The electronic structure,magnetic,and optical properties of two-dimensional(2D)GaSe doped with rare earth elements X(X=Sc,Y,La,Ce,Eu)were calculated using the first-principles plane wave method based on den-sity funct...The electronic structure,magnetic,and optical properties of two-dimensional(2D)GaSe doped with rare earth elements X(X=Sc,Y,La,Ce,Eu)were calculated using the first-principles plane wave method based on den-sity functional theory.The results show that intrinsic 2D GaSe is a p-type nonmagnetic semiconductor with an indi-rect bandgap of 2.6611 eV.The spin-up and spin-down channels of Sc-,Y-,and La-doped 2D GaSe are symmetric,they are non-magnetic semiconductors.The magnetic moments of Ce-and Eu-doped 2D GaSe are 0.908μ_(B)and 7.163μ_(B),which are magnetic semiconductors.Impurity energy levels appear in both spin-up and spin-down chan-nels of Eu-doped 2D GaSe,which enhances the probability of electron transition.Compared with intrinsic 2D GaSe,the static dielectric constant of the doped 2D GaSe increases,and the polarization ability is strengthened.The ab-sorption spectrum of the doped 2D GaSe shifts in the low-energy direction,and the red-shift phenomenon occurs,which extends the absorption spectral range.The optical reflection coefficient of the doped 2D GaSe is improved in the low energy region,and the improvement of Eu-doped 2D GaSe is the most obvious.展开更多
In this study,a pulsed,high voltage driven hollow-cathode electron beam sources through an optical trigger is designed with characteristics of simple structure,low cost,and easy triggering.To validate the new design,t...In this study,a pulsed,high voltage driven hollow-cathode electron beam sources through an optical trigger is designed with characteristics of simple structure,low cost,and easy triggering.To validate the new design,the characteristics of hollow-cathode discharge and electron beam characterization under pulsed high voltage drive are studied experimentally and discussed by discharge characteristics and analyses of waveform details,respectively.The validation experiments indicate that the pulsed high voltage supply significantly improves the frequency and stability of the discharge,which provides a new solution for the realization of a high-frequency,high-energy electron beam source.The peak current amplitude in the high-energy electron beam increases from 6.2 A to 79.6 A,which indicates the pulsed power mode significantly improves the electron beam performance.Besides,increasing the capacitance significantly affects the highcurrent,lower-energy electron beam more than the high-energy electron beam.展开更多
The electron optical column for the variable rectangular-shaped beam lithographysystem DJ-2 is described,with emphasis on the analysis of the optical configuration and theshaping deflection compensation.In this column...The electron optical column for the variable rectangular-shaped beam lithographysystem DJ-2 is described,with emphasis on the analysis of the optical configuration and theshaping deflection compensation.In this column the variable spot shaping is performed with aminimum number of lenses by a more reasonable optical scheme.A high-sensitivity electrostaticshaping deflector with sequential parallel-plates is implemented for high-speed spot shaping.With a precise linear and rotational approach,the spot current density,the edge resolution aswell as the position of spot origin remain unchanged when the spot size varies.Experiments showthat the spot current density of over 0.4 A/cm^2 is obtained with a tungsten hairpin cathode,andthe edge resolution is better than 0.2μm within a 2×2 mm^2 field size.展开更多
Cyclo[18]carbon has received considerable attention thanks to its novel geometric configuration and special electronic structure.Superalkalis have low ionization energy.Doping a superalkali in cyclo[18]carbon is an ef...Cyclo[18]carbon has received considerable attention thanks to its novel geometric configuration and special electronic structure.Superalkalis have low ionization energy.Doping a superalkali in cyclo[18]carbon is an effective method to improve the optical properties of the system because considerable electron transfer occurs.In this paper,the geometry,bonding properties,electronic structure,absorption spectrum,and nonlinear optical(NLO)properties of superalkaline M_(3)O(M=Li,Na)-doped cyclo[18]carbon were studied by using density functional theory.M_(3)O and the C_(18) rings are not coplanar.The C_(18) ring still exhibits alternating long and short bonds.The charge transfer between M_(3)O and C_(18) forms stable[M_(3)O]+[C_(18)]-ionic complexes.C_(18)M_(3)O(M=Li,Na)shows striking optical nonlinearity,i.e.,their first-and second-order hyperpolarizability(βvec andγ||)increase considerably atλ=1907 nm and 1460 nm.展开更多
Structural, electronic and optical properties of Sc-based aluminum-nitride alloy have been carried out with first-principles methods using both local density approximation (LDA) and Heyd-Scuseria-Ernzerhof (HSE) hybri...Structural, electronic and optical properties of Sc-based aluminum-nitride alloy have been carried out with first-principles methods using both local density approximation (LDA) and Heyd-Scuseria-Ernzerhof (HSE) hybrid functional. This latter provides a more accurate description of the lattice parameters, enthalpy of formation, electronic and optical properties of our alloy than standard DFT. We found the transition from wurtzite to rocksalt structures at 61% of Sc concentration. By increasing the scandium concentration, the lattice parameters and the band gap decrease. The HSE band gap is in good agreement with available experimental data. The existence of the strong hybridization between Sc 3d and N 2p indicates the transport of electrons from Sc to N atoms. Besides, it is shown that the insertion of the Sc atom leads to the redshift of the optical absorption edge. The optical absorption of Sc<sub>x</sub>Al<sub>1-x</sub>N is found to decrease with increasing Sc concentrations in the low energy range. Because of this, Sc<sub>x</sub>Al<sub>1-x</sub>N have a great potential for applications in photovoltaics and photocatalysis.展开更多
The band structure,DOSs,and optical properties of(Y_(0.75)Ca_(0.25))(Cu_(0.75)Mn_(0.25))SO,including dielectric function,absorption function,reflection function,and energy loss spectrum were studied by using the first...The band structure,DOSs,and optical properties of(Y_(0.75)Ca_(0.25))(Cu_(0.75)Mn_(0.25))SO,including dielectric function,absorption function,reflection function,and energy loss spectrum were studied by using the first-principles calculation.The calculation results indicate that(Y_(0.75)Ca_(0.25))(Cu_(0.75)Mn_(0.25))SO is a direct bandgap semiconductor with a bandgap of 1.1 eV.The Fermi surface is asymmetric and exhibits spin splitting phenomenon.The new type of dilute magnetic semiconductor(Y_(0.75)Ca_(0.25))(Cu_(0.75)Mn_(0.25))SO exhibits significant light loss around 70 eV,with light reflection gradually increasing after 30 eV,and light absorption mainly occurring around 8-30 eV.These results also provide a basis for the discovery of more types of 1111 phase new dilute magnetic semiconductors in the future.展开更多
This paper describes a prototype power delivery system developed for high voltage electronic current transformer (ECT) that uses laser light to transfer power to and communicates with the primary converter. The desi...This paper describes a prototype power delivery system developed for high voltage electronic current transformer (ECT) that uses laser light to transfer power to and communicates with the primary converter. The design is based on optical-to-electrical power converters, solid-state diode lasers and optical fibers. Command signals are transmitted via the same up-fiber used to send power from secondary power supply to primary converter. The upward data transmission is completed during the brief interruption of power delivery without affecting steady power-supply. A simple comparator added to the primary converter can take the command data. Experimental results show that the fibers can provide reliable up-link for data transmission at 200 kb/s from the secondary to the primary converter. Based on the delivery system, the secondary converter can control three auxiliary channels to provide additional information. These monitoring channels are used in a time-multiplexing mode to provide information about the operation temperature, voltage and current at the remote unit for monitoring the ECT. This preventive maintenance or built-in test can increase reliability by giving early warning for necessary maintenance request.展开更多
X-ray laser based on OFI is a promising way to realize the table-top X-ray laser.A simple model to describe the electron energy distribution in plasma produced by circularly polarized optical-field-induced ionization ...X-ray laser based on OFI is a promising way to realize the table-top X-ray laser.A simple model to describe the electron energy distribution in plasma produced by circularly polarized optical-field-induced ionization is constructed on the basis of ADK tunneling ionization theory.The ionization rate,threshold intensity,residual energy and electron energy distribution of Pd-like Xe system based on optical-field-induced ionization are calculated.The results are useful to further experments on X-ray laser of Pa-like Xe system.展开更多
The comparative analysis of modem mathematical models for 3D problems in electron optics is presented. The new approach to solve the electron optics problems in three dimensions is presented. It is based on the princi...The comparative analysis of modem mathematical models for 3D problems in electron optics is presented. The new approach to solve the electron optics problems in three dimensions is presented. It is based on the principal ray method suggested by G. Grinberg in 1948. That perspective approach was not realized before for full three-dimensional electron optic systems, probably because of the complexity of its mathematical apparatus. We describe the analytical technique of the BEM (boundary element method) for the field evaluation, and 3rd order aberration expansion for the trajectory analysis. The first version of such computer code "OPTICS-3" and some results of numerical simulations with this code were presented.展开更多
The decomposition method was successfully used in solving of 3D problems with complex geometry shape in electron optics for the FDM (Finite Difference Method) and FEM (Finite Element Method) mostly to implement fa...The decomposition method was successfully used in solving of 3D problems with complex geometry shape in electron optics for the FDM (Finite Difference Method) and FEM (Finite Element Method) mostly to implement fast and robust parallel algorithms and computer codes. We suggest a new version of similar approach for the BEM (Boundary Element Method) based on the alternating method by Schwartz. This approach substantially reduce the dimension of dense global matrix of algebraic system produced by BEM algorithm to solve a complex problem on as single CPU (Central Processor Unit) desktop computer. New algorithm is iterative one, but exponential convergence for the Schwatlz's algorithm creates the fast numerical procedures. We describe the results of numerical simulation for a multi electrode ion transport system. The algorithms were implemented in the computer code "POISSON-3".展开更多
Power-electronic devices are widely used in various applications, such as voltage and frequency control for transmitting and converting electric power. As these devices are becoming increasingly important, there is a ...Power-electronic devices are widely used in various applications, such as voltage and frequency control for transmitting and converting electric power. As these devices are becoming increasingly important, there is a need to reduce their losses and improve their performance to reduce electric power consumption. Current power semiconductor devices, such as inverters, are made of silicon (Si), but the performance of these Si power devices is reaching its limit due to physical properties and energy bandgap. To address this issue, recent developments in wide bandgap (WBG) semiconductor materials, such as silicon carbide (SiC) and gallium nitride (GaN), offer the potential for a new generation of power semiconductor devices that can perform significantly better than silicon-based devices. In this research, a green synthesized copper-zinc-tin-sulfide (CZTS) nanoparticle is proposed as a new WBG semiconductor material that could be used for optical and electronic devices. Its synthesis, consisting of the production methods and materials used, is discussed. The characterization is also discussed, and further research is recommended in the later sections to enable the continual advancement of this technology.展开更多
Rare earth luminescent materials have attracted significant attention due to their wide-ranging applications in the field of optoelectronics. This study aims to delve into the electronic structure and optical properti...Rare earth luminescent materials have attracted significant attention due to their wide-ranging applications in the field of optoelectronics. This study aims to delve into the electronic structure and optical properties of rare earth luminescent materials, with the goal of uncovering their importance in luminescence mechanisms and applications. Through theoretical calculations and experimental methods, we conducted in-depth analyses on materials composed of various rare earth elements. Regarding electronic structure, we utilized computational techniques such as density functional theory to investigate the band structure, valence state distribution, and electronic density of states of rare earth luminescent materials. The results indicate that the electronic structural differences among different rare earth elements notably influence their luminescence performance, providing crucial clues for explaining the luminescence mechanism. In terms of optical properties, we systematically examined the material’s optical behaviors through fluorescence spectroscopy, absorption spectroscopy, and other experimental approaches. We found that rare earth luminescent materials exhibit distinct absorption and emission characteristics at different wavelengths, closely related to the transition processes of their electronic energy levels. Furthermore, we studied the influence of varying doping concentrations and impurities on the material’s optical properties. Experimental outcomes reveal that appropriate doping can effectively regulate the emission intensity and wavelength, offering greater possibilities for material applications. In summary, this study comprehensively analyzed the electronic structure and optical properties of rare earth luminescent materials, providing deep insights into understanding their luminescence mechanisms and potential value in optoelectronic applications. In the future, these research findings will serve as crucial references for the technological advancement in fields such as LEDs, lasers, and bioimaging.展开更多
A loop diagram approach to the nonlinear optical conductivity of an electron-phonon system is introduced. This approach can be categorized as another Feynman-like scheme because all contributions to the self-energy te...A loop diagram approach to the nonlinear optical conductivity of an electron-phonon system is introduced. This approach can be categorized as another Feynman-like scheme because all contributions to the self-energy terms can be grouped into topologically-distinct loop diagrams. The results for up to the first order nonlinear conductivity are identical to those derived using the KC reduction identity (KCRI) and the state- dependent projection operator (SDPO) introduced by the present authors. The result satisfies the “population criterion” in that the population of electrons and phonons appear independently or the Fermi distributions are multiplied by the Planck distributions in the formalism. Therefore it is possible, in an organized manner, to present the phonon emissions and absorptions as well as photon absorptions in all electron transition processes. In additions, the calculation needed to obtain the line shape function appearing in the energy denominator of the conductivity can be reduced using this diagram method. This method shall be called the “KC loop diagram method”, since it originates from proper application of KCRI’s and SDPO’s.展开更多
文摘The electronic structure,magnetic,and optical properties of two-dimensional(2D)GaSe doped with rare earth elements X(X=Sc,Y,La,Ce,Eu)were calculated using the first-principles plane wave method based on den-sity functional theory.The results show that intrinsic 2D GaSe is a p-type nonmagnetic semiconductor with an indi-rect bandgap of 2.6611 eV.The spin-up and spin-down channels of Sc-,Y-,and La-doped 2D GaSe are symmetric,they are non-magnetic semiconductors.The magnetic moments of Ce-and Eu-doped 2D GaSe are 0.908μ_(B)and 7.163μ_(B),which are magnetic semiconductors.Impurity energy levels appear in both spin-up and spin-down chan-nels of Eu-doped 2D GaSe,which enhances the probability of electron transition.Compared with intrinsic 2D GaSe,the static dielectric constant of the doped 2D GaSe increases,and the polarization ability is strengthened.The ab-sorption spectrum of the doped 2D GaSe shifts in the low-energy direction,and the red-shift phenomenon occurs,which extends the absorption spectral range.The optical reflection coefficient of the doped 2D GaSe is improved in the low energy region,and the improvement of Eu-doped 2D GaSe is the most obvious.
基金supported by National Natural Science Foundation of China(No.12102099)the National Key R&D Program of China(No.2021YFC2202700)the Outstanding Academic Leader Project of Shanghai(Youth)(No.23XD1421700),respectively。
文摘In this study,a pulsed,high voltage driven hollow-cathode electron beam sources through an optical trigger is designed with characteristics of simple structure,low cost,and easy triggering.To validate the new design,the characteristics of hollow-cathode discharge and electron beam characterization under pulsed high voltage drive are studied experimentally and discussed by discharge characteristics and analyses of waveform details,respectively.The validation experiments indicate that the pulsed high voltage supply significantly improves the frequency and stability of the discharge,which provides a new solution for the realization of a high-frequency,high-energy electron beam source.The peak current amplitude in the high-energy electron beam increases from 6.2 A to 79.6 A,which indicates the pulsed power mode significantly improves the electron beam performance.Besides,increasing the capacitance significantly affects the highcurrent,lower-energy electron beam more than the high-energy electron beam.
文摘The electron optical column for the variable rectangular-shaped beam lithographysystem DJ-2 is described,with emphasis on the analysis of the optical configuration and theshaping deflection compensation.In this column the variable spot shaping is performed with aminimum number of lenses by a more reasonable optical scheme.A high-sensitivity electrostaticshaping deflector with sequential parallel-plates is implemented for high-speed spot shaping.With a precise linear and rotational approach,the spot current density,the edge resolution aswell as the position of spot origin remain unchanged when the spot size varies.Experiments showthat the spot current density of over 0.4 A/cm^2 is obtained with a tungsten hairpin cathode,andthe edge resolution is better than 0.2μm within a 2×2 mm^2 field size.
基金Project supported by the Natural Science Foundation of Anhui Province(Grant No.1908085MA12)the National Natural Science Foundation of China(Grant No.21703222)。
文摘Cyclo[18]carbon has received considerable attention thanks to its novel geometric configuration and special electronic structure.Superalkalis have low ionization energy.Doping a superalkali in cyclo[18]carbon is an effective method to improve the optical properties of the system because considerable electron transfer occurs.In this paper,the geometry,bonding properties,electronic structure,absorption spectrum,and nonlinear optical(NLO)properties of superalkaline M_(3)O(M=Li,Na)-doped cyclo[18]carbon were studied by using density functional theory.M_(3)O and the C_(18) rings are not coplanar.The C_(18) ring still exhibits alternating long and short bonds.The charge transfer between M_(3)O and C_(18) forms stable[M_(3)O]+[C_(18)]-ionic complexes.C_(18)M_(3)O(M=Li,Na)shows striking optical nonlinearity,i.e.,their first-and second-order hyperpolarizability(βvec andγ||)increase considerably atλ=1907 nm and 1460 nm.
文摘Structural, electronic and optical properties of Sc-based aluminum-nitride alloy have been carried out with first-principles methods using both local density approximation (LDA) and Heyd-Scuseria-Ernzerhof (HSE) hybrid functional. This latter provides a more accurate description of the lattice parameters, enthalpy of formation, electronic and optical properties of our alloy than standard DFT. We found the transition from wurtzite to rocksalt structures at 61% of Sc concentration. By increasing the scandium concentration, the lattice parameters and the band gap decrease. The HSE band gap is in good agreement with available experimental data. The existence of the strong hybridization between Sc 3d and N 2p indicates the transport of electrons from Sc to N atoms. Besides, it is shown that the insertion of the Sc atom leads to the redshift of the optical absorption edge. The optical absorption of Sc<sub>x</sub>Al<sub>1-x</sub>N is found to decrease with increasing Sc concentrations in the low energy range. Because of this, Sc<sub>x</sub>Al<sub>1-x</sub>N have a great potential for applications in photovoltaics and photocatalysis.
文摘The band structure,DOSs,and optical properties of(Y_(0.75)Ca_(0.25))(Cu_(0.75)Mn_(0.25))SO,including dielectric function,absorption function,reflection function,and energy loss spectrum were studied by using the first-principles calculation.The calculation results indicate that(Y_(0.75)Ca_(0.25))(Cu_(0.75)Mn_(0.25))SO is a direct bandgap semiconductor with a bandgap of 1.1 eV.The Fermi surface is asymmetric and exhibits spin splitting phenomenon.The new type of dilute magnetic semiconductor(Y_(0.75)Ca_(0.25))(Cu_(0.75)Mn_(0.25))SO exhibits significant light loss around 70 eV,with light reflection gradually increasing after 30 eV,and light absorption mainly occurring around 8-30 eV.These results also provide a basis for the discovery of more types of 1111 phase new dilute magnetic semiconductors in the future.
基金Project supported by the National Natural Science Foundation of China (Grant No.50447006)
文摘This paper describes a prototype power delivery system developed for high voltage electronic current transformer (ECT) that uses laser light to transfer power to and communicates with the primary converter. The design is based on optical-to-electrical power converters, solid-state diode lasers and optical fibers. Command signals are transmitted via the same up-fiber used to send power from secondary power supply to primary converter. The upward data transmission is completed during the brief interruption of power delivery without affecting steady power-supply. A simple comparator added to the primary converter can take the command data. Experimental results show that the fibers can provide reliable up-link for data transmission at 200 kb/s from the secondary to the primary converter. Based on the delivery system, the secondary converter can control three auxiliary channels to provide additional information. These monitoring channels are used in a time-multiplexing mode to provide information about the operation temperature, voltage and current at the remote unit for monitoring the ECT. This preventive maintenance or built-in test can increase reliability by giving early warning for necessary maintenance request.
基金Sponsored by the National Natural Science Foundation of China(Grant No.10774033)the Harbin Science and Technology Innovation Fund(Grant No.RC2007QN017030)+1 种基金the HIT Foundation(Grant No.HIT2003.05)the Program of Excellent Team in Harbin Institute of Technology
文摘X-ray laser based on OFI is a promising way to realize the table-top X-ray laser.A simple model to describe the electron energy distribution in plasma produced by circularly polarized optical-field-induced ionization is constructed on the basis of ADK tunneling ionization theory.The ionization rate,threshold intensity,residual energy and electron energy distribution of Pd-like Xe system based on optical-field-induced ionization are calculated.The results are useful to further experments on X-ray laser of Pa-like Xe system.
文摘The comparative analysis of modem mathematical models for 3D problems in electron optics is presented. The new approach to solve the electron optics problems in three dimensions is presented. It is based on the principal ray method suggested by G. Grinberg in 1948. That perspective approach was not realized before for full three-dimensional electron optic systems, probably because of the complexity of its mathematical apparatus. We describe the analytical technique of the BEM (boundary element method) for the field evaluation, and 3rd order aberration expansion for the trajectory analysis. The first version of such computer code "OPTICS-3" and some results of numerical simulations with this code were presented.
文摘The decomposition method was successfully used in solving of 3D problems with complex geometry shape in electron optics for the FDM (Finite Difference Method) and FEM (Finite Element Method) mostly to implement fast and robust parallel algorithms and computer codes. We suggest a new version of similar approach for the BEM (Boundary Element Method) based on the alternating method by Schwartz. This approach substantially reduce the dimension of dense global matrix of algebraic system produced by BEM algorithm to solve a complex problem on as single CPU (Central Processor Unit) desktop computer. New algorithm is iterative one, but exponential convergence for the Schwatlz's algorithm creates the fast numerical procedures. We describe the results of numerical simulation for a multi electrode ion transport system. The algorithms were implemented in the computer code "POISSON-3".
文摘Power-electronic devices are widely used in various applications, such as voltage and frequency control for transmitting and converting electric power. As these devices are becoming increasingly important, there is a need to reduce their losses and improve their performance to reduce electric power consumption. Current power semiconductor devices, such as inverters, are made of silicon (Si), but the performance of these Si power devices is reaching its limit due to physical properties and energy bandgap. To address this issue, recent developments in wide bandgap (WBG) semiconductor materials, such as silicon carbide (SiC) and gallium nitride (GaN), offer the potential for a new generation of power semiconductor devices that can perform significantly better than silicon-based devices. In this research, a green synthesized copper-zinc-tin-sulfide (CZTS) nanoparticle is proposed as a new WBG semiconductor material that could be used for optical and electronic devices. Its synthesis, consisting of the production methods and materials used, is discussed. The characterization is also discussed, and further research is recommended in the later sections to enable the continual advancement of this technology.
文摘Rare earth luminescent materials have attracted significant attention due to their wide-ranging applications in the field of optoelectronics. This study aims to delve into the electronic structure and optical properties of rare earth luminescent materials, with the goal of uncovering their importance in luminescence mechanisms and applications. Through theoretical calculations and experimental methods, we conducted in-depth analyses on materials composed of various rare earth elements. Regarding electronic structure, we utilized computational techniques such as density functional theory to investigate the band structure, valence state distribution, and electronic density of states of rare earth luminescent materials. The results indicate that the electronic structural differences among different rare earth elements notably influence their luminescence performance, providing crucial clues for explaining the luminescence mechanism. In terms of optical properties, we systematically examined the material’s optical behaviors through fluorescence spectroscopy, absorption spectroscopy, and other experimental approaches. We found that rare earth luminescent materials exhibit distinct absorption and emission characteristics at different wavelengths, closely related to the transition processes of their electronic energy levels. Furthermore, we studied the influence of varying doping concentrations and impurities on the material’s optical properties. Experimental outcomes reveal that appropriate doping can effectively regulate the emission intensity and wavelength, offering greater possibilities for material applications. In summary, this study comprehensively analyzed the electronic structure and optical properties of rare earth luminescent materials, providing deep insights into understanding their luminescence mechanisms and potential value in optoelectronic applications. In the future, these research findings will serve as crucial references for the technological advancement in fields such as LEDs, lasers, and bioimaging.
文摘A loop diagram approach to the nonlinear optical conductivity of an electron-phonon system is introduced. This approach can be categorized as another Feynman-like scheme because all contributions to the self-energy terms can be grouped into topologically-distinct loop diagrams. The results for up to the first order nonlinear conductivity are identical to those derived using the KC reduction identity (KCRI) and the state- dependent projection operator (SDPO) introduced by the present authors. The result satisfies the “population criterion” in that the population of electrons and phonons appear independently or the Fermi distributions are multiplied by the Planck distributions in the formalism. Therefore it is possible, in an organized manner, to present the phonon emissions and absorptions as well as photon absorptions in all electron transition processes. In additions, the calculation needed to obtain the line shape function appearing in the energy denominator of the conductivity can be reduced using this diagram method. This method shall be called the “KC loop diagram method”, since it originates from proper application of KCRI’s and SDPO’s.