Structure-sensitive biodiesel synthesis over MgO nanocrystals

Size-controlled MgO nanocrystals were synthesised via a simple sol-gel method and their bulk and surface properties characterised by powder XRD, HRTEM and XPS. Small, cubic MgO single crystals, generated by low temperature processing, expose weakly basic (100) surfaces. High temperature annealing transforms these into large, stepped cuboidal nanoparticles of periclase MgO which terminate in more basic (110) and (111) surfaces. The size dependent evolution of surface electronic structure correlates directly with the associated catalytic activity of these MgO nanocrystals towards glyceryl tributyrate transesterification, revealing a pronounced structural preference for (110) and (111) facets. © 2009 The Royal Society of Chemistry.

Annealing and temperature coefficient study of type IA fibre Bragg gratings inscribed under strain and no strain - Implications to optical fibre component reliability

The annealing properties of Type IA Bragg gratings are investigated and compared with Type I and Type IIA Bragg gratings. The transmission properties (mean and modulated wavelength components) of gratings held at predetermined temperatures are recorded from which decay characteristics are inferred. Our data show critical results concerning the high temperature stability of Type IA gratings, as they undergo a drastic initial decay at 100°C, with a consequent mean index change that is severely reduced at this temperature However, the modulated index change of IA gratings remains stable at lower annealing temperatures of 80°C, and the mean index change decays at a comparable rate to Type I gratings at 80°C. Extending this work to include the thermal decay of Type IA gratings inscribed under strain shows that the application of strain quite dramatically transforms the temperature characteristics of the Type IA grating, modifying the temperature coefficient and annealing curves, with the grating showing a remarkable improvement in high temperature stability, leading to a robust grating that can survive temperatures exceeding 180°C. Under conditions of inscription under strain it is found that the temperature coefficient increases, but is maintained at a value considerably different to the Type I grating. Therefore, the combination of Type I and IA (strained) gratings make it possible to decouple temperature and strain over larger temperature excursions.

Typical performance of regular low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Relationship between the free energy in statistical-mechanics approach and the mutual information used in the information-theory literature is established within a general framework; Gallager and MacKay-Neal codes are studied as specific examples of LDPC codes. It is shown that basic properties of these codes known for particular channels, including their potential to saturate Shannon's bound, hold for general symmetric channels. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel models.

Existence of Global Solutions to Supercritical Semilinear Wave Equations

∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.

Projective Methods of Image Recognition

We propose a method for image recognition on the base of projections. Radon transform gives an opportunity to map image into space of its projections. Projection properties allow constructing informative features on the base of moments that can be successfully used for invariant recognition. Offered approach gives about 91-97% of correct recognition.

Self-Learning Fuzzy Spiking Neural Network as a Nonlinear Pulse-Position Threshold Detection Dynamic System Based on Second-Order Critically Damped Response Units

Architecture and learning algorithm of self-learning spiking neural network in fuzzy clustering task are outlined. Fuzzy receptive neurons for pulse-position transformation of input data are considered. It is proposed to treat a spiking neural network in terms of classical automatic control theory apparatus based on the Laplace transform. It is shown that synapse functioning can be easily modeled by a second order damped response unit. Spiking neuron soma is presented as a threshold detection unit. Thus, the proposed fuzzy spiking neural network is an analog-digital nonlinear pulse-position dynamic system. It is demonstrated how fuzzy probabilistic and possibilistic clustering approaches can be implemented on the base of the presented spiking neural network.

Best Constant in the Weighted Hardy Inequality: The Spatial and Spherical Version

Mathematics Subject Classification: 26D10.

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mathematics Subject Classification: Primary 35R10, Secondary 44A15

Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

On Limiting Case of the Stein-Weiss Type Inequality for the B-Riesz Potentials

Mathematics Subject Classification: Primary 42B20, 42B25, 42B35

On Hankel Transform of Generalized Mathieu Series

Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20

Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions

Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30

Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization

Mathematics Subject Classification: 26A33, 93B51, 93C95

Computation of some Differential Operators in Toric Coordinates

Toric coordinates and toric vector field have been introduced in [2]. Let A be an arbitrary vector field. We obtain formulae for the divA, rotA and the Laplace operator in toric coordinates.