Spectral reciprocity and matrix representations of unbounded operators

Motivated by potential theory on discrete spaces, we study a family of unbounded Hermitian operators in Hilbert space which generalize the usual graph-theoretic discrete Laplacian. These operators are discrete analogues of the classical conformal Laplacians and Hamiltonians from statistical mechanics. For an infinite discrete set $X$, we consider operators acting on Hilbert spaces of functions on $X$, and their representations as infinite matrices; the focus is on $\ell^2(X)$, and the energy space $\mathcal{H}_{\mathcal E}$. In particular, we prove that these operators are always essentially self-adjoint on $\ell^2(X)$, but may fail to be essentially self-adjoint on $\mathcal{H}_{\mathcal E}$. In the general case, we examine the von Neumann deficiency indices of these operators and explore their relevance in mathematical physics. Finally we study the spectra of the $\mathcal{H}_{\mathcal E}$ operators with the use of a new approximation scheme.Comment: 20 pages, 1 figure. To appear: Journal of Functional Analysi

The influence of bench geometry on blasting effects for vertical cylindrical charges

Blasting phenomena are affected by many factors. Previous investigators have studied many of these factors, however, the influence of charge length and explosive detonation velocity have apparently not been thoroughly examined. It was found by this investigation that the detonation pressure of a commercial explosive is closely controlled by the detonation velocity. The detonation velocity, in turn, will largely determine the necessary blast geometry that can be successfully employed. Relationships were derived between the detonation velocity, in relation to the rock energy propagation velocity, and blast geometry for both bottom and collar primed blasts. The resultant force magnitude and direction at a point in the medium was found to be influenced by the charge length and the velocity ratio. A graphical analysis of the forces in the medium indicated that the direction of the resultant forces along the reflected pulse front is not perpendicular to this wave front. Observed blasting phenomena appear to substantiate the theoretical investigation --Abstract, page i

Dopexamine can attenuate the inflammatory response and protect against organ injury in the absence of significant effects on hemodynamics or regional microvascular flow

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