A tight Hermite–Hadamard inequality and a generic method for comparison between residuals of inequalities with convex functions

Periodica Mathematica Hungarica - We present a tight parametrical Hermite–Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value...     

Reciprocally convex functions

We say that f is reciprocally convex if x?f(x) is concave and x?f(1/x) is convex on (0,+∞). Reciprocally convex functions generate a sequence of quasi-arithmetic means, with the first one between harmonic and arithmetic mean and others above the arithmetic mean. We present several examples related to the gamma function and we show that if f is a Stieltjes transform, then −f is reciprocally convex. An application in probability is also presented.     

Magnetic and Electrical Properties, Eu Mössbauer Spectroscopy, and Chemical Bonding of REAgMg (RE=La, Ce, Eu, Yb) and EuAuMg

Single-phase samples of REAgMg (RE=La, Ce, Eu, Yb) and EuAuMg were prepared by reacting the elements in sealed tantalum tubes in a high-frequency furnace. LaAgMg and CeAgMg adopt the hexagonal ZrNiAl-type structure, while EuAgMg, YbAgMg, and EuAuMg crystallize with the orthorhombic TiNiSi type. Chemical bonding was exemplarily investigatedfor EuAgMg and EuAuMg on the basis of TB-LMTO-ASAcalculations. Magnetic susceptibility measurements indicatePauli paramagnetism for LaAgMg and YbAgMg with room-temperature susceptibilities of 2.4(1)×10⁻⁹ and 1.5(1)×10⁻⁹ m³/mol, respectively. CeAgMg remains paramagnetic down to 2 K. The experimental magnetic moment of 2.52(2) μ_B/Ce above 50 K is compatible with trivalent cerium. EuAgMg and EuAuMg are paramagnetic above 50 K with experimentalmagnetic moments of 7.99(5) μ_B/Eu for the silver and 7.80(5) μ_B/Eu for the gold compound, indicating divalent europium. Ferromagnetic ordering is detected at T_C=22.0(3) K (EuAgMg) and T_C=36.5(5) K (EuAuMg). At 4.2 K and 5 T the saturation magnetizations are 7.1(1) and 7.3(1) μ_B/Eu for EuAgMg and EuAuMg, respectively. According to the very small hysteresis, EuAgMg and EuAuMg may be classified as soft ferromagnets. All compounds are metallic conductors. For EuAgMg and EuAuMg freezing of spin-disorder scattering is observed below T_C. At 78 K ¹⁵¹Eu Mössbauer spectra show isomer shifts of −9.00(4) and −8.72(8) mm/s for EuAgMg and EuAuMg, respectively. Full magnetic hyperfine field splitting is detected at 4.2 K with hyperfine fields of 17.4(1) and 18.3(2) T at the europium nuclei of EuAgMg and EuAuMg.     

Vanadium(V) environments in bismuth vanadates: A structural investigation using Raman spectroscopy and solid state V NMR

The Bi₂O₃---V₂O₅ system was examined using Raman spectroscopy and solid state ⁵¹V wideline, magic-angle spinning (MAS), and nutation NMR spectroscopy. The methods are shown to be complementary in the identification of the various phases and in the characterization of their vanadium site symmetries. Most of the compositions examined (1:1 ≤ Bi:V ≤ 60:1) are multiphasic. Depending on the Bi:V ratio, the following phases have been identified: BiVO₄, Bi₄V₂O₁₁, a triclinic type-II phase, a cubic type-I phase, γ-Bi₂O₃ doped with V(V) (sillenite), and β-Bi₂O₃. Detailed spectroscopic characterization reveals that vanadium is tetrahedrally coordinated in all these compounds, and that the degree of symmetry increases with increasing Bi:V ratio. At the highest Bi:V ratios, the combined interpretation of the Raman and NMR data provides strong evidence for the presence of Bi⁵⁺O₄ tetrahedra.     

Structural integration of tellurium oxide into mixed-network-former glasses: connectivity distribution in the system NaPO(3)-TeO(2).

Sodium phosphate tellurite glasses in the system (NaPO(3))(x)(TeO(2))(1-) (x) were prepared and structurally characterized by thermal analysis, vibrational spectroscopy, X-ray photoelectron spectroscopy (XPS) and a variety of complementary solid-state nuclear magnetic resonance (NMR) techniques. Unlike the situation in other mixed-network-former glasses, the interaction between the two network formers tellurium oxide and phosphorus oxide produces no new structural units, and no sharing of the network modifier Na(2)O takes place. The glass structure can be regarded as a network of interlinked metaphosphate-type P(2) tetrahedral and TeO(4/2) antiprismatic units. The combined interpretation of the O 1s XPS data and the (31)P solid-state NMR spectra presents clear quantitative evidence for a nonstatistical connectivity distribution. Rather, the formation of homoatomic P--O--P and Te--O--Te linkages is favored over mixed P--O--Te connectivities. As a consequence of this chemical segregation effect, the spatial sodium distribution is not random, as also indicated by a detailed analysis of (31)P/(23)Na rotational echo double-resonance (REDOR) experiments.     

On Suhl's dispersion equations for dilute magnetic alloys in a finite magnetic field

A one dimensional, nonlinear, singular integral equation was recently shown to be equivalent to Suhl's dispersion equations for the Kondo-problem of a half-spin magnetic impurity in a finite magnetic field. We investigate this integral equation further analytically and numerically and obtain numerical solutions which we use for a calculation of transport coefficients. The normal part of the scattering potential of the magnetic impurity is included via ans-wave phase shift. The transport coefficients are universal functions of the ratiosT/T _K andB/B _K of the temperatureT and the zero magnetic field Kondo-temperatureT _K and of the magnetic inductionB and the Kondo magnetic inductionB _K. We find maxima in the electrical and thermal resistivities as functions ofT/T _K forBB _K. These are typical Kondo phenomena, and can be influenced by. Interference of and the phases of Kondo-scattering amplitudes leads to dramatic effects in the thermopower and the Hall coefficient.SFB 125The numerical part of this work was performed at the Institut für Festkörperforschung, Kernforschungsanlage Jülich, F.R. Germany     

Investigation of the Crystallisation Behaviour of Lead Titanate (PT), Lead Zirconate (PZ) and Lead Zirconate Titanate (PZT) by EXAFS-Spectroscopy and X-Ray Diffraction

Two solid solutions of lead zirconium titanates PbZr _x Ti_{1 – x} O₃ (x = 0.1 and 0.35) as well as the reference compounds lead titanate and lead zirconate were prepared from zirconium and titanium n-propoxide, dissolved in 2-methoxyethanol, by sol-gel process. The amorphous products after pyrolysis of the dried gels and the crystalline phases were studied by EXAFS spectroscopy to monitor the structural changes from the amorphous oxide mixture to the crystalline ceramics after calcination. Additionally, the crystalline phases were identified by X-ray diffraction (XRD).It follows from the analysis of the EXAFS data that the local order of the amorphous phases seems to be completely different from that of the crystalline phase. There is no indication of a preformation of the local order of the perovskite structure. The analysis of our EXAFS spectra can be interpreted very consistently with the assumption that in the amorphous samples a segregation exists on molecular level and the low crystallisation temperatures are a consequence of very short diffusion paths.