THE BERGMAN KERNEL FUNCTION

In this note, we point out that a large family of n x n matrix valued kernel functions defined on the unit disc D subset of C, which were constructed recently in [9], behave like the familiar Bergman kernel function on ID in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered using this likeness.

Slow m=1 instabilities of softened gravity Keplerian discs

We present the simplest model that permits a largely analytical exploration of the m =1 counter-rotating instability in a `hot' nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using the Wentzel-Kramers-Brillouin approximation. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian discm must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.

Boxicity and cubicity of asteroidal triple free graphs

The boxicity of a graph G, denoted box(G), is the least integer d such that G is the intersection graph of a family of d-dimensional (axis-parallel) boxes. The cubicity, denoted cub(G), is the least dsuch that G is the intersection graph of a family of d-dimensional unit cubes. An independent set of three vertices is an asteroidal triple if any two are joined by a path avoiding the neighbourhood of the third. A graph is asteroidal triple free (AT-free) if it has no asteroidal triple. The claw number psi(G) is the number of edges in the largest star that is an induced subgraph of G. For an AT-free graph G with chromatic number chi(G) and claw number psi(G), we show that box(G) <= chi(C) and that this bound is sharp. We also show that cub(G) <= box(G)([log(2) psi(G)] + 2) <= chi(G)([log(2) psi(G)] + 2). If G is an AT-free graph having girth at least 5, then box(G) <= 2, and therefore cub(G) <= 2 [log(2) psi(G)] + 4. (c) 2010 Elsevier B.V. All rights reserved.

Raman and infra-red spectra of crystalline ammonium sulphamate

Raman spectrum of a single crystal of ammonium sulphamate has been recorded for the two different orientations using λ 2537 resonance radiation of the mercury as the exciter. Thirty-four Raman lines have been observed of which eight belong to the lattice oscillations. Weak hydrogen bonding of NH2 group in the crystal was predicted. The infra-red absorption spectrum of the substance was taken in the powder form in potassium bromide disc, using Carl Zeiss UR10 IR spectrometer. Thirty-five absorption maxima could be identified.

Raman and infra-red spectra of crystalline potassium sulphamate

Raman spectrum of a single crystal of potassium sulphamate has been recorded for the first time using λ 2536 radiation of mercury as the exciter. Thirty-three Raman lines have been observed of which nine belong to the lattice oscillations. The infra-red absorption spectrum of the substance was taken in the powder form in potassium bromide disc using Carl Zeiss UR 10 IR spectrometer. Thirty-six absorption maxima could be identified of which twenty-five have been recorded for the first time. The analysis clearly shows that the N-H bond in the crystalline potassium sulphamate is not hydrogen-bonded to any appreciable extent.

Studies in bubble formation - IV: bubble formation at porous discs

Bubble formation from porous discs submerged in liquids of different physical properties has been investigated. It is found the number of sites effective for bubble formation is much smaller than the total potentially available sites. The number of effective sites is found to be a function of the surface tension, viscosity, and density of the liquid and the gas flow rate through the disc. A model proposed on the basis of bubble formation from an isolated nozzle and the close packed arrangement of the formed bubbles, explains the phenomenon adequately. © 1970.

Flow of non-newtonian fluid between torsionally oscillating discs

The flow of an incompressible non-Newtonian viscous fluid contained between two torsionally oscillating infinite parallel discs is investigated. The two specific cases studied are (i) one disc only oscillates while the other is at rest and (ii) both discs oscillate with the same frequency and amplitude but in opposite directions. Assuming that the amplitude of oscillation,Ω/n, is small and neglecting the squares and higher powers ofΩ/n, the equations of motion have been solved exactly for velocity and pressure satisfying all the boundary conditions. The effect of both positive and negative coefficients of cross-viscosity on the steady components of the flow has been represented graphically.

Drosophila indirect flight muscle specific Act88F actin mutants as a model system for studying congenital myopathies of the human ACTA1 skeletal muscle actin gene

Most human ACTA1 skeletal actin gene mutations cause dominant, congenital myopathies often with severely reduced muscle function and neonatal mortality. High sequence conservation of actin means many mutated ACTA1 residues are identical to those in the Drosophila Act88F, an indirect flight muscle specific sarcomeric actin. Four known Act88F mutations occur at the same actin residues mutated in ten ACTA1 nemaline mutations, A138D/P, R256H/L, G268C/D/R/S and R372C/S. These Act88F mutants were examined for similar muscle phenotypes. Mutant homozygotes show phenotypes ranging from a lack of myofibrils to almost normal sarcomeres at eclosion. Aberrant Z-disc-like structures and serial Z-disc arrays, ‘zebra bodies’, are observed in homozygotes and heterozygotes of all four Act88F mutants. These electron-dense structures show homologies to human nemaline bodies/rods, but are much smaller than those typically found in the human myopathy. We conclude that the Drosophila indirect flight muscles provide a good model system for studying ACTA1 mutations.

Effect of densification and TiB2 reinforcement on the wear of molybdenum disilicide

Wear tests were done in a pin-on-disc machine by sliding MoSi2 pins against hard-steel discs in a normal load range of 5-140 N and a speed of 0.5 m/s under nominally dry conditions in the ambient. The specific wear rate of the pin undergoes two transitions: severe to mild at low load and mild to severe at high load. The mild-wear domain is distinguished by the formation of a protective mechanically mixed layer of steel and its oxides, transferred from the counterface in particulate form. Increasing the hardness by densification and TiB2 reinforcement lowers the specific wear rate and expands the mild-wear load domain. However, even when the volume wear rate is normalised with respect to the real contact area (load/hardness) the non-dimensional wear factor is still seen to decrease with densification and reinforcement. This indicates that fracture toughness may also play an important role in determining the wear-resistance of these materials. The surface coverage on the pin by the mechanically mixed layer increases with densification and reinforcement.

Sorghum proteinase inhibitors: purification and some biochemical properties

An investigation has been carried out on the proteinase inhibitors of grain sorghum (Sorghum bicolor (L.) Moench). One of the inhibitors has been isolated in a pure form and characterized. The proteinase inhibitor was extracted from the acetone-defatted sorghum meal and purified by selective thermal denaturation, ammonium sulfate fractionation, Sephadex gel filtration and DEAE-cellulose chromatography (DEAE-preparation II). This preparation was demonstrated to be a mixture of three inhibitor components by polyacrylamide disc gel electrophoresis. Further resolution of this mixture into Inhibitors I to III was achieved by QAE-Sephadex chromatography. Sorghum Inhibitor III was homogeneous by the criteria of disc gel electrophoresis and has been more fully characterized. A molecular weight of 25,000 was obtained for Inhibitor III by gel filtration and was in agreement with the value calculated from the amino acid composition of the inhibitor. The N-terminal amino acid residue of Inhibitor III, a single chain protein, was isoleucine. Sorghum proteinase inhibitors inhibit specifically the serine proteinases and are inactive towards the other classes of proteinases. Inhibitor III is primarily a chymotrypsin inhibitor, whereas Inhibitors I and II inhibit both trypsin and chymotrypsin.

Changes to near-surface region of PTFE during dry sliding against steel

PTFE specimens were slid against an EN24 disc. The unworn and worn surfaces as well as the wear debris were examined by X-ray diffraction. Sliding was found to introduce (i) shrinkage of the unit cell, (ii) enlargement of crystallites and (iii) residual stresses in the slid PTFE surface. No conformational changes in the 157 helix could be observed due to sliding. The wear debris was found to be 1 mgrm thick warped laminates.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Purification of goat serum retinol-binding protein and preparation of its antibodies

The method for the purification of goat serum retinol-binding protein consists of DEAE-cellulose chromatography of the serum followed by preparative polyacrylamide disc gel electrophoresis. After electrophoresis, the retinol-binding protein containing zone is identified by the specific fluorescence of retinol. For raising the antibodies, the portion of the gel containing retinol binding protein is homogenized and injected intradermally and intramuscularly to rabbits. The availability of this simple method for the isolation of retinol-binding protein and production of its antibodies enables the development of a radioimmunoassay for this protein.

Lubricated Tribology of a Eutectic Aluminium-Silicon Alloy in the Ultra-Mild Wear and Mild Wear Regimes for Long Sliding Times

Aluminium-silicon alloy, an important material used for the construction of internal combustion engines, exhibit pressure induced distinct regimes of wear and friction; ultra-mild and mild. In this work the alloy is slid lubricated against a spherical steel pin at contact pressures characteristic of the two test regimes, at a very low sliding velocity. In both cases, the friction is controlled at the initial stages of sliding by the abrasion of the steel pin by the protruding silicon particles of the disc. The generation of nascent steel chips helps to breakdown the additive in the oil by a cationic exchange that yields chemical products of benefits to the tribology. The friction is initially controlled by abrasion, but the chemical products gain increasing importance in controlling friction with sliding time. After long times, depending on contact pressure, the chemical products determine sliding friction exclusively. In this paper, a host of mechanical and spectroscopic techniques are used to identify and characterize mechanical damage and chemical changes. Although the basic dissipation mechanisms are the same in the two regimes, the matrix remains practically unworn in the low-pressure ultra-mild wear regime. In the higher pressure regime at long sliding times a small but finite wear rate prevails. Incipient plasticity in the subsurface controls the mechanism of wear.

Numerical estimation of hotspot temperatures in electrodes subjected to pulsed electron beam heating in vacuum

A numerical solution for the transient temperature distribution in a cylindrical disc heated on its top surface by a circular source is presented. A finite difference form of the governing equations is solved by the Alternating Direction Implicit (ADI) time marching scheme. This solution has direct applications in analyzing transient electron beam heating of target materials as encountered in the prebreakdown current enhancement and consequent breakdown in high voltage vacuum gaps stressed by alternating and pulsed voltages. The solution provides an estimate of the temperature for pulsed electron beam heating and the size of thermally activated microparticles originating from anode hot spots. The calculated results for a typical 45kV (a.c.) electron beam of radius 2.5 micron indicate that the temperature of such spots can reach melting point and could give rise to microparticles which could initiate breakdown.