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A new decomposition of exact solutions to the scalar wave equation into bidirectional, forward and backward, traveling plane wave solutions is described. The resulting representation is a natural basis for synthesizing pulse solutions that can be tailored to give directed energy transfer in...
For his metric space construction Meyer incorrectly derived several results. Meyer’s proofs are corrected or disproved by counterexamples. The physical relevance of his construction is further examined.
This paper deals with fluid space‐times within the framework of general relativity and subject to a metric symmetry (self‐similarity and conformal or conformal collineation). Via the investigation of the kinematic properties of such fluids, it is shown that the conformal collineation symmetry...
It is proved that the path‐space measure for the Dirac equation in four space‐time dimensions does not exist. The origin of the nonexistence of the measure turns out to be the dependence of the solution on the first derivative of the initial condition.
For higher‐order Kadomtsev–Petviashvili (KP) equations, the existence of explicitly time‐dependent constants of motion is discussed. Generalizing the results for the ordinary KP equation, constants T ( m ) n , l polynomial in t are constructed for each l th order KP equation, for all n ≥...
The multi‐Hamiltonian structure, conservation laws, and higher order symmetries for the Born–Infeld equation are exhibited. A new transformation of the Born‐Infeld equation to the equations of a Chaplygin gas is presented and explored. The Born–Infeld equation is distinguished among...
A theory of characteristic classes for complex super vector bundles over supermanifolds is developed. Such characteristic classes are proved to fulfill the usual properties, and it is shown that, under suitable conditions, they can be represented in terms of supersmooth curvature forms.
The Lanczos spin tensor C. Lanczos, Rev. Mod. Phys. 3 4 , 379 (1962) is obtained for arbitrary space‐times type III, N , or o .
In this paper, the methods of nucleons outside the closed shell (NOCS) and nucleons inside the closed shell (NICS) is introduced into the composite‐particle systems, and Glauber’s multiple scattering theory is used to divide the multiple scattering amplitude (between two composite particle...
Recent results of the shift operator matrix technique are utilized to calculate an exact expression for the lattice coverage of simple indistinguishable interacting molecules adsorbed on a semi‐infinite two‐dimensional M ×∞ rectangular lattice. As an illustrated example, parameters are...
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