Contact-eutectic-lens fabrication technique

Method enables use of crystal or semiconductor materials with selective spectral-response characteristics (ultraviolet, visible, or infrared wavelengths) in fabrication of contact lenses, reading glasses, and photographic processing equipment

Frequency and Phase Synchronization in Neuromagnetic Cortical Responses to Flickering-Color Stimuli

In our earlier study dealing with the analysis of neuromagnetic responses (magnetoencephalograms - MEG) to flickering-color stimuli for a group of control human subjects (9 volunteers) and a patient with photosensitive epilepsy (a 12-year old girl), it was shown that Flicker-Noise Spectroscopy (FNS) was able to identify specific differences in the responses of each organism. The high specificity of individual MEG responses manifested itself in the values of FNS parameters for both chaotic and resonant components of the original signal. The present study applies the FNS cross-correlation function to the analysis of correlations between the MEG responses simultaneously measured at spatially separated points of the human cortex processing the red-blue flickering color stimulus. It is shown that the cross-correlations for control (healthy) subjects are characterized by frequency and phase synchronization at different points of the cortex, with the dynamics of neuromagnetic responses being determined by the low-frequency processes that correspond to normal physiological rhythms. But for the patient, the frequency and phase synchronization breaks down, which is associated with the suppression of cortical regulatory functions when the flickering-color stimulus is applied, and higher frequencies start playing the dominating role. This suggests that the disruption of correlations in the MEG responses is the indicator of pathological changes leading to photosensitive epilepsy, which can be used for developing a method of diagnosing the disease based on the analysis with the FNS cross-correlation function.Comment: 21 pages, 14 figures; submitted to "Laser Physics", 2010, 2

Space-time symplectic extension

It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time local structure group. A discrete sequence of the metric space-times of the fixed dimensionalities d=(2l)^2 and signatures, with l(2l-1) time-like and l(2l+1) space-like directions, defined over the set of the Hermitian second-rank spin-tensors is considered as an alternative to the pseudo-Euclidean extra dimensional space-times. The basic concepts of the symplectic framework are developed in general, and the ordinary and next-to-ordinary space-time cases with l=1,2, respectively, are elaborated in more detail. In particular, the scheme provides the rationale for the four-dimensionality and 1+3 signature of the ordinary space-time.Comment: 15 pp, LaTe

Lax pairs, Painlev\'e properties and exact solutions of the alogero Korteweg-de Vries equation and a new (2+1)-dimensional equation

We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2+1)-dimensional case and thereby propose a new equation in (2+1) dimensions. We named this the (2+1)-dimensional CKdV equation. We show that the CKdV equation as well as the (2+1)-dimensional CKdV equation are integrable in the sense that they possess the Painlev\'e property. Some exact solutions are also constructed