Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m ₂) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m ₂ memory may be chosen for a particular application. Memory retentiveness (m ₂) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined.     

Effect of preparation and metal content on the introduction of Fe in BEA zeolite, studied by DR UV-vis, EPR and Mössbauer spectroscopy

Fe-containing SiBEA zeolites were prepared by a two-step postsynthesis method: creation of vacant T-sites by dealumination of tetraethylammonium BEA zeolite with nitric acid and then impregnation of the resulting SiBEA zeolite with an aqueous solution of Fe(NO₃)₃. X-ray diffraction shows that iron is incorporated in SiBEA at lattice sites. The presence of Fe in its oxidation state +3 and at isolated tetrahedral sites for low metal content, was demonstrated by diffuse reflectance UV-vis, EPR and Mössbauer spectroscopy. For high iron content, diffuse reflectance UV-vis and Mössbauer spectra revealed the additional presence of extra-lattice FeO_x oligomers and superparamagnetic Fe-oxyhydroxide. Mössbauer spectroscopy identified superparamagnetic Fe-oxyhydroxide as the main phase when basic conditions are used for the preparation.     

Densely-packed self-assembled monolayers on gold surfaces from a conformationally constrained helical hexapeptide

A novel hexapeptide was functionalized at the N-terminus by a lipoyl group for binding to gold substrates. Owing to the high content of α-aminoisobutyric acid residues, the peptide adopts a rigid helical conformation despite the shortness of its main chain. Binding of the peptide to gold was investigated by quartz crystal microbalance, cyclic voltammetry, X-ray photoelectron spectroscopy, and scanning tunneling microscopy under ultra-high vacuum conditions. Scanning tunneling microscopy experiments revealed that the peculiar self-assembly properties of this short helical peptide determine the complex morphology of the monolayer, showing ‘stripes’, i.e. peptide aggregates horizontally layered on the gold surface, and ‘holes’, i.e. Au vacancy islands coated by the peptide monolayer.     

Performance analysis of 1300 nm SLEDs – impact of temperature and length scaling

The impact of self-heating and cavity length on the spectral emission properties of SLEDs is investigated using a state-of-the-art simulation tool. Simulated data are compared to measurements for two InP-based benchmark devices operating around 1300 nm, and excellent agreement is achieved in either case.     

Laguerre geometry of surfaces with plane lines of curvature

We study surfaces with plane lines of curvature in the framework of Laguerre geometry and provide explicit representation formulae for these surfaces in terms of a potential function. As an application, we explicitly integrate allL- minimal surfaces with plane curvature lines. Partially supported by MURST 40.