We present a solution to the phase problem in near-field x-ray (propagation) imaging. The three-dimensional complex-valued index of refraction is reconstructed from a set of projections recorded in the near-field (Fresnel) setting at a single detector distance. The solution is found by an iterative algorithm based only on the measured data and the three-dimensional tomographic (Helgason-Ludwig)...

When generating Gaussian stationary random fields, a standard method based on circulant matrix embedding usually fails because some of the associated eigenvalues are negative. The eigenvalues can be shown to be nonnegative in the limit of increasing sample size. Computationally feasible large sample sizes, however, rarely lead to nonnegative eigenvalues. Another solution is to extend suitably t...

Suppose p is a homogeneous polynomial over a field K. Let p(D) be the differential operator defined by replacing each occurrence of xj in p by xj , defined formally in case K is not a subset of C. (The classical example is p(x1 , ..., xn)= j xj , for which p(D) is the Laplacian { .) In this paper we solve the equation p(D) q=0 for homogeneous polynomials q over K, under the restriction that K b...

We present a unified scheme of quantum measurements containing the aspects of amplification processes, or translation to macro-levels on the basis of [1], a joint work with Prof. I. Ojima. This formulation is based on micro-macro duality [2] as a mathematical expression of the general idea of quantum-classical correspondence. An essential difference between classical physics and quantum physics...

This paper reports on an investigation of voicing and aspiration of stops in Southern American English (SAE) and discusses theoretical implications of the findings for the features of contrast in SAE. Languages that have a two-way stop contrast generally fall into two categories: voicing languages (Russian, Dutch, Spanish) and aspirating languages (German, English, Mandarin). Many phonologists ...

6 Hermann, R., "A Poisson kernel for certain homogeneous spaces," Proc. Am. Math. Soc., 12, 892-899 (1961). 7Segal, I. E., "A class of operator algebras determined by groups," Duke Math. J., 18, 221-265 (1951). 8 Inonu, E., and E. Wigner, "On the contraction of Lie groups and their representations," these PROCEEDINGS, 39, 510-524 (1953). 9 Saletan, E., "Contraction of Lie groups," J. Math. Phys...

In Cartan’s original proof, the fixed point theorem was about Riemannian spaces of negative curvature, but I’ll use instead a simpler geometric notion due to [Bruhat-Tits:1972]. This allows an argument that is somewhat shorter and more direct than the standard one presented, for example, in [Helgason:1968]. The original application of the criterion of Bruhat-Tits was to buildings, as explained ...

In analogy with radiation fields for asymptotically Euclidean manifolds, introduced by F.G. Friedlander, we define radiation fields for asymptotically hyperbolic manifolds. We use them to give a translation representation of the wave group and to obtain the scattering matrix for such manifolds. Furthermore, we prove a support theorem for the radiation fields which generalizes to this setting th...