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Initial‐value problems for the generalized Burgers equation (GBE) u t + u β u x +λ u α =(δ/2) u x x are discussed for the single hump type of initial data—both continuous and discontinuous. The numerical solution is carried to the self‐similar ‘‘intermediate asymptotic’’ regime...
There are N equal particles interacting through a repulsive potential V ( r )= A / r β ( β>0) placed insided the sphere. For β=1 (Coulomb case) and for all β<1, the minimum energy configuration will have all N particles on the inner surface of the sphere for any integer N . It is shown that...
Starting from the affinely parametrized supersymmetric Dirac particle model a Grassmannian path integral expression for the propagator of the Dirac equation, minimally coupled to an external electromagnetic field, is derived. A purely ‘‘bosonic’’ path integral representation of the...
Field contents for scalar superfields in different numbers of dimensions are tabulated. Tables of field contents for some irreducible superfields included in the scalar superfield in 11 dimensions are also given.
Recent works on the hydrogen‐oscillator connection are extended to cover in a systematic (and easily computarizable) way the problem of the expansion of an R 3 hydrogen wave function in terms of R 4 oscillator wave functions. Passage formulas from oscillator to hydrogen wave functions are...
Local properties of a quantum system are defined as the expectation values of its observables in a microstate of some complete set of commuting observables. An equation for the time evolution of local properties is obtained for any system whose statistical operator (density matrix) evolves by...
A method for generating exact Bianchi type II cosmological models with a perfect fluid distribution of matter is presented. Two new classes of Bianchi type II solutions have been generated from Lorenz’s solution D. Lorenz, Phys. Lett. A 7 9 , 19 (1980). A detailed study of physical and...
The integral representation of the inverse of a determinant and the Grassmann representation of a determinant are used to derive an expression for the average resolvent for a Gaussian orthogonal ensemble. The expression is compared with the one obtained using Lagrangian formalism.
The set of all pair (and in fact higher‐order) distributions that are representable in quantum mechanics is characterized and compared with the classical range. Various interference phenomena yield pair distributions that are not classical; a few examples are discussed. These results shed light...
The problem of the determination of the asymptotic density of states of the quark–gluon gas is reconsidered. A general method emerges, which unifies and simplifies previous derivations that can be found in the literature. It takes due account of various constraints on the configurations of the...
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