An approximation method using approximate approximations

The aim of this paper is to extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the Laplace equation in two dimensions using approximate approximations. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

On a 3D-Hypersingular Equation of a Problem for a Crack

MSC 2010: 45DB05, 45E05, 78A45

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{potential $Q=|Z|^2$ we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials.

Characterization, physicochemical stability, and evaluation of in vitro digestibility of solid lipid microparticles produced with palm kernel oil and tristearin

Solid lipid particles have been investigated by food researchers due to their ability to enhance the incorporation and bioavailability of lipophilic bioactives in aqueous formulations. The objectives of this study were to evaluate the physicochemical stability and digestibility of lipid microparticles produced with tristearin and palm kernel oil. The motivation for conducting this study was the fact that mixing lipids can prevent the expulsion of the bioactive from the lipid core and enhance the digestibility of lipid structures. The lipid microparticles containing different palm kernel oil contents were stable after 60 days of storage according to the particle size and zeta potential data. Their calorimetric behavior indicated that they were composed of a very heterogeneous lipid matrix. Lipid microparticles were stable under various conditions of ionic strength, sugar concentration, temperature, and pH. Digestibility assays indicated no differences in the release of free fatty acids, which was approximately 30% in all analises. The in vitro digestibility tests showed that the amount of palm kernel in the particles did not affect the percentage of lipolysis, probably due to the high amount of surfactants used and/or the solid state of the microparticles.

Xyloglucan nano-aggregates: Physico-chemical characterisation in buffer solution and potential application as a carrier for camptothecin, an anti-cancer drug

In this work, native xyloglucan was extracted from Tamarindus indica seeds (XGT), and its properties in phosphate buffer solution (PBS) were evaluated in comparison with a commercial tamarind kernel powder (TKP). The physico-chemical characteristics of the polysaccharides such as molar mass, critical concentration and intrinsic viscosity were determined. Furthermore, using spectroscopic and microscopy techniques, it was observed that the XGs tested can be considered macromolecules able to aggregate as nano-entities of 60-140 nm. The XGT tended to an ordered and compact spherical conformation determined by the Huggins constant, circular dichroism, atomic force microscopy and transmission electron microscopy. After the determination of the properties in PBS the XGs, at concentrations of 25% above their critical aggregation concentration, were used to encapsulate camptothecin, an anti-cancer drug. The XGT sample showed an encapsulation efficiency of 42% and first-order drug delivery kinetics. These results demonstrated the importance of knowledge of the physico-chemical properties of polysaccharides, for example, to better conduct their biotechnological applications as drug carriers. (C) 2010 Elsevier Ltd. All rights reserved.

Nucleon-nucleon interaction: Central potential and pion production

We show that the tail of the chiral two-pion exchange nucleon-nucleon potential is proportional to the pion-nucleon (πN) scalar form factor and discuss how it can be translated into effective scalar meson interactions. We then construct a kernel for the process NN → πNN, due to the exchange of two pions, which may be used in either three-body forces or pion production in NN scattering. Our final expression involves a partial cancellation among three terms, due to chiral symmetry, but the net result is still important. We also find that, at large internucleon distances, the kernel has the same spatial dependence as the central NN potential and we produce expressions relating these processes directly.

Accurate ab initio potential energy surfaces for the (3)A '' and (3)A ' electronic states of the O(P-3) plus HBr system

In this work, we report the construction of potential energy surfaces for the (3)A '' and (3)A' states of the system O(P-3) + HBr. These surfaces are based on extensive ab initio calculations employing the MRCI+Q/CBS+SO level of theory. The complete basis set energies were estimated from extrapolation of MRCI+Q/aug-cc-VnZ(-PP) (n = Q, 5) results and corrections due to spin-orbit effects obtained at the CASSCF/aug-cc-pVTZ(-PP) level of theory. These energies, calculated over a region of the configuration space relevant to the study of the reaction O(P-3) + HBr -> OH + Br, were used to generate functions based on the many-body expansion. The three-body potentials were interpolated using the reproducing kernel Hilbert space method. The resulting surface for the (3)A '' electronic state contains van der Waals minima on the entrance and exit channels and a transition state 6.55 kcal/mol higher than the reactants. This barrier height was then scaled to reproduce the value of 5.01 kcal/mol, which was estimated from coupled cluster benchmark calculations performed to include high-order and core-valence correlation, as well as scalar relativistic effects. The (3)A' surface was also scaled, based on the fact that in the collinear saddle point geometry these two electronic states are degenerate. The vibrationally adiabatic barrier heights are 3.44 kcal/mol for the (3)A '' and 4.16 kcal/mol for the (3)A' state. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705428]

Predicting class II MHC-Peptide binding:a kernel based approach using similarity scores

Background - Modelling the interaction between potentially antigenic peptides and Major Histocompatibility Complex (MHC) molecules is a key step in identifying potential T-cell epitopes. For Class II MHC alleles, the binding groove is open at both ends, causing ambiguity in the positional alignment between the groove and peptide, as well as creating uncertainty as to what parts of the peptide interact with the MHC. Moreover, the antigenic peptides have variable lengths, making naive modelling methods difficult to apply. This paper introduces a kernel method that can handle variable length peptides effectively by quantifying similarities between peptide sequences and integrating these into the kernel. Results - The kernel approach presented here shows increased prediction accuracy with a significantly higher number of true positives and negatives on multiple MHC class II alleles, when testing data sets from MHCPEP [1], MCHBN [2], and MHCBench [3]. Evaluation by cross validation, when segregating binders and non-binders, produced an average of 0.824 AROC for the MHCBench data sets (up from 0.756), and an average of 0.96 AROC for multiple alleles of the MHCPEP database. Conclusion - The method improves performance over existing state-of-the-art methods of MHC class II peptide binding predictions by using a custom, knowledge-based representation of peptides. Similarity scores, in contrast to a fixed-length, pocket-specific representation of amino acids, provide a flexible and powerful way of modelling MHC binding, and can easily be applied to other dynamic sequence problems.

Design, Synthesis And Biological Evaluation Of Hybrid Bioisoster Derivatives Of N-acylhydrazone And Furoxan Groups With Potential And Selective Anti-trypanosoma Cruzi Activity.

Hybrid bioisoster derivatives from N-acylhydrazones and furoxan groups were designed with the objective of obtaining at least a dual mechanism of action: cruzain inhibition and nitric oxide (NO) releasing activity. Fifteen designed compounds were synthesized varying the substitution in N-acylhydrazone and in furoxan group as well. They had its anti-Trypanosoma cruzi activity in amastigotes forms, NO releasing potential and inhibitory cruzain activity evaluated. The two most active compounds (6, 14) both in the parasite amastigotes and in the enzyme contain the nitro group in para position of the aromatic ring. The permeability screening in Caco-2 cell and cytotoxicity assay in human cells were performed for those most active compounds and both showed to be less cytotoxic than the reference drug, benznidazole. Compound 6 was the most promising, since besides activity it showed good permeability and selectivity index, higher than the reference drug. Thereby the compound 6 was considered as a possible candidate for additional studies.

Antimicrobial And Antiproliferative Potential Of Anadenanthera Colubrina (vell.) Brenan.

The aim of the present study was to perform an in vitro analysis of the antimicrobial and antiproliferative potential of an extract from Anadenanthera colubrina (Vell.) Brenan (angico) and chemically characterize the crude extract. Antimicrobial action was evaluated based on the minimum inhibitory concentration (MIC), minimum bactericidal/fungicidal concentration, and the inhibition of formation to oral biofilm. Cell morphology was determined through scanning electron microscopy (SEM). Six strains of tumor cells were used for the determination of antiproliferative potential. The extract demonstrated strong antifungal activity against Candida albicans ATCC 18804 (MIC = 0.031 mg/mL), with similar activity found regarding the ethyl acetate fraction. The extract and active fraction also demonstrated the capacity to inhibit the formation of Candida albicans to oral biofilm after 48 hours, with median values equal to or greater than the control group, but the difference did not achieve statistical significance (P > 0.05). SEM revealed alterations in the cell morphology of the yeast. Regarding antiproliferative activity, the extract demonstrated cytostatic potential in all strains tested. The present findings suggest strong antifungal potential for Anadenanthera colubrina (Vell.) Brenan as well as a tendency toward diminishing the growth of human tumor cells.

Whole Cortical And Default Mode Network Mean Functional Connectivity As Potential Biomarkers For Mild Alzheimer's Disease.

The search for an Alzheimer's disease (AD) biomarker is one of the most relevant contemporary research topics due to the high prevalence and social costs of the disease. Functional connectivity (FC) of the default mode network (DMN) is a plausible candidate for such a biomarker. We evaluated 22 patients with mild AD and 26 age- and gender-matched healthy controls. All subjects underwent resting functional magnetic resonance imaging (fMRI) in a 3.0 T scanner. To identify the DMN, seed-based FC of the posterior cingulate was calculated. We also measured the sensitivity/specificity of the method, and verified a correlation with cognitive performance. We found a significant difference between patients with mild AD and controls in average z-scores: DMN, whole cortical positive (WCP) and absolute values. DMN individual values showed a sensitivity of 77.3% and specificity of 70%. DMN and WCP values were correlated to global cognition and episodic memory performance. We showed that individual measures of DMN connectivity could be considered a promising method to differentiate AD, even at an early phase, from normal aging. Further studies with larger numbers of participants, as well as validation of normal values, are needed for more definitive conclusions.

Antioxidant And Anti-diabetic Potential Of Passiflora Alata Curtis Aqueous Leaves Extract In Type 1 Diabetes Mellitus (nod-mice).

Leaves of Passiflora alata Curtis were characterized for their antioxidant capacity. Antioxidant analyses of DPPH, FRAP, ABTS, ORAC and phenolic compounds were made in three different extracts: aqueous, methanol/acetone and ethanol. Aqueous extract was found to be the best solvent for recovery of phenolic compounds and antioxidant activity, when compared with methanol/acetone and ethanol. To study the anti-inflammatory properties of this extract in experimental type 1 diabetes, NOD mice were divided into two groups: the P. alata group, treated with aqueous extract of P. alata Curtis, and a non-treated control group, followed by diabetes expression analysis. The consumption of aqueous extract and water ad libitum lasted 28 weeks. The treated-group presented a decrease in diabetes incidence, a low quantity of infiltrative cells in pancreatic islets and increased glutathione in the kidney and liver (p<0.05), when compared with the diabetic and non-diabetic control-groups. In conclusion, our results suggest that the consumption of aqueous extract of P. alata may be considered a good source of natural antioxidants and compounds found in its composition can act as anti-inflammatory agents, helping in the control of diabetes.

Bioremediation Potential Of Microorganisms Derived From Petroleum Reservoirs.

Bacterial strains and metagenomic clones, both obtained from petroleum reservoirs, were evaluated for petroleum degradation abilities either individually or in pools using seawater microcosms for 21 days. Gas Chromatography-Flame Ionization Detector (GC-FID) and Gas Chromatography-Mass Spectrometry (GC-MS) analyses were carried out to evaluate crude oil degradation. The results showed that metagenomic clones 1A and 2B were able to biodegrade n-alkanes (C14 to C33) and isoprenoids (phytane and pristane), with rates ranging from 31% to 47%, respectively. The bacteria Dietzia maris CBMAI 705 and Micrococcus sp. CBMAI 636 showed higher rates reaching 99% after 21 days. The metagenomic clone pool biodegraded these compounds at rates ranging from 11% to 45%. Regarding aromatic compound biodegradation, metagenomic clones 2B and 10A were able to biodegrade up to 94% of phenanthrene and methylphenanthrenes (3-MP, 2-MP, 9-MP and 1-MP) with rates ranging from 55% to 70% after 21 days, while the bacteria Dietzia maris CBMAI 705 and Micrococcus sp. CBMAI 636 were able to biodegrade 63% and up to 99% of phenanthrene, respectively, and methylphenanthrenes (3-MP, 2-MP, 9-MP and 1-MP) with rates ranging from 23% to 99% after 21 days. In this work, isolated strains as well as metagenomic clones were capable of degrading several petroleum compounds, revealing an innovative strategy and a great potential for further biotechnological and bioremediation applications.

Genetic Diversity Of Giardia Duodenalis: Multilocus Genotyping Reveals Zoonotic Potential Between Clinical And Environmental Sources In A Metropolitan Region Of Brazil.

Giardia duodenalis is a flagellate protozoan that parasitizes humans and several other mammals. Protozoan contamination has been regularly documented at important environmental sites, although most of these studies were performed at the species level. There is a lack of studies that correlate environmental contamination and clinical infections in the same region. The aim of this study is to evaluate the genetic diversity of a set of clinical and environmental samples and to use the obtained data to characterize the genetic profile of the distribution of G. duodenalis and the potential for zoonotic transmission in a metropolitan region of Brazil. The genetic assemblages and subtypes of G. duodenalis isolates obtained from hospitals, a veterinary clinic, a day-care center and important environmental sites were determined via multilocus sequence-based genotyping using three unlinked gene loci. Cysts of Giardia were detected at all of the environmental sites. Mixed assemblages were detected in 25% of the total samples, and an elevated number of haplotypes was identified. The main haplotypes were shared among the groups, and new subtypes were identified at all loci. Ten multilocus genotypes were identified: 7 for assemblage A and 3 for assemblage B. There is persistent G. duodenalis contamination at important environmental sites in the city. The identified mixed assemblages likely represent mixed infections, suggesting high endemicity of Giardia in these hosts. Most Giardia isolates obtained in this study displayed zoonotic potential. The high degree of genetic diversity in the isolates obtained from both clinical and environmental samples suggests that multiple sources of infection are likely responsible for the detected contamination events. The finding that many multilocus genotypes (MLGs) and haplotypes are shared by different groups suggests that these sources of infection may be related and indicates that there is a notable risk of human infection caused by Giardia in this region.