Shades of orthodoxy in Rees-Sushkevich varieties

It is shown that, within the class of Rees-Sushkevich varieties that are generated by completely (0-) simple semigroups over groups of exponent dividing n, there is a hierarchy of varieties determined by the lengths of the products of idempotents that will, if they fall into a group ℋ-class, be idempotent. Moreover, the lattice of varieties generated by completely (0-) simple semigroups over groups of exponent dividing n, with the property that all products of idempotents that fall into group ℋ-classes are idempotent, is shown to be isomorphic to the direct product of the lattice of varieties of groups with exponent dividing n and the lattice of exact subvarieties of a variety generated by a certain five element completely 0-simple semigroup.     

General quantum mechanical canonical point transformations

Problems related to the operator form of the generalized canonical momenta in quantum mechanics are resolved by use of the general quantum mechanical canonical point transformation method. This method can be applied to any general canonical point transformation irrespective of the relationship between the domains of the original and transformed variables. The differential representation of the original canonical momenta p_i in the original coordinate space is ?i \(\begin{array}{*{20}c} / \\ h \\ \end{array}\) ?/?x _i and of the transformed canonical momentap _i ′ in the transformed coordinate space is ?i \(\begin{array}{*{20}c} / \\ h \\ \end{array}\) ?/?x _i ′. Relationships are derived between the eigenvalues of the original and transformed momenta in either space. The ordering problem for general point transformations is discussed and is shown to be solved. As an example of the generality of the method, it is demonstrated on the point transformation in three dimensions from Cartesian rectilinear to spherical rectilinear coordinates.     

Über die Reduktion von Metalloxyden mit Aluminiumkarbid

Analytical and Bioanalytical Chemistry -     

Ein neues Barometer

Ohne Zusammenfassung     

Thermodynamics of ionic solid solutions: II. Discontinuous series: A new treatment of existing distribution data

A method of finding the activity coefficients of salts, anhydrous or hydrated, in binary solid solutions, described in an earlier paper as it applies to continuous series, has been applied to discontinuous series. The salts must differ with respect to only one ion. The method requires isothermal distribution data for equilibria between liquid (aqueous) and solid solutions in the ternary system consisting of the two salts and water. The following salt pairs were used for illustration: K(I/Br) at 0, 15, 25, 35, and 50°C., (NH₄/K)SCN at 0, 30, 60, and 90°C., (K/Tl)C10₃ at 10°C., and (NH₄/K)SO₃NH₂, (NH₄/K)Br, (Mg/Co)SO₄-7H₂O, and (Mn/Cu) SO₄.n H₂O-all at 25°C. Two kinds of behavior were noted and treated differently: systems in which the two series have the same, and those in which they have different crystal lattices. For two salts, A and B, which have the same lattice, and whose rational activity coefficients, f _A and f _B , can be described by 2-suffix Margules equations (regular solutions), lnf _A =B_sx _B ² and lnf _B =B_sx _A ² to be partially miscible, B_s>2, but this requirement does not apply if the lattices are different. In each series, distribution constants for the equilibria were also determined. Where possible, the calculated activities of the salts or the Gibbs excess energies of the solid solutions were compared with values reported by others who determined them by other methods. All the salt pairs studied show slight or strong positive deviations from ideality.     

Use of net present value analysis to evaluate a publicly funded biomass-to-ethanol research,development, and demonstration program and valuate expected private sector participation

One of the functions of government is to invest tax dollars in programs, projects, and properties that will result in greater public benefit than would have resulted from leaving the tax dollars in the private sector or using them to pay off the public debt. This paper describes the use of Net Present Value(npv) as an approach to analyze and select investment opportunities for government money in public research, development, and demonstration (RD&D) programs and to evaluate potential private sector participation in the programs. This approach is then applied to a specific biomass-to-ethanol opportunity in California.