Some error estimates for the finite volume element method for a parabolic problem

We study spatially semidiscrete and fully discrete finite volume element methods for the homogeneous heat equation with homogeneous Dirichlet boundary conditions and derive error estimates for smooth and nonsmooth initial data. We show that the results of our earlier work \cite{clt11} for the lumped mass method carry over to the present situation. In particular, in order for error estimates for initial data only in $L_2$ to be of optimal second order for positive time, a special condition is required, which is satisfied for symmetric triangulations. Without any such condition, only first order convergence can be shown, which is illustrated by a counterexample. Improvements hold for triangulations that are almost symmetric and piecewise almost symmetric

Mafic alkaline metasomatism in the lithosphere underneath East Serbia: evidence from the study of xenoliths and the host alkali basalts

Effects of mafic alkaline metasomatism have been investigated by a combined study of the East Serbian mantle xenoliths and their host alkaline rocks. Fertile xenoliths and tiny mineral assemblages found in depleted xenoliths have been investigated. Fertile lithologies are represented by clinopyroxene (cpx)-rich lherzolite and spinel (sp)-rich olivine websterite containing Ti–Al-rich Cr-augite, Fe-rich olivine, Fe–Al-rich orthopyroxene and Al-rich spinel. Depleted xenoliths, which are the predominant lithology in the suite of East Serbian xenoliths, are harzburgite, cpx-poor lherzolite and rare Mg-rich dunite. They contain small-scale assemblages occurring as pocket-like, symplectitic or irregular, deformation-assisted accumulations of metasomatic phases, generally composed of Ti–Al- and incompatible element-rich Cr-diopside, Cr–Fe–Ti-rich spinel, altered glass, olivine, apatite, ilmenite, carbonate, feldspar, and a high-TiO2 (c. 11 wt%) phlogopite. The fertile xenoliths are too rich in Al, Ca and Fe to simply represent undepleted mantle. By contrast, their composition can be reproduced by the addition of 5–20 wt% of a basanitic melt to refractory mantle. However, textural relationships found in tiny mineral assemblages inside depleted xenoliths imply the following reaction: opx+sp1 (primary mantle Cr-spinel) ±phlogopite+Si-poor alkaline melt=Ti–Al-cpx+sp2 (metasomatic Ti-rich spinel)±ol±other minor phases. Inversion modelling, performed on the least contaminated and most isotopically uniform host basanites (87Sr/86Sr=c. 0.7031; 143Nd/144Nd=c. 0.5129), implies a source that was enriched in highly and moderately incompatible elements (c. 35–40× chondrite for U–Th–Nb–Ta, 2× chondrite for heavy rare earth elements (HREE), made up of clinopyroxene, carbonate (c. 5%), and traces of ilmenite (c. 1%) and apatite (c. 0.05%). A schematic model involves: first, percolation of CO2- and H2O-rich fluids and precipitation of metasomatic hydrous minerals; and, second, the subsequent breakdown of these hydrous minerals due to the further uplift of hot asthenospheric mantle. This model links intraplate alkaline magmatism to lithospheric mantle sources enriched by sublithospheric melts at some time in the past

Variations in the squamous part of the occipital bone in medieval and contemporary cranial series from Bulgaria

The squamous part of the occipital bone is a place of many different variations. They are a result of faulty ossification in the occipital squama or due to the presence of sutural bones in the lambda region. As their differentiation is intricate because of the various criteria used, the issue of their recognition in the adult skull still remains difficult even though they can be clearly distinguished at a younger age. The aim of the present study was to compare the frequency of interparietal, preinterparietal and sutural bones in the lambda region in medieval male and female cranial series as well as between medieval and contemporary male series from Bulgaria. We also discuss the development of the occipital squama in order to set clearer criteria for further differentiation of such variations in the adult skull. In the reviewed 3 cranial series, the variations in the squamous portion of the occipital bone were observed with a low frequency. The incidence of preinterparietal bones was more common than the interparietal ones. The sutural bones in the lambda region were numerous in the series. No statistically significant sex or intergroup differences were established. So even if these anatomical variations are relatively rare, the understanding of them is of significance for many disciplines like anthropology, comparative and developmental anatomy, clinical and forensic medicine.

Radiofrequency catheter ablation in a child with Wolff-Parkinson-White syndrome and congenitally corrected transposition of the great arteries

The case is presented of a five-year-old boy with Wolff-Parkinson-White syndrome, who had undergone three surgical palliations because of congenitally corrected transposition of the great arteries, ventricular septal defect and pulmonary trunk near-atresia. Successful and uncomplicated radiofrequency catheter ablation of an accessory pathway located across the systemic atrioventricular valve ring was performed. The procedure was motivated by forthcoming corrective surgery, which would preclude venous access to the heart. This case emphasizes the need for precise timing of ablative therapy in such patients and shows that surgery itself may facilitate catheter ablation. (Cardiol J 2007; 14: 500-503

Facial soft tissue thicknesses in Bulgarian adults: relation to sex, body mass index and bilateral asymmetry

Background: The aim of the study is to measure the facial soft tissue thicknesses (STTs) in Bulgarians, to evaluate the relation of the STTs to the nutritional status, sex and bilateral asymmetry, and to examine the correlations between the separate STTs as well as between the STTs and body weight, height, and body mass index (BMI). In the present study, the facial STTs were measured on computed tomography scans of the head of Bulgarian adults. Materials and methods: The STTs were measured at 7 midline and 9 bilateral landmarks. The measurements were performed in the free software InVesalius in the axial and sagittal planes. The mean, standard deviation, minimum and maximum values, median and coefficient of variation were reported for the STT at each landmark according to the sex and BMI category. The BMI, sex and bilateral differences were assessed for statistical significance. Pearson correlation analysis was applied to assess the strength and direction of the relationships between the STTs and body height, weight and BMI, as well as between separate STTs. Results and Conclusions: The facial soft tissues in Bulgarian adults changed in accordance with the nutritional status of the individual and in both sexes all STTs augmented with the increasing BMI. For both normal and overweight BMI categories, males had more soft tissue at the majority of facial points than females, as the only exceptions were observed in the cheek zone, where STTs were thicker in females. Significant bilateral differences were observed in either sex and BMI category. Stronger correlations were established for the STTs in the jaw region and between the cheek and jaw soft tissues. Besides, the correlations between the homologous bilateral landmarks were among the strongest ones

Human Subtilase SKI-1/S1P Is a Master Regulator of the HCV Lifecycle and a Potential Host Cell Target for Developing Indirect-Acting Antiviral Agents

HCV infection is a major risk factor for liver cancer and liver transplantation worldwide. Overstimulation of host lipid metabolism in the liver by HCV-encoded proteins during viral infection creates a favorable environment for virus propagation and pathogenesis. In this study, we hypothesize that targeting cellular enzymes acting as master regulators of lipid homeostasis could represent a powerful approach to developing a novel class of broad-spectrum antivirals against infection associated with human Flaviviridae viruses such as hepatitis C virus (HCV), whose assembly and pathogenesis depend on interaction with lipid droplets (LDs). One such master regulator of cholesterol metabolic pathways is the host subtilisin/kexin-isozyme-1 (SKI-1) – or site-1 protease (S1P). SKI-1/S1P plays a critical role in the proteolytic activation of sterol regulatory element binding proteins (SREBPs), which control expression of the key enzymes of cholesterol and fatty-acid biosynthesis. Here we report the development of a SKI-1/S1P-specific protein-based inhibitor and its application to blocking the SREBP signaling cascade. We demonstrate that SKI-1/S1P inhibition effectively blocks HCV from establishing infection in hepatoma cells. The inhibitory mechanism is associated with a dramatic reduction in the abundance of neutral lipids, LDs, and the LD marker: adipose differentiation-related protein (ADRP)/perilipin 2. Reduction of LD formation inhibits virus assembly from infected cells. Importantly, we confirm that SKI-1/S1P is a key host factor for HCV infection by using a specific active, site-directed, small-molecule inhibitor of SKI-1/S1P: PF-429242. Our studies identify SKI-1/S1P as both a novel regulator of the HCV lifecycle and as a potential host-directed therapeutic target against HCV infection and liver steatosis. With identification of an increasing number of human viruses that use host LDs for infection, our results suggest that SKI-1/S1P inhibitors may allow development of novel broad-spectrum biopharmaceuticals that could lead to novel indirect-acting antiviral options with the current standard of care

Bi-Legendrian manifolds and paracontact geometry

We study the interplays between paracontact geometry and the theory of bi-Legendrian manifolds. We interpret the bi-Legendrian connection of a bi-Legendrian manifold M as the paracontact connection of a canonical paracontact structure induced on M and then we discuss many consequences of this result both for bi-Legendrian and for paracontact manifolds. Finally new classes of examples of paracontact manifolds are presented.Comment: to appear in Int. J. Geom. Meth. Mod. Phy