Pyroxene inclusions in paleo-Christian mosaic tesserae: a new tool for constraining the glass manufacturing temperature

The mineral inclusions of two orange glass tesserae from paleo-Christian mosaics were investigated in order to derive the melting temperature reached during their production (sourced from Padua and Vicenza, Veneto region, Italy). In particular, clinopyroxene crystals were studied by single-crystal X-ray diffraction and electron microprobe WDS analysis. The crystals show C2/c symmetry, typical of disordered Ca/Na and Mg/Al distributions indicating high-temperature of formation (>700°C). The cation site populations were obtained by combining results from the two experimental techniques enabled us to derive the following stoichiometric formula:

Eu2+ and Eu3+ based “concentrated phosphors” as converters for UV LED light: two approaches and two new examples

The absolute majority of phosphors are composed of a host lattice and some percentage of an activator. At higher activator concentrations the concentration quenching occurs. However, there are phosphors in which only minor quenching of the emission occurs with increasing of the activator content. Based on the existence of two different valence states of the Eu ion (2+ and 3+), two approaches for the development of “concentrated phosphors”, i.e. light emitting materials in which the activator ion is a main part of the crystal lattice, are discussed. In both approaches, reduced energy migration leading to the luminescence quenching is considered as a main condition to reach a high quantum efficiency of a concentrated phosphor. Two kinds of phosphors—Eu²⁺-doped alumosilicate and Eu³⁺-doped oxyfluoride—are used as an experimental basis for this discussion. Starting from the stoichiometric Ca_1-xEu_x²⁺Al₂Si₂O₈\mathrm{Ca}_{1-x}\mathrm{Eu}_{x}^{2+}\mathrm{Al}_{2}\mathrm{Si}_{2}\mathrm{O}_{8} anorthite and Eu³⁺OF oxyfluorides, the non-stoichiometric powders with Eu²⁺_0.92Al_1.76Si_2.24O₈\mathrm{Eu}^{2+}_{0.92}\mathrm{Al}_{1.76}\mathrm{Si}_{2.24}\mathrm{O}_{8}, Eu³⁺(O, F)_2,35 and Eu³⁺(O, F)_2,16 compositions were synthesized by a solid state reaction and investigated. It was shown that—in spite of the almost 100% Eu concentration—light converters with high quantum efficiency of more than 45% can be realized. A possible application of these materials as UV LED light converters for white light emitting diodes are discussed as well.     

基于深度残差网络的脱机手写汉字识别研究

摘 要: 手写汉字识别是模式识别与机器学习的重要研究方向和应用领域。近年来,随着深度学习理论方法的完善、新技术的层出不穷,深度神经网络在图像识别分类、图像生成等典型应用中取得了突破性的进展,其中,深度残差网络作为最新的研究成果,已成功应用于手写数字识别、图片识别分类等多个领域。本文将研究深度残差网络在脱机孤立手写汉字识别中的应用方法,通过改进残差学习模块的单元结构,优化深度残差网络性能,同时通过对训练集的预处理,从数据层面实现训练生成模型性能的提升,最后设计实验,验证深度残差网络、End-to-End模式在脱机手写汉字识别中的可行性,分析、总结存在的问题及今后的研究方向。     

Quantum Marginal Inequalities and the Conjectured Entropic Inequalities

A conjecture – the modified super-additivity inequality of relative entropy – was proposed in Zhang et al. (Phys. Lett. A 377:1794–1796, 2013): There exist three unitary operators \(U_{A}\in \mathrm {U}(\mathcal {H}_{A}), U_{B}\in \mathrm {U}(\mathcal {H}_{B})\) , and \(U_{AB}\in \mathrm {U}(\mathcal {H}_{A}\otimes \mathcal {H}_{B})\) such that $$\mathrm{S}\left(U_{AB}\rho_{AB}U^{\dagger}_{AB}||\sigma_{AB}\right)\geqslant \mathrm{S}\left(U_{A}\rho_{A}U^{\dagger}_{A}||\sigma_{A}\right) + \mathrm{S}\left(U_{B}\rho_{B}U^{\dagger}_{B}||\sigma_{B}\right), $$ where the reference state σ is required to be full-ranked. A numerical study on the conjectured inequality is conducted in this note. The results obtained indicate that the modified super-additivity inequality of relative entropy seems to hold for all qubit pairs.     

Kinetically modified non-minimal inflation with exponential frame function

We consider supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the \(\phi ^n\) potential with \(n=2\) or 4. We show that the coexistence of an exponential non-minimal coupling to gravity \(f_\mathcal{R}=\mathrm{e}^{c_\mathcal{R}\phi ^{p}}\) with a kinetic mixing of the form \(f_{\mathrm{K}}=c_{\mathrm{K}}f_\mathcal{R}^m\) can accommodate inflationary observables favored by the Planck and Bicep2/Keck Array results for \(p=1\) and 2, \(1\le m\le 15\) and \(2.6\times 10^{-3}\le r_{\mathcal {R}\mathrm{K}}=c_\mathcal{R}/c_{\mathrm{K}}^{p/2}\le 1,\) where the upper limit is not imposed for \(p=1\). Inflation is of hilltop type and it can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale. The supergravity embedding of these models is achieved employing two chiral gauge singlet supefields, a monomial superpotential and several (semi)logarithmic or semi-polynomial Kähler potentials.     

Ultrafast delocalization of hydrogen atoms in allene in intense laser fields

Ultrafast delocalization of hydrogen atoms in allene (CH₂=C=CH₂) induced by intense laser fields was investigated by the Coulomb explosion coincidence momentum imaging method. On the basis of the kinetic energy distributions of the fragment ions produced through the two three-body Coulomb explosion pathways, C₃H₄³⁺ ? H⁺ + CH⁺ + C₂H₂⁺\mathrm{C}_{3}\mathrm{H}_{4}^{3+} \rightarrow \mathrm{H}^{+} + \mathrm{CH}^{+} + \mathrm{C}_{2}\mathrm{H}_{2}^{+} and C₃H₄³⁺ ? H⁺ + C₂H⁺ +CH₂⁺\mathrm{C}_{3}\mathrm{H}_{4}^{3+} \rightarrow \mathrm{H}^{+} + \mathrm{C}_{2}\mathrm{H}^{+} +\mathrm{CH}_{2}^{+}, and the proton maps for both pathways, it was shown that the decomposition proceeds in a stepwise manner as well as in a concerted manner. The time scale of the hydrogen migration within an allene molecule was estimated to be ∼20 fs.     

Shift and broadening of emission lines in Nd<Superscript>3+</Superscript>:YAG laser crystal influenced by input energy

Spectroscopic properties of the flashlamp-pumped Nd ³⁺:YAG laser as a function of input energy were studied over the range of 18–75 J. The spectral widths and shifts of quasi-three-level and four-level inter-Stark emissions within the respective intermanifold transitions of \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -2.7pt}\mathrm {I}_{\mathrm {9/2}}\) and \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -2.7pt}\mathrm {I}_{\mathrm {11/2}}\) were investigated. The emission lines of \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -2.7pt}\mathrm {I}_{\mathrm {9/2}}\) shifted towards longer wavelength (red shift) and broadened, while the positions and linewidths of the \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -3.5pt}\mathrm {I}_{\mathrm {11/2}}\) transition lines remained constant by increasing the pumping energy. This is attributed to the thermal population as well as one-phonon and multiphonon emission processes in the ground state. This phenomenon degrades the output performance of the lasers.     

Confinement, average forces, and the Ehrenfest theorem for a one-dimensional particle

The topics of confinement, average forces, and the Ehrenfest theorem are examined for a particle in one spatial dimension. Two specific cases are considered: (i) A free particle moving on the entire real line, which is then permanently confined to a line segment or ‘a box’ (this situation is achieved by taking the limit V ₀?→?∞ in a finite well potential). This case is called ‘a particle-in-an-infinite-square-well-potential’. (ii) A free particle that has always been moving inside a box (in this case, an external potential is not necessary to confine the particle, only boundary conditions). This case is called ‘a particle-in-a-box’. After developing some basic results for the problem of a particle in a finite square well potential, the limiting procedure that allows us to obtain the average force of the infinite square well potential from the finite well potential problem is re-examined in detail. A general expression is derived for the mean value of the external classical force operator for a particle-in-an-infinite-square-well-potential, $\hat{F}$ . After calculating similar general expressions for the mean value of the position ( $\hat{X}$ ) and momentum ( $\hat{P}$ ) operators, the Ehrenfest theorem for a particle-in-an-infinite-square-well-potential (i.e., $\mathrm{d}\langle\hat{X}\rangle/\mathrm{d}t=\langle\hat{P}\rangle/M$ and $\mathrm{d}\langle\hat{P}\rangle/\mathrm{d}t=\langle\hat{F}\rangle$ ) is proven. The formal time derivatives of the mean value of the position ( $\hat{x}$ ) and momentum ( $\hat{p}$ ) operators for a particle-in-a-box are re-introduced. It is verified that these derivatives present terms that are evaluated at the ends of the box. Specifically, for the wave functions satisfying the Dirichlet boundary condition, the results, $\mathrm{d}\langle\hat{x}\rangle/\mathrm{d}t=\langle\hat{p}\rangle/M$ and $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\mathrm{b.t.}+\langle\hat{f}\rangle$ , are obtained where b.t. denotes a boundary term and $\hat{f}$ is the external classical force operator for the particle-in-a-box. Thus, it appears that the expected Ehrenfest theorem is not entirely verified. However, by considering a normalized complex general state that is a combination of energy eigenstates to the Hamiltonian describing a particle-in-a-box with v(x)?=?0 ( $\Rightarrow\hat{f}=0$ ), the result that the b.t. is equal to the mean value of the external classical force operator for the particle-in-an-infinite-square-well-potential is obtained, i.e., $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t$ is equal to $\langle\hat{F}\rangle$ . Moreover, the b.t. is written as the mean value of a quantity that is called boundary quantum force, f _B. Thus, the Ehrenfest theorem for a particle-in-a-box can be completed with the formula $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\langle{{f_\mathrm{B}}}\rangle$ .     

Local structure of Fe-doped In 2 O 3 films investigated by X-ray absorption fine structure spectroscopy

$(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ $(x=0.07, 0.09, 0.16, 0.22, 0.31)$ films were deposited on Si (100) substrates by RF-magnetron sputtering technique. The influence of Fe doping on the local structure of films was investigated by X-ray absorption spectroscopy (XAS) at Fe K-edge and L-edge. For the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ films with $x=0.07, 0.09 \mbox{ and } 0.16$ , Fe ions dissolve into $\mathrm{In}_{2}\mathrm{O}_{3}$ and substitute for $\mathrm{In}^{3+}$ sites with a mixed-valence state ( $\mathrm{Fe}^{2+}/\mathrm{Fe}^{3+}$ ) of Fe ions. However, a secondary phase of Fe metal clusters is formed in the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ films with $x=0.22 \mbox{ and } 0.31$ . The qualitative analyses of Fe-K edge extended X-ray absorption fine structure (EXAFS) reveal that the Fe–O bond length shortens and the corresponding Debye–Waller factor ( $\sigma^{2}$ ) increases with the increase of Fe concentration, indicating the relaxation of oxygen environment of Fe ions upon substitution. The anomalously large structural disorder and very short Fe–O distance are also observed in the films with high Fe concentration. Linear combination fittings at Fe L-edge further confirm the coexistence of $\mathrm{Fe}^{2+}$ and $\mathrm{Fe}^{3+}$ with a ratio of ${\sim}3:2$ ( $\mathrm{Fe}^{2+}: \mathrm{Fe}^{3+}$ ) for the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ film with $x=0.16$ . However, a significant fraction ( ${\sim}40~\mbox{at\%}$ ) of the Fe metal clusters is found in the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ film with $x=0.31$ .     

W diffusion in paramagnetic and ferromagnetic <Emphasis Type="Italic">α</Emphasis>-Fe

Diffusion of W in the 723–1153 K temperature range both in paramagnetic and ferromagnetic α-Fe was studied, diffusion couples were manufactured by W evaporation onto high-purity Fe samples. Measurements were made using the Heavy Ion Rutherford Backscattering (HIRBS) technique as the analysis tool. A straight Arrhenius plot was obtained in the paramagnetic region with a break at the Curie temperature (1043 K) followed by a curved plot at lower temperatures as a product of the effect of ferromagnetism on diffusion. A straight Arrhenius plot was obtained in the paramagnetic region with a break at the Curie temperature (1043 K) followed by a curved plot at lower temperatures resulting from the effect of ferromagnetism on diffusion. A previous developed model for the diffusion of non-magnetic impurities in ferromagnetic Fe fits the data perfectly well, giving a temperature dependent diffusivity according to

Effect of Y3+ substitution on the structural,dielectric, and electrical properties of nanosized ZnAl 2 O 4 spinel

In the present work, we have studied the structural, dielectric, and electrical properties of a series of nanosized $\mathrm{ZnAl}_{2-2x}\mathrm{Y}_{2x}\mathrm{O}_{4}$ ( $x = 0.00$ , 0.01, 0.02, 0.03, 0.04, 0.05, 0.07, and 0.10) system prepared by chemical coprecipitation method. Powder X-ray diffraction (XRD) was carried out to study the influence of $\mathrm{Y}^{3+}$ substitution on the crystal structure of these samples. High Resolution Transmission Electron Microscopy (HRTEM) images reveal the nanocrystalline nature of the samples. The Fourier Transform Infrared (FTIR) spectra confirmed the preference of $\mathrm{Y}^{3+}$ ions at the octahedral B site. The variation of dielectric constant and loss tangent (1 kHz to 1 MHz) at room temperature for all the samples show the normal behavior of spinel compounds. AC conductivity study reveals that the conduction is due to small polaron hopping. The electrical modulus analysis shows that nanocrystalline $\mathrm{ZnAl}_{2-2x}\mathrm{Y}_{2x}\mathrm{O}_{4}$ system exhibits non-Debye-type relaxation. The DC electrical resistivity measured in the temperature range 303–373 K was found to increase with temperature and yttrium content.     

A measurement of semileptonic B decaysto narrow orbitally-excited charm mesons

The decay chain is identified in a sample of 3.9 million hadronic Z decays collected with the OPAL detector at LEP. The branching ratio BR is measured to be for the J ^P =1⁺ (D⁰ ₁) state. For decays into the J ^P =2⁺ (D₂ ^*0) state, an upper limit of 1.4 x 10^-3 is placed on the branching ratio at the 95% confidence level.Received: 20 December 2002, Revised: 15 April 2003, Published online: 12 September 2003     

Time evolution of the Infrared Laser Induced Breakdown Spectroscopy of DNA bases Guanine and Adenine

Laser-Induced Breakdown Spectroscopy (LIBS) of DNA bases Guanine and Adenine was studied using a high-power CO₂ pulsed laser (λ=10.591 μm, τ _FWHM=64 ns and fluences ranging from 25 to 70 J/cm²). The strong emission of the adenine and guanine plasma, collected using a high-resolution spectrometer, at medium-vacuum conditions (4 Pa) and at 1 mm from the target, exhibits excited molecular bands of CN (B² Σ ⁺–X² Σ ⁺) and excited neutral H and ionized N⁺ and C⁺. The medium-weak emission is due to excited species C²⁺, C³⁺, N, O, O⁺, O²⁺ and molecular band systems of $\mathrm{C}_{2}(\mathrm{d}^{3}\varPi_{\mathrm{g}}\mbox{--}\mathrm{a}^{3}\varPi_{\mathrm{u}};\ \mathrm{D}^{1}\varSigma_{\mathrm{u}}^{+}\mbox{--}\mathrm{X}^{1}\varSigma_{\mathrm{g}}^{+})$ , OH(A² Σ ⁺–X² Π), NH(A³ Π–X³ Σ ^?), CH(A² Π–X² Π), $\mathrm{N}_{2}^{+}(\mathrm{B}^{2}\varSigma_{\mathrm{u}}^{+}\mbox{--} \mathrm{X}^{2}\varSigma_{\mathrm{g}}^{+})$ and N₂(C³ Π _u–B³ Π _g). We focus our attention on the temporal evolution of different atomic/ionic and molecular species. The velocity distributions for various (different) species were obtained from time-of-flight (TOF) measurements. Intensities of some lines from C⁺ were used for determining electron temperature and their Stark-broadened profiles were employed to estimate the temporal evolution of electron density.     

Effects of Si and Ti impurities on electrical properties of sol–gel-derived amorphous SrTa2O6 thin films by UV/O3 treatment

Sol–gel-derived SrTa₂O₆ thin films were fabricated at a low temperature of 500 °C. To improve their leakage current properties, additional UV/O₃-assisted annealing was performed from room temperature to 290 °C. UV/O₃ treatment at 290 °C gave a very low leakage current that was six orders of magnitude lower than that of an untreated thin film. During UV/O₃-assisted annealing, Si and Ti ions diffused from the substrates into the SrTa₂O₆ thin films and occupied the Ta⁵⁺ sites, subsequently generating Si^? and Ti^?. At a heating temperature of 290 °C, large amounts of Ti ions diffused throughout the SrTa₂O₆ thin film. These Ti ions contributed to the generation of inactive combinations of $(\mathrm{Si}^{-}\mbox{--}\mathrm{V}_{\mathrm{o}}^{+})^{+}\mbox{--}\mathrm{Ti}^{-}$ and $(\mathrm{Ti}^{-}\mbox{--}\mathrm{V}_{\mathrm{o}}^{+})^{+}\mbox{--}\mathrm{Ti}^{-}$ , which greatly reduced oxygen vacancies (V_o). Thus, the leakage current was significantly reduced.     

Reexploration of interacting holographic dark energy model: cases of interaction term excluding the Hubble parameter

In this paper, we make a deep analysis for the five typical interacting holographic dark energy models with the interaction terms \(Q=3\beta H_{0}\rho _\mathrm{{de}}\), \(Q=3\beta H_{0}\rho _\mathrm{{c}}\), \(Q=3\beta H_{0}(\rho _\mathrm{{de}}+\rho _\mathrm{c})\), \(Q=3\beta H_{0}\sqrt{\rho _\mathrm{{de}}\rho _\mathrm{c}}\), and \(Q=3\beta H_{0}\frac{\rho _\mathrm{{de}}\rho _{c}}{\rho _\mathrm{{de}}+\rho _\mathrm{c}}\), respectively. We obtain observational constraints on these models by using the type Ia supernova data (the Joint Light-Curve Analysis sample), the cosmic microwave background data (Planck 2015 distance priors), the baryon acoustic oscillations data, and the direct measurement of the Hubble constant. We find that the values of \(\chi _\mathrm{min}^2\) for all the five models are almost equal (around 699), indicating that the current observational data equally favor these IHDE models. In addition, a comparison with the cases of an interaction term involving the Hubble parameter H is also made.     

Search for charged Higgs bosons at LEP in general two Higgs doublet models

A search for pair-produced charged Higgs bosons was performed in the data collected by the DELPHI detector at LEP II at centre-of-mass energies from 189 GeV to 209 GeV. Five different final states, , , , and were considered, accounting for the major expected decays in type I and type II Two Higgs Doublet Models. No significant excess of data compared to the expected Standard Model processes was observed. The existence of a charged Higgs boson with mass lower than 76.7 GeV/c² (type I) or 74.4 GeV/c² (type II) is excluded at the 95% confidence level, for a wide range of the model parameters. Model independent cross-section limits have also been calculated.Received: 30 September 2003, Revised: 12 February 2004, Published online: 8 April 2004     

Spectroscopic properties of Ho 3 + -doped K–Sr–Al phosphate glasses

Trivalent holmium-doped K–Sr–Al phosphate glasses ( $\mathrm{P}_{2}\mathrm{O}_{5}$ – $\mathrm{K}_{2}\mathrm{O}$ –SrO– $\mathrm{Al}_{2}\mathrm{O}_{3}$ – $\mathrm{Ho}_{2}\mathrm{O}_{3}$ ) were prepared, and their spectroscopic properties have been evaluated using absorption, emission, and excitation measurements. The Judd–Ofelt theory has been used to derive spectral intensities of various absorption bands from measured absorption spectrum of 1.0 mol% $\mathrm{Ho}_{2}\mathrm{O}_{3}$ -doped K–Sr–Al phosphate glass. The Judd–Ofelt intensity parameters ( $\varOmega_{\lambda}$ , $\times10^{-20}~\mathrm{cm}^{2}$ ) have been determined of the order of $\varOmega_{2} = 11.39$ , $\varOmega_{4} = 3.59$ , and $\varOmega_{6} = 2.92$ , which in turn used to derive radiative properties such as radiative transition probability, radiative lifetime, branching ratios, etc. for excited states of $\mathrm{Ho}^{3+}$ ions. The radiative lifetimes for the ${}^{5}F_{4}$ , ${}^{5}S_{2}$ , and ${}^{5}F_{5}$ levels of $\mathrm{Ho}^{3+}$ ions are found to be 169, 296, and 317 μs, respectively. The stimulated emission cross-section for 2.05-μm emission was calculated by the McCumber theory and found to be $9.3\times10^{-2 1}~\mathrm{cm}^{2}$ . The wavelength-dependent gain coefficient with population inversion rate has been evaluated. The results obtained in the titled glasses are discussed systematically and compared with other $\mathrm{Ho}^{3+}$ -doped systems to assess the possibility for visible and infrared device applications.     

Oriented Percolation in One–dimensional 1/|<Emphasis Type="Italic">x</Emphasis>−<Emphasis Type="Italic">y</Emphasis>|<Superscript>2</Superscript> Percolation Models

We consider independent edge percolation models on ℤ, with edge occupation probabilities

Bimodal/schizophrenic neutrino as a bridge between inflation and dark energy

We consider the possibility to combine inflection point inflation and growing neutrino dark energy in a particular setup of bimodal/schizophrenic neutrino model in the framework of MSSM\(\otimes U(1)_{\mathrm{B}\mbox{--}\mathrm{L}}\). In order to obtain a varying neutrino mass, we make an assumption that a soft mass of \(\tilde{Z'}_{\mathrm{BL}}\) depends on a scalar field which plays the role of a cosmon field. We also investigate the possible effects of the cosmon field in the early universe such as modulated reheating and found that the induced density perturbation is negligible.     

Cluster generation under pulsed laser ablation of zinc oxide

Neutral and cationic Zn _n O _m clusters of various stoichiometry have been produced by nanosecond laser ablation of ZnO in vacuum and investigated by time-of-flight mass spectrometry. Particular attention was paid to the effect of laser wavelength (in the range from near-IR to UV) on cluster composition. Under 193-nm laser ablation, the charged clusters are essentially substoichiometric with Zn_nO_n-1⁺\mathrm{Zn}_{n}\mathrm{O}_{n-1}^{+} and Zn_nO_n-3⁺\mathrm{Zn}_{n}\mathrm{O}_{n-3}^{+} being the most abundant series. Both sub- and stoichiometric cationic clusters are generated in abundance at 532- and 1064-nm ablation whose composition depends on the cluster size. The reactivity of small stoichiometric Zn_nO_n⁺\mathrm{Zn}_{n}\mathrm{O}_{n}^{+} clusters (n<11) toward hydrogen is found to be high, while oxygen-deficient species are less reactive. The neutral plume particles are mainly stoichiometric with Zn₄O₄ tetramer being a magic cluster. It is suggested that the Zn₄O₄ loss is the dominant fragmentation channel of large zinc oxide clusters upon electron impact. Plume expansion conditions under ZnO ablation with visible and IR laser pulses are shown to be favorable for stoichiometric cluster formation.