Augmented Zagreb index

Inspired by recent work on the atom-bond connectivity (ABC) index we propose here a new topological index, augmented Zagreb index (AZI). The tight upper and lower bounds for chemical trees are obtained. Moreover, it has been shown that among all trees the star has the minimum AZI value. Characterizing trees with maximal augmented Zagreb index remains an open problem for future research.     

Heat Kernel Upper Estimates for Symmetric Jump Processes with Small Jumps of High Intensity

We consider the following non-local operator

Optical technologies for the read out and quality control of DNA and protein microarrays

Microarray formats have become an important tool for parallel (or multiplexed) monitoring of biomolecular interactions. Surface-immobilized probes like oligonucleotides, cDNA, proteins, or antibodies can be used for the screening of their complementary targets, covering different applications like gene or protein expression profiling, analysis of point mutations, or immunodiagnostics. Numerous reviews have appeared on this topic in recent years, documenting the intriguing progress of these miniaturized assay formats. Most of them highlight all aspects of microarray preparation, surface chemistry, and patterning, and try to give a systematic survey of the different kinds of applications of this new technique. This review places the emphasis on optical technologies for microarray analysis. As the fluorescent read out of microarrays is dominating the field, this topic will be the focus of the review. Basic principles of labeling and signal amplification techniques will be introduced. Recent developments in total internal reflection fluorescence, resonance energy transfer assays, and time-resolved imaging are addressed, as well as non-fluorescent imaging methods. Finally, some label-free detection modes are discussed, such as surface plasmon microscopy or ellipsometry, since these are particularly interesting for microarray development and quality control purposes.     

Multistep liquid-phase lithography for fast prototyping of microfluidic free-flow-electrophoresis chips

We present a fast and versatile method to produce functional micro free-flow electrophoresis chips. Microfluidic structures were generated between two glass slides applying multistep liquid-phase lithography, omitting troublesome bonding steps or cost-intensive master structures. Utilizing a novel spacer-less approach with the photodefinable polymer polyethyleneglycol dimethacrylate (PEG-DA), microfluidic devices with hydrophilic channels of only 25 μm in height were generated. The microfluidic chips feature ion-permeable segregation walls between the electrode channels and the separation bed and hydrophilic surfaces. The performance of the chip is demonstrated by free-flow electrophoretic separation of fluorescent xanthene dyes and fluorescently labeled amino acids.     

Rapid quantitative determination of ephedra alkaloids in tablet formulations and human urine by microchip electrophoresis

Microchip electrophoresis with fluorescence detection has been applied for fast separation and determination of ephedra alkaloids in pharmaceutical formulations and body fluids. A custom epifluorescence microscope setup was employed and the compounds were separated within 40?s, allowing the detection of less than 200?ng/L for both analytes. Quantitation of the two stimulants was performed via a derivatization step using FITC without any extraction or preconcentration steps. The effects of different microchip types and excitation light sources were investigated and the method was successfully applied for the analysis of these compounds in tablet formulations, yielding recovery rates from 100.2 to 101.1% and relative standard deviations from 1.5 to 3.4%. Analysis of ephedrines was also carried out with human urine samples at detection limits of 500-1000?ng/L and relative standard deviations from 2.2 to 3.3% using argon ion LIF detection.     

Harnack Inequality and Hölder Regularity Estimates for a Lévy Process with Small Jumps of High Intensity

We consider a Lévy process in ? ^d (d≥3) with the characteristic exponent $$\varPhi(\xi)=\frac{|\xi|^2}{\ln(1+|\xi|^2)}-1.$$ The scale invariant Harnack inequality and a priori estimates of harmonic functions in Hölder spaces are proved.     

Molecular engineering for panchromatic absorbing oligothiophene donor-π-acceptor organic semiconductors

A series of three novel organic semiconductor molecules based on the donor-π-bridge-acceptor (D-π-A) modular design have been designed, synthesised and characterised. These small organic molecules have a common donor (triphenylamine), π-bridge (an alkylated tetrathiophene) and various acceptors to provide tuning of optical and electronic properties. The examined acceptors were dicyanovinylidene, cyanopyridone and oxoindenemalononitrile groups. These compounds were highly soluble in common organic solvents, such as chloroform, toluene and chlorobenzene. As acceptor strength increased from dicyanovinylidene to cyanopyridone to oxoindenemalononitrile groups, the wavelength of the longest wavelength absorption maximum increased (518, 587, 619 nm (solution)), the respective extinction coefficients increased (4.9×10⁴, 6.3×10⁴, 7.4×10⁴ M⁻¹ cm⁻¹) and with increasing acceptor strength the band gap narrowed (1.63, 1.42 1.38 eV). Panchromatic absorbance was observed for the compounds comprising the cyanopyridone and oxoindenemalononitrile acceptors.     

Atom-bond connectivity index of trees

The recently introduced atom-bond connectivity (ABC) index has been applied up to now to study the stability of alkanes and the strain energy of cycloalkanes. Here, mathematical properties of the ABC index of trees are studied. Chemical trees with extremal ABC values are found. In addition, it has been proven that, among all trees, the star tree, S_n, has the maximal ABC value.