The Curvature and Index of Completely Positive Maps

We study conjugacy invariants for completely positive maps thatare inspired by the concept of curvature introduced for commutingd-tuples of contractions by Arveson. 2000 Mathematics SubjectClassification 46L53, 46L55, 46L57, 46L87, 47L55, 46L07, 46L08     

Statistical-mechanics theory of active mode locking with noise

Actively mode-locked lasers with noise are studied employing statistical mechanics. A mapping of the system to the spherical model (related to the Ising model) of ferromagnets in one dimension that has an exact solution is established. It gives basic features, such as analytical expressions for the correlation function between modes, and the widths and shapes of the pulses [different from the Kuizenga-Siegman expression; IEEE J. Quantum Electron. QE-6, 803 (1970)] and reveals the susceptibility to noise of mode ordering compared with passive mode locking.     

Frequency shifting of microwave signals by use of a general temporal self-imaging (Talbot) effect in optical fibers

A simple and practical microwave frequency-shifting technique based on a general temporal self-imaging (GTSI) effect in optical fiber is proposed, formulated, and experimentally demonstrated. The proposed technique can be applied to an arbitrary periodic microwave signal (e.g., a microwave tone) and provides unparalleled design flexibility to increase the frequency of the input microwave signal up to the desired value (limited only by the photodetector's bandwidth). For instance, we demonstrate frequency upshifting of microwave tones from approximately 10 to approximately 50 GHz and from approximately 40 to approximately 354 GHz. These results also represent what is to the authors' knowledge the first experimental observation of GTSI phenomena.     

A New Twist of the Method of Successive Approximations to Yield Closed-Form Solutions for Inhomogeneous Vibrating Beams by Integral Method

The finite element method for stochastically inhomogeneous structures is now under active development. Very often the conventional finite element is used in conjunction with the Monte Carlo method. It appears imperative, therefore, to have benchmark solutions for the deterministic problems. This paper is devoted to fill the gap. The old (but not obsolete) method of successive approximations is newly interpreted to yield closed-form solution for vibrating beams.     

Dynamic equivalence,self-equilibrated excitation and Saint-Venant’s principle for an elastic strip

The distinction between the near and far-fields for a semi-infinite, elastic strip has been exploited to derive conditions under which different dynamic excitations can be considered as equivalent. These different excitations are equivalent in the sense that they produce the same displacement field far from the excited end. It is shown that dynamically equivalent excitations degenerate to statically equivalent loads in the limit of a vanishing frequency. The no-radiation condition is derived, and its relation to self-equilibrated, dynamic and static loads is presented. Dynamically equivalent excitations are utilized to formulate a dynamic version of Saint-Venant’s principle for symmetric excitations with frequencies below the first cut-off frequency of a strip. It has been shown that the requirement of self-equilibrium of a load for the decay of end effects for static fields can be deduced from the requirement of zero average power for the dynamic fields.     

Absolute Continuity,Interpolation and the Lyapunov Order

We extend our Nevanlinna–Pick theorem for Hardy algebras and their representations to cover interpolation at the absolutely continuous points of the boundaries of their discs of representations. The Lyapunov order plays a crucial role in our analysis.     

Measurement of fiber chromatic dispersion using spectral interferometry with modulation of dispersed laser pulses

We propose and experimentally demonstrate a method for fiber dispersion measurement based on the modulation of laser pulses stretched by the fiber under test. The measured spectrum of the modulated pulses is the result of the interference between the stretched pulse spectra shifted by the modulation harmonics. The interference pattern is processed as in Fourier transform spectral interferometry. Unlike to conventional spectral interferometry, environmental conditions do not affect the interferogram due to the lack of any interferometer; additionally, large dispersions can be characterized by the method proposed. Its high accuracy is demonstrated in experimental comparison with the widely used phase shift technique.     

Some properties of the Cauchy-type integral for the time-harmonic Maxwell equations

We study the analog of the Cauchy-type integral for the theory of time-harmonic electromagnetic fields in case of a piece-wise Liapunov surface of integration and we prove the Sokhotski-Plemelj theorem for it as well as the necessary and sufficient condition for the possibility to extend a given pair of vector fields from such a surface up to a solution of the time-harmonic Maxwell equations in a domain. Formula for the square of the singular Cauchy-type integral is given. The proofs of all these facts are based on intimate relations between time-harmonic solutions of the Maxwell equations and some versions of quaternionic analysis.     

A Bessel identity for the theta correspondence

We establish a spectral identity between global Bessel distributions with respect to generic cuspidal representations of an odd orthogonal group and the metaplectic cover of a symplectic group which are related by the theta correspondence. We also provide analogous local identities for square-integrable representations.