A Note on PIN Polynomials and PRIN Rational Functions

This brief presents a necessary and sufficient condition for testing positive, real, imaginary, and negative rational functions. A related term, the positive, imaginary, and negative polynomial, is defined and two necessary and sufficient conditions for testing it are given.     

Fuzzy Learning of Talbot Effect Guides Optimal Mask Design for Proximity Field Nanopatterning Lithography

Processing methods used in photonics and nanotechnology possess many limitations restricting their application areas such as high cost, inability to produce fine details, problems with scalability, and long processing time. Proximity field nanopatterning is a lithography method which surpasses these limitations. By using interference patterns produced by a two-dimensional phase mask, the technique is able to generate a submicron detailed exposure on a millimeter-size slab of light sensitive photopolymer, which is then developed like a photographic plate to reveal three-dimensional interference patterns from the phase mask. While it is possible to use simulations to obtain the interference patterns produced by a phase mask, realizing the mask dimensions necessary for producing a desired interference pattern is analytically challenging due to the intricacies of light interactions involved in producing the final interference pattern. An alternative method is to iteratively optimize the phase mask until the interference patterns obtained converge to the desired pattern. However, depending on the optimization technique used, one either risks a significant probability of failure or requires a prohibitive number of iterations. We argue that an optimization technique that is to take advantage of the physics of the problem using machine learning methods (here fuzzy learning) can lead to competent mask design. This technique is described in this letter.     

Energy-efficient video streaming over Bluetooth using rateless coding

Energy-efficient error control for IEEE 802.15.1 (Bluetooth) video communication is proposed. The scheme is based on block-oriented incremental redundancy provided by rateless coding and receiver feedback. Results are presented for time-sensitive video streaming applications under a Markovian channel model. When the proposed algorithm is compared to variations of Bluetooth forward error control, there are improvements of around 3 dB in received video quality and of over 10% in energy efficiency.     

Symmetrized Split-Step Fourier Scheme to Control Global Simulation Accuracy in Fiber-Optic Communication Systems

Analytical expressions involving both system parameters and step-size are proposed to represent the local simulation error for the symmetrized split-step Fourier (SSSF) simulation method. This analytical expression can be used for a step-size selection rule to achieve comparable local simulation accuracy for SSSF simulations. This can lead to computational savings since there is no waste of computation in each simulation step. Furthermore, based on the local error expression, scaling rules are derived to achieve comparable global simulation accuracy for wide ranges of key system parameter values. This is significant in enhancing the computational efficiency in optical fiber communication system design and optimization. Extensive validation tests were performed to explore the application range of the proposed step-size selection and scaling rules. The desired global accuracy can be achieved with the use of our local error expression and scaling rules by only a couple of test trial simulation runs for a variety of practical applications.     

Naphthyl azomesogens with lateral chloro groups

A homologous series of azomesogens, 2″-[4-(4′-n-alkoxybenzoyloxy)-2-chlorophenylazo] naphthalenes, with lateral chloro groups was synthesised. All the homologues synthesized exhibit enantiotropic nematic mesophase. The mesomorphic properties of the present series are compared with other structurally related series to evaluate the effect of lateral chloro group and its position on mesomorphism This paper was presented at the 10th National Conference on Liquid Crystals held at Bangalore, India during 9–11 October 2003.     

Indeterminacy Criteria for the Stieltjes Matrix Moment Problem

In this paper, we obtain criteria for the indeterminacy of the Stieltjes matrix moment problem. We obtain explicit formulas for Stieltjes parameters and study the multiplicative structure of the resolvent matrix. In the indeterminate case, we study the analytic properties of the resolvent matrix of the moment problem. We describe the set of all matrix functions associated with the indeterminate Stieltjes moment problem in terms of linear fractional transformations over Stieltjes pairs.     

A classical no-interaction theorem for bosonic strings and its quantum significance

We show that, in dimensions equal or greater than three, classical strings do not join or split. This is part of a no-interaction theorem that is also proved. The quantum theory is considered.     

Photoconductive Terahertz antenna with radial symmetry

It has been demonstrated recently that it is possible to guide broadband Terahertz pulses utilising a novel coaxial waveguide. This technique is hindered by the difficulty in exciting the radially polarised fundamental mode of the waveguide. To optimise mode matching, a novel radially symmetric photoconductive Terahertz antenna is proposed. Using finite element method simulations and analytical calculations, it is shown that this antenna can generate the desired radial polarisation.     

Investigation of multicomponent fluoride optical materials in the UV spectral region: I. Single crystals of Ca1−x R xF2+x (R = Sc, Y, La, Yb, Lu) solid solutions

Crystalline materials that are transparent in the vacuum UV spectral region and currently used have been reviewed. Transmission of crystals of solid solutions with the fluorite structure Ca_1?x R _xF_2+x (R = Sc, Y, La, Yb, Lu) in the UV and vacuum UV spectral regions has been investigated. It is shown that application of different methods of purification of fluorides from some impurities can significantly improve the optical quality of fluoride multicomponent crystals in the short-wavelength spectral region.     

Nanolayered lightweight flexible shields with multidirectional optical transparency

New nanolayered coatings are designed and deposited on flexible plastic substrate having the thickness of 100 /spl mu/m, in order to realize lightweight ultrathin transparent shielding foils. The structure of the coating is optimized considering three figures of merit: the average transmittance in the visible range for normal incidence, the normalized average transmittance for oblique incidence at 550 nm, and the transmittance quality factor. The nanotechnology exploited for the deposition of the transparent metals is the dual ion beam sputtering. Tests of durability, optical transmission, and shielding effectiveness demonstrate that the film has a high adhesion under mechanical solicitation, high resistance against aging, peak transmittance in the visible range higher than 70%, omnidirectional properties in the range 0/spl deg/-60/spl deg/, and shielding effectiveness of 40 dB up to 6 GHz.