A new mechanical framework is introduced to describe bodies with time-continuous mass

variation, incorporating a functional dependence on mass. In this approach, the dynamics

are governed by momentum balance equations formulated using Caputo fractional

derivatives, which adhere to a weak form of Galilean invariance. The formulation is

particularly focused on the Meshchersky kinetics, accounting for both mass and velocity

changes. As a practical example, this paper presents a novel model for the motion of a

material body with continuously varying mass in a constant gravitational field—leading to

a time-fractional version of the Tsiolkovsky rocket equation, augmented by a dissipative

term. Under time-based approximation, deviations from vertical projectile motion are

analyzed to assess the internal consistency of the proposed model.

A three-parameter generalization of the Tsallis entropy based on the properties of the power functions and Weyl fractional calculus like extension of quantum calculus, are introduced. The generalization of the Shannon-Khinchin axioms corresponding to the fractional Tsallis entropy is verified and proposed. These axioms uniquely characterize new entropy function. For a certain sets of parameter values satisfied the second and third law of thermodynamics, the Lesche and thermodynamic stability criteria.

Thin films deposited on glass surfaces can be produced by various

methods, including physical methods (thermal evaporation in

vacuum, sputtering, etc.) and chemical methods (chemical

deposition, chemical vapor deposition, thermal chemical analysis,

etc.). In this paper, thin films were deposited on glass slides using

the plasma-enhanced chemical vapor deposition (PECVD)

technique at pressures (10,30 and 50 mTorr) for varying durations

of (5,10 and 15 minutes). In addition, the results indicates that

increasing the deposition time significantly influenced the film

thickness while the adhesion does not directly depend on time.

The specific activities of twenty-five soil samples have been measured with gamma ray spectrometry system using a High Purity Germanium (HPGe) detector in order to evaluate the radiological hazard effects of the natural radioactivity, the activity utilization index(AUI), Gamma Index (𝐼𝛾), alpha index (𝐼𝛼) and the radiation exposure rate (I), The annual effective dose indoor AEDE(Sv y-1)indoor , and outdoor AEDE(Sv y-1)outdoor have been calculated.

The activity utilization index values ranged from 0.06 to 0.34 with an average 0.15, and Gamma Index (𝐼𝛾) values ranged from 0.142 to 0.372 with an average of 0.2028, while the alpha index values ranged from 0.025 to 0.117 with an average 0.049, and the values of

radiation exposure rate (I) ranged from 39.02 μR/h to 102.66 μR/h with an average value of 56.34 μR/h.

Nanoparticles thin films of the titanium dioxide (TiO₂) exhibit many interesting properties that can be exploited in a variety of applications such as such as a Photocatalysts, Dye-sensitized solar cell, Gas sensors, Electronic devices and an insulator (buffer layer) in the dielectric bolometer sensor, which are very important to investigate and study the properties of its current density. This review discusses the applications and syntheses of titanium dioxide (TiO2) and outlines methods of preparation that allow control over the size, morphology, surface treatment.

Two new fractional entropy functions, first, based on extension of

Ubriaco and Shafee approach, and second, the generalization

through the use of concept of expansion of linear fractional

distributed order derivative, is proposed. The first entropies are the

two-parametric functions. The second entropy is a linear

combination of the above functions. Then they have the same

properties as the Shannon entropy except additivity. For q1, q2 

(0,1], these entropies satisfy the third law of thermodynamics in

the Bento sense, and, for q1 ≤ 1 and q2 ≥ 1, the Lesche stability

criteria.

In this paper we introduce a new fractional generalization of the

Smith's formula for the classical generalization of the Drude

equation. The generalized Drude formula described was proposed

originally to account for the unusual behavior of the optical

properties of mercury and its amalgams, it can be used for liquid

tellurium and some quasicrystals.

In this study, generalized Lorentz model is basic one-particle model in the framework of dielectric, conductive and/or magnetic responses of materials. AC conductivity studies of various BaTiO3 or similar ceramics produced equivalent circuits with impedance spectra, usually within the framework of RCPE elements serial connection (CPE - constant phase element) or Cole element. This element, in the generalized Lorentz model, corresponds to Caputo fractional derivative, who, as operator, contains a singular integral kernel in itself. However, in the literature, fractional derivatives with a non singular integral kernels have recently emerged. One of them is a Caputo-Fabrizio fractional derivative. In this work, physical basics and all three behaviors (dielectric, conductive and magnetic) of materials and their relationships are considered in the case of electric or magnetic alternate fields, which are the tools for experimental measurements

This paper presents a study of two commercial hollow-cathode lamps (HCLs) with the intention of demonstrating different phenomena in gas discharges. The optogalvanic effect in both HCLs is produced by a laser diode radiated at the wavelength that corresponds to neon transition 1s2–2p2 at 659.89 nm. The voltage–current characteristics of the lamps are explained using a classical theory of hollow-cathode discharge, while the optogalvanic signal is treated as a small perturbation of the discharge current. For certain values of voltage self-sustained current oscillations are observed in one of the HCLs. In the same HCL laser-induced optogalvanic dumped oscillations are detected. A phenomenological model that includes the effective circuit parameters of the discharge is used to explain the oscillation characteristics.

Van Siclen (1988 Am. J. Phys. 56 1142) reported a curious property of a dielectric sphere in the field of an external point charge: the field outside the sphere generated by the combination of the original charge exterior and the Kelvin image charge interior to the sphere is independent of the permittivity of the sphere. In this paper, we simplify and correct the original derivation and give a detailed analysis of the sources of the field. We also present various checks for the theory, providing instructive exercises for advanced undergraduates.

The Kelvin image theory for a conducting sphere is extended to the case of a conducting oblate spheroid in uniform motion along its axis of revolution (a Heaviside ellipsoid) using the well-known method provided by Special Relativity. The results derived are checked in various ways.