Stabilization in relation to wavenumber in HDG methods

Simulation of wave propagation through complex media relies on proper understanding of the properties of numerical methods when the wavenumber is real and complex. Numerical methods of the Hybrid Discontinuous Galerkin (HDG) type are considered for simulating waves that satisfy the Helmholtz and Maxwell equations. It is shown that these methods, when wrongly used, give rise to singular systems for complex wavenumbers. A sufficient condition on the HDG stabilization parameter for guaranteeing unique solvability of the numerical HDG system, both for Helmholtz and Maxwell systems, is obtained for complex wavenumbers. For real wavenumbers, results from a dispersion analysis are presented. An asymptotic expansion of the dispersion relation, as the number of mesh elements per wave increase, reveal that some choices of the stabilization parameter are better than others. To summarize the findings, there are values of the HDG stabilization parameter that will cause the HDG method to fail for complex wavenumbers. However, this failure is remedied if the real part of the stabilization parameter has the opposite sign of the imaginary part of the wavenumber. When the wavenumber is real, values of the stabilization parameter that asymptotically minimize the HDG wavenumber errors are found on the imaginary axis. Finally, a dispersion analysis of the mixed hybrid Raviart-Thomas method showed that its wavenumber errors are an order smaller than those of the HDG method

The Yoneda algebra of a graded Ore extension

Let A be a connected-graded algebra with trivial module k, and let B be a graded Ore extension of A. We relate the structure of the Yoneda algebra E(A) := Ext_A(k,k) to E(B). Cassidy and Shelton have shown that when A satisfies their K_2 property, B will also be K_2. We prove the converse of this result.Comment: 9 page

Angular Resolution of an EAS Array for Gamma Ray Astronomy at Energies Greater Than 5 x 10 (13) Ev

A 24 detector extensive air shower array is being operated at Ootacamund (2300 m altitude, 11.4 deg N latitude) in southern India for a study of arrival directions of showers of energies greater than 5 x 10 to the 13th power eV. Various configurations of the array of detectors have been used to estimate the accuracy in determination of arrival angle of showers with such an array. These studies show that it is possible to achieve an angular resolution of better than 2 deg with the Ooty array for search for point sources of Cosmic gamma rays at energies above 5 x 10 to the 13th power eV

\u3ci\u3eIn vivo\u3c/i\u3e Liver Endocytosis Followed by Purification of Liver Cells by Liver Perfusion

The liver is the metabolic center of the mammalian body and serves as a filter for the blood. The basic architecture of the liver is illustrated in figure 1 in which more than 85% of the liver mass is composed of hepatocytes and the remaining 15% of the cellular mass is composed of Kupffer cells (KCs), stellate cells (HSCs), and sinusoidal endothelial cells (SECs). SECs form the blood vessel walls within the liver and contain specialized morphology called fenestrae within in the cytoplasm. Fenestration of the cytoplasm is the appearance of holes (˜100 μm) within the cells so that the SECs act as a sieve in which most chylomicrons, chylomicron remnants and macromolecules, but not cells, pass through to the hepatocytes and HSCs 1 (Fig. 1). Due to the lack of a basement membrane, the gap between the SECs and hepatocytes form the Space of Disse. HSCs occupy this space and play a prominent role in regulation and response to injury, storage of retinoic acid and immunoregulation of the liver 2. SECs are among the most endocytically active cells of the body displaying an array of scavenger receptors on their cell surface 3. These include SR-A, Stabilin-1 and Stabilin-2. Generally, small colloidal particles less than 230 nm and macromolecules in buffer phase are taken up by SECs, whereas, large particles and cellular debris is endocytosed (phagocytosed) by KCs 4. Thus, the bulk clearance of extracellular material such as the glycosaminoglycans from blood is largely dependent on the health and endocytic functions of SECs 5,6. For example, an increase in blood hyaluronan levels is indicative of liver disease ranging from mild to more severe forms 7. With the exception of one report 8, there are no immortalized SEC cell lines in existence. Even this immortalized cell line is de-differentiated in that it does not express scavenger receptors that are present on primary SECs (our data, not shown). All cell biological studies must be performed on primary cells obtained freshly from the animal. Unfortunately, SECs dedifferentiate under standard culture conditions and must be used within 1 or 2 days upon isolation from the animal. Differentiation of SECs is marked by the expression of Stabilin-2 or HARE receptor 9 , CD31, and the presence of cytoplasmic fenestration 1. Differentiation of SECs can be extended by the addition of VEGF in culture media or by culturing cells in hepatocyte conditioned medium 10,11. In this report, we will demonstrate the endocytic activity of SECs in the intact organ using radio-labeled heparin for hyaluronan for the SECspecific Stabilin-2 receptor. We will then purify hepatocytes and SECs from the perfused liver to measure endocytosis

Phytochemical screening and antimicrobial activity of Capsicum chinense Jacq.

The present study investigated on the comparative evaluation of the extraction, quantification, phytochemical and antimicrobial activity of Capsaicin from acetone and acetonitrile extracts of Capsicum chinense Jacq. The polar aprotic solvent extracts showed high amount of Capsaicin with pungency level of 1,529,500 Scoville Heat Units. The Thin layer chromatography method is providing a fingerprint of plant extract. The Capsaicin extracted in the solvents on TLC chromatogram was viewed under UV 254 nm and UV 366 nm and documented. The extraction and estimation of chlorophyll and Carotenoids were also performed for the plant sample following standard procedure. Phytochemical analysis shows that acetone and acetonitrile extract of callus, leaf, shoot, fruit and seed which shows abundant presence of alkaloids, flavonoids, phenols, saphonins etc. The acetone and acetonitrile extract showed maximum zone of inhibition of Klebsiella pneumonia and Staphylococcus aureus against the gram positive and gram negative bacteria respectively through agar well diffusion method. The acetone and acetonitrile extract was found to be more effective at different concentration against all the tested bacteria and fungi. The results revealed that the Capsaicin and other secondary metabolites present in the acetone and acetonitrile extract of Capsicum chinense would contribute for the further extraction and purification of capsaicin as an antimicrobial agent

In vivo Liver Endocytosis Followed by Purification of Liver Cells by Liver Perfusion

The liver is the metabolic center of the mammalian body and serves as a filter for the blood. The basic architecture of the liver is illustrated in figure 1 in which more than 85% of the liver mass is composed of hepatocytes and the remaining 15% of the cellular mass is composed of Kupffer cells (KCs), stellate cells (HSCs), and sinusoidal endothelial cells (SECs). SECs form the blood vessel walls within the liver and contain specialized morphology called fenestrae within in the cytoplasm. Fenestration of the cytoplasm is the appearance of holes (˜100 μm) within the cells so that the SECs act as a sieve in which most chylomicrons, chylomicron remnants and macromolecules, but not cells, pass through to the hepatocytes and HSCs 1 (Fig. 1). Due to the lack of a basement membrane, the gap between the SECs and hepatocytes form the Space of Disse. HSCs occupy this space and play a prominent role in regulation and response to injury, storage of retinoic acid and immunoregulation of the liver 2