of Fe into FeO.

In recent years, interest in studying quantum well semiconductor structures has been driven by their potential application as nanotechnological devices operating in the nanoscale range, as well as in various spintronic devices. The main reason why scientists are so interested in these quantum-scale structures is that the physical properties of such materials have a number of interesting scientific processes, which allow us to more fully understand the fundamental changes in these processes under the influence of various external factors. In particular, one of such external factors is a quantizing magnetic field and a strong electromagnetic wave, which change the trajectories of charged particles moving freely along the crystal lattice of bulk or smallsized materials. This leads to the emergence of quantum-physical phenomena such as the quantum Hall effect, the Shubnikov-de Haas and de Haas-van Alphen effects.

The optical and morphological properties of C₇₀ fullerene in binary xylene/tetrahydrofuran solutions were systematically studied using UV-Vis absorption and Raman spectroscopy, refractometry, pycnometry, and dynamic light scattering (DLS). It was found that during storage of a molecular solution, the increase in intermolecular interactions and the onset of the self-assembly process of C70 molecules significantly affect the properties of the solution. A correlation was established between the formation of C₇₀ nanoaggregates in solution and the changes in their properties (optical absorption, refractive index, density, and Raman spectra).

This study explores a comprehensive approach to analyzing laser power stability by combining statistical evaluation with machine learning-based predictive modeling and anomaly detection. Power data from an Erbium-doped femtosecond fiber laser operating at 775 nm are analyzed to assess variability, trends, and potential instabilities. Statistical analysis revealed moderate fluctuations in power output. Advanced anomaly detection techniques, including Isolation Forest and K-means clustering, identified distinct deviations in the data, with K-means achieving a Silhouette Score of 0.73. Predictive modeling using linear regression and ARIMA demonstrated robust forecasting capabilities. The ARIMA model effectively captured both short-term fluctuations and long-term trends, projecting stabilization of laser power over a 300-minute extension, indicative of equilibrium behavior. This study highlights the integration of statistical and machine learning tools as a valuable framework for enhancing precision and stability in high-performance laser applications.

The present study investigates the flow dynamics of viscous fluid threads interacting with a less viscous fluid and their stability as they flow through a Hele-Shaw microfluidic cell. We study multiple liquid pairs and identify for the first time several flow regimes, including the well-known Kelvin-Helmholtz instability.

In this study, numerical methods were employed to investigate the effect of grid configuration, lug position, and wire angles on the stress-deformed state of double rectangular and diagonal grids made of Pb–0.7%Sn–0.08%Ca alloy for VRLA-batteries. The maximum values of stress and displacement were calculated using SolidWorks and ANSYS programs of finite element analysis. The recommendations were given to optimize design and prevent deformation and distortion of the double grids after solidification, which were confirmed in production conditions.

This study investigates the physical and microstructural properties of EDM-machined steel under varying electrical discharge machining (EDM) conditions. An experimental approach is adopted to evaluate the influence of pulse time ($T$on), rest time ($T$off), and discharge current (I) on material removal rate (MRR) and surface roughness (Ra). The effect of discharge energy on crater formation, debris evolution, and microstructural transformations is analyzed. Surface integrity is assessed through microscopic roughness analysis, crater morphology measurements, and X-ray diffraction (XRD) to reveal phase transformations induced by electrothermal effects.