Fock representations and BRST cohomology inSL(2) current algebra

We investigate the structure of the Fock modules overA ₁ ⁽¹⁾ introduced by Wakimoto. We show that irreducible highest weight modules arise as degree zero cohomology groups in a BRST-like complex of Fock modules. Chiral primary fields are constructed as BRST invariant operators acting on Fock modules. As a result, we obtain a free field representation of correlation functions of theSU(2) WZW model on the plane and on the torus. We also consider representations of fractional level arising in Polyakov's 2D quantum gravity. Finally, we give a geometrical, Borel-Weil-like interpretation of the Wakimoto construction.     

New Weyl groups forA 1 (1) and characters of singular highest weight modules

We consider singular Verma modules overA ₁ ⁽¹⁾ , i.e., Verma modules for which the central charge is equal to minus the dual Coxeter number. We calculate the characters of certain factor modules of these Verma modules. In one class of cases we are able to prove that these factor modules are actually the irreducible highest modules for those highest weights. We introduce new Weyl groups which are infinitely generated abelian groups and are proper subgroups or isomorphic between themselves. Using these Weyl groups we can rewrite the character formulae obtained in the paper in the form of the classical Weyl character formula for the finite-dimensional irreducible representations of semisimple Lie algebras (respectively Weyl-Kac character formula for the integrable highest weight modules over affine Kac-Moody algebras) so that the new Weyl groups play the role of the usual Weyl group (respectively affine Weyl group).     

A Weyl group for the Virasoro andN=1 super-Virasoro algebras

We introduce a Weyl group for the highest weight modules over the Virasoro algebra and the Neveu-Schwarz and Ramond superalgebras. Using this group we rewrite the character formulae for the irreducible highest weight modules over these algebras in the form of the classical Weyl character formula for the finite-dimensional irreducible representations of semi-simple Lie algebras (and also of the Weyl-Kac character formula for the integrable highest weight modules over affine Kac-Moody algebras). This is the same group we introduced recently in order to rewrite in a similar manner the characters of the singular highest weight modules over the affine Kac-Moody algebraA ₁ ⁽¹⁾ .     

Fusion and singular vectors inA 1 (1) highest weight cyclic modules

We show how the interplay between the fusion formalism of conformal field theory and the Knizhnik-Zamolodchikov equation leads to explicit formulae for the singular vectors in the highest weight representations ofA ₁ ⁽¹⁾ .Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique     

Structures,vibrational spectra,and relative energetics of FC(O)ONO and FC(O)NO2 isomers at DFT and ab initio levels

The structural and vibrational parameters of FC(O)ONO and FC(O)NO₂ isomers were examined theoretically using the B3LYP/6-311+G(3df) and CCSD(T)/6-311G(d) methods. Four conformers of FC(O)ONO isomer and one FC(O)NO₂ isomer are found here. Among them, the trans–cis and cis–cis FC(O)ONO configuration are new conformers. The energetics were refined with G3//B3LYP and CBS-QB3 calculations. The trans–trans conformer of the FC(O)ONO isomer is found to be the lowest energy structure, with an estimated heat of formation of ?104.9 kcal mol^?1 at 0 K as determined from CBS-QB3 theory. The next lowest structure is the cis–trans FC(O)ONO lying 1.7 kcal mol^?1 above the trans–trans structural form. The highest energy structure is the FC(O)NO₂ isomer with a predicted heat of formation of ?84.8 kcal mol^?1. A comparison of the relative stability of the FCNO₃ isomers with the isomers of ClCNO₃ shows that the Cl analogues follow the same pattern of stability, as do the F isomers. However, the chlorine isomers are unstable relative to their fluorine analogues.     

Left regular representation and contraction of sl q (2) to e q (2)

The left regular representation of the quantum algebras sl _q (2) and e _q (2) are discussed and shown to be related by contraction. The reducibility is studied andq-difference intertwining operators are constructed.     

Highest Weight Modules Over Quantum Queer Superalgebra {U_q(\mathfrak {q}(n))}

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra U_q(\mathfrak q(n)){U_q(\mathfrak {q}(n))}. The key ingredients are the triangular decomposition of U_q(\mathfrak q(n)){U_q(\mathfrak {q}(n))} and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for U_q(\mathfrak q(n)){U_q(\mathfrak {q}(n))}-modules in the category O_q ^{3 0}{\mathcal {O}_{q}^{\geq 0}}.     

Dielectric spectra of LiTFSI-doped chitosan/PEO blends

Solid-polymer-blend electrolyte consisting of chitosan and polyethylene oxide (PEO) in a 1:1 weight ratio and doped with lithium trifluoromethanesulfonimide (LiTFSI) salt was prepared by solution cast technique. The highest conducting film with conductivity value of 1.40 × 10^-6 S cm⁻¹ at room temperature consists of 30 wt% LiTFSI. The temperature dependence for the highest conducting film obeyed Arrhenius relationship. From loss tangent–frequency plots at different temperatures, the frequency f _max at which the plot is a maximum was obtained. From this, ln f _max vs 10³/T was plotted. The activation energy value obtained from the log σ vs 10³/T plot and ln f _max vs 10³/T plot is about the same, suggesting that the processes of conductivity and relaxation for the charge carriers are the same. This paper was presented at the International Conference on Solid State Science and Technology 2006, Kuala Terengganu, Malaysia, Sept. 4–6, 2006.     

Temperature‐dependent Raman scattering of KDP:Mn (0.9% weight of Mn) crystal

Low temperature polarized Raman scattering measurements of KDP:Mn (0.9% weight of Mn) were performed at temperatures ranging from 14 to 300 K, over the spectral range 50–1250 cm⁻¹. In the present results we can see that the spectra of undoped and doped samples at room temperature are very different. Doped samples maintain the KDP structure as tetragonal, with the same factor group D_2d but with a different class of the space group, different from the original 12. The results show that the crystal undergoes a phase transition at temperature between 115 and 97 K, which is much lower than the phase transition temperature of undoped KDP that occurs at 122 K, where the crystal changes from the para‐electric to the ferroelectric phase. Further, at very low temperature (14 K) we can see that the spectra of KDP:Mn (0.9% weight of Mn) present a behavior very different from the behavior presented by the spectra of KDP doped with low Mn concentration. Copyright © 2010 John Wiley & Sons, Ltd.     

The electronic structure of the nitridoosmate(VIII) ion,OsO3N-

The electronic spectrum of the nitridoosmate(VIII) ion, OsO₃N^-, has been measured at liquid helium temperatures for thin films of the n-tetrabutyl-ammonium salt and for oriented, doped LiClO₄. 3H₂O single crystals. Four structured band systems, all individually composed of superimposed A ₁ ← A ₁ and E←A ₁ transitions, are observed at energies comparable to those of the two lowest ¹ T ₂←¹ A ₁ transitions of OsO₄. Prominent vibronic structure assigned to ν(Os-N) is observed for all of the bands. The bands are assigned to transitions to completely spin-orbit mixed states. The highest filled orbitals of OsO₃N^- are oxygen-localized and π non-bonding. The nitrido ligand appears to ‘dominate’ the π-bonding in the ion.     

Universal Schwinger cocycles of current algebras in (D+1)-dimensions: Geometry and physics

We discuss the universal version of the Schwinger terms of current algebra (we call it the universal Schwinger cocycle) forp=3 (herep denotes the class of the Schatten idealI _p , which is related to the (D+1) space-time dimensions byp=(D+1)/2) in detail, and give a conjecture of the general form of the cocycle for anyp. We also discuss the infinite charge renormalizations, the highest weight vector and state vectors forp=3. Last, we give brief comments on the problems caused by the difficulties to construct the measure of infinite-dimensional Grassmann manifolds.     

Strong Anisotropic Thermal Conductivity in Polycrystalline Layers of (AgxSn1-xS)1.2(TiS2)2 with Prospects Toward Improved Thermoelectric Performance

Anisotropic tuning is of crucial importance for designing and developing high-performance thermoelectric materials. Here, a prominent anisotropic thermoelectric characteristic of Ag-substituted misfit-layered (SnS)_1.2(TiS₂)₂ alloys is investigated in the perpendicular (in-plane) and parallel (out-of-plane) to the pressing direction. In the in-plane direction, the (Ag_xSn_1-xS)_1.2(TiS₂)₂ alloys possess a highest power factor of 0.86 mW K⁻² m⁻¹ at 520 K, while in the out-of-plane direction the lowest lattice thermal conductivity (0.37 W K⁻¹ m⁻¹) is achieved, which is driven by the natural intercalated structure where the out-of-plane phonon is strongly scattered without affecting the in-plane mobility. Moreover, along the in-plane orientation, the introduced point defects due to the substitution of Sn by Ag trigger a significant reduction of lattice thermal conductivity. In contrast, along the out-of-plane orientation, the decreased carrier concentration enables a large Seebeck coefficient and power factor, ultimately ensuring high thermoelectric performance. The present finding in the misfit-layered chalcogenide opens up a new route to manipulating thermoelectrics via anisotropy engineering.     

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.     

Realization ofU q (so(N)) within the differential algebra onR q N

We realize the Hopf algebraU _q–1 (so(N)) as an algebra of differential operators on the quantum Euclidean spaceR _q ^N . The generators are suitableq-deformed analogs of the angular momentum components on ordinaryR ^N . The algebra Fun(R _q ^N ) of functions onR _q ^N splits into a direct sum of irreducible vector representations ofU _q–1 (so(N)); the latter are explicitly constructed as highest weight representations.     

SU(2)L×SU(2)R×U(1) gauge model

We determine here the most general electroweak interaction based on the groupSU(2)_L×SU(2)_R×U(1). When we rotate theZ ₁,Z ₂ basis to theZ,D basis such that the total interaction ofZ with the right-handed current is zero, we obtain an interaction that is free of triangle anomalies. This condition enables us to know the angle through whichZ ₁,Z ₂ basis is to be rotated. We show that the triangle anomaly free interaction obtained by others is contained here as a special case. We also determine the triangle anomaly free weak interaction whenever the neutral (Z,D) bosons are mass eigenstates and show that it reduces to the neutral sector of the standard model whenever g _R ² goes to infinity. The charged sector is also developed here. The most general elements of the masssquared matrix of theZ,D bosons are evaluated. The masses of the left- and right-handed charged bosons are also determined.     

Laser-induced fluorescence of Na2 at the Na(3s → 5s) two-photon transition (6022.3 Å)

Na₂ excited from the X¹Σ_g⁺ state to the A¹Σ_u⁺ state by a narrow band (3 MHz) Rhodamine-6G dye laser at 6022.3 Å, the same wavelength at which Na undergoes the 3s–5s two-photon transition, gives four fluorescence series from A¹Σ_u⁺ levels (v′ = 21, J′ = 26), (18, 33), (33, 19), and (34, 50). The last two series are much weaker in intensity, and at long wavelengths many doublets are lost in the background noise. The same (34, 50) fluorescence series was found by other workers in the lab using a Kr⁺ (5682 Å) laser as excitation source. Their analysis agrees very well with the findings in the work.     

Soliton equations and fundamental representations of A 2l (2)

Fundamental representations of the Euclidean Lie algebra A _2l ⁽²⁾ is constructed by decomposing the vertex representations of gI(∞). For l=1 the multiplicities of highest weights are determined. Soliton equations associated with each of these representations are also discussed.     

Radiation chemistry of tris(acetylacetonato) cobalt(iii) in aqueous solutions

Abstract

On radiolysis tris(acetylacetonato) cobalt(III) in aqueous solutions is found to get reduced by reaction with (1) hydrated electrons, (2) H atoms, (3) OH radicals and (4) C₂H₂OH radicals. The bimolecular rate constants for the first three reactions, determined by competition kinetics are: 4 × 10¹⁰, 2.3 × 10⁹ and 4.7 × 10⁹ M^?1sec^?1 respectively. Absorption spectra of the irradiated solutions indicate the formation of bis(acetylacetonato) cobalt(II) from reaction (1), but not from (3). The total cobaltous yield in air-free solutions is given byG(Co⁺⁺) = 5.6 and 6.5 at pH 6.5 and 1 respectively. It appears that G_eaq- ∽ _H ⁺ G_oH ∽ 2.8 in neutral solutions. Considerations of material balance for the primary yields of radiolysis of water suggest the possibility that the so-called independent H-atoms in neutral solutions are probably excited water molecules or ion-pairs.     

Synthesis and characterization of proton-conducting polymer electrolyte based on polyacrylonitrile (PAN)

Solid polymer electrolytes based on polyacrylonitrile (PAN) doped with ammonium iodide (NH₄I) have been prepared by solution casting method with different molar ratios of polymer and salt using DMF as solvent. The XRD pattern confirms the dissociation of salt. The FTIR analysis confirms the complex formation between the polymer and the salt. A shift in glass transition temperature (T _g ) of the PAN/NH₄I electrolytes has been observed from the DSC thermograms, which indicates the interaction between the polymer and the salt. The conductivity analysis shows that the polymer electrolyte with 20 mol% NH₄I has the highest conductivity equal to 1.106 × 10⁻³ S cm⁻¹ at room temperature. The activation energy (E _a ) has been found to be low for the highest conductivity sample. The dielectric permittivity (ε*) and modulus (M*) have been calculated from the alternating current (AC) impedance spectroscopy in the frequency range 42 Hz–1 MHz. The DC polarization measurement shows that the conductivity is mainly due to ions.