Zeros of analytic functions, with or without multiplicities

The classical Mason-Stothers theorem deals with nontrivial polynomial solutions to the equation $a+b=c$. It provides a lower bound on the number of distinct zeros of the polynomial $abc$ in terms of the degrees of $a$, $b$ and $c$. We extend this to general analytic functions living on a reasonable bounded domain $\Omega\subset\mathbb C$, rather than on the whole of $\mathbb C$. The estimates obtained are sharp, for any $\Omega$, and a generalization of the original result on polynomials can be recovered from them by a limiting argument.Comment: This is a retitled and slightly revised version of my paper arXiv:1004.359

Comparison of pressure, magnetic field and excess manganese effects on transport properties of film and bulk ceramic La–Ca manganites

The pressure, magnetic field and excess manganese effects on transport and magnetoresistance effect (MRE) have been studied in both the epitaxial films and bulk ceramics of manganites (La₀.₇Ca₀.₃)₁₋xMn₁₊xO₃₋y (x = 0–0.2). A comparison of electrical behavior in both kinds of samples of similar composition at hydrostatic pressures of up to 1.8 GPa and in a magnetic fields of up to 8 kOe has been performed. The pressure and magnetic field effects are shown to increase with increasing manganese content. Experimental data show that the pressure and magnetic field effects on temperatures of both metal–insulator transition (TMD) and MRE peak (TMR) are considerably stronger in the films than in ceramics. The hydrostatic pressure increases TMD and TMR. Magnetoresistance effect for both types of samples was shown to be favored by the pressure and magnetic field in an opposite way. A direct correlation is established between TMD and conductivity bandwidth as well as between MRE and concentration of charge carriers at applied pressure. The differences in the values of pressure effect on resistance, MRE and TMD temperature in the films and ceramics are connected with both granular structure of ceramics and the oxygen nonstoichiometry in ceramic and film samples of the same content as well as with the film strain induced by lattice mismatch between the film and the substrate. The origin of pressure–magnetic field effects is analyzed in the framework of double exchange interaction and small polaron hopping, and variable range hopping models

The spectrum features of UHECRs below and surrounding GZK

The energy spectrum of UHECRs is discussed on the basis of the Yakutsk array database analysis. In the region E=0.1 to 30 EeV the showers are detected under trigger-500, while at energies above 30 EeV the whole acceptance area for trigger-1000 is used in order to utilize all the data available in the region of GZK cutoff.Comment: Invited talk at CRIS2004: GZK and surroundings, Catania, Italy, 31.05.04. To appear in Nucl. Phys. B Proc. Supp

Quantum phase transitions and thermodynamic properties in highly anisotropic magnets

The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models and of quantum phi^4 model is established. A scaling analysis is performed for the ground-state properties. The influence of the external longitudinal magnetic field on the ground-state properties is investigated, and the corresponding magnetic susceptibility is calculated. Finite-temperature properties are considered with the use of the scaling analysis for the effective classical model proposed by Sachdev. Analytical results for the ordering temperature and temperature dependences of the magnetization and energy gap are obtained in the case of a small ground-state moment. The forms of dependences of observable quantities on the bare splitting (or magnetic field) and renormalized splitting turn out to be different. A comparison with numerical calculations and experimental data on systems demonstrating magnetic and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure

The magnetic properties of potassium holmium double tungstate

The magnetic investigations of potassium holmium double tungstate KHo(WO⁴)² have been performed. The results of measurements of magnetic susceptibility and magnetization as a function of temperature (T from 0.3 K up to 100 K) and magnetic field (up to 1.5 T) are presented. A strong anisotropy of magnetic properties was found. The magnetic measurements data were used to calculate the interaction energy. It was shown that the interactions between nearest neighbors Ho³⁺ ions have antiferromagnetic character

Low-temperature magnetic behavior of the organic-based magnet Na[FeO₆(C₁₀H₆N)₃]

The static and dynamic aspects of magnetic behavior of the complex of iron with 1-nitroso-2-naphthol Na[FeO₆(C₁₀H₆N)₃] as a function of temperature, frequency and magnetic field have been analysed. The ac susceptibility ( ac) and dc magnetization (Mdc) were measured over a temperature range of 1.5–200 K in external magnetic field up to 90 kOe and over a frequency range of 95–2000 Hz. The experimental data indicate the absence of magnetic long range order in this complex. The magnetization does not reach a saturation in field of 90 kOe at 1.5 K. At low temperatures, the following characteristic peculiarities of magnetic behavior of complex studied have been found, namely : cusp-like anomalies in the ac susceptibility and zero field coold (ZFC) magnetization at Tcusp = = 17 K; frequency dependence of the Tcusp temperature; remanence and time-dependent relaxation of ZFC magnetization. Attempts were made to compare the ac and Mdc anomalies in complex studied with those of other magnetic systems. Comparison of characteristic peculiarities of magnetic behavior of the spin-glasses and superparamagnets was also performed. Although superparamagnetic behavior should not be completely ruled out as an explanation of the freezing phenomena in sample studied, the analysis of experimental results strongly suggests that the spin-glasslike behavior is a more consistent explanation

Electrostatic layer-by-layer assembly of poly-3,4-ethylene dioxythiophene functional nanofilms

Method of electrostatic layer-by-layer assembly is used for preparation of the ultra thin functional films based on anionic complex of poly-3.4-ethylene dioxythiophene (PEDOT) — polystyrene sulfoacid (PSS) on the surface of the transparent indium-tin-oxide substrates. For the first time N-cetyl pyridinium chloride (CPC) was used as a cationic surfactant. It has been shown that nanofilms obtained in the presence of CPC demonstrate the optical properties and electrochemical behavior similar to PEDOT-PSS functional films that promises their application in electrochromic devices