Direct observation of Raman shifts in a fir superradiant laser

Fabry-Perot frequency measurements of FIR superradiant emission from D₂O at 99 μm are reported. Several Fabry-Perot scans at different frequency settings of the CO₂ pump laser show a shift in the FIR output spectrum equal, within experimental error, to the shift in input frequency of the CO₂ pump. The “superradiant” emission therefore of the D₂O 10_1,10(010) → 9_0,9(010) transition at 99 μm contains a strong Raman component.     

Thermionic constants and electron reflection for Ta (100) by the shelton retarding field method

The Shelton retarding field method has been employed to determine the thermionic constants of the (100) surface of tantalum in the temperature range 1500 to 1730 K: φ* = = 4.16 ± 0.05 V, dφdT= 56 ± 5 μ V/K, and A_R = 122 ± 26 A/cm²K².φ = 4.24 ± 0.05 V at300 K. A refined analysis of the Shelton method shows the importance of four reflection coefficients, because of which, A_R cannot be identified unambiguously as the preexponental constant appearing in the Richardson equation. The dependence on incident energy of the electron reflection coefficient of Ta(100) was observed in the range 0–100 eV. The positions at 4.5, 8.0, 11.3, and 17.0 eV of relative reflection maxima agree closely with those observed by others for W(100). Advances are described in instrumentation, in experimental technique, and in acquisition and analysis of data.     

Electronic structure of the valence bands of SnCl2 and SnBr2 studied by ultraviolet photoelectron spectroscopy

A photoelectron study of the outermost bands of solid-phase SnCl₂ and SnBr₂ using 40.81 eV photons is reported. The main features of the spectra are successfully interpreted in terms of molecular orbital theory for the appropriate isolated molecules.     

Characterization of polycrystalline (Na,K)β/β′- alumina ceramics

K β′-alumina is unstable at >1300°C. Mixed alkali β′-alumina has a variable stability depending on the alkali ratio, [K⁺]/([Na⁺]+[K⁺]). For f(β)<[K⁺]/([Na⁺]+[K⁺]), the β′-Al₂O₃ phase decomposes to Kβ-Al₂O₃ 0997 0815 V 3 and a solid solution of Na β′-Al₂O₃ and K β′-Al₂O₃. For f(β)=[K⁺]/([Na⁺]+[K⁺], the ceramic consists of K β-Al₂O₃ and Naβ′-Al₂O₃ and for f(β)>[K⁺]/([Na⁺]+[K⁺]), the excess Na⁺ after Na β′-Al₂O₃ dissolves in the β phase, giving Na β-Al₂O₃/K β-Al₂O₃ solid solution and Na β′-Al₂O₃. These sequences were confirmed by measuring the dependence of the c-axis lattice parameters of β- and β′-Al₂O₃ phases on the f(β), and the change of these parameters during the ion-exchange of Na⁺ and K⁺ ions.     

Stationary response of combined linear dynamic systems to stationary excitation

The stationary response of a broad class of combined linear systems to stationary random excitation is determined by the normal mode method. The systems are characterized by a viscously damped simple beam (or string, membrane, thin plate or shell, etc.) connected at discrete points to a multiplicity of viscously damped linear oscillators and/or masses. The solution of the free vibration problem by way of Green functions and the deterministic forced vibration problem by modal analysis for both proportional and non-proportional damping is reviewed. The orthogonality relation for the natural modes of vibration is used to derive a unique relationship between the cross-spectral density functions of the applied forces and the cross-spectral density functions of the generalized forces. Finally, the response spectral density functions and the mean square responses of the beam and oscillators are derived in closed form, exact for the proportionally damped system and approximate for the non-proportionally damped system.     

A commutativity theorem

LetR be an associative ring with identity which satisfies the identities(xy) ^k =(yx) ^k and(xy) ^l =(yx) ^l , wherek andl are relatively prime positive integers, depending onx andy. ThenR is commutative. Moreover, examples are given which show thatR need not be commutative if either of the above identities is dropped. This theorem is also true for groups. Presented by N. S. Mendelsohn.     

Spray-drying and fabrication of superionic conducting sodium rare-earth silicates

Fine precursor powders of particle diameter of 0.50–7 μm and high surface area (9 m²/g) for superionic conducting Na₅RESi₄O₁₂ (RE=Gd, Y) were successfully produced by spray-drying and an optimised calcination procedure. Using these powders, dense sinters (>98% of theoretical) with ?(NGS) or $\text{?(}\text{NGS}\text{)=1.0}$ (the proposed parameter for purity) were obtained under normal sintering conditions. 300°C ionic resistivities were calculated from ac impedance and had values of 5.6 Ω cm with an activation energy for conduction of 4.5 kcal/mol for Na₅GdSi₄O₁₂ and 7.7 Ω cm and 5.9 kcal/mol for Na₅YSi₄O₁₂. These values were dependent on the ?(NGS) or ?(NYS).     

Electrostatically mediated specific adsorption of small molecules in metallo-organic frameworks

We investigate the interaction of ethylene and ethane with a Cu-tricarboxylate complex and show that at low loadings the lighter molecule has a higher binding energy as a result of an increased interaction with the framework Cu and stronger hydrogen bonding with the basic framework oxygens. This leads to selective adsorption of ethylene by a factor of about 2 at low pressure, which is overcome by the stronger van der Waals interaction of ethane at high loadings, explaining recent literature data. The results suggest the possibility of separation of light hydrocarbons at low pressures or in trace amounts.     

<Emphasis FontCategory="NonProportional">pyomo.dae</Emphasis>: a modeling and automatic discretization framework for optimization with differential and algebraic equations

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.