Laser-diode-excited Blue Upconversion in Tm3+/Yb3+-codoped TeO2-Ga2O3-R2O (R=Li, Na, K) Glasses

This paper reports on intense blue upconversion in Tm³⁺/Yb³⁺ codoped TeO₂-Ga₂O₃-R₂O(R=Li, Na, K) glasses upon excitation with commercial available laser diode (LD). Effects of alkali ions on the Raman spectra, thermal stability and spectroscopic properties of the tellurite-gallium glasses have also been investigated. Energy transfer and the involved upconversion mechanisms have been discussed. Intense blue upconversion emission centered at 476 nm along with a weak red emission at 650 nm has been observed upon excitation of 977 nm LD, assigned to the transitions of , and and/or of Tm³⁺, respectively. The blue upconversion intensity has a cubelike dependence on incident pump laser power, indicating a three-photon process. However, a quadratic dependence of the 476 nm upconversion intensity on the incident pump laser power has been observed when samples under excitation of 808 nm LD due to a two-photon absorption process. Enhanced upconversion luminescence have been observed with replacing K⁺ for Na⁺ and Li⁺.     

Cohomology of $${\mathfrak{osp}}(1|2)$$ Acting on Linear Differential Operators on the Supercircle S1|1

We compute the first cohomology spaces of the Lie superalgebra with coefficients in the superspace of linear differential operators acting on weighted densities on the supercircle S ^1|1. The structure of these spaces was conjectured in (Gargoubi et al. in Lett Math Phys 79:5165, 2007). In fact, we prove here that the situation is a little bit more complicated.      

Feynman Graphs,Rooted Trees,and Ringel-Hall Algebras

We construct symmetric monoidal categories of rooted forests and Feynman graphs. These categories closely resemble finitary abelian categories, and in particular, the notion of Ringel-Hall algebra applies. The Ringel-Hall Hopf algebras of , are dual to the corresponding Connes-Kreimer Hopf algebras on rooted trees and Feynman diagrams. We thus obtain an interpretation of the Connes-Kreimer Lie algebras on rooted trees and Feynman graphs as Ringel-Hall Lie algebras.     

An Infinite Genus Mapping Class Group and Stable Cohomology

We exhibit a finitely generated group whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus g with n boundary components, for any g ≥ 0 and n > 0. We construct a representation of into the restricted symplectic group of the real Hilbert space generated by the homology classes of non-separating circles on , which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first universal Chern class in is the pull-back of the Pressley-Segal class on the restricted linear group via the inclusion . L. F. was partially supported by the ANR Repsurf:ANR-06-BLAN-0311.     

Ion exchange equilibrium between cation exchange membranes and aqueous solutions of K+/Na+, K+/Ca2+, and Na+/Ca2+

Equilibrium between synthetic ion exchangers and solutions of cations has been the subject of this investigation. Competitive ion exchange reactions were studied for two cation exchange membranes (CMX and CRP) involving K⁺, Na⁺, and Ca²⁺ ions. The ionic strength of the equilibrating solutions was maintained constant, but the molar fraction varied; all experiments were conduced with nitrate as nonexchanging anions at 25 °C. Adsorption isotherm for the three binaries systems: K⁺/Na⁺, K⁺/Ca²⁺, and Na⁺/Ca²⁺ were studied. The obtained results show that potassium was the most strongly sorbed and the selectivity order for CMX and CRP membranes is K⁺>Ca²⁺>Na⁺ at 0.1 M, under the experimental conditions. Selectivity coefficients , , and for the three binaries and for the two membranes were determined at an ionic strength of 0.1 M and at a constant temperature of 25 °C. We remark that all the selectivity coefficient values are quite different from the unit. Ternary equilibrium was taken for the Ca²⁺/K⁺/Na⁺ system. It was found that binary selectivity data could be successfully used to predict the ternary ion exchange equilibrium.     

Spectral Measure of Heavy Tailed Band and Covariance Random Matrices

We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N × N symmetric matrix whose (i, j) entry is , where (x _ij , 1 ≤ i ≤ j < ∞) is an infinite array of i.i.d real variables with common distribution in the domain of attraction of an α-stable law, , and σ is a deterministic function. For random diagonal D _N independent of and with appropriate rescaling a _N , we prove that converges in mean towards a limiting probability measure which we characterize. As a special case, we derive and analyze the almost sure limiting spectral density for empirical covariance matrices with heavy tailed entries. Supported in part by a Discovery grant from the Natural Sciences and Engineering Research Council of Canada and a University of Saskatchewan start-up grant. Research partially supported by NSF grant #DMS-0806211.     

A Negative Mass Theorem for the 2-Torus

Let M be a closed surface. For a metric g on M, denote the area element by dA and the Laplace-Beltrami operator by Δ = Δ _g . We define the Robin mass m(p) at the point to be the value of the Green function G(p, q) at q = p after the logarithmic singularity has been subtracted off, and we define trace . This regularized trace can also be obtained by regularization of the spectral zeta function and is hence a spectral invariant which heuristically measures the total wavelength of the surface.We define the Δ-mass of (M, g) to equal , where is the Laplacian on the round sphere of area A. This scale invariant quantity is a non-trivial analog for closed surfaces of the ADM mass for higher dimensional asymptotically flat manifolds.In this paper we show that in each conformal class for the 2-torus, there exists a metric with negative Δ-mass. From this it follows that the minimum of the Δ-mass on is negative and attained by some metric . For this minimizing metric g, one gets a sharp logarithmic Hardy-Littlewood-Sobolev inequality and an Onofri-type inequality.We remark that if the flat metric in is sufficiently long and thin then the minimizing metric g is non-flat. The proof of our result depends on analyzing the ordinary differential equation which is equivalent to h′′ = 1 − 1/h. The solutions are periodic and we need to establish quite delicate, asymptotically sharp inequalities relating the period to the maximum value. The author was supported by the National Science Foundation #DMS-0302647.     

Solid Substrate-Room Temperature Phosphorescence Method for the Determination of Trace Mn(II) Based on Oxidizing Reaction of Hydrogen Peroxide Using α,α′-Bipyridine as Sensitizer

A new solid substrate-room temperature phosphorescence (SS-RTP) method for the determination of trace manganese (II) has been established. It bases on the fact that fullerol (R) emits strong and stable room temperature phosphorescence (RTP) on filter paper substrate. H₂O₂ can oxidize R to cause the SS-RTP quenching. But manganese (II) can obstruct H₂O₂ to oxidize R, and enhance the RTP of R. α,α′-Bipyridine (Bipy) can sensitize the RTP. After adding Bipy, the ΔI _p enhances 7 times than that without Bipy. Under the optimum conditions, the linear dynamic range of this method is 0.016–1.12 pg spot⁻¹ with a detection limit (L.D.) of 4.6 fg spot⁻¹ ( is the absolute mass of Mn²⁺), and the regression equation of working curve is ΔI _p=25.20 + 63.55 (pg spot⁻¹), n=6, r=0.9983. For 0.016 and 1.12 pg spot⁻¹ Mn²⁺, RSDS are 4.3 and 4.8%, respectively (n=7). This method has been applied to the determination of trace manganese (II) in actual sample with high sensitivity and good selection. And the reaction mechanism of SS-RTP is discussed.     

The Fluorosolvatochromism of Brooker's Merocyanine in Pure and in Mixed Solvents

The fluorescence-based solvatochromism (fluorosolvatochromism) of 4-[(1-methyl-4(1H)-pyridinylidene)-ethylidene]-2,5-cyclohexadien-1-one (Brooker's merocyanine) was studied. The results revealed that the fluorescence emission band of the dye was dependent on the medium ( nm in water and nm in DMF). The fluorescence quantum yields (φ _f) were calculated for the dye in the solvents investigated. Low φ _f values ( < 10%) were obtained for the dye and in order to better comprehend the radiative and nonradiative decay processes of this dye, its fluorescence lifetime in methanol was measured and was found to be very short (230 ps). The results suggest that the dye in the excited state decays rapidly through nonradiative processes. The behavior of the probe in binary mixtures including a hydrogen-bond accepting solvent (acetonitrile, N,N-dimethylformamide, and dimethylsulfoxide) and a hydroxylic solvent (water, methanol, ethanol, propan-2-ol, and butan-1-ol) was also investigated. All data were successfully fitted to a model based on solvent exchange equilibria, which allowed the separation of the different contributions of the solvent species in the solvation shell of the dye. The data obtained for the mixed solvents were explained based on solute–solvent and solvent–solvent interactions.     

Direct ammonia proton-conducting solid oxide fuel cells prepared by a modified suspension spray

A dense (BCSO) membrane was fabricated by a modified suspension spraying on porous NiO–BCSO anode support. In the process, the suspension was directly prepared by ball-milling the BaCO₃, CeO₂, and Sm₂O₃ powders in ethanol. A dense and uniform electrolyte layer in the thickness of 10 μm was successfully prepared on porous anode support by suspension spray process after co-sintering at 1,400 °C for 5 h. With (NSMO) cathode, a single cell was assembled and tested with hydrogen and ammonia as fuels, respectively. The hydrogen-fueled cell exhibits 1.01 V for open circuit voltage (OCV) and 560 mW/cm² for peak power density at 700 °C. In comparison, the cell in ammonia displays a similar performance (1.02 V for OCV and 530 mW/cm² for output), which indicates the liquid ammonia is a promising substitute for hydrogen. Moreover, the fuel cell displays good interface contacts. To sum up, ammonia-fueled solid oxide fuel cells prepared by this simple suspension spray is an alternative way to promote the commercialization.     

Baxter Operator and Archimedean Hecke Algebra

In this paper we introduce Baxter integral -operators for finite-dimensional Lie algebras and . Whittaker functions corresponding to these algebras are eigenfunctions of the -operators with the eigenvalues expressed in terms of Gamma-functions. The appearance of the Gamma-functions is one of the manifestations of an interesting connection between Mellin-Barnes and Givental integral representations of Whittaker functions, which are in a sense dual to each other. We define a dual Baxter operator and derive a family of mixed Mellin-Barnes-Givental integral representations. Givental and Mellin-Barnes integral representations are used to provide a short proof of the Friedberg-Bump and Bump conjectures for G = GL(ℓ + 1) proved earlier by Stade. We also identify eigenvalues of the Baxter -operator acting on Whittaker functions with local Archimedean L-factors. The Baxter -operator introduced in this paper is then described as a particular realization of the explicitly defined universal Baxter operator in the spherical Hecke algebra , K being a maximal compact subgroup of G. Finally we stress an analogy between -operators and certain elements of the non-Archimedean Hecke algebra .     

Er-Yb Codoped Ferroelectrics for Controlling Visible Upconversion Emissions

Under a 980 nm laser pumping, quenching of green upconversion (UC) emission accompanied with enhancement of red UC emission observed was dominated by the energy back-transfer (EBT) process in Er³⁺ and Yb³⁺ co-doped PbTiO₃, BaTiO₃, and SrTiO₃ polycrystalline powders. The efficiency of the EBT process depends not only on Yb³⁺ concentration but also on level match of the doped Er³⁺ and Yb³⁺ ions caused by the crystal fields with different symmetries. Our UC emission spectra and X-ray diffraction confirm that the centrosymmetric crystal field arising from reducing tetragonality causes level match of transition of Er³⁺ and of Yb³⁺. This level match is responsible for enhancing red UC emission.     

On the Uniqueness of Weak Weyl Representations of the Canonical Commutation Relation

Let (T, H) be a weak Weyl representation of the canonical commutation relation (CCR) with one degree of freedom. Namely T is a symmetric operator and H is a self-adjoint operator on a complex Hilbert space satisfying the weak Weyl relation: for all (the set of real numbers), e^−itH D(T) ⊂ D(T) (i is the imaginary unit and D(T) denotes the domain of T) and . In the context of quantum theory where H is a Hamiltonian, T is called a strong time operator of H. In this paper we prove the following theorem on uniqueness of weak Weyl representations: Let be separable. Assume that H is bounded below with and , where is the set of complex numbers and, for a linear operator A on a Hilbert space, σ(A) denotes the spectrum of A. Then ( is the closure of T) is unitarily equivalent to a direct sum of the weak Weyl representation on the Hilbert space , where is the multiplication operator by the variable and with . Using this theorem, we construct a Weyl representation of the CCR from the weak Weyl representation . This work is supported by the Grant-in-Aid No.17340032 for Scientific Research from Japan Society for the Promotion of Science (JSPS).     

Chemical stability of hydroxysulphate green rust synthetised in the presence of foreign anions: carbonate, phosphate and silicate

Hydroxysulphate green rust species were precipitated in the presence of various anions. is stable at ∼pH 7 and is transformed into a mixture of magnetite and ferrous hydroxide when the pH raised at ∼12. In the presence of carbonate species, is partially transformed into a mixture of magnetite and siderite at ∼pH 8.5. This transformation is stopped when silicate anions are present in the solution. As already observed for phosphate anions, the adsorption of silicate anions on the lateral faces of the crystals may explain this stabilization effect. Sulphate anions are easily exchanged by carbonate species at ∼pH 10.5. In contrast, anionic exchange between sulphate and phosphate anions was not observed.     

Torelli Theorem for the Deligne–Hitchin Moduli Space

Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let denote the corresponding Deligne–Hitchin moduli space. We prove that the complex analytic space determines (up to an isomorphism) the unordered pair , where is the Riemann surface defined by the opposite almost complex structure on X.     

The Automorphism Group of a Simple Tracially AI Algebra

The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group .     

Bicross-Product Structure of Affine Quantum Groups

We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.     

Small magnetic polaron effect in lithium iron phosphates

The small polarons in LiFePO₄ are associated with the presence of Fe³⁺ ions introduced by the native defects in relative concentration in the samples known to be optimized with respect to their electrochemical properties. The nearest iron neighbours around the central polaron site are spin-polarized by the indirect exchange mediated by the electronic charge in excess. These small magnetic polarons are responsible for the interplay between electronic and magnetic properties that are quantitatively and self-consistently analysed. Comparison is made with other magnetic polaron effects in other members of the family of magnetic semiconductors to which this material belongs. Paper presented at the 11th Euro-Conference on Science and Technology of Ionics, Batz-sur-Mer, France, 9–15 September 2007.     

Diffusion Coefficients of Several Rhodamine Derivatives as Determined by Pulsed Field Gradient–Nuclear Magnetic Resonance and Fluorescence Correlation Spectroscopy

Rhodamine derivatives are popular, photostable fluorophores that are used in a number of fluorescent based techniques, including fluorescence correlation spectroscopy (FCS). Indeed, in FCS, both rhodamine 6G (R6G) and rhodamine 110 (R110) are used as calibration standards to determine the dimensions of the instrument confocal volume. In spite of a requirement for precise values of the diffusion coefficients, literature values are scarce and vary over an order of magnitude. In this paper, the diffusion coefficients of four rhodamine fluorophores (rhodamine 6G (R6G), rhodamine B (RB), rhodamine 123 (R123), rhodamine 110 (R110)) were determined by pulsed field gradient nuclear magnetic resonance (PFG-NMR) spectrometry and then validated by comparison with fluorescence correlation spectroscopy. With the objective of validating the FCS calibration, diffusion coefficients of several dextrans and a polystyrene nanoparticle were also determined and compared with literature values or theoretical values that were based upon the Stoke–Einstein equation. The work presented here lead us to conclude that the diffusion coefficients for R6G and R110 have generally been underestimated in the literature. We propose revised values of 4.4 × 10⁻¹⁰ m² s⁻¹ for R110 and 4.0 × 10⁻¹⁰ m² s⁻¹ for R6G. Using the revised D value for R110 to calibrate the FCS instrument, diffusion coefficients have then been systematically determined for different conditions of pH, ionic strength and concentration. To correct for differences due to solvent effects (D₂O vs. H₂O), an isotopic correction factor, of 1.23, was determined from both FCS and from the solvent auto-diffusion coefficients obtained by NMR.