On the Idempotents of Hecke Algebras

We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational functions thus providing a new version of the fusion procedure for the Hecke algebras. We show that the normalization factors which occur in the procedure are related to the Ocneanu–Markov trace of the idempotents.      

Electron paramagnetic resonance in Y1−cH1.92:Erc

We have investigated the EPR of isotopically enriched ¹⁶⁸Er³⁺ in Y_1?cH_1.92:Er_c where c = 100 and 1400 ppm, at both 1.4 and 9 GHz and between 1.5 and 50 K. Resonance lines were observed from Er³⁺ ions in both sites of cubic symmetry and sites of axial symmetry. We determine the numbers of Er³⁺ in cubic, and C_4v axial symmetry to be in the ratio 2:1. The cubic site resonance line is at g = 6.85 ± 0.07 and is attributed to a Γ₇ doublet. The linewidth has a linear thermal broadening of 3.9 ± 0.05 gauss K^-1 below circa 7 K. From the nonlinear thermal broadening above this temperature we determine the first excited state, in the cubic crystal field scheme, to be a Γ₈ at 35 ± 10 K above the Γ₇ ground state. We have investigated the origins of the (T = 0) residual linewidth for the ions in cubic symmetry, and conclude there to be a small but significant contribution due to unresolved transferred hyperfine structure from the surrounding hydrogen nuclei.     

Lithium aluminum nitride,Li3AlN2 as a lithium solid electrolyte

Single phase of Li₃AlN₂ was prepared from the mixture of Li₃N/AlN = 1.2 to 1.5 in molar ratio at 700°C and at 900°C. It crystalizes in the cubic system derived from antifluorite-type structure having the lattice parameter $\text{a = 9.470}\text{A}\text{?}$. It is a pure ionic conductor having conductivity of 5 × 10^?8ω^?1cm^?1 at room temperature and an activation energy of 52 kJ/ mol. Its decomposition voltage was 0.85 V at 104°C. The TiS₂/Li₃AlN₂/Li cell could be discharged at a constant current of 45 μA/cm² at 104°C.     

Property (RD) for Hecke Pairs

As the first step towards developing noncommutative geometry over Hecke C ^∗-algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the subgroup H in a Hecke pair (G, H) is finite, we show that the Hecke pair (G, H) has (RD) if and only if G has (RD). This provides us with a family of examples of Hecke pairs with property (RD). We also adapt Paul Jolissant’s works in Jolissaint (J K-Theory 2:723–735, 1989; Trans Amer Math Soc 317(1):167–196, 1990) to the setting of Hecke C ^∗-algebras and show that when a Hecke pair (G, H) has property (RD), the algebra of rapidly decreasing functions on the set of double cosets is closed under holomorphic functional calculus of the associated (reduced) Hecke C ^∗-algebra. Hence they have the same K ₀-groups.     

Intrinsic and impurity luminescence of rare earth ions doped KYF4 nanophosphors

The KYF₄ nanopowders, non-doped and doped with Ce³⁺ or Tb³⁺, having well-crystallized, unaggregated, monodisperse (±15%) nanoparticles with the cubic (the size in the range from ∼15 to ∼30 nm) or hexagonal (from ∼30 to ∼50 nm) crystal structure have been successfully synthesized by microwave-hydrothermal treatment of as-precipitated gels. In KYF₄ hexagonal nanopowders an intense STE-type luminescence at ∼4.4 eV was observed which is not quenched at room temperature. In contrast to single crystals or cubic nanopowders, in KYF₄ hexagonal nanopowders doped with Ce³⁺ or Tb³⁺, a rather efficient energy transfer is observed from the host to Ce³⁺ or Tb³⁺ ions, respectively, because of overlapping the emission spectrum of STE-type luminescence and the spectrum of efficient absorption on 4f-5d transitions in Ce³⁺ or Tb³⁺.     

Pulsed EPR spectroscopy of Gd3+ centers in Ca1−x R x F2+x (R=La, Y) mixed crystals

A study of Gd³⁺ centers in Ca_1?x R _x F_2+x (R=La, Y) crystals using pulsed EPR spectroscopy is presented. The echo-induced EPR (ESE-EPR) spectrum shows, besides the signal of slightly perturbed cubic Gd³⁺ centers, a broad signal at g≈2 due to Gd³⁺ centers at low symmetry sites. To describe the effects of R³⁺ ions on the EPR Gd³⁺, a model, including cubic and linear R³⁺?2F _i ^? centers, is developed. Its predictions are compared with the experimental results. The composition dependence of the EPR signal due to slightly perturbed cubic Gd³⁺ centers in mixed Ca_1?x R _x F_2+x crystals is explained taking into account the different clustering tendency in La and Y crystals. Moreover, the formation of mixed clusters involving R³⁺ and Gd³⁺ ions is proposed for both series of samples. A greater clustering trend is found in the Y crystals than in the La ones. Gd³⁺ ions are found to be a “non innocent” paramagnetic probe for structural studies in these mixed crystals.     

Mechanosynthesis,magnetic and Mössbauer characterization of pure and Ti4+-doped cubic phase BiFeO3 nanocrystalline particles

The mechanosynthesis of cubic γ-phase pure BiFeO₃ and Ti⁴⁺-doped BiFeO₃ nanocrystalline particles and their preliminary characterization with magnetic measurements and Mössbauer spectroscopy are reported. The BiFeO₃ nanoparticles (5–40 nm) were prepared by heating a 48 h pre-milled 1:1 molar mixture of α-Bi₂O₃ and α-Fe₂O₃ at 400 °C for (1 h). Doping α-Fe₂O₃ in the initial mixture of reactants with Ti⁴⁺ was found to lead to the formation of Ti⁴⁺-doped BiFeO₃ nanoparticles by milling the reactants for 32 h. The magnetization of the BiFeO₃ nanoparticles is found to be tripled under a maximum external field of 1.35 T and their magnetic hardness increases by ～15 times relative to those of the corresponding bulk. The Ti⁴⁺-doped BiFeO₃ nanoparticles exhibit higher magnetization relative to the pure ones. These observations are related to the spiral modulated spin structure of the compound. The Mössbauer data show ～12 % of the BiFeO₃ nanocrystalline particles to be superparamagnetic having blocking temperatures of less than 78 K. The quadrupole shift values of the magnetic spectral component favor the cubic structural symmetry. These observations were mainly associated with possible collective magnetic excitations as well as transverse relaxation of canted surface spins. The Ti-doped BiFeO₃ nanoparticles gave statistically-poor Mössbauer spectra with no signs of a superparamagnetic behavior.     

Structural, thermal and morphological studies of magnesium substituted-lithium manganese oxide spinels

Coexistence of two phases having space groups of Fd3m and P4₃32 in the Mg-doped LiMn₂O₄ spinel is being reported for the first time in this article. Mg-doped LiMn₂O₄ powders have been synthesized by sol-gel method using citric acid as a chelating agent. X-ray powder diffraction (XRD) studies show that the crystal structure of LiMg_xMn_2−xO₄ for x<0.25 is a single-phase cubic spinel, which has space group of Fd3m. The cubic spinel structures having space group of Fd3m and P4₃32 are found to coexist in the compound for x=0.25. The structure becomes single-phase cubic spinel with space group P4₃32 for x>0.25. Field emission scanning electron microscopy (FESEM) shows that particle size of various synthesized powders ranges from 100 to 350 nm. Particle size decreases with increase in Mg content. Differential thermal analysis (DTA) and thermogravimetry (TG) studies show an exponential decay relationship between Mg-doping content and the decomposition temperature to form nonstoichiometry (LiMg_xMn_2−xO_4−δ) in air atmosphere. Fourier transform infrared spectroscopy (FTIR) analysis shows increase in the number of vibrational bands with increase in Mg content, which indicates ordering of the ions in the case of ordered spinel structure, and consequent reduction of the space group symmetry from O_h⁷ to O⁷.     

Photoluminescence investigations of cubic boron nitride doped with neodymium during high-pressure synthesis

Micropowders of cubic boron nitride doped with neodymium are prepared under high-pressure and high-temperature conditions. The phase composition of the micropowders is studied using X-ray diffractometry and X-ray fluorescence analysis. The photoluminescence, photoluminescence excitation spectra, and the life-time of the ⁴ F _3/2 excited state of Nd ions introduced into cubic boron nitride are investigated. In photoluminescence spectra of the micropowders, structured bands are recorded in the range of the ⁴ F _3/2 → ⁴ I _9/2 and ⁴ F _3/2 → ⁴ I _11/2 electronic transitions. A higher intensity of the first structured band indicates that the corresponding photoluminescence in cubic boron nitride doped with neodymium is excited by the “three-level scheme.” It is demonstrated that an increase in the concentration of the neodymium compound in the growth batch leads to the formation of two luminescence centers Nd1 and Nd2 formed by neodymium ions located in different low-symmetry crystal fields in the micropowders. This is confirmed by X-ray diffraction investigations and the study of the photoluminescence decay curves. The ⁴ F _3/2 short-lived state is assigned to the Nd ions forming the Nd1 centers, and the long-lived state is attributed to the Nd ions forming the Nd2 centers.     

Van Vleck paramagnetism of the thulium garnet Tm3Al5O12

The magnetic susceptibility of the garnet-type single crystal Tm₃Al₅O₁₂ exhibits the typical Van Vleck temperature independent paramagnetism below ≈8 K. The temperature dependence of the susceptibility over the range 2.0-300 K has been analyzed on the assumption that the cubic crystal-electric-field dominates the energy level on ³H₆ (J=6) ground multiplet for Tm³⁺ ion having 12-electrons in 4f shell. The ground state of the ³H₆ is nonmagnetic with Γ₂ singlet, avoiding the Kramers doublet. The energy separation between Γ₂ and the first excited state Γ⁽²⁾₅ triplet is evaluated to be 68.0 K. The whole energy interval Δ between Γ₂ and the highest state Γ₁ in ³H₆ is estimated to be 339.5 K.     

EPR study of Fe3+ and Mn2+ in CeO2 and ThO2

Attempts were made to grow CeO₂ and ThO₂ single crystals doped with transition metal ions. Only Fe³⁺ and Mn²⁺ could be detected by the EPR technique. The EPR spectrum of Fe³⁺ in CeO₂ exhibits the well-known fine structure in cubic fields. The parameters areg=2.0044(1) anda=15.6(1)·10^?4 cm^?1. The hyperfine constantA for⁵⁷Fe in hexahedral coordination was found to be 8.9(1)·10^?4 cm^?1. The EPR spectrum of Mn²⁺ in CeO₂ reveals two cubic Mn²⁺ centers. The parameters for center 1 areg=1.9999(1) andA=86.9(1)·10^?4 cm^?1 and for center 2g=1.9984(1) andA=87.0(1)·10^?4 cm^?1. Heating the Mn doped CeO₂ samples in hydrogen, the Mn²⁺ centers transform from cubic into trigonal centers with approximate values ofg=1.9988(2),A=84.5(6)·10^?4 cm^?1 andD=203(1)·10^?4 cm^?1. The two observed Mn²⁺ centers in ThO₂ exhibita priori axial symmetry with approximate values ofg=2.0006(2),A=88.9(4)·10^?4 cm^?1 andD=33(3)·10^?4 cm^?1.     

Magnetic properties of rare earth ion (Sm) added nanocrystalline Mg-Cd ferrites, prepared by oxalate co-precipitation method

Nanocrystalline ferrite powder having the general formula Mg_1−xCd_xFe₂O₄+5% Sm³⁺ (x=0, 0.2, 0.4, 0.6, 0.8 and 1.0) was synthesized by chemical oxalate co-precipitation technique. The synthesized powder was characterized by X-ray, IR and SEM techniques. The XRD analysis confirms cubic spinel phase with orthoferrite secondary phase. The lattice constant increases with increase in Cd²⁺ content (x). It is smaller than that for pure Mg-Cd ferrites. The average crystallite size lies in the range 28.69-32.66 nm. Saturation magnetization and magnetic moment increase with cadmium content up to x=0.4 and decrease thereafter. This is attributed to the existence of localized canted spin. The decrease in saturation magnetization and magnetic moment beyond x=0.4 is due to the presence of triangular spin arrangement on B-site. Coercivity and remanent magnetization decrease while Y-K angles increase with Cd²⁺ content. The Sm³⁺ addition improves the magnetic properties.     

Structure, electric and dielectric studies of indium-substituted magnesium copper manganese ferrites

The structure, electric and dielectric properties of In-substituted Mg-Cu-Mn ferrites having the general formula of Mg_0.9Cu_0.1Mn_0.1In_xFe_1.9−xO₄ with 0.0≤x≤0.4 have been studied. X-ray diffraction (XRD) patterns of the samples indicated the formation of single-phase cubic spinel structure up to 0.2 and mixed phase (cubic and tetragonal phase) for samples x≥0.3. The relation of conductivity with temperature revealed a semiconductor to semimetal behavior as In⁺³ concentration increases. Variation in the universal exponent s with temperature indicates the presence of two hopping conduction mechanisms: the correlated barrier hopping (CHB) at low In⁺³ content x≤0.1 and small-polaron (SP) hopping at In⁺³ content x≥0.2. The variation in dielectric permittivity (ε′, ε″) with temperature at different frequencies shows a normal behavior for the studied compounds, while the variation in dielectric loss tangent with frequency at different temperatures shows abnormal behavior with more than relaxation peak. The conduction mechanism used in the present study has been discussed in the light of electron exchange between Fe³⁺ and Fe²⁺ ions and hole hopping between Mn²⁺ and Mn³⁺ ions at the octahedral B-sites.     

Study of the electronic structure of rhenium and tungsten oxides on the O K-edge

Oxygen K-edge x-ray absorption spectra were studied on the electrochromic amorphous thin film a-WO₃ in the comparison with crystalline oxides having variable electronic (d⁰, d¹, d²) and atomic structure: monoclinic m-WO₃ (insulator - d⁰), cubic Na_0.6WO₃ (metal - d¹), cubic ReO₃ (metal - d¹), layered-type hexagonal h-WO₃, WO₃H₂O and with intercalated H_xReO₃ (metal - d²), H_xWO₃ oxides having a metal-isulating transition. The changes in the XANES range 10–15 eV above the absorption edge are interpreted based on the known band-structure calculations. The high-energy features are related to the multiple-scattering processes (EXAFS) on the nearest atoms. The intensity of the feature at 550–560 eV is attributed for the first time to the value of the metal-oxygen-metal bond angle. Paper presented at the 5th Euroconference on Solid State Ionics, Benalmádena, Spain, Sept. 13–20, 1998.     

Adaptive phase plates for optical encoding systems invariant to second-order aberrations

Certain optical aberrations of imaging systems yield low resolution images. Wavefront coding has proven to minimise this problem by means of hybrid optical-digital imaging systems. The optical part usually involves a phase plate described in terms of cubic polynomials whose shape is a linear combination of (x³ + y³) and (x²y + xy²). Optimization is achieved by seeking the most appropriate linear combination with respect to the optical system's constraints. Here, we propose the shape of two pairs of phase plates such that by means of relative rotations they allow for variation of the linear combination of the cubic terms. This will enable adaptive optimization of the cubic phase to the optical system's constraints when these vary in time. Results will be illustrated with numerical simulations.     

Development of superhard materials,sintered diamond and cubic boron nitride

Abstract

Recent advances on the preparation technique of sintered diamond and cubic boron nitride containing small amount of sintering additives having superior thermal and mechanical properties is reviewed. Sintered diamond of lower metallic content (1–5 vol%) shows high hardness (100–150 GPa) and high electrical resistivity (10⁸ ohm-cm) at room temperature. Reaction sintered cubic boron nitride contained 1–3 mole % of magnesium boron nitride shows high thermal conductivity. (7 watt/cm K at RT)     

EPR of cadmium ferric voltaite above the ferrimagnetic transition

A single isotropic EPR line of Fe³⁺ in synthetic cadmium ferric voltaite, (NH₄)₂Cd₅Fe₃Al(SO₄)₁₂ · 18H₂O, was observed in a wide temperature range from 295 to 1.57°K. The ferrimagnetic transition temperature of CdFe voltaite was determined to be ～ 0.7°K using the temperature dependence of the g-factor and the line width. The cubic crystal field parameter, a, for Fe³⁺ in CdFe voltaite is extracted from the EPR line width measurement using the exchange-narrowed line width model of Anderson and Weiss. The parameter a for Fe³⁺ in CdFe voltaite at 4.2°K is 157 × 10^-4cm^-1 which is consistent with the corresponding values for Fe³⁺ in other cubic structures.     

Far infrared electronic transitions in rare earth doped barium fluoride

Single crystals of barium fluoride doped with different rare earth ions (Tb-Sm-Nd-Pr-Dy-Ho-Er) have been grown in a He atmosphere. The far infrared (FIR) spectra observed at 1.4 K show common features at 75.5-125-131 and 156 cm⁻¹. They are explained in terms of localised vibration of the compensation F⁻ ion in a cubic site (v̇_c = 131 cm⁻¹), a tetragonal one (v̇_L = 75.5 cm⁻¹ ; v̇_T = 156 cm⁻¹) and a trigonal one (v̇_L = 125 cm⁻¹). The different frequencie can be calculated in the assumption of a cubic harmonic oscillator (v̇_c = 131 cm⁻¹) with Coulomb perturbations due to the RE ion at different positions.Special features are observed at 41.2 cm⁻¹ for BaF₂: Dy⁺³; 37 cm⁻¹ and 50.4 cm⁻¹ for BaF₂: Ho³⁺; 69.2 and 70.3 cm⁻¹ for BaF₂: Er³⁺. They arise from electronic transitions. The Zeeman effect gives information on the Landé g factors of both ground and excited levels with magnetic fields smaller than 50 kG.     

On the Li Coefficients for the Hecke L-functions

In this paper, we compute and verify the positivity of the Li coefficients for the Hecke L-functions using an arithmetic formula established in Omar and Mazhouda, J. Number Theory 125(1), 50–58 (2007) and J. Number Theory 130(4), 1098–1108 (2010) and the Serre trace formula. Additional results are presented, including new formulas for the Li coefficients and a formulation of a criterion for the partial Riemann hypothesis. Basing on the numerical computations made below, we conjecture that these coefficients are increasing in n.     

Magnetic properties in silica-coated CoFe2O4 nanoparticles: Quantitative test for a theory of single-domain particles with cubic anisotropy

We report magnetic properties of silica-coated CoFe₂O₄ nanoparticles (about 32 nm) in a wide temperature range (4-700 K). Coating CoFe₂O₄ nanoparticles with amorphous silica yields an assembly of noninteracting single-domain particles with cubic magnetocrystalline anisotropy. We find that the reduced remanence is about 0.81-0.82 at low temperatures (?100 K), very close to the theoretical prediction (0.83) for cubic anisotropy. The room-temperature anisotropy constant K₁ inferred from the data is also in quantitative agreement with the bulk value (1.8×¹⁰⁶ erg/cm³). The current work thus provides a quantitative test for a theory of noninteracting single-domain particles with cubic anisotropy.