The paper considers the phase retrieval problem in N dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a union of subspaces, respectively. A stable analytic reconstruction procedure of low complexity is given. Additionally it is proven that signal recovery from thes...

This thesis explores the relative complexity of proofs produced by the automatic theorem proving procedures of analytic tableaux, linear resolution, the connection method, tree resolution and the Davis-Putnam procedure. It is shown that tree resolution simulates the improved tableau procedure and that SL-resolution and the connection method are equivalent to restrictions of the improved tableau...

A general procedure to obtain analytic solutions of the linearized lattice Boltzmann equation for simple ows is developed. As examples, the solutions for the Poiseuille and the plane Couette ows in two-dimensional space are obtained and studied in detail. The solutions not only have a component which is the solution of the Navier-Stokes equation, they also include a kinetic component which cann...

Exact analytic expressions are developed for the average power of the Benjamini and Hochberg false discovery control procedure. The result is based on explicit computation of the joint probability distribution of the total number of rejections and the number of false rejections, and expressed in terms of the cumulative distribution functions of the p-values of the hypotheses. An example of anal...

We develop a calculable analytic approach to marginal deformations in open string field theory using wedge states with operator insertions. For marginal operators with regular operator products, we construct analytic solutions to all orders in the deformation parameter. In particular, we construct an exact time-dependent solution that describes D-brane decay and incorporates all α′ corrections....

Using a geometric approach, we derive the minimum number of applications needed for an arbitrary controlled-unitary gate to construct a universal quantum circuit. An analytic construction procedure is presented and shown to be either optimal or close to optimal. This result can be extended to improve the efficiency of universal quantum circuit construction from any entangling gate. In addition,...

In this paper, a semi-analytic thermal stress computation for single crystals with cubic anisotropy is developed, by introducing a new anisotropic factor. Based on a suitable splitting of the differential operators, a convergence series for general elasticity problem with cubic anisotropy is derived. Each term of the series is related to an isotropic elasticity problem. Using the analytic solut...

Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a neighborhood of the origin in the complex plane, we associate a vector field and its dual, an operator version of Fourier transform. The construction extends natur...

The paper considers the phase retrieval problem in N dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a union of subspaces, respectively. A stable analytic reconstruction procedure of low complexity is given. Additionally it is proven that signal recovery from thes...

At times, sufficient accumulated validity evidence is available for a selection procedure to justify its use in a new situation without conducting a local validation research study. In these instances, use of the selection procedure may be based on demonstration of the generalized validity inferences from that selection procedure, coupled with a compelling argument for its applicability to the ...