Lattice instabilities in Cs2MFe(CN)6 (M = Mg2+, Ca2+, and Sr2+): The crystal structure of Cs2BaFe(CN)6·2H2O

The room temperature Raman spectra of Cs₂MFe(CN)₆ (M = Mg²⁺, Ca²⁺, and Sr²⁺) suggest that these salts undergo phase transformations similar to those found in Cs₂LiCr(CN)₆ where the distortion from the high-symmetry phase proceeds primarily along two modes of vibration. The distortion involves an antiferroelectric rotation of the hexacyanide moiety and a cesium translation. On the basis of the spectra a correlation has been made between the size of M and the apparent transition temperature. In going down the alkaline earths, the apparent transition temperature increases. The structure of the barium salt determined at room temperature shows the crystal latitce contains two waters of hydration. Many similarities have been found between Cs₂BaFe(CN)₆·2H₂O and the low-symmetry phase structure of Cs₂LiCr(CN)₆.     

Current fluctuations from various crystal faces of a clean tungsten field emitter

The temperature, frequency and current dependence of current fluctuations have been measured for the (310), (112) and (100) planes of a tungsten field emitter. The rms percent fluctuation of the current at 900 K was 8.7, 1.5 and 0.13% and the threshold temperature for current fluctuation was 300, 650 and 1000 K for the (310), (112) and (100) planes respectively. Based on the results reported here it is concluded that the current fluctuations arise from the generation of mobile atoms on net plane terraces.     

Oscillation of nonlinear vector differential equations

Summary Oscillation criteria are obtained for vector partial differential equations of the type Δv+b(x, v)v=0, x∈G, v∈E^m, where G is an exterior domain in E_n, and b is a continuous nonnegative valued function in G × E^m. A solution v: G→E^m is called h-oscillatory in G whenever the scalar product [v(x), h] (|h|=1) has zeros x in G with |x| arbitrarily large. It is shown that the spherical mean of [v(x), h] over a hypersphere of radius r in Eⁿ satisfies a nonlinear ordinary differential inequality. As a consequence, the main theorems give sufficient conditions on b(x, t), depending upon the dimension n, for all solutions v to be h-oscillatory in G. Entrata in Redazione il 26 giugno 1975.     

A Stochastic Model for Bidding

Competitive bidding situations involve considering a multiplicity of factors. Organizations must be able to weigh the relative probability of potential projects based on resource usage, project duration and competitor actions to decide which of many possible bids to submit. A bidding strategy designed to maximize expected long run return is crucial, since an organization can usually submit only one bid per project.This paper presents a family of stochastic dynamic programming models considering different bidding situations. Several projects, each with several potential bids, are available for each situation. The objective is to determine what bidding strategy will maximize expected returns. Models are developed for two principle bidding situations: sequential, where projects are bid individually; and simultaneous, where several projects are bid at one time. Next, the effects of over- or under-commitment of resources are incorporated into the models. Finally, changes in project timing and the resultant effects on bidding strategy are included.A numerical example traces the changes in bidding strategy which occur as the models are expanded. The general formulation of bidding problems is also discussed, including changing the bid success probabilities due to competitor actions, the possibility of crashing projects and alternate methods of performing projects.