Exchange energy calculation of He-He with supermolecular one-matrix

Exch~nge energy of the He-He system is calculated using the one-density matrix which has been modified according to the supermolecular density formula quoted by Kolos. The exchange energy integrals are computed analytically and by the Monte Carlo method. The results obtained from both ways compared favourably,with the results obtained from the SCF program HONDO

Reactions of polyhalogenated aromatic compounds and related ethers with metal/ammonia solutions

This work contains the results of a series of reduction studies on polyhalogenated aromatic compounds and related ethers using alkali metals in liquid ammonia. In general, polychlorobenzenes were reduced to t he parent aromatic hydrocarbon or to 1 ,4-cyc1ohexadiene, and dipheny1ethers were cleaved to the aroma tic hydrocarbon and a phenol. Chlorinated dipheny1ethers were r eductive1y dechlorinated in the process. For example, 4-chlorodipheny1- ether gave benzene and phenol. Pentach1orobenzene and certain tetrachlorobenzenes disproportionated to a fair degree during the reduction process if no added proton source was present. The disproportionation was attributed to a build-up of amide ion. Addition of ethanol completely suppressed the formation of any disproportionation products. In the reductions of certain dipheny1ethers , the reduction of one or both of the dipheny1ether rings occurred, along with the normal cleavage. This was more prevalent when lithium was the metal used . As a Sidelight, certain chloropheno1s were readily dechlorinated. In light of these results, the reductive detoxification of the chlorinated dibenzo-1,4-dioxins seems possible with alkali metals in l iquid ammonia.

Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.

Some Travelling Wave Solutions of KdV-Burgers Equation

In this paper we study the extended Tanh method to obtain some exact solutions of KdV-Burgers equation. The principle of the Tanh method has been explained and then apply to the nonlinear KdV- Burgers evolution equation. A finnite power series in tanh is considered as an ansatz and the symbolic computational system is used to obtain solution of that nonlinear evolution equation. The obtained solutions are all travelling wave solutions.

Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.