Consistency of a linear system of inequalities

We show that a consistency check of a linear system of inequalitiesAxb reduces to check whetherQb0 for a certain matrixQ. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values ofb, one need not run a numerical algorithm for eachb.On leave at the Electronics Research Laboratory of the University of California at Berkeley in a CNRS/NSF Exchange Program.     

Lifshitz tails for periodic plus random potentials

We prove that the integrated density of states () for a potentialW =V _per +V has Lifshitz tails where V_per is a periodic potential with reflection symmetry andV is a random potential, e.g., of the formV =q _i ()f(x–i).research partially supported by DFG.research partially supported by USNSF under grant No. MCS-81-20833.     

Bianchi type-V perfect fluid models

A study of the nontilted diagonal Bianchi type-V perfect fluid models is undertaken in the nonlocally rotationally symmetric case. It is shown that in such a model, the singularity is necessarily velocity dominated and the upper bound for the ratio of the shear to the expansion is 1/3. A class of such exact models is also presented; the structure of the singularity and the effect of the anisotropy on the scale are discussed. Lastly, an attempt is made to solve exactly the equations of motion for the coordinates of the null geodesics.     

Rigorous justification of the Friedlander-Keller formulas

In the paper an asymptotic expansion (as , the wave number) is proved for the Green function of the problem of diffraction by a smooth convex body in two cases: when one of the points of the source or observer lies on the boundary while the other is an arbitrary distance from the boundary and also when both points lie off the boundary but not far from it. The two-dimensional Dirichlet problem is considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 140, pp. 49–60, 1984.     

The constant-volume-velocity nature of hearing aids: conclusions based on computer simulations

In the literature there are several references which imply that various parts of a hearing aid are sources of constant volume velocity. Reported herein are the findings of an investigation of the validity of such statements. A computer scheme, referenced elsewhere, for modeling in situ hearing aids was utilized to test the constant-volume-velocity hypothesis. In particular, capabilities of the receiver, ear hook, and earmold tip to deliver constant volume velocity were investigated via a computer. To facilitate such an investigation, a universal receiver/earmold model was created. This model was broken down into "source" and "load"at three locations: the receive output, output of the ear hook, and medial tip of the earmold. At each location comparisons were made between computed values of source and load impedance. The constant-volume-velocity hypothesis was assumed to be valid for those cases where source impedance was much, much greater than load impedance. Plots of such impedances show that, for the cases investigated, this rarely occurred, except over certain frequency bands. With the exception of in-the-ear hearing aids, these results appear to contradict inferences made in the literature about the constant-volume-velocity nature of hearing aids.