Heavy-tailed targets and (ab)normal asymptotics in diffusive motion

We show that, under suitable confinement conditions, the ordinary Fokker-Planck equation may generate non-Gaussian heavy-tailed probability density functions (pdfs) (like, for example, Cauchy or more general Lévy stable distributions) in its long-time asymptotics. In fact, all heavy-tailed pdfs known in the literature can be obtained this way. For the underlying diffusion-type processes, our main focus is on their transient regimes and specifically the crossover features, when an initially infinite number of pdf moments decreases to a few or none at all. The time dependence of the variance (if in existence), ∼t^γ with 0<γ<2, may in principle be interpreted as a signature of subdiffusive, normal diffusive or superdiffusive behavior under confining conditions; the exponent γ is generically well defined in substantial periods of time. However, there is no indication of any universal time rate hierarchy, due to a proper choice of the driver and/or external potential.     

Riesz-Haviland criterion for incomplete data

The aim of this paper is to analyze a “support-free” version of the Riesz-Haviland theorem proved recently by the present authors, which characterizes truncations of the complex moment problem via positivity condition on appropriate families of polynomials in z and . The attention is focused on modifications of the positivity condition as well as the assumption on admissible truncations. The former results in truncations for which the corresponding “support-free” Riesz-Haviland condition locates a representing measure on the distinguished subset of the complex plane, while the latter effects a non-integral variant of the Riesz-Haviland theorem.     

Simultaneous quantification of Panax and Epimedium species using Rapid Resolution Liquid Chromatography (RRLC)

Two Rapid Resolution Liquid Chromatography (RRLC) methods have been developed and validated for simultaneous quantification of eight major ginsenosides from Panax species, namely, R1, Rg1, Re, Rf, Rb1, Rb2, Rc, and Rd, and flavonoids from Epimedium species, namely, epimedins A, B, and C and icariin. The analyses were performed using an Agilent 1200 series RRLC system with Phenomenex Luna C18-HST and Zorbax Eclipse XDB columns. The separation was performed with a gradient mobile phase of A (pure water) and B (acetonitrile) at a flow rate of 1.0 mL/min and 2.5 mL/min, respectively. Both columns were kept at 40 degrees C with the detection wavelength set at 203 nm. Specific eluted compounds were identified by using reference samples of ginsenosides R1, Rg1, Re, Rf, Rb1, Rc, Rb2, and Rd, and epimedins A, B, C and icariin. Baseline separation was achieved in less than 15 minutes for the Phenomenex Luna column and 4 minutes for the Zorbax Eclipse column. Characteristic RRLC profiles were established for complex mixtures of ginsenosides from Panax species and flavonoids from Epimedium species. Both methods developed here are effective for the quality control of formulated products containing both Panax and Epimedium varieties.     

Rapid resolution liquid chromatography (RRLC) analysis for quality control of Rhodiola rosea roots and commercial standardized products

A simple, sensitive and reliable reversed phase Rapid Resolution Liquid Chromatography (RRLC) method was developed and validated for six biologically active compounds (salidroside, tyrosol, rosarin, rosavin, rosin and rosiridin) in Rhodiola rosea L. roots and powder extracts. The method uses a Phenomenex C18 (2)-HST column at 40 degrees C with a neutral gradient system mobile phase (H20 and acetonitrile), a flow rate of 1.0 mL/min, and UV detection wavelengths set at 205 and 254 nm, simultaneously. Baseline separation of the six active compounds was achieved within 8 minutes. The average percentages of rosavins (rosarin, rosavin, and rosin) in authentic R. rosea roots and root powder extracts were quantitatively determined and a characteristic R. rosea roots RRLC profile was established. The RRLC method is accurate and sensitive; in addition, it effectively increases the sample analysis throughput compared with conventional HPLC.     

X-ray absorption near edge structure and extended X-ray absorption fine structure analysis of Fe(II) aqueous and acetone solutions

X-ray absorption spectroscopy measurements were used to determine the structure of the first coordination shell of Fe(II) ions in aqueous and acetone based solutions. Extended X-ray absorption fine structure analysis coupled with ab initio X-ray absorption near edge structure calculations confirms the octahedral coordination of the iron ion in water based solution. Data collected for acetone rich solutions can be reproduced assuming coexistence of the octahedral Fe(H(2)O)(6)(2+) and tetrahedral [FeCl(4)](2-) complexes. Distortion of the tetrahedral coordination of ion was detected in some of the acetone based solutions.     

Exploring a reaction mechanism for acetato ligand replacement in paddlewheel tetrakisacetatodirhodium (II,II) complex by ammonia: computational density functional theory study

This study focuses on the first step of interaction between DNA and the paddle-wheel dirhodium complex. The ammonia molecule was used to model the oligonucleotide sequence. The reaction was considered in neutral and acidic conditions, in gas phase, and in solvent, using the COSMO model. Molecular structures of the complexes were optimized in both models at the B3PW91/6-31G(d) level. The B3LYP functional and aug-cc-pvdz basis set were employed for single-point energy determination and electron distribution analyses. It was shown that in neutral solution the replacement of axial aqua ligand is mildly exoergic. The reaction is characterized by a relatively low activation barrier (10-12 kcal/mol), and, according to Eyring transition state theory, it proceeds very quickly. The breaking of the Rh-O(ac) bond in neutral solution is mildly endoergic (less than 1 kcal/mol) with an activation barrier of about 21 kcal/mol. However, this process can occur much more spontaneously (ΔG of -14 kcal/mol) when the dirhodium complex is protonated at the acetyl oxygen in remote position.     

Dielectric properties of the multicomponent PZT-type solid solution

In this paper the multicomponent PZT-type solid solution doped by barium, calcium, strontium, bismuth and germanium with composition: Pb_0.975Ba_0.01Ca_0.01Sr_0.005(Zr_0.52Ti_0.48)O₃ + 1.4 wt.% Bi₂O₃ + 0.3 wt.% GeO obtained by hot uniaxial pressing method is described. The results of structural, dielectric, ferroelectric and electromechanical studies of these ceramics are presented. It has been stated that introduction to the basic composition PZT admixtures of the barium, calcium, strontium, bismuth and germanium has a positive effect on the electro-physic parameters of obtained ceramic samples. This material has good microstructure, with high value of the dielectric permittivity (with the high temperature of phase transition) as well as low dielectric losses. It allows considering this material as elements for low frequency and high temperature electromechanical transducers.     

Electrochemical and Biological Studies on Reactivity of [VO(oda)(H2O)2], [Co(oda)(H2O)2]·H2O,and [Ni(oda)­(H2O)3]·1.5H2O Towards Superoxide Free Radicals

The reactivity of superoxide free radicals (O₂ ^{· –}) generated electrochemically towards the oxydiacetate metal complexes, namely [VO(oda)(H₂O)₂], [Co(oda)(H₂O)₂] · H₂O, and [Ni(oda)(H₂O)₃] · 1.5H₂O (oda = oxydiacetate) was examined by cyclic voltammetry. The measurements were carried out in DMSO solution using a platinum electrode. Based on the height of the anodic peak E_a that corresponds to electrochemical oxidation O₂ ^{· –} → O₂ + e, in the absence and in the presence of the compounds in the mixture, their O₂ ^{· –} scavenge ability was assessed. The influence of the type of the complex was briefly discussed. H₂O₂ was used to induce cellular injury in a mouse hippocampal cell line (HT22). The cytoprotection of chemical compounds was tested at the mitochondrial (MTT test) and plasma membrane level (LDH leakage). Dose‐dependent effect (10 and 100 μM of the complex) of investigated compounds was observed.     

A Convenient Synthesis of ω-(2-Aryl-4-oxothiazolidin-3-Yl)alkylphosphonic Acids via In Situ–Generated Arylideneaminoalkylphosphonic Acids

ω-(2-Aryl-4-oxothiazolidin-3-yl)alkylphosphonic acids are prepared in an easy workup procedure by the addition of methyl mercaptoacetate to in situ–generated arylideneaminoalkyl phosphonic acids.