An active area of research in quantum information theory is expanding the operational approach of resource theory (RT) to all quantum correlations. In the context of quantum resource theories we define a measure using resource destroying maps that can be interpreted as the upper bound on any information present in dynamical systems.

We investigate diffusion equations which have concentration dependent diffusion coefficients with physically two relevant Ansätze, the self-similar and the traveling wave Ansatz. We found that for power-law concentration dependence some of the results can be expressed with a general analytic implicit formulas for both trial functions. For the self-similar case some of the solutions can be given with a formula containing the hypergeometric function. For the traveling wave case different analytic formulas are given for different exponents. For some physically reasonable parameter sets the direct solutions are given and analyzed in details.

An effective neural network method is proposed to solve the fractional Duffing system in this paper. First, a multi-layer neural network is designed and the output is assumed as the solution. Secondly, by numerical discretization of the Caputo derivative using the L₁ scheme, a discrete optimization problem is obtained. The famous Adam algorithm is used to train the neural network and parallel computing is suggested to reduce the computational cost. The neural network experimental results show that the analytical solution has a high accuracy and is in a good agreement with the numerical one.

New features of the light beam localization in radial direction in an optical medium with a spatial saturation of the refractive index are described analytically. A new model of radial-dependent distribution of the dielectric function, which allows obtaining the exact analytical solutions to the wave equation, is formulated. Two types of waveguide modes characterized by different transverse electric field distributions are found. The first type of modes is characterized by minimum of the electric field at the core center maximum inside the core. These modes correspond to different values of the angular distribution number. The second type of modes is characterized by oscillations of the electric field inside the core. These modes correspond to different numbers of the dispersion equation solution with fixed values of the angular distribution number. The light intensity increases and the beam localization radius increases with the growth of the core radius. An increase of the value of change in the dielectric constant over the cladding leads to a slight increase of the light intensity but the beam localization radius stays almost the same. The propagation constant enlarges monotonically with the growth of the core radius and it decreases very little with the growth of the value of change in the dielectric constant over the cladding. The minimum core radius, starting from which it is possible to excite the waveguide mode, and the critical core radius for which the power flow is minimal, are found. It is derived analytically that the confinement factor monotonically increases with the growth of the core radius.

Materials exhibiting up-conversion luminescence with rare earth ions have found extensive applications in anti-counterfeiting technologies. However, the practical realization of dual-mode photoluminescence poses challenges in meeting the increasingly complex requirements of modern anti-counterfeiting measures. This study introduces a novel approach, successfully synthesizing dual-mode excitation, dual-color emission Yb³⁺/Er³⁺ co-doped BaGeTeO₆ phosphors through a single-step high-temperature solid-state method. The BaGeTeO₆:Yb³⁺/Er³⁺ phosphors demonstrates simultaneous green and red emission under 980 nm excitation, with the emitted color transitioning from green to red by controlling the dopant concentrations. Conversely, under 1550 nm excitation, primarily a single-band red emission is observed. The inclusion of multi-color emissions enhances the security of multi-mode anti-counterfeiting measures. The potential up-conversion mechanisms under different excitation sources at 980 and 1550 nm were systematically investigated. Additionally, the anti-counterfeiting efficacy of the synthesized phosphor was assessed based on the intensity ratio of red and green emissions. Furthermore, it has been found that optimizing the molar ratio between Er³⁺ and Yb³⁺ ions improves the performance of the examined materials, making them suitable for use as a high-quality optical thermometer employing the FIR technique. Our results indicate promising prospects for the application of BaGeTeO₆:Er³⁺/Yb³⁺ in the field of anti-counterfeiting.

In this paper the authors want to demonstrate new possibilities of the generalized Pareto distribution (GPD) that contains two or three power-law exponents. The eigen-coordinates method allows to detect these exponents that can contain complexconjugated terms also. This GPD is applied successfully to Cosmic Microwave Background (CMB) data from the ESA’s Planck space mission. The data analyzed in the paper are CMB temperature fluctuations around the 2.725 K mean, measured by Planck instruments at the frequencies of 100 GHz, 143 GHz, 217 GHz, and 353 GHz. Planck CMB temperature maps are provided by ESA in HEALPix nested format based on the division of the sky into 12 regions, called primary pixels. Because the data are really huge, we considered only one of the twelve primary pixels for each frequency mentioned above. For us it is important only to read these data quantitatively and prove that the detected distribution does not coincides with conventional one as the Gaussian. For this purpose, we used the GPD for description the temperature fluctuation envelopes. This distribution demonstrates its efficiency and can be used for more detailed description of many data.

In this work, the influence of light on the temperature dependence of transverse magnetoresistance oscillations is studied. A generalized mathematical expression that calculates the temperature and light dependence of the quasi-Fermi levels of smallscale p-type semiconductor structures in a quantizing magnetic field is derived. New analytical expressions have been found to represent the temperature dependence of transverse differential magnetoresistance ossillations in dark and light situations, taking into account the effect of light on the ossillations of the Fermi energy of small-scale semiconductor structures. A mathematical model has been developed that determines the light dependence of the second-order derivative of the transverse magnetoresistance oscillations of p-type semiconductors with quantum wells by magnetic field induction. A new theory is proposed, which explains the reasons for the significant shift of the differential magnetoresistance oscillations along the vertical axis measured in the experiment for dark and light conditions.

To increase the spatial resolution of available TEC maps, an existing technique has been modified to better fit the context of Romania and to minimize computational time. The resulting maps have a resolution of 55 km² and require sparse data interpolation to fill in missing data. The method yields results close to the reference values from IGS, with approximately 45% of maps having an absolute mean difference lower than 10 TECU, proving the viability of the method even at such high spatial resolutions.

Three-dimensional (3D) numerical studies closer to real physical scenarios have received increasing academic attention for providing a better design reference for electrohydrodynamic (EHD) pumping technology. A 3D computational model of a cylindrical EHD cascade actuator based on needle-to-ring electrodes is established in this paper, in which the effects of injection, field-enhanced dissociation, and surface charge accumulation are jointly involved. We explore the strongly coupling behavior of the EHD flow pattern with charge motion in an isothermal incompressible dielectric liquid, analyzing the flow rate, dynamic pressure, and current. It is found that an asymmetrical 3D vortex structure appears within the 2D axisymmetric actuator body, which is attributed to the motion of opposite charges.

Damages produced by cavitation on the materials under their action must be carefully monitored to determine the material's mass loss and changes in its properties. Moreover, describing the process evolution is important for practical applications related to the failure of components made of a certain material. In this context, this article investigates the long-range dependence of the mass loss of a copper alloy sample under ultrasound cavitation.

Reusing and recycling wastes to produce new materials are seen as costeffective, sustainable solution for the economic and environmental problems especially in the agricultural and construction sectors in the worldwide. In the paper, four groups of waste samples including both agricultural and industrial wastes (tincal waste, Bayburt stone waste, tea waste, eggshell waste, marble dust waste and peanut shell waste) were produced by mixing in different ratios. The radiation protection parameters were found by Phy-X/PSD code and radiation shielding abilities of the samples were examined. Mass attenuation coefficient data were also compared by Xcom. In addition, spectroscopic results were provided based on XRD and SEM-EDS spectroscopic techniques. It is obtained that the shielding performances of the samples including tincal waste and Bayburt stone waste with the highest amount of marble dust waste and eggshell waste are the highest, respectively. The lowest protection property is obtained for the sample with Bayburt stone waste with marble dust waste and peanut shell waste consisting of lower Ca and higher C contents. It is observed that there is a direct relation between the amount of Ca and the radiation shielding capability of the samples. It is also determined that neutron shielding potential is the highest for tincal waste with marble dust and tea waste. It can be concluded that the newly prepared samples consisting of wastes in order to support reusing and recycling have good protective properties and use of the samples as replacement materials instead of cement or aggregate can be recommended.