Traces of Intertwiners for Quantum Affine {\mathfrak{sl}}_2 and Felder–Varchenko Functions

We show that the traces of \({U_q({\widehat{\mathfrak{sl}}}_2)}\)-intertwiners of [ESV02] valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction of Felder–Varchenko’s hypergeometric solutions to the q-KZB heat equation given in [FV02]. This gives the first proof that such a trace function converges and resolves the first case of the Etingof–Varchenko conjecture of [EV00]. As applications, we prove a symmetry property for traces of intertwiners and prove Felder–Varchenko’s conjecture in [FV04] that their elliptic Macdonald polynomials are related to the affine Macdonald polynomials defined as traces over irreducible integrable \({U_q({\widehat{\mathfrak{sl}}}_2)}\)-modules in [EK95]. In the trigonometric and classical limits, we recover results of [EK94,EV00]. Our method relies on an interplay between the method of coherent states applied to the free field realization of the q-Wakimoto module of [Mat94], convergence properties given by the theta hypergeometric integrals of [FV02], and rationality properties originating from the representation-theoretic definition of the trace function.     

Structural, thermal and transport properties of {\text{B}}{{\text{i}}_4}{{\text{V}}_{2 - {\text{x}}}}{\text{G}}{{\text{a}}_{\text{x}}}{{\text{O}}_{11 - \delta }} (0 ≤ x ≤ 0.4)

Solid electrolytes are mostly used in solid oxide fuel cells (SOFC). In the present study, gallium-substituted compounds ( $ {\text{B}}{{\text{i}}_4}{{\text{V}}_{2 - {\text{x}}}}{\text{M}}{{\text{e}}_{\text{x}}}{{\text{O}}_{11 - \delta }} $ ; Me?=?Ga³⁺; 0≤x≤0.4) were prepared by solid-state reaction technique for its use as an electrolyte in SOFC. Structural and conductivity behavior was studied as a function of the Ga³⁺ substitution on vanadium site. The compounds remain in the orthorhombic α-phase for x?=?0 and 0.1 whereas higher concentration of dopant leads to β-phase stabilization. The highest and lowest ionic conductivity were observed in x?=?0.2 and x?=?0.4 samples, respectively. The prepared samples were studied by using alternating current conductivity, differential thermal analysis and X-ray diffraction techniques. The results are discussed on the basis of formation of oxygen vacancy and its ordering.     

The Sixth Painlevé Equation as Similarity Reduction of $${\widehat{\mathfrak{gl}}_3}$$ Generalized Drinfel’d–Sokolov Hierarchy

Scaling symmetry of -type Drinfel’d–Sokolov hierarchy is investigated. Applying similarity reduction to the hierarchy, one can obtain the Schlesinger equation with (n + 1) regular singularities. Especially in the case of n = 3, the hierarchy contains the three-wave resonant system and the similarity reduction gives the generic case of the Painlevé VI equation. We also discuss Weyl group symmetry of the hierarchy.      

The Decrease of the ESEEM Frequency of $${\text{P}}_{700}^{ + } {\text{A}}_{1}^{ - }$$ Ion-Radical Pair in Photosystem I Embedded in Trehalose Glassy Matrix at Room Temperature can be Explained by Acceleration of Spin–Lattice Relaxation

The main observation in this work is a decrease in the modulation frequency of the primary electron spin-echo decay (ESEEM) of the \({\text{P}}_{ 7 0 0}^{ + }\) cofactor in the reaction center of Photosystem I (PS I) from cyanobacteria Synechocystis sp. PCC 6803 embedded in dry trehalose matrix as the temperature rises from 150 K to room temperature. From the previous studies of the EPR spectrum shape of this system, it is known that, in dry trehalose matrix at room temperature, the distance between \({\text{P}}_{ 7 0 0}^{ + }\) and \({\text{A}}_{ 1}^{ - }\) spins does not increase compared to the distance measured in glycerol–water solution at cryogenic temperature. From the present ESEEM study, we conclude that the decrease of modulation frequency with rising temperature in trehalose matrix can be fully attributed to the influence of accelerated spin–lattice relaxation of \({\text{A}}_{ 1}^{ - }\). Our calculations show that this requires a decrease in the spin–lattice relaxation time from 3 to 1 μs. To the best of our knowledge, this is the first time that a shift in the ESEEM frequency due to the dipole–dipole interaction between the spins is observed that is caused by spin–lattice relaxation. Based on the above-mentioned results, we formulate a model of the protective effect of trehalose matrix on the electron transfer in the reaction center of PS I that is based on different hydrogen-bond networks between trehalose, local water, and protein.     

The MV formalism for $${\mathrm{IBL}}_\infty $$- and $${\mathrm{BV}}_\infty $$BV∞-algebras

We develop a new formalism for the quantum master equation \(\Delta e^{S/\hbar } = 0\) and the category of \(\mathrm{IBL}_\infty \)-algebras and simplify some homotopical algebra arising in the context of oriented surfaces with boundary. We introduce and study a category of MV-algebras, which, on the one hand, contains such important categories as those of \(\mathrm{IBL}_\infty \)-algebras and \(\mathtt{L}_\infty \)-algebras and, on the other hand, is homotopically trivial, in particular allowing for a simple solution of the quantum master equation. We also present geometric interpretation of our results.     

Properties of the _{69}^{150}{\text{T}}{{\text{m}}_{81}} 6− β-decaying isomer

Decay experiments for ¹⁴⁸Ho 6^? and ¹⁵⁰Tm 6^? were carried out at the GSI On-line mass separator using 5 MeV/A ⁵⁸Ni-beams on ⁹⁴Mo and ⁹⁶Ru targets. Gammaγ-and γX-coincidences established the ¹⁵⁰Tm 6^? decay scheme, and e^? gave firm I^π assignments for ¹⁴⁸Dy and ¹⁵⁰Er levels fed in the decays. It was found that the previously unknown \(6_1^ -\) state in ¹⁵⁰Er receives significant β-strength, which strongly suggests \(\pi {h_{11/2}}\nu s_{1/2}^{ - 1}\) character for the ¹⁵⁰Tm 6^? isomer. The results are discussed in terms of the expected GT strength function. Shell model calculations for the \(\pi h_{11/2}^4\) yrast states are presented.     

Neutron Pairing Correlations in an {\alpha}–{n}–{n} Three-Cluster Model of the {^{6}}He Nucleus

An \({\alpha}\)–n–n three-cluster model of the \({^6}\)He nucleus is studied by solving the Faddeev equations, where the cluster potential between \({\alpha}\) and n takes into account the Pauli exclusion correction, using the Fish-Bone Optical Model (Schmid in Z Phys A 297:105, 1980). The resulting binding energy of the ground state (\({0^+}\)) is 0.831 MeV and the resonance energy of the first excited state (\({2^+}\)), 0.60–i0.012 MeV, is extracted from the three-cluster break-up threshold. These theoretical values are in reasonable agreement with the experimental data: 0.973 MeV and 0.824–i0.056 MeV, respectively. In order to investigate the structure of these states, we calculate the angle density matrix for the \({\angle n_1 \alpha n_2}\) angle in the triangle formed by the three clusters. The angle density matrix of the ground state has two peaks and the configuration of \({0^+}\) wave function corresponding to the peaks constitutes a mixture of an acute-angled triangle structure and an obtuse-angled one. This finding is consistent with the former result from a variational approach (Hagino and Sagawa in Phys Rev C 72:044321, 2005). On the other hand, in the case of \({2^+}\) state only a single peak is obtained.     

The Quantum Superalgebra {\mathfrak{osp}_{q}(1|2)} and a q-Generalization of the Bannai–Ito Polynomials

The Racah problem for the quantum superalgebra \({\mathfrak{osp}_{q}(1|2)}\) is considered. The intermediate Casimir operators are shown to realize a q-deformation of the Bannai–Ito algebra. The Racah coefficients of \({\mathfrak{osp}_q(1|2)}\) are calculated explicitly in terms of basic orthogonal polynomials that q-generalize the Bannai–Ito polynomials. The relation between these q-deformed Bannai–Ito polynomials and the q-Racah/Askey–Wilson polynomials is discussed.     

$\ensuremath{\mathcal{P}}$$\ensuremath{\mathcal{T}}$ Symmetry vs. Hermiticity

The relation between the P\ensuremath{\mathcal{P}} T\ensuremath{\mathcal{T}} symmetry and Hermiticity is discussed. In the finite-dimensional linear space, any Hermitian matrix is a special case of P\ensuremath{\mathcal{P}} T\ensuremath{\mathcal{T}}-symmetric matrices. Explicit results in 2×2 are shown. The early belief that the P\ensuremath{\mathcal{P}} T\ensuremath{\mathcal{T}}-symmetric quantum mechanics is a generalization of the conventional Hermitian quantum mechanics is confirmed.     

Two-parameter Quantum Affine Algebra $$U_{r,s}(\widehat{\mathfrak {sl}_n})$$, Drinfel’d Realization and Quantum Affine Lyndon Basis

We further define two-parameter quantum affine algebra (n > 2) after the work on the finite cases (see [BW1,BGH1,HS,BH]), which turns out to be a Drinfel’d double. Of importance for the quantum affine cases is that we can work out the compatible two-parameter version of the Drinfel’d realization as a quantum affinization of and establish the Drinfel’d Isomorphism Theorem in the two-parameter setting, via developing a new combinatorial approach (quantum calculation) to the quantum affine Lyndon basis we present (with an explicit valid algorithm based on the use of Drinfel’d generators). N.H., supported in part by the NNSF (Grants 10431040, 10728102), the PCSIRT, the TRAPOYT and the FUDP from the MOE of China, the SRSTP from the STCSM, die Deutche Forschungsgemeinschaft (DFG), as well as an ICTP long-term visiting scholarship. H.Z., supported by a Ph.D. Program Scholarship Fund of ECNU 2006.     

Dirac multimode ket-bra operators’ \mathfrak{Q}-ordered and \mathfrak{P}-ordered integration theory and general squeezing operator

We develop quantum mechanical Dirac ket-bra operator’s integration theory in $\mathfrak{Q}$ -ordering or $\mathfrak{P}$ -ordering to multimode case, where $\mathfrak{Q}$ -ordering means all Qs are to the left of all Ps and $\mathfrak{P}$ -ordering means all Ps are to the left of all Qs. As their applications, we derive $\mathfrak{Q}$ -ordered and $\mathfrak{P}$ -ordered expansion formulas of multimode exponential operator $e^{ - iP_l \Lambda _{lk} Q_k } $ . Application of the new formula in finding new general squeezing operators is demonstrated. The general exponential operator for coordinate representation transformation $\left| {\left. {\left( {_{q_2 }^{q_1 } } \right)} \right\rangle \to } \right|\left. {\left( {_{CD}^{AB} } \right)\left( {_{q_2 }^{q_1 } } \right)} \right\rangle $ is also derived. In this way, much more correpondence relations between classical coordinate transformations and their quantum mechanical images can be revealed.     

Back to the Amitsur–Levitzki Theorem: a Super Version for the Orthosymplectic Lie Superalgebra $${\mathfrak{o}}{\mathfrak{s}}{\mathfrak{p}}\left( {1,2n} \right)$$

We prove an Amitsur–Levitzki type theorem for the Lie superalgebras $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left( {1,2n} \right)$ ) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras $\mathfrak{g}\mathfrak{l}\left( {p,q} \right)$ cannot satisfy an Amitsur–Levitzki type super identity if pq≠0 and conjecture that neither can any other classical simple Lie superalgebra with the exception of $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left( {1,2n} \right)$ .     

Backbending Phenomena in Even–Even $${}^{\boldsymbol{162{-}172}}$$ Hf Isotopes

Physics of Atomic Nuclei - This study probes the backbending phenomena in even–even $${}^{162{-}172}$$ Hf isotopes. Experimental ground-state rotational energies up to $$J^{\pi}=36^{+}$$...     

Cool white light emission on Ca3−(l+n)MgSi2O8:\mathrm{Ce}_{\mathrm{l}}^{3+}, \mathrm{Eu}_{n}^{2+} phosphors and analysis of energy transfer mechanism

Rare earth ions (Ce³⁺, Eu²⁺) activated Ca₃MgSi₂O₈ (CMSO) phosphors have been synthesized using solid-state reaction method in 95%N₂+5%H₂ reduction atmosphere at elevated temperatures by varying Eu²⁺ concentration from 0.0075 to 0.0300 at the fixed Ce_0.03 concentration to study their photoluminescence (PL) properties. An energy transfer occurs from Ce³⁺ to Eu²⁺ through a significant overlap of Eu²⁺ excitation spectrum with Ce³⁺ emission spectrum in CMSO, together with the systematic relative decrease and increase in emission bands of Ce³⁺ and Eu²⁺, respectively, have been observed. To support the phenomenon, diffuse reflectance spectra show various absorption levels corresponding to Ce³⁺, Eu²⁺, and/or mixture of both rare earth ions. An optimum emission was realized at 0.0150 of Eu²⁺ via. energy transfer from Ce³⁺ ion. By utilizing the principle of energy transfer, the critical distance (R _c ) between activator ions was found to be 18.64 Å. The CIE chromaticity coordinates measured on the Ca₃MgSi₂O₈:Ce³⁺, Eu²⁺ phosphors excited under ultraviolet (365 nm) source shows the values lie in cool white light region could be applied to solid state lighting.     

Top polarization and exploration of \mathbf{\emph{t}} \boldsymbol{\bar t} forward–backward asymmetry?

The large forward?Cbackward asymmetry in top pair-production observed at the Tevatron has generated much excitement in recent times. Many different models have been proposed as possible explanations for this anomaly. We discuss how the measurement of the polarization of the top quark can be used to establish the role of new physics in generating the observed asymmetry and to characterize and discriminate among various models.     

Role of the Λ(1600) in the ${K}^{-}p \rightarrow {\rm{\Lambda }}{\pi }^{0}{\pi }^{0}$ reaction

Role of the Λ(1600) is studied in the ${K}^{-}p\to {\rm{\Lambda }}{\pi }^{0}{\pi }^{0}$ reaction by using the effective Lagrangian approach near the threshold. We perform a calculation for the total and differential cross sections by considering the contributions from the Λ(1600) and Λ(1670) intermediate resonances decaying into ${\pi }^{0}{{\rm{\Sigma }}}^{* 0}(1385)$ with ${{\rm{\Sigma }}}^{* 0}(1385)$ decaying into ${\pi }^{0}{\rm{\Lambda }}$. Additionally, the non-resonance process from u-channel nucleon pole is also taken into account. With our model parameters, the current experimental data on the total cross sections of the ${K}^{-}p\to {\rm{\Lambda }}{\pi }^{0}{\pi }^{0}$ reaction can be well reproduced. It is shown that we really need the contribution from the Λ(1600) with spin-parity ${J}^{P}=1/{2}^{+}$, and that these measurements can be used to determine some of the properties of the Λ(1600) resonance. Furthermore, we also plot the π⁰Λ invariant mass distributions which could be tested by the future experimental measurements.     

基于Spalart-Allmaras-γ-\begin{document} ${\overline {Re} _{\theta {\rm{t}}}}$ \end{document}转捩模型的横流不稳定性转捩预测方法

传统的应用稳定性理论对横流不稳定性转捩现象的预测很难与现代CFD并行化计算结合, 为了解决这个问题, 文章基于SA-γ-${\overline {Re} _{\theta {\rm{t}}}}$转捩模型, 使用不可压三维边界层相似性解实现横流位移损失厚度Reynolds数在流场中的当地化求解, 结合亚音速试验数据-C1准则构建横流不稳定性转捩判据, 从而实现了横流不稳定性转捩预测方法的当地化并行求解.首先采用SA-γ-${\overline {Re} _{\theta {\rm{t}}}}$转捩模型对NLF(1)-0416翼型进行了流向转捩预测, 证实了该模型的正确性.然后应用所建立的横流转捩模型对45°前缘后掠角的NLF(2)-0415无限展长机翼和DLR-F5机翼, 以及标准6:1椭球标模进行了横流不稳定转捩数值模拟, 计算结果显示转捩位置均与试验数据吻合较好, 证明了文章所建立的方法在不可压边界层转捩预测具有较高的预测精度.