Let E be an elliptic curve defined over Q and P ∈ E(Q) a rational point of infinite order. Suppose that E has complex multiplication by an order in the quadratic imaginary field k. Denote by ME,P the set of rational primes ` such that ` splits in k, E has good reduction at `, and P is a primitive point modulo `. Under the generalized Riemann hypothesis, we can determine the positivity of the de...

We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solut...

We describe a technique for accurately measuring the ratio between the imaginary and real parts of the third-order nonlinearity in optical waveguides. Unlike most other methods, it does not depend on precise knowledge of the coupling efficiencies, optical propagation loss, or optical pulse shape. We apply the method to characterize a silicon waveguide, a GaAs waveguide, and AlGaAs waveguides wi...

We present a new algorithm for computing the ideal class group of an imaginary quadratic order which is based on the multiple polynomial version of the quadratic sieve factoring algorithm. Although no formal analysis is given, we conjecture that our algorithm has sub-exponential complexity, and computational experience shows that it is signiicantly faster in practice than existing algorithms.

Angle-resolved photoemission spectroscopy ARPES spectra hold a wealth of information about the manybody interactions in a correlated material. However, the quantitative analysis of ARPES spectra to extract the various coupling parameters in a consistent manner is extremely challenging, even for a model Fermi liquid system. We propose a fitting procedure which allows quantitative access to the i...

We complete the construction of the renormalization group equation (RGE) for the Color Glass Condenstate begun in Paper I. This is the equation which governs the evolution with rapidity of the statistical weight function for the color glass field. The coefficients in this equation — one-loop real and virtual contributions — are computed explicitly, to all orders in the color glass field. The re...

In this paper, we derive a negative imaginary and a strict negative imaginary lemma based on Riccati equations. The resulting negative imaginary lemma is used to solve a controller synthesis problem. For a given uncertain system, a static controller is constructed to force the system to satisfy the negative imaginary property. As a result, the closed-loop system can be guaranteed to be robustly...

The exact ground state of a strongly interacting quantum many-body system can be obtained by evolving a trial state with finite overlap with the ground state to infinite imaginary time. In many cases, since the convergence is exponential, the system converges essentially to the exact ground state in a relatively short time. Thus a short-time evolved wave function can be an excellent approximati...