A stable and easily sintering {\text{BaCe}}_{0.7} {\text{Sn}}_{0.1} {\text{Gd}}_{0.2} {\text{O}}_{3 - \delta } electrolyte for solid oxide fuel cells

${\text{BaCe}}_{0.7} {\text{Sn}}_{0.1} {\text{Gd}}_{0.2} {\text{O}}_{3 - \sigma } $ (BCSG) and ${\text{BaCe}}_{0.8} {\text{Gd}}_{0.2} {\text{O}}_{3 - \sigma } $ (BCG) powders were prepared by solid-state reaction method. After exposure in 5% CO₂?+?5% H₂O?+?90% N₂ at 500 °C for 5 h, the BCSG powders were hardly affected while the BCG powders decomposed into CeO₂ and BaCO₃ phases. Moreover, the relative density of BCSG reaches 97%, while the BCG just displays 91% after sintering at 1,400 °C. The BCSG displays a conductivity of 0.01 S/cm at 700 °C in humid hydrogen, which is quite close to 0.012 S/cm for BCG. A fuel cell with BCSG exhibits 1.02 V for open circuit voltage, 420 mW/cm² for peak performance and 0.23 Ω cm² for interfacial resistance at 700 °C, respectively.     

Universal behaviors of mutual information in one-dimensional ${\sf J}_1-{\sf J}_2$ model

The critical behaviors of the entropy correlation effects in the one dimensional J₁-J₂ Heisenberg model are studied. It is shown that the mutual information or the correlation entropy captures the key features of information about critical fluctuations and can be used to quantify the quantum and finite-temperature phase transitions. At the critical point, the mutual information is power-law decay and the entanglement correlation length is infinite. While far away from the critical point, the mutual information is exponential decay and the entanglement correlation length is finite. A universal property of the mutual information is also found. Based on the critical behaviors of the mutual information, a new method to quantify the infinite order phase transition in the system is proposed.     

Intensity ratios of mesonic x-ray linesK_{\alpha _1 } , K_{\alpha _2 } andL_{\alpha _1 } , L_{\beta _2 }

Intensity ratios ofμ-mesonic x-rays in some heavy elements are discussed. Intensity ratios of the \(K_{\alpha _1 } /K_{\alpha _2 } \) and \(L_{\alpha _1 } /L_{\beta _2 } \) lines have been calculated for²⁰⁶Pb,²⁰⁹Bi and²³⁸U with relativistic wavefunctions and retardation effect. Though for a refined calculation, it is necessary to take into consideration several features that are peculiar to mesonic atoms, the present calculations have shown that the observed intensity ratios of mesonic x-rays are not anomalous.     

Impurity effects of the Λhyperon in the hypernuclear systems ${}_{{\rm{\Lambda }}}^{25}\mathrm{Mg}$ and ${}_{{\rm{\Lambda }}}^{29}\mathrm{Si}$

Based on the beyond-mean-field Skyrme–Hartree–Fock model, impurity effects of the Λhyperon in the hypernuclear systems ${}_{\,{\rm{\Lambda }}}^{25}$ Mg and ${}_{\,{\rm{\Lambda }}}^{29}$ Si are investigated, respectively. Four cases, in which the Λhyperon occupies the single-particle orbitals ${\rm{\Lambda }}$[000]${\tfrac{1}{2}}^{+}$, ${\rm{\Lambda }}$[110]${\tfrac{1}{2}}^{-}$, ${\rm{\Lambda }}$[101]${\tfrac{3}{2}}^{-}$ and ${\rm{\Lambda }}$[101]${\tfrac{1}{2}}^{-}$, are focused. In each case, the potential energy surface and the energy curves projected on certain angular momenta are employed to show the influence of the Λhyperon on the nuclear core. Beside the shrinkage effect that is induced by the Λhyperon occupying the s_Λ orbital, it is found that the Λhyperon on the p_Λ orbital, ${\rm{\Lambda }}$[110]${\tfrac{1}{2}}^{-}$, drives the nuclear core toward a prolate shape, while the ones on the other two p_Λ orbitals, ${\rm{\Lambda }}$[101]${\tfrac{3}{2}}^{-}$ and ${\rm{\Lambda }}$[101]${\tfrac{1}{2}}^{-}$, drive the nuclear core toward an oblate shape. The energy spectra and the corresponding intra-band E2 transition rates for the rotational bands are given as a prediction for future experiments.     

Characteristics of splat-cooled Sn- \hbox{Bi}_{5} - \hbox{Pb}_{\bi x} alloys

A Sn-5 \, wt.%Bi binary master alloy was prepared by melt spinning. Ternary alloys with different Pb contents ( x = 0 - 2.5\,\hbox{wt.}\% ) were prepared with the same technique. All the alloys were irradiated with 1.2\,\hbox{MGy} \gamma -radiation at room temperature. The internal friction, Q^{-1} , the thermal diffusivity D_{\rm th} and the Young's modulus Y obtained by applying the resonance technique were measured at room temperature before and after irradiation. DTA thermograms and X-ray diffraction patterns were obtained for the tested alloys. The results showed a remarkable dependence on both the amounts of the ternary addition and irradiation with \gamma -rays. The observed changes in the measured values were attributed to a composition inhomogeneity, caused by the distribution mode of the third element in the matrix and the defects induced by irradiation.     

Reversibility of 1D Cellular Automata with Periodic Boundary over Finite Fields $\pmb{ {\mathbb{Z}}}_{p}$

The reversibility problem for linear cellular automata with null boundary defined by a rule matrix in the form of a pentadiagonal matrix was studied recently over the binary field ℤ₂ (del Rey and Rodriguez Sánchez in Appl. Math. Comput., 2011, doi:). In this paper, we study one-dimensional linear cellular automata with periodic boundary conditions over any finite field ℤ _p . For any given p≥2, we show that the reversibility problem can be reduced to solving a recurrence relation depending on the number of cells and the coefficients of the local rules defining the one-dimensional linear cellular automata. More specifically, for any given values (from any fixed field ℤ _p ) of the coefficients of the local rules, we outline a computer algorithm determining the recurrence relation which can be solved by testing reversibility of the cellular automaton for some finite number of cells. As an example, we give the full criteria for the reversibility of the one-dimensional linear cellular automata over the fields ℤ₂ and ℤ₃.     

Modeling of Spin Hamiltonian Parameters for Vanadyl-Doped {\bf\hbox{K}_2\hbox{SO}_4{-}\hbox{Na}_2\hbox{SO}_4{-}\hbox{ZnSO}_4} Glass

A full ligand-field energy matrix diagonalization treatment for 3d ¹ ions in tetragonal symmetry is developed on the basis of the two spin?Corbit coupling parameter model, and the contributions of the spin?Corbit coupling of the ligand ions to the optical and electron paramagnetic resonance spectra are included. Spin Hamiltonian parameters of the tetragonal ${\rm V}^{4+}$ center in $\hbox{K}_2\hbox{SO}_4 {-} \hbox{Na}_2\hbox{SO}_4{-}\hbox{ZnSO}_4$ glass are calculated from the complete energy matrix diagonalization and the perturbation theory methods. The results calculated by both methods are not only close to each other but also in good agreement with the experimental values. Furthermore, the compressed defect structure of the ${\rm (VO_6)^{8-}}$ cluster is discussed.     

On q-Deformed {\mathfrak{gl}_{\ell+1}}-Whittaker Function II

A representation of a specialization of a q-deformed class one lattice ${\mathfrak{gl}_{\ell+1}}$ -Whittaker function in terms of cohomology groups of line bundles on the space ${\mathcal{QM}_d(\mathbb{P}^{\ell})}$ of quasi-maps ${\mathbb{P}^1 \to \mathbb{P}^{\ell}}$ of degree d is proposed. For ? = 1, this provides an interpretation of the non-specialized q-deformed ${\mathfrak{gl}_{2}}$ -Whittaker function in terms of ${\mathcal{QM}_d(\mathbb{P}^1)}$ . In particular the (q-version of the) Mellin-Barnes representation of the ${\mathfrak{gl}_2}$ -Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important role of q-version of Γ-function as a topological genus in semi-infinite geometry. A relation with the Givental-Lee universal solution (J-function) of q-deformed ${\mathfrak{gl}_2}$ -Toda chain is also discussed.     

On q-Deformed {\mathfrak{gl}_{\ell+1}} -Whittaker Function I

We propose a new explicit form of q-deformed Whittaker functions solving q-deformed ${\mathfrak{gl}_{\ell+1}}A representation of a specialization of a q-deformed class one lattice \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker function in terms of cohomology groups of line bundles on the space QM_d(\mathbbP^l){\mathcal{QM}_d(\mathbb{P}^{\ell})} of quasi-maps \mathbbP¹ ? \mathbbP^l{\mathbb{P}^1 \to \mathbb{P}^{\ell}} of degree d is proposed. For ℓ = 1, this provides an interpretation of the non-specialized q-deformed \mathfrakgl₂{\mathfrak{gl}_{2}}-Whittaker function in terms of QM_d(\mathbbP¹){\mathcal{QM}_d(\mathbb{P}^1)}. In particular the (q-version of the) Mellin-Barnes representation of the \mathfrakgl₂{\mathfrak{gl}_2}-Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important role of q-version of Γ-function as a topological genus in semi-infinite geometry. A relation with the Givental-Lee universal solution (J-function) of q-deformed \mathfrakgl₂{\mathfrak{gl}_2}-Toda chain is also discussed.     

Study of semileptonic decay of ${\bar{B}}_{s}^{0} \rightarrow \phi {l}^{+}{l}^{-}$ in QCD sum rule

In this work we study the semileptonic decay of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) with the QCD sum rule method. We calculate the ${\bar{B}}_{s}^{0}\to \phi $ translation form factors relevant to this semileptonic decay, then the branching ratios of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) decays are calculated with the form factors obtained here. Our result for the branching ratio of ${\bar{B}}_{s}^{0}\to \phi {\mu }^{+}{\mu }^{-}$ agree very well with the recent experimental data. For the unmeasured decay modes such as ${\bar{B}}_{s}^{0}\to \phi {e}^{+}{e}^{-}$ and ${\bar{B}}_{s}^{0}\to \phi {\tau }^{+}{\tau }^{-}$, we give theoretical predictions.     

Time-resolved photoelectron spectroscopy of $\mathrm{Al}_{3}\mathrm{O}_{3}^{-}$: photoisomerization versus photofragmentation

In general, clusters are unstable and in many cases several metastable isomers exist even at low temperature. Therefore, a cluster may react with a dramatic geometry change to a small disturbance such as a weak field or to the absorption of a low-energy photon. Here, we study the response of Al₃O₃^-\mathrm{Al}_{3}\mathrm{O}_{3}^{-} to photoexcitation using time-resolved photoelectron spectroscopy. Earlier experimental and theoretical studies suggested that this cluster anion undergoes a geometry change after photoexcitation. In contrast, our time-resolved spectra indicate that photoexcitation triggers ultra-fast fragmentation. This example demonstrates that ultra-fast processes in clusters are not well understood and that it is still difficult to gain reliable experimental data about such processes.     

{^6_{\Lambda} \rm{H}} Modeled as {^4_{\Lambda} \rm{H}} + n + n

A three-body calculation for the \({^4_{\Lambda} \rm{He}}\) and \({^6_{\Lambda}{\rm H}}\) hypernuclei has been undertaken. The respective cores are \({^4_{\Lambda}{\rm H}}\) . The interactions in the \({^6_{\Lambda}{\rm He}}\) system, modeled as \({^4_{\Lambda} {\rm H+p+n}}\) , are reasonably well known. For example, the p n interaction is well determined by the p n scattering data, the \({^4_{\Lambda}{\rm H}}\) –p interaction can be fitted to the \({^5_{\Lambda}{\rm He}}\) binding energy. The \({^4_{\Lambda}{\rm He}}\) –n interaction can be fitted to α–n scattering data. For the ⁴He–n system the s-wave can be modeled alternatively as a repulsive potential or as an attractive potential with a forbidden bound state. We explore these alternatives in ⁶He, because the interaction comes into play in modeling \({^6_{\Lambda}{\rm He}}\) as well as in our \({^4_{\Lambda}{\rm H}}\) + n + n model of \({^6_{\Lambda}{\rm H}}\) , where the valence neutrons are Pauli blocked from the s-shell of the core nucleus.     

Photoionization Cross Section for H@Cn${\text{H@C}}_{n}$ Implanted in Nonideal Classical Plasmas

In this study, photoionization cross sections of guest hydrogen atom in endohedral fullerene (${\text{H@C}}_n$) modeled by the Woods–Saxon confinement potential implanted in the nonideal classical plasma (NICP) under spherical confinement are reported for the first time in the related literature. The relevant wave equation is solved numerically via the tridiagonal matrix method and then the energy levels, bound and continuum wave functions are interpreted. Plasma effect is examined by considering plasma temperature and density and is evaluated in the photoionization process. Since the plasma modifies the discrete and continuum spectra by changing the potential energy of hydrogen atom, it closely affects the overlapping of the wave functions of ground state and continuum state. This effect has a distinct response on photoionization resonances. Using different values of endohedral confinement parameters, which means regarding different types of fullerenes, detailed analysis of energy levels, bound and continuum wave functions, and photoionization cross sections are provided by evaluating confinement width, depth, smoothing effect and distance from the spherical encompassement center. The photoionization process of ${\text{H@C}}_n$ implanted in the NICP (nonideal classical plasma) is highly sensitive to both plasma and endohedral confinement. At this sensitivity, Cooper resonance character is like an encoder for fullerene structure.     

Tau Leptonic Decay τ→lVlVτ in Littlest Higgs Model＊

We consider the τ leptonic decay $\tau\rightarrow l\bar{\nu}_{l}\nu_{\tau}$ in the framework of the littlest Higgs (LH) model and calculate the corrections of new particles to this decay. We find that the contributions of the charged scalars can be safely ignored and the LH model is in perfect agreement with the universality of the couplings of the SU gauge bosons to the leptonic charged currents. The corrections of the LH model to the τ leptonic decay $\tau\rightarrow l\bar{\nu}_{l}\nu_{\tau}$ are not sensitive to the parameter c, but depend strongly on the parameters f and x. The precision measured data about the τ leptonic decay demand that the parameter f approximately equal 3.5 TeV and x>0.1, while agree with the general expectation based on other phenomenological explorations.