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.     

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.     

Semi-Classical Twists for {\mathfrak{sl}}_{3} and {\mathfrak{sl}}_{4} Boundary r-Matrices of Cremmer–Gervais Type

We obtain explicit formulas for the semi-classical twists deforming the coalgebraic structure of $U({\mathfrak{sl}}_{3})$ and $U({\mathfrak{sl}}_{4})$ . In rank 2 and 3 the corresponding universal R-matrices quantize the boundary r-matrices of Cremmer–Gervais type defining Lie Frobenius structures on the maximal parabolic subalgebras in ${\mathfrak{sl}}_{n}$ .     

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.     

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.     

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.     

A complete $\mathcal{O}(\alpha_{\mathrm{S}}^{2})$ calculation of the signal–background interference for the Higgs diphoton decay channel

We analyze a noncommutative model of BTZ spacetime based on deformation of the standard symplectic structure of phase space, i.e., a modification of the standard commutation relations among coordinates and momenta in phase space. We find a BTZ-like solution that is nonperturbative in the non-trivial noncommutative structure. It is shown that the use of deformed commutation relations in the modified non-canonical phase space eliminates the horizons of the standard metric.     

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.      

Determination of the strong coupling αS from hadronic event shapes with \mathcal{O}(\ensuremath {\alpha _{\mathrm {S}}}^{3}) and resummed QCD predictions using JADE data

Event Shape Data from e⁺e^? annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV are used to determine the strong coupling α_S. QCD predictions complete to next-to-next-to-leading order (NNLO), alternatively combined with resummed next-to-leading-log-approximation (NNLO?+?NLLA) calculations, are used. The combined value from six different event shape observables at the six JADE centre-of-mass energies using the NNLO calculations is $$\begin{array}{rcl}\ensuremath {\ensuremath {\alpha _{\mathrm {S}}}(\ensuremath {m_{\ensuremath {\mathrm {Z^{0}}}}})}&=&0.1210\pm 0.0007\ensuremath {\mathrm {(stat.)}}\pm 0.0021\ensuremath {\mathrm {(exp.)}}\\[6pt]&&{}\pm 0.0044\ensuremath {\mathrm {(had.)}}\pm 0.0036\ensuremath {\mathrm {(theo.)}}\end{array}$$ and with the NNLO?+?NLLA calculations the combined value is $$\begin{array}{rcl}\ensuremath {\ensuremath {\alpha _{\mathrm {S}}}(\ensuremath {m_{\ensuremath {\mathrm {Z^{0}}}}})}&=&0.1172\pm 0.0006\ensuremath {\mathrm {(stat.)}}\pm 0.0020\ensuremath {\mathrm {(exp.)}}\\[6pt]&&{}\pm 0.0035\ensuremath {\mathrm {(had.)}}\pm 0.0030\ensuremath {\mathrm {(theo.)}}.\end{array}$$ The stability of the NNLO and NNLO?+?NLLA results with respect to missing higher order contributions, studied by variations of the renormalisation scale, is improved compared to previous results obtained with NLO?+?NLLA or with NLO predictions only. The observed energy dependence of α_S agrees with the QCD prediction of asymptotic freedom and excludes absence of running with 99% confidence level.     

Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(_3)

In this paper,we prove one case of conjecture given by Hernandez and Leclerc.We give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group Uq(3).As a conclusion,for every exchange relation of cluster algebra,there exists an exact sequence of the full subcategory corresponding to it.     

Exact solutions of perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity by improved $${\textbf{tan}} \left( {\frac{{\boldsymbol{\phi}} \left( {\boldsymbol{\xi}} \right)}{{\textbf{2}}}} \right)$$-expansion method

This paper carries out exact solutions of the perturbed nonlinear Schödinger’s equation withy Kerr law nonlinearity by using the improved tan\(\left( {\frac{\phi \left( \xi \right)}{2}} \right)\)-expansion method. The exact solutions contain four types: hyperbolic function solution, trigonometric function solution, exponential solution, and rational solution. The method appears to be easier and faster by means of symbolic computational system and can be applied to the other nonlinear evolution equations in mathematical physics.     

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.     

Point defect diagrams for pure and doped cobalt oxide $$ {hbox{C}}{{hbox{o}}_{{{1} - }}}_{delta }{hbox{O}} $$ in the temperature range of 1,173–1,673 K ( I)

The point defect diagram in non-stoichiometric cobalt oxide Co_{1 - d}O {hbox{C}}{{hbox{o}}_{{{1} - }}}_{delta }{hbox{O}} , pure and doped with M³⁺ and M⁺ metal ions, taking into consideration all of the types of defects in the cation sublattice are presented in this work. A new method was used for the calculations of the diagrams. This method is based on the derived relations between the standard Gibbs energies of formation of cobalt vacancies and the intrinsic ionic and electronic defects; it also uses the experimental values of the deviation from the stoichiometry. The calculations were performed using the results of studies obtained by many authors in the temperature range of 1,173–1,673 K.     

Bannai–Ito algebras and the universal R-matrix of $$\pmb {\mathfrak {osp}}(1|2)$$osp(1|2)

Letters in Mathematical Physics - The Bannai–Ito algebra BI(n) is viewed as the centralizer of the action of $$\mathfrak {osp}(1|2)$$ in the n-fold tensor product of the universal algebra of...     

Study on the A~2Π_(3/2u), B~2Δ_(3/2u), and X~2Π_(3/2g) states of Cl_2~+ including its isotopologues

Adopting the experimentally available vibrational constants in a recent analysis of the strong perturbation between the A22Π3/2u and BΔ3/2u states of Cl+2in the A–X band system [Gharaibeh et al. 2012 J. Chem. Phys. 137 194317], an unambiguous vibrational assignment of the bands reported previously is carried out. The equilibrium rotational constants Be and α e of the X2Π3/2g and A2Π3/2u states for35Cl+2and35Cl37Cl+and those of the B2Δ3/2u state for35Cl+2are obtained by fitting the experimental values of Bυ. In addition, the values of Be and α e of these three states for the minor isotopologues35Cl37Cl+and37Cl+2are predicted by employing the isotopic effect. The values of equilibrium internuclear distance Re of the three states for the three isotopologues are calculated as well.     

Fundamental Role of the H-Bond Interaction in the Dissociation of NH_{3} on Si(001)-(2×1)

Further insight into the dissociative adsorption of NH_{3} on Si(001) has been obtained using a combined computational and experimental approach. A novel route leading to the dissociation of the chemisorbed NH_{3} is proposed, based on H-bonding interactions between the gas phase and the chemisorbed NH_{3} molecules. Our model, complemented by synchrotron radiation photoelectron spectroscopy measurements, demonstrates that the low temperature dissociation of molecular chemisorbed NH_{3} is driven by the continuous flux of ammonia molecules from the gas phase.     

The CUORICINO 130Te ββ-decay experiment and a new limit on T_{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^{0\nu } (\beta \beta )

The CUORICINO ββ-decay detector is an array of 62 TeO2 bolometers; 44 are 5×5×5-cm crystals made with natural tellurium (33.8% ¹³⁰Te). There are 18, 3×3×6-cm crystals, 14 of which are made of natural tellurium, 2 are isotopically enriched to 75% in ¹³⁰Te, and 2 are enriched to 82.3% in ¹²⁸Te. The total mass of ¹³⁰Te is ～ 11 kg. The background rate is 0.23 ± 0.04 counts/keV/kg/yr in the energy interval 2480 to 2600 keV. During the cooling process, some of the wires became disconnected and only 32 of the large and 16 of the smaller crystals could be read out. The data presented here come from 29 of the 5×5×5-cm crystals containing 6.2 kg of ¹³⁰Te. The new limit on the half-life is $T_{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}^{0\nu } \geqslant 5 \times 10^{23} yr$ , corresponding to an effective Majorana mass of the electron neutrino 〈m _ν〉 between 0.42 and 2.05 eV, depending on the nuclear model used to analyze the data.