Finite element solution of a linear mixed-type functional differential equation

This paper is devoted to the approximate solution of a linear first-order functional differential equation which involves delayed and advanced arguments. We seek a solution x, defined for t?∈?(0, k???1],(k?∈?IN ), which takes given values on the intervals [???1, 0] and (k???1, k]. Continuing the work started in previous articles on this subject, we introduce and analyse a computational algorithm based on the finite element method for the solution of this problem which is applicable both in the case of constant and variable coefficients. Numerical results are presented and compared with the results obtained by other methods.     

Alternating Sign Multibump Solutions of Nonlinear Elliptic Equations in Expanding Tubular Domains

Let Γ denote a smooth simple curve in ? ^N , N ≥ 2, possibly with boundary. Let Ω _R be the open normal tubular neighborhood of radius 1 of the expanded curve RΓ: = {Rx | x ∈ Γ??Γ}. Consider the superlinear problem ? Δu + λu = f(u) on the domains Ω _R , as R → ∞, with homogeneous Dirichlet boundary condition. We prove the existence of multibump solutions with bumps lined up along RΓ with alternating signs. The function f is superlinear at 0 and at ∞, but it is not assumed to be odd. If the boundary of the curve is nonempty our results give examples of contractible domains in which the problem has multiple sign changing solutions.     

Suiformes orthologous satellite DNAs as a hallmark of Pecari tajacu and Tayassu pecari (Tayassuidae) evolutionary rearrangements

In a broad general way, eukaryotic satellite DNA sequences are characterized by a highly dynamic molecular behavior due to concerted evolution that leads to rapid change between repeat sequences of different species, achieved by amplification of new variants during speciation or by gradual sequence evolution due to the accumulation of nucleotide substitutions. There are, although exceptions for this almost universal rule. We isolated variants from both the Mc1 and Ac2 pig (Sus scrofa, Suidae) satellite DNA families from the genomes of two Tayassuidae members: Pecari tajacu and Tayassu pecari, which have highly derived karyotypes. The presence of these sequences in both families’ genomes (Suidae and Tayassuidae) implies their existence in a common ancestor, what confers to the variants the status of orthology and the approximate age of, at least 40 million years.While at the molecular composition level these orthologous sequences are highly homologous, cross-species physical mapping revealed a completely different chromosomal location in Suidae versus Tayassuidae families, most probably, reflecting the high level of divergence and chromosomes evolution pathways after radiation of each family. Detailed comparative analysis of the satellites assignment on the peccary's chromosomes revealed its co-localization with homologous evolutionary breakpoints in both species, suggesting their involvement in the rearrangement events. The complex behavior of the repeats evolution in the pig/peccaries genomes is here clearly illustrated. These sequences are molecularly preserved for a considerable period of time and display slow rates of sequence change, but show a dynamic motion behavior throughout the peccary's genomes that accompanied the great architectonic reorganization of Tayassuidae chromosomes during evolution.     

Determination of dimethylarginine levels in rats using HILIC-MS/MS: an in vivo microdialysis study

Nitric oxide (NO) is one of the most important mediators and neurotransmitters and its levels change under pathological conditions. NO production may be regulated by endogenous nitric oxide synthase (NOS) inhibitors, in particular asymmetric dimethylarginine (ADMA). Most of the interest is focused on ADMA, since this compound is present in plasma and urine and accumulation of ADMA has been described in many disease states but little is known about cerebrospinal fluid (CSF) concentrations of this compound and of its structural isomer symmetric dimethylarginine (SDMA). To determine the levels of methylarginines, we here present a new hydrophilic interaction chromatography (HILIC)-MS/MS method for the precise determination of these substances in CSF from microdialysis samples of rat prefrontal cortex (PFC). The method requires only minimal sample preparation and features isotope-labelled internal standards.     

Homophymine A, an anti-HIV cyclodepsipeptide from the sponge Homophymia sp

A new anti-HIV cyclodepsipeptide, homophymine A, was isolated from a New Caledonian collection of the marine sponge Homophymia sp. The structure of homophymine A was determined by interpretation of spectroscopic data, acid hydrolysis, and LC-MS analysis. Homophymine A contains 11 amino acid residues and an amide-linked 3-hydroxy-2,4,6-trimethyloctanoic acid moiety. Along with four D-, two L-, and one N-methyl amino acids, it also contains four unusual amino acid residues: (2S,3S,4R)-3,4-diMe-Gln, (2R,3R,4S)-4-amino-2,3-dihydroxy-1,7-heptandioic acid, L-ThrOMe, and (2R,3R,4R)-2-amino-3-hydroxy-4,5-dimethylhexanoic acid. In a cell-based XTT assay, homophymine A exhibited cytoprotective activity against HIV-1 infection with a IC50 of 75 nM.     

Structure-based approach for identification of novel phenylboronic acids as serine-β-lactamase inhibitors

β-Lactamases are bacterial enzymes conferring resistance to β-lactam antibiotics in clinically-relevant pathogens, and represent relevant drug targets. Recently, the identification of new boronic acids (i.e. RPX7009) paved the way to the clinical application of these molecules as potential drugs. Here, we screened in silico a library of ~1400 boronic acids as potential AmpC β-lactamase inhibitors. Six of the most promising candidates were evaluated in biochemical assays leading to the identification of potent inhibitors of clinically-relevant β-lactamases like AmpC, KPC-2 and CTX-M-15. One of the selected compounds showed nanomolar K _i value with the clinically-relevant KPC-2 carbapenemase, while another one exhibited broad spectrum inhibition, being also active on Enterobacter AmpC and the OXA-48 class D carbapenemase.     

Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces

A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz.