Monotone numerical schemes for a Dirichlet problem for elliptic operators in divergence form

We consider a second‐order differential operator A( x )=?∑?_ia_ij( x )?_j+ ∑?_j(b_j( x )·)+c( x ) on ?^d, on a bounded domain D with Dirichlet boundary conditions on ?D, under mild assumptions on the coefficients of the diffusion tensor a_ij. The object is to construct monotone numerical schemes to approximate the solution of the problem A( x )u( x )=µ( x ), x ∈D, where µ is a positive Radon measure. We start by briefly mentioning questions of existence and uniqueness introducing function spaces needed to prove convergence results. Then, we define non‐standard stencils on grid‐knots that lead to extended discretization schemes by matrices possessing compartmental structure. We proceed to discretization of elliptic operators, starting with constant diffusion tensor and ending with operators in divergence form. Finally, we discuss W‐convergence in detail, and mention convergence in C and L₁ spaces. We conclude by a numerical example illustrating the schemes and convergence results. Copyright © 2008 John Wiley & Sons, Ltd.     

Edge searching weighted graphs

In traditional edge searching one tries to clean all of the edges in a graph employing the least number of searchers. It is assumed that each edge of the graph initially has a weight equal to one. In this paper we modify the problem and introduce the Weighted Edge Searching Problem by considering graphs with arbitrary positive integer weights assigned to its edges. We give bounds on the weighted search number in terms of related graph parameters including pathwidth. We characterize the graphs for which two searchers are sufficient to clear all edges. We show that for every weighted graph the minimum number of searchers needed for a not-necessarily-monotonic weighted edge search strategy is enough for a monotonic weighted edge search strategy, where each edge is cleaned only once. This result proves the NP-completeness of the problem.     

Micellar enhanced ultrafiltration of cadmium

The preconcentration of cadmium from aqueous colloid solution containing 8-hydroxyquinoline as extractant, laurylsulphate natrium as surfactant,n-butanol as co-surfactant was performed using micellar ultrafiltration technique. Filters with different pore size and materials were used to achieve a separation from liquid solutions. The cadmium recoveries depending on different conditions (pH, concentration of surfactant) were determined and the results are explained in the terms of colloidal parameters in the compare with the classical solvent extraction.     

Tetrahalidometallate(II) Ionic Liquids with More than One Metal: The Effect of Bromide versus Chloride

Fifteen N-butylpyridinium salts – five monometallic [C₄Py]₂[MBr₄] and ten bimetallic [C₄Py]₂[M_0.5^aM_0.5^bBr₄] (M=Co, Cu, Mn, Ni, Zn) – were synthesized, and their structures and thermal and electrochemical properties were studied. All the compounds are ionic liquids (ILs) with melting points between 64 and 101 °C. Powder and single-crystal X-ray diffraction show that all ILs are isostructural. The electrochemical stability windows of the ILs are between 2 and 3 V. The conductivities at room temperature are between 10⁻⁵ and 10⁻⁶ S cm⁻¹. At elevated temperatures, the conductivities reach up to 10⁻⁴ S cm⁻¹ at 70 °C. The structures and properties of the current bromide-based ILs were also compared with those of previous examples using chloride ligands, which illustrated differences and similarities between the two groups of ILs.     

Isometric artifacts from polymerase chain reaction-massively parallel sequencing analysis of short tandem repeat loci: An emerging issue from a new technology?

The recent introduction of polymerase chain reaction (PCR)-massively parallel sequencing (MPS) technologies in forensics has changed the approach to allelic short tandem repeat (STR) typing because sequencing cloned PCR fragments enables alleles with identical molecular weights to be distinguished based on their nucleotide sequences. Therefore, because PCR fidelity mainly depends on template integrity, new technical issues could arise in the interpretation of the results obtained from the degraded samples. In this work, a set of DNA samples degraded in vitro was used to investigate whether PCR-MPS could generate “isometric drop-ins” (IDIs; i.e., molecular products having the same length as the original allele but with a different nucleotide sequence within the repeated units). The Precision ID GlobalFiler NGS STR panel kit was used to analyze 0.5 and 1 ng of mock samples in duplicate tests (for a total of 16 PCR-MPS analyses). As expected, several well-known PCR artifacts (such as allelic dropout, stutters above the threshold) were scored; 95 IDIs with an average occurrence of 5.9 IDIs per test (min: 1, max: 11) were scored as well. In total, IDIs represented one of the most frequent artifacts. The coverage of these IDIs reached up to 981 reads (median: 239 reads), and the ratios with the coverage of the original allele ranged from 0.069 to 7.285 (median: 0.221). In addition, approximately 5.2% of the IDIs showed coverage higher than that of the original allele. Molecular analysis of these artifacts showed that they were generated in 96.8% of cases through a single nucleotide change event, with the C > T transition being the most frequent (85.7%). Thus, in a forensic evaluation of evidence, IDIs may represent an actual issue, particularly when DNA mixtures need to be interpreted because they could mislead the operator regarding the number of contributors. Overall, the molecular features of the IDIs described in this work, as well as the performance of duplicate tests, may be useful tools for managing this new class of artifacts otherwise not detected by capillary electrophoresis technology.     

Analysis of tetrapyrrolic pigments and derivatives in sediments by high performance liquid chromatography/atmospheric pressure chemical ionization mass spectrometry

A new application is described of the on-line high-performance liquid chromatography/positive and negative ion atmospheric pressure chemical ionization mass spectrometry (APCI(+/–)-MS) to the identification of tetrapyrrolic compounds in sediment samples containing complex mixtures of natural pigments and their diagenetic products. The method relies on the production of radical anions in order to determine the molecular masses of the molecules which yield abundant fragment ions when analyzed in the positive mode. This approach allows to verify the occurrence of coeluting components by examining their negative ion spectra and to complete their identification on the basis of their fragment ions produced in the positive ion spectra. Received: 24 September 1998 / Revised: 23 December 1998 / Accepted: 29 December 1998     

DNA fragment separations by on‐line combination of capillary isotachophoresis–capillary zone electrophoresis with UV detection

A high‐speed DNA fragment separation system based on an on‐line combination of capillary ITP with CZE (CITP‐CZE) and using UV detection at 260 nm was developed. A novel CITP‐CZE buffer system of pH 6.1 was designed for the separation of ten DNA fragments with sizes ranging from 100 to 1000 bp. An effect of underivatized α‐, β‐ and γ‐cyclodextrins on the resolution of DNA fragments in the CZE step of the CITP‐CZE combination was systematically investigated. Methylhydroxyethylcellulose present in the BGE was used to eliminate the EOF. DNA ladder fragments were separated within 10 min with LODs in the range of 1–5 ng/μL (S/N = 3). The RSDs of the migration time and peak area of individual DNA fragments were in the range of 1–3 and 3–9%, respectively. The developed CITP‐CZE system was further applied to the analysis of digest plasmid DNA samples.     

Ex Vivo and In Vitro Studies on the Cytotoxicity and Immunomodulative Properties of Poly(2‐isopropenyl‐2‐oxazoline) as a New Type of Biomedical Polymer

Poly(2‐alkenyl‐2‐oxazoline)s are promising functional polymers for a variety of biomedical applications, such as drug delivery systems, peptide conjugates, or gene delivery. In this study, poly(2‐isopropenyl‐2‐oxazoline) (PIPOx) is prepared through free‐radical polymerization initiated with azobisisobutyronitrile. Reactive 2‐oxazoline units in the side chain support an addition reaction with different compounds containing a carboxylic group, which facilitates the preparation of polymers labeled with two different fluorescent dyes. The cytotoxicities of 2‐oxazoline monomers, PIPOx, and fluorescently labeled PIPOx are evaluated in vitro using an 3‐(4,5‐Dimethyldiazol‐2‐yl)‐2,5‐diphenyl tetrazolium bromide assay and ex vivo using a cell proliferation assay with adenosine triphosphate bioluminescence. The cell uptake of labeled PIPOx is used to determine the colocalization of PIPOx with cell organelles that are part of the endocytic pathway. For the first time, it is shown that poly(2‐isopropenyl‐2‐oxazoline) is a biocompatible material and is suitable for biomedical applications; further, its immunomodulative properties are evaluated.