Regularity properties of distributions through sequences of functions

We give necessary and sufficient criteria for a distribution to be smooth or uniformly Hölder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations ${(T\ast\phi_{n})}$ .     

Global Representatives of Colombeau Holomorphic Generalized Functions

It is proved that a holomorphic generalized function in the sense of Colombeau has a representative consisting of a net of holomorphic functions. More generally, the existence of global representatives of Colombeau solutions to elliptic partial differential equations is proved. Further, it is shown that a generalized holomorphic function on Ω, which is equal to zero in an open set , is equal to zero. First author partially supported by FWF (Austria), grants P16820 and Y237. Third author partially supported by MNZŽ (Serbia), project 144016.     

A flexible microfluidic processor for molecular biology: application to microarray sample preparation

We describe a programmable microfluidic system with onboard pumps and valves that has the ability to process reaction volumes in the sub-microlitre to hundred microlitre range. The flexibility of the architecture is demonstrated with a commercial molecular biology protocol for mRNA amplification, implemented without significant modification. The performance of the microchip system is compared to conventional bench processing at each stage of the multistep protocol, and DNA microarrays are used to assess the quality and performance of bench- and microchip-amplified RNA. The results show that the microchip system reactions are similar to bench control reactions at each step, and that the microchip- and bench-derived amplified RNAs are virtually indistinguishable in differential microarray analyses.     

On the convolution of Roumieu ultradistributions through the \epsilon tensor product

The equivalence of several definitions of convolution of two Roumieu ultradistributions is proved. For that purpose, the $\varepsilon $ tensor product of $\dot{\tilde{\mathcal{B }}}^{\{M_p\}}$ and a locally convex space $E$ is considered.     

The influence of electrolyte on photocatalytic activity of PEO coatings with incorporated Ce-ZSM5 formed on aluminum

Journal of Solid State Electrochemistry - The preparation and characterization of oxide coatings made by plasma electrolytic oxidation (PEO) process on aluminum in two different electrolyte...     

Real analytic generalized functions

Real analytic generalized functions are introduced and investigated. The analytic singular support and analytic wave front of a generalized function in are introduced and described. Authors’ addresses: S. Pilipović, Department of Mathematics and Informatics, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, Serbia; D. Scarpalezos, U.F.R. de Mathématiques, Université Paris 7, 2 Place Jussieu, Paris 5^e, 75005, France; V. Valmorin, Université des Antilles et de la Guyane, Département Math-Info, Campus de Fouillole, 97159 Pointe á Pitre Cedex, France     

Full-field technique for measuring the spectral evolution of reconfigurable photonic filters

This Letter demonstrates a measurement technique based on frequency-to-time mapping and coherent detection, which enables the complete (i.e., amplitude and phase) characterization of dynamically reconfigurable photonic filters. We apply this technique to a unit cell from a silicon CMOS-compatible photonic lattice filter that has a rapidly changing transfer function with an 8.33 ns update time, 120 MHz spectral resolution, and 12 GHz bandwidth. These dynamic measurements allow characterization of transients, thermal effects, filter fidelity, and other time-dependent phenomena during switching.     

Indigo Carmine in a Food Dye: Spectroscopic Characterization and Determining Its Micro-Concentration through the Clock Reaction

Indigo carmine is a commonly used industrial blue dye. To determine its concentration in a commercially available food dye composed of a mixture of indigo carmine and D-glucose, this paper characterizes it through (ATR, KBr) FTIR micro-Raman as well as UV/Vis and clock: Briggs–Rauscher (BR) oscillatory reaction methods. The indigo carmine was detected in the bulk food dye only by applying micro-Raman spectroscopy, indicating a low percentage of the indigo carmine present. This research provides an improvement in the deviations from the experimental Raman spectrum as calculated by the B97D/cc-pVTZ level of theory one, resulting in a better geometrical optimization of the indigo carmine molecule compared to data within the literature. The analytical curves used to determine indigo carmine concentrations (and quantities) in an aqueous solution of food dye were applied by means of UV/Vis and BR methods. BR yielded significantly better analytical parameters: 100 times lower LOD and LOQ compared to commonly used UV/Vis. The remarkable sensitivity of the BR reaction towards indigo carmine suggests that not only does indigo carmine react in an oscillatory reaction but also its decomposition products, meaning that the multiple oxidation reactions have an important role in the BR’s indigo carmine mechanism. The novelty of this research is the investigation of indigo carmine using a clock BR reaction, opening new possibilities to determine indigo carmine in other complex samples (pharmaceutical, food, etc.).