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 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.

The single-phase polycrystalline samples of Y2(Cu1xMgx)2O5, x = 0.0, 0.05, 0.15 were successfully synthesized by a modified self-propagating high temperature synthesis. Effects of Mg+2 substitution for Cu+2 in

metamagnetic Y2Cu2O5 on its crystal structure and magnetic properties have been analyzed by X-ray

diffraction and magnetic measurements performed within 2–300 K range. Mg doping was found to introduce small distortions in the main intradimmer superexchange paths so that ferromagnetic correlations

decrease with Mg concentration. More significant impact of Cu substitution was found on the low

temperature magnetism due to the breaking of infinite Cu–O chains. The formation of finite size chains

introduces low temperature paramagnetic contribution and reduction in Néel temperature. Overall

results give a strong indication that the antiferromagnetic ordering as well as metamagnetism persists

up to the 15% of the Mg concentration.

Polycrystalline samples of Y2Cu2O5 were for the first time sintered from precursors obtained by two combustion routes – the glycine–nitrate method (sample S1) and a modified self-propagating high-temperature synthesis (sample S2). The detailed X-ray diffraction analysis has confirmed that both samples are

well crystallized and single phase, with the high crystallization degree and cation ordering within a Cu

sublattice. Magnetic characterization has shown magnetic behavior typical of pure Y2Cu2O5. The distinctive advantages of these new synthesis routes in comparison to the ceramic sintering are in simplification

of the overall proce dure as well as in a significant reduction of synthesis duration from several days down

to 31 h (S1) or 12 h (S2).

The electron-doped magnetic nanoparticles of Ca1–xYxMnO3 (x = 0, 0.05, 0.10, 0.15, 0.20,

and 0.30) manganite with an average particle size of 50 nm are analyzed and discussed in relation to their bulk counterparts. Nanoparticle samples show dominant anti-ferromagnetic ordering with a significant increase of coercivity, with the maximum value of 0.9 T for x = 0.

Par ti cle size re duction in Ca1–xYxMnO3 retains the bulk-like magnetic behavior of samples

having up to 15% of Y3+, with the small fer ro mag netic contri bu tion from dis or dered sur face

spins. Sup pres sion of charge order ing state and en hance ment of sat ura tion mag ne ti zation

were found in samples with higher Y3+ con cen tra tion (x = 0.2, 0.3), indicating high ferromag netic contri bu tion in these sam ples

A new synthesis route for obtaining a single-phase hexagonal YMnO3 was developed, based on the annealing of the amorphous

precursor powder obtained by the glycine–nitrate combustion method. The process was monitored by XRD as well as by magnetic and

heat capacity measurements. The analysis of these data shows that precursor powder undergoes a gradual phase transformation that

depends on the annealing temperature. The metastable orthorhombic YMnO3 phase is the first to appear at temperatures below 700 1C,

while a mixture of ortho- and hexa-phases was found to exist within the 700–900 1C range. An almost complete conversion to hexaphase occurs at 900–1000 1C, but to obtain the pure, well crystallized h-YMnO3 phase an annealing temperature of 1300 1C was

necessary. The synthesis method applied in this work has been proved to be more convenient for obtaining single-phase h-YMnO3 than

by a solid state reaction. In addition, it is capable of producing sample free of parasitic phases that are often present in specimens

obtained by other synthesis methods.

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.