On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

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.

A MAS NMR investigation of aluminosilicate, silicophosphate, and aluminosilicophosphate gels and the evolution of crystalline structures on heating the gels

Gels of various composition containing SiO2, Al2O3, and P2O5 have been investigated by employing high resolution magic-angle-spinning (MAS) 27Al, 29Si, and 31P NMR spectroscopy. Changes occurring in the NMR spectra as the gels are progressively heated have been examined to understand the nature of structural changes occurring during the crystallization of the gels. 27Al resonance is sensitive to changes in the coordination number even when the Al concentration is as low as 1 mol%. As the percentage of Al increases, the hydroxyl groups tend to be located on the Al sites while Si remains as SiO4/2 (Q4). Mullite is the major phase formed at higher temperature in the aluminosilicate gels. In the case of the silicophosphate gels, Si is present in the form of Q4 and Q3 species. There is a change in the coordination of Si from four to six as the gel is heated. The formation of six-coordinated Si is facilitated even at lower temperatures (~673 K) when the P2O5 content is high. The phosphorus atoms present as orthophosphoric acid units in the xerogels change over to metaphosphate-like units as the gel is heated to higher temperatures. In aluminosilicophosphates, Si is present as Q4 and Q3 species while P is present as metaphosphate units; Al in these gels seems to be inducted into the tetrahedral network positions.

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.

Heterogeneous nucleation of solidification of cadmium particles embedded in an aluminium matrix

A hypomonotectic alloy of Al-4.5wt%Cd has been manufactured by melt spinning and the resulting microstructure examined by transmission electron microscopy. As-melt spun hypomonotectic Al-4.5wt%Cd consists of a homogeneous distribution of faceted 5 to 120 nm diameter cadmium particles embedded in a matrix of aluminium, formed during the monotectic solidification reaction. The cadmium particles exhibit an orientation relationship with the aluminium matrix of {111}Al//{0001}Cd and lang110rangAlAl//lang11¯20> Cd, with four cadmium particle variants depending upon which of the four {111}Al planes is parallel to {0001}Cd. The cadmium particles exibit a distorted cuboctahedral shape, bounded by six curved {100}Al//{20¯23}Cd facets, six curved {111}Al/{40¯43}Cd facets and two flat {111}Al//{0001}Cd facets. The as-melt spun cadmium particle shape is metastable and the cadmium particles equilibrate during heat treatment below the cadmium melting point, becoming elongated to increase the surface area and decrease the separation of the {111}Al//{0001}Cd facets. The equilibrium cadmium particle shape and, therefore, the anisotropy of solid aluminium-solid cadmium and solid aluminium -liquid cadmium surface energies have been monitored by in situ heating in the transmission electron microscope over the temperature range between room temperature and 420 °C. The anisotropy of solid aluminium-solid cadmium surface energy is constant between room temperature and the cadmium melting point, with the {100}Al//{20¯23}Cd surface energy on average 40% greater than the {111}Al//{0001}Cd surface energy, and 10% greater than the {111}Al//{40¯43Cd surface energy. When the cadmium particles melt at temperatures above 321 °C, the {100}Al//{20¯23}Cd facets disappear and the {111}Al//{40¯43}Cd and {111}A1//{0001}Cd surface energies become equal. The {111}Al facets do not disappear when the cadmium particles melt, and the anisotropy of solid aluminium-liquid cadmium surface energy decreases gradually with increasing temperature above the cadmium melting point. The kinetics of cadmium solidification have been examined by heating and cooling experiments in a differential scanning calorimeter over a range of heating and cooling rates. Cadmium particle solidification is nucleated catalytically by the surrounding aluminium matrix on the {111}Al faceted surfaces, with an undercooling of 56 K and a contact angle of 42 °. The nucleation kinetics of cadmium particle solidification are in good agreement with the hemispherical cap model of heterogeneous nucleation.

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.

Sign Of The Order Parameter In Oriented Systems And Its Utility In The Study Of The Dynamic Properties Of Molecules

Novel one and two dimensional NMR techniques are proposed and utilized for the determination of the signs of the order parameters used for the study of the mobility of the fatty acid chains. The experiments designed to extract this information involve the use of the intensities of the side bands in the spectra of oriented systems spinning at the magic angle. Advantages of the two dimensional technique over the one dimensional method are discussed. The utility of the method in the study of the dynamic properties of membranes and model systems is pointed out.

Plant aspartate transcarbamylase: An affinity chromatographic method for the purification of the enzyme from germinated seedlings

A simple and rapid affinity chromatographic method for the isolation of aspartate transcarbamylase from germinated seedlings of mung bean (Phaseolus aureus) was developed. A partially purified preparation of the enzyme was chromatographed on an affinity column containing aspartate linked to CNBr-activated Sepharose 4B. Aspartate transcarbamylase was specifically eluted from the column with 10 mImage aspartate or 0.5 Image KCl. The enzyme migrated as a single sharp band during disc electrophoresis at pH 8.6 on polyacrylamide gels. Electrophoresis of the sodium dodecyl sulfate-treated enzyme showed two distinct protein bands, suggesting that the mung bean aspartate transcarbamylase was made up of nonidentical subunits. Like the enzyme purified by conventional procedures, this enzyme preparation also exhibited positive homotropic interactions with carbamyl phosphate and negative heterotropic interactions with UMP. This method was extended to the purification of aspartate transcarbamylase from Lathyrus sativus, Eleucine coracona, and Trigonella foenum graecum.

Isolation and characterization of thiamin-binding protein from chicken egg white

A thiamin-binding protein was isolated and characterized from chicken egg white by affinity chromatography on thiamin pyrophosphate coupled to aminoethyl-Sepharose. The high specificity of interaction between the thiamin-binding protein and the riboflavin-binding protein of the egg white, with a protein/protein molar ratio of 1.0, led to the development of an alternative procedure that used the riboflavin-binding protein immobilized on CNBr-activated Sepharose as the affinity matrix. The thiamin-binding protein thus isolated was homogeneous by the criteria of polyacrylamide-gel disc electrophoresis, double immunodiffusion and sodium dodecyl sulphate/polyacrylamide-gel electrophoresis, had a mol.wt. of 38,000 +/- 2000 and was not a glycoprotein. The protein bound [14C]thiamin was a molar ratio of 1.0, with dissociation constant (Kd) 0.3 micrometer.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

On some results of A. E. Livingston and coefficient problems for concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of a bounded convex set. We call these functions concave univalent functions. In 1994, Livingston presented a characterization for these functions. In this paper, we observe that there is a minor flaw with this characterization. We obtain certain sharp estimates and the exact set of variability involving Laurent and Taylor coefficients for concave functions. We also present the exact set of variability of the linear combination of certain successive Taylor coefficients of concave functions.