Fundamental solutions of singular SPDEs

This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Lévy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator which enables us to express the solution as u = sA ◊ I^◊(−1), where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.     

Optimization Study of Plumbane Generation and Preconcentration in Hydride Generation-Graphite Furnace Atomic Absorption Spectrometry

Optimization of lead hydride generation has been performed and a regression model of the efficiency (chemical yield, E %) of plumbane generation has been derived from experimental data. The effect of various chemical and instrumental parameters on hydride generation and trapping in an absorbing solution of Ce(IV)-KI, with subsequent determination of lead by graphite-furnace atomic absorption spectrometry (GF-AAS) has been studied, in an effort to optimize conditions for preconcentration and determination of nanogram amount of lead. Characteristic concentrations are 1 μg/1 in absorbing solution and 0.2 μg/1 in a 50-ml aliquot of sample solution and the corresponding limits of detection are ca. 4 and 1 μg/1, respectively.     

Targeting a Large Active Site: Structure-Based Design of Nanomolar Inhibitors of Trypanosoma brucei Trypanothione Reductase

Trypanothione reductase (TR) plays a key role in the unique redox metabolism of trypanosomatids, the causative agents of human African trypanosomiasis (HAT), Chagas’ disease, and leishmaniases. Introduction of a new, lean propargylic vector to a known class of TR inhibitors resulted in the strongest reported competitive inhibitor of Trypanosoma (T.) brucei TR, with an inhibition constant K_i of 73 nm , which is fully selective against human glutathione reductase (hGR). The best ligands exhibited in vitro IC₅₀ values (half-maximal inhibitory concentration) against the HAT pathogen, T. brucei rhodesiense, in the mid-nanomolar range, reaching down to 50 nm. X-Ray co-crystal structures confirmed the binding mode of the ligands and revealed the presence of a HEPES buffer molecule in the large active site. Extension of the propargylic vector, guided by structure-based design, to replace the HEPES buffer molecule should give inhibitors with low nanomolar K_i and IC₅₀ values for in vivo studies.     

Characterization of winemaking yeast by cell number-size distribution analysis through flow field-flow fractionation with multi-wavelength turbidimetric detection

Yeasts are widely used in several areas of food industry, e.g. baking, beer brewing, and wine production. Interest in new analytical methods for quality control and characterization of yeast cells is thus increasing. The biophysical properties of yeast cells, among which cell size, are related to yeast cell capabilities to produce primary and secondary metabolites during the fermentation process. Biophysical properties of winemaking yeast strains can be screened by field-flow fractionation (FFF). In this work we present the use of flow FFF (FlFFF) with turbidimetric multi-wavelength detection for the number-size distribution analysis of different commercial winemaking yeast varieties. The use of a diode-array detector allows to apply to dispersed samples like yeast cells the recently developed method for number-size (or mass-size) analysis in flow-assisted separation techniques. Results for six commercial winemaking yeast strains are compared with data obtained by a standard method for cell sizing (Coulter counter). The method here proposed gives, at short analysis time, accurate information on the number of cells of a given size, and information on the total number of cells.     

Hybrid Systems and Hybrid Computation 1st Part: Hybrid Systems

In the first part of this paper we will give a short historical survey of the field of hybrid systems, a precise definition of a hybrid system and some comments on the definition. In a second paper (Hybrid systems and hybrid computation – 2nd part: Hybrid computation) we will concentrate on a particular aspect of the theory closely related to scientific computation, that we have called hybrid computation.     

Programmed Synthesis by Stimuli‐Responsive DNAzyme‐Modified Mesoporous SiO2 Nanoparticles

DNAzyme‐capped mesoporous SiO₂ nanoparticles (MP SiO₂ NPs) are applied as stimuli‐responsive containers for programmed synthesis. Three types of MP SiO₂ NPs are prepared by loading the NPs with Cy3‐DBCO (DBCO=dibenzocyclooctyl), Cy5‐N₃, and Cy7‐N₃, and capping the NP containers with the Mg²⁺, Zn²⁺, and histidine‐dependent DNAzyme sequences, respectively. In the presence of Mg²⁺ and Zn²⁺ ions as triggers, the respective DNAzyme‐capped NPs are unlocked, leading to the “click” reaction product Cy3‐Cy5. In turn, in the presence of Mg²⁺ ions and histidine as triggers the second set of DNAzyme‐capped NPs is unlocked leading to the Cy3‐Cy7 conjugated product. The unloading of the respective NPs and the time‐dependent formation of the products are followed by fluorescence spectroscopy (FRET). A detailed kinetic model for the formation of the different products is formulated and it correlates nicely with the experimental results.     

Platinum(II), palladium(II), rhodium(III) and lead(II) voltammetric determination in sites differently influenced by vehicle traffic

The present work reports analytical results relevant to voltammetric determination of Pt(II), Pd(II), Rh(III) [Platinum Group Metals (PGMs)] and Pb(II) in superficial water sampled in sites differently influenced by vehicle traffic, especially considering their temporal behaviour. For all the elements, in addition to detection limits, precision, expressed as relative standard deviation (s(r) %) and accuracy, expressed as percentage recovery (R %) are also reported. In all cases they show to be good, being the former lower than 6% and the latter in the range 94-105%. A critical comparison with spectroscopic measurements is also discussed.     

Proton,carbon-13 and fluorine-19 NMR studies of 9,10,11,12-tetra-fluoro-5,6-dihydrobenzo[b]naphth[2,1-f]oxepin: ‘Through-space’ carbon-fluorine coupling was revealed

The ¹H, ¹³C and ¹⁹F nmr spectra of 9,10,11,12-tetrafluoro-5,6-dihydrobenzo[b]naphth[2,1-f]oxepin ( 1 ) were totally assigned using a combination of two-dimensional nmr techniques. Unequivocal interpretation of the spectral data allowed the complete assignments of the resonances. In addition, the spectra of compound 1 revealed an unusual through-space carbon-fluorine coupling which was further supported by NOE and modeling experiments.