Vertex operators of quantum affine Lie algebrasU q (D n (1) )

We give an explicit formula for the vertex operators related to the level 1 representations of the quantum affine Lie algebrasU _q (D _n ⁽¹⁾ ) in terms of bosons. As an application, we derive an integral formula for the correlation functions of the vertex models withU _q (D _n ⁽¹⁾ )-symmetry.NJ was supported in part by NSA grant MDA904-93-H-3005 and University of Kansas General Research allocation.SJK was supported in part by Basic Science Research Institute Program, Ministry of Education of Korea, BSRI-94-1414 and GARC-KOSEF at Seoul National University, Korea.     

Construction of the affine Lie algebraA 1 (1)

We give an explicit construction of the affine Lie algebraA ₁ ⁽¹⁾ as an algebra of differential operators on [x ₁,x ₃,x ₅, ...]. This algebra is spanned by the creation and annihilation operators and by the homogeneous components of a certain exponential generating function which is strikingly similar to the vertex operator in the string model.Partially supported by a Sloan Foundation Fellowship and NSF grant MCS 76-10435Most of this work was done while the author was a Visiting Fellow at Yale University, supported in part by NSF grant MCS 77-03608 and in part by a Faculty Academic Study Plan grant from Rutgers University     

Fusion Rules for the Vertex Operator Algebras <Emphasis Type="Italic">M</Emphasis>(1)<Superscript>+</Superscript> and <Emphasis Type="Italic">V</Emphasis><Superscript>+</Superscript><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>

The fusion rules for the vertex operator algebras M(1)⁺ (of any rank) and V⁺_L (for any positive definite even lattice L) are determined completely.Supported by JSPS Research Fellowships for Young ScientistsPartially supported by NSF grants and a research grant from the Committee on Research, UC Santa CruzPartially supported by a NSA grant and a grant from Rutgers University Research Council     

Tm3+掺杂硅酸镓镧(La3Ga5SiO14)晶体的结构与光学性能研究

利用X射线粉末衍射确定了Tm³⁺掺杂硅酸镓镧(La₃Ga₅SiO₁₄,LGS)晶体的晶体结构;运用DICVOL91程序计算了该晶体不同部位的晶胞参数;测定了Tm：LGS晶体的室温吸收谱和470nm光激发下的发射光谱;根据Judd-Ofelt理论拟合了Tm³⁺的三个晶场调节参数Ω_t(t=2,4,6),分别为2.694×10^-20cm²,1.842×10^-20cm²,0.030×10^-20cm²;计算了各个能级跃迁的谱线强度、振子强度、吸收截面等,进而计算了³H₄和³F₄态的自发跃迁概率、辐射寿命、荧光分支比和积分发射截面,并对结果进行了分析. 关键词： Tm：LGS晶体 吸收谱 Judd-Ofelt理论 光谱参数     

Production of excited charm and charm-strange mesons at HERA

The production of excited charm, D ₁(2420)⁰ and D ₂^*(2460)⁰, and charm-strange, D _s1(2536)^±, mesons in ep collisions was measured with the ZEUS detector at HERA using an integrated luminosity of 126 pb⁻¹. Masses, widths and helicity parameters were determined. The measured yields were converted to the rates of c quarks hadronising as a given excited charm meson and to the ratios of the dominant D ₂^*(2460)⁰ and D _s1(2536)^± branching fractions. A search for the radially excited charm meson, D ^*′(2640)^±, was also performed. The results are compared with those measured previously and with theoretical expectations. Dedicated to the memory of our colleague Pavel Ermolov. Deceased. Also affiliated with University College London, UK. Now at BayesForecast, Madrid, Spain. Also at Institut of Theoretical and Experimental Physics, Moscow, Russia. Also at INP, Cracow, Poland. Also at FPACS, AGH-UST, Cracow, Poland. Partly supported by Moscow State University, Russia. Royal Society of Edinburgh, Scottish Executive Support Research Fellow. Also affiliated with DESY, Germany. Also at University of Tokyo, Japan. Now at Kobe University, Japan. Supported by DESY, Germany. Now at University of Salerno, Italy. Partly supported by Russian Foundation for Basic Research grant no. 05-02-39028-NSFC-a. Partially supported by Warsaw University, Poland. This material was based on work supported by the National Science Foundation, while working at the Foundation. Now at University of Kansas, Lawrence, USA. Also at Max Planck Institute, Munich, Germany, Alexander von Humboldt Research Award. Now at KEK, Tsukuba, Japan. Now at Nagoya University, Japan. Member of Department of Radiological Science, Tokyo Metropolitan University, Japan. Now at SunMelx Co. Ltd., Tokyo, Japan. PPARC Advanced fellow. Supported by the research grant no. 1 P03B 04529 (2005–2008). Also at Hamburg University, Inst. of Exp. Physics, Alexander von Humboldt Research Award and partially supported by DESY, Hamburg, Germany. Also at Łódź University, Poland. Member of Łódź University, Poland. Now at Lund Universtiy, Lund, Sweden. This work was supported in part by the Marie Curie Actions Transfer of Knowledge project COCOS (contract MTKD-CT-2004-517186). Now at University of Bonn, Germany. Now at DESY group FEB, Hamburg, Germany. Now at University of Liverpool, UK. Now at CERN, Geneva, Switzerland. Now at Bologna University, Bologna, Italy.     

The Yamada polynomial of spacial graphs and knit algebras

The Yamada polynomial for embeddings of graphs is widely generalized by using knit semigroups and polytangles. To construct and investigate them, we use a diagrammatic method combined with the theory of algebrasH _N,M(a,q), which are quotients of knit semigroups and are generalizations of Iwahori-Hecke algebrasH _n(q). Our invariants are versions of Turaev-Reshetikhin's invariants for ribbon graphs, but our construction is more specific and computable.This research was supported in part by NSF grant DMS-9100383     

Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model

We consider infinite Jacobi matrices with ones off-diagonal, and independent identically distributed random variables with distributionF(v)dv on-diagonal. IfF has compact support and lies in some Sobolev spaceL ¹ , then we prove that the integrated density of states,k(E), isC inE.Research partially supported by USNSF under Grant MCS-81-20833Research partially supported by USNSF under Grant MCS-82-01766A01     

DSC study of superionic phase transition in (NH4)4H2(SeO4)3 single crystals

DSC and complex impedance studies of the protonic conductor (NH₄)₄H₂(SeO₄)₃, which undergoes a superionic phase transition of first order at T_s = 378 K show that the activation energy of ionic conductivity d(lg σ)/dt and the ordering enthalpy ΔC_p of the crystal are proportional: d(lg σ)/dT = XΔC_p/RT_s + const, as found for MAg₄I₅ crystals undergoing a second-order superionic phase transition. Thus the short-range order environment of the species involved in fast-ion transport plays the main role in the superionic phase transition. This is also supported by the value of the entropy change at T_s, ΔS = 43 J/mole·K. A new metastable phase was found to be induced on heating the (NH₄)₄H₂(SeO₄)₃ crystal above T_s.     

Action of monoatomic cations on the structure and spectra of Mx(1)M1-x(2)UO2(NO3)3 crystals

The action of the monovalent M⁺ cations on the luminescent properties of the mixed M _x ⁽¹⁾ M _1-x ⁽²⁾ UO₂(NO₃)₃ crystals, where M is Na, K, Rb, Cs, or NH₄ , has been investigated. It has been established that the spectral positions of the bands of vibronic transitions depend linearly on the ratio between the concentrations of the M⁽¹⁰⁾ and M⁽²⁾ cations. It is shown that the crystals considered are composed of l[RbUO₂(NO₃)₃]n[CsUO₂(NO₃)₃] clusters, where l/n = x/(1 - x). The spectral regularities revealed are determined by the partial contributions of the M⁽¹⁾ and M⁽²⁾ cations to their combined, polarizing action on the uranyl complex and are explained by the ligand nature of its highest occupied molecular orbital.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 827–830, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Crystal structure and thermochemical properties of phase change materials bis(1-octylammonium) tetrachlorochromate

A new crystalline complex (C₈H₁₇NH₃)₂CdCl₄(s) (abbreviated as C₈Cd(s)) is synthesized by liquid phase reaction. The crystal structure and composition of the complex are determined by single crystal X-ray diffraction, chemical analysis, and elementary analysis. It is triclinic, the space group is P-1 and Z = 2. The lattice potential energy of the title complex is calculated to be U_POT (C₈Cd(s))=978.83 kJ·mol^-1 from crystallographic data. Low-temperature heat capacities of the complex are measured by a precision automatic adiabatic calorimeter over a temperature range from 78 K to 384 K. The temperature, molar enthalpy, and entropy of the phase transition for the complex are determined to be 307.3± 0.15 K, 10.15± 0.23 kJ·mol^-1, and 33.05± 0.78 J·K^-1·mol^-1 respectively for the endothermic peak. Two polynomial equations of the heat capacities each as a function of temperature are fitted by the least-square method. Smoothed heat capacity and thermodynamic functions of the complex are calculated based on the fitted polynomials.     

TheA n /(1) face models

Presented here is the construction of solvable two-dimensional lattice models associated with the affine Lie algebraA _n ^/(1) and an arbitrary pair of Young diagrams. The models comprise two kinds of fluctuation variables; one lives on the sites and takes on dominant integral weights of a fixed level, the other lives on edges and assumes the weights of the representations ofsl(n+1, C) specified by Young diagrams. The Boltzmann weights are elliptic solutions of the Yang-Baxter equation. Some conjectures on the one point functions are put forth.     

CO adsorption on small Aun（n=1-7） clusters supported on a reduced rutile TiO2（110） surface:a first-principles study

CO adsorption on small Au n(n = 1-7) clusters which are supported by a partially reduced rutile TiO 2(110) surface has been investigated by the first-principles method.The low coordinated sites of Au clusters are favorable for CO adsorption.CO-Au n-TiO 2 system displays surface magnetism.There is a strong interaction between the adsorbed CO molecule and the supported Au clusters.     

Strong connections on quantum principal bundles

A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as those that are induced from the base space of a quantum bundle. Examples of both strong and non-strong connections are provided. In particular, such connections are constructed on a quantum deformation of the two-sphere fibrationS ²→RP ². A certain class of strongU _q (2)-connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with theq-dependent hermitian metric. A particular form of the Yang-Mills action on a trivialU _q (2)-bundle is investigated. It is proved to coincide with the Yang-Mills action constructed by A. Connes and M. Rieffel. Furthermore, it is shown that the moduli space of critical points of this action functional is independent ofq. This work was in part supported by the NSF grant 1-443964-21858-2. Writing up the revised version was partially supported by the KBN grant 2 P301 020 07 and by a visiting fellowship at the International Centre for Theoretical Physics in Trieste.     

Spectral characterization and energy levels of Cr:Sc2(MoO4)3 crystal

This paper reports the spectral properties and energy levels of Cr³⁺:Sc₂(MoO₄)₃ crystal. The crystal field strength Dq, Racah parameter B and C were calculated to be 1408 cm⁻¹, 608 cm⁻¹ and 3054 cm⁻¹, respectively. The absorption cross sections σ_α of ⁴A₂→⁴T₁ and ⁴A₂→⁴T₂ transitions were 3.74×10⁻¹⁹ cm² at 499 nm and 3.21×10⁻¹⁹ cm² at 710 nm, respectively. The emission cross section σ_e was 375×10⁻²⁰ cm² at 880 nm. Cr³⁺:Sc₂(MoO₄)₃ crystal has a broad emission band with a broad FWHM of 176 nm (2179 cm⁻¹). Therefore, Cr³⁺:Sc₂(MoO₄)₃ crystal may be regarded as a potential tunable laser gain medium.     

Structure of 2-(2-(anthracen-9-ylmethylene)hydrazinyl)-4-(3-methyl-3-phenylcyclobutyl)thiazole by combined X-Ray crystallographic and molecular modelling studies

A single crystal of 2-(2-(anthracen-9-ylmethylene)hydrazinyl)-4-(3-methyl-3-phenylcyclobutyl)thiazole (C₂₉H₂₅N₃S) containing anthracene, thiazole and cyclobutane rings has been synthesised. The synthesised crystal structure was characterised using IR, ¹H-NMR and ¹³C-NMR spectroscopic and X-Ray analysis techniques. In the crystal, neighbouring molecules formed chains along [110] by interconnecting with N–H···N hydrogen bonding and π–π interactions. The geometrical parameters of the title compound were optimised by Gaussian 09 software in the gas phase and Quantum-Espresso software under Periodic Boundary Conditions (PBC) in the solid phase. Theoretically, IR, NMR spectra, Mulliken, NPA and AIM atomic charges, Hirshfeld surface and frontier molecular orbitals (FMOs) of the title compound were examined. Using the Hirshfeld surface and two-dimensional (2D) fingerprint graphics, the presence of intermolecular interactions in the crystal packing were analysed. The energies of these interactions and their distribution on the crystal structure were shown graphically. In general, it was seen that theoretical calculations were consistent with X-Ray results.     

Dependence of intramolecular valence delocalization on crystal form in mixed-valence trinuclear iron phenylacetate [Fe 2 III FeIIO(PhCH2CO2)6(py)3]

A dependence of intramolecular valence delocalization on crystal form in mixed-valence trinuclear iron phenylacetate [Fe ₂ ^III Fe^IIO(PhCH₂CO₂)₆(py)₃] was found. This complex was obtained in two different crystal forms: a columnar and a needle crystal form. Mössbauer spectra of the columnar crystals show a temperature-dependent valence delocalization, while the needle crystals show a trapped mixed-valence state from a lower temperature up to room temperature.     

Anomalies in the Young modulus at structural phase transitions in rare-earth cobaltites RBaCo<Subscript>4</Subscript>O<Subscript>7</Subscript> (R = Y,Tm-Lu)

The elastic properties of rare-earth cobaltites RBaCo₄O₇ (R = Y, Tm-Lu) have been experimentally studied in the temperature range of 80–300 K. The strong softening of the Young modulus ΔE(T)/E ₀ ≈ −(0.1–0.2) of cobaltites with Lu and Yb ions has been revealed, which is due to the instability of the crystal structure upon cooling and is accompanied by an inverse jump at the second-order structural phase transition. The softening of the Young modulus and the jump at the phase transition decrease by an order of magnitude and the transition temperature T _s and hysteresis ΔT _s increase from a compound with Lu to that with Tm. A large softening of the Young modulus at the structural transition in Lu- and Yb cobaltites indicates that the corresponding elastic constant goes to zero, whereas this constant in Tm cobaltite is not a “soft” mode of the phase transition. It has been found that the structural phase transition in Lu- and Yb cobaltites is accompanied by a large absorption maximum at the phase transition point and an additional maximum in the low-temperature phase and absorption anomalies in Tm cobaltite is an order of magnitude smaller.     

Graph theory,SO(n) current algebra and the Virasoro master equation

We announce an isomorphism between a set of generically irrational affine-Virasoro constructions onSO(n) and the unlabelled graphs of ordern. On the one hand, the conformal constructions are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. High-level expansion provides a strong argument that each construction is unitary down to some finite critical level.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY85-15857     

Twist deformations for algebras of motion

We study the twist deformations of algebras of motiong ^H ⊂ sl(N) with the Cartan subalgebraH(g^H) equal toH(sl(N)). The proposed deformations are maximal in the sense that their carrier algebrasg _c coincide withg ^H. The algebraic properties are demonstrated forg ^H ⊂ sl(5). Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. This work has been partially supported by the Russian Foundation for Fundamental Research under the grant N 00-01-00500.