Discontinuous approximate molecular electronic wave-functions

Following Kohn (reference 4), Schlosser and Marcus (reference 3), and Weare and Parr (reference 2), an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh–Ritz method in the replacement of the usual kinetic energy operators T?(μ) with operators T?′(μ) = T?(μ) + Î(μ), where Î(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the ?Ψ · ?Ψ way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of ?Ψ and the change of ?Ψ across surfaces of discontinuity.     

Zur Bestimmung des Gesamt-Kohlenstoffs in Kohlen und Bodenarten

Ohne Zusammenfassung     

Zur Bestimmung der Halogene, des Phosphors und Arsens in organischen Substanzen

Ohne Zusammenfassung     

Complexity of chaotic binary sequence and precision of its numerical simulation

Numerical simulation is one of primary methods in which people study the property of chaotic systems. However, there is the effect of finite precision in all processors which can cause chaos to degenerate into a periodic function or a fixed point. If it is neglected the precision of a computer processor for the binary numerical calculations, the numerical simulation results may not be accurate due to the chaotic nature of the system under study. New and more accurate methods must be found. A quantitative computable method of sequence complexity evaluation is introduced in this paper. The effect of finite precision is evaluated from the viewpoint of sequence complexity. The simulation results show that the correlation function based on information entropy can effectively reflect the complexity of pseudorandom sequences generated by a chaotic system, and it is superior to the other measure methods based on entropy. The finite calculation precision of the processor has significant effect on the complexity of chaotic binary sequences generated by the Lorenz equation. The pseudorandom binary sequences with high complexity can be generated by a chaotic system as long as the suitable computational precision and quantification algorithm are selected and behave correctly. The new methodology helps to gain insight into systems that may exist in various application domains such as secure communications and spectrum management.