On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

The Linker Region in Receptor Guanylyl Cyclases Is a Key Regulatory Module MUTATIONAL ANALYSIS OF GUANYLYL CYCLASE C

Receptor guanylyl cyclases are multidomain proteins, and ligand binding to the extracellular domain increases the levels of intracellular cGMP. The intracellular domain of these receptors is composed of a kinase homology domain (KHD), a linker of similar to 70 amino acids, followed by the C-terminal guanylyl cyclase domain. Mechanisms by which these receptors are allosterically regulated by ligand binding to the extracellular domain and ATP binding to the KHD are not completely understood. Here we examine the role of the linker region in receptor guanylyl cyclases by a series of point mutations in receptor guanylyl cyclase C. The linker region is predicted to adopt a coiled coil structure and aid in dimerization, but we find that the effects of mutations neither follow a pattern predicted for a coiled coil peptide nor abrogate dimerization. Importantly, this region is critical for repressing the guanylyl cyclase activity of the receptor in the absence of ligand and permitting ligand-mediated activation of the cyclase domain. Mutant receptors with high basal guanylyl cyclase activity show no further activation in the presence of non-ionic detergents, suggesting that hydrophobic interactions in the basal and inactive conformation of the guanylyl cyclase domain are disrupted by mutation. Equivalent mutations in the linker region of guanylyl cyclase A also elevated the basal activity and abolished ligand-and detergent-mediated activation. We, therefore, have defined a key regulatory role for the linker region of receptor guanylyl cyclases which serves as a transducer of information from the extracellular domain via the KHD to the catalytic domain.

Flow Studies in Non Circular Tubes with Wall Injection

An analysis of inviscid incompressible flow in a tube of sinusoidally perturbed circular cross section with wall injection has been made. The velocity and pressure fields have been obtained. Measurements of axial velocity profiles and pressure distribution have been made in a simulated star shaped tube with wall injection. The static pressure at the star recess is found to be more than that at the star point, this feature being in conformity with the analytical result. Flow visualisation by photography of injected smoke seems to show simple diffusion rather than strong vortices in the recess.

Non-enzymatic reactions involving vitamin B6: Spectroscopic investigations on the effect of pH and metal ions on the decyclization reactions of the pyridoxal-histamine cyclized Schiff base

The effect of pH and metal ions (Cu2+, Zn2+, Cd2+, Mn2+, Cr3+, Co3+, and Mg2+) on the decyclization reactions of pyridoxal-histamine cyclized Schiff base has been studied using electronic spectroscopy. The study reveals that the cyclization reaction is irreversible with respect to pH and metal ions. Interest in this work derives from the possible involvement of cyclization reactions in the inhibitory activity of a number of pyridoxal-dependent enzymes.

Nucleotide sequence of the 3' terminal region of belladonna mottle virus-Iowa (renamed Physalis mottle virus) RNA and an analysis of the relationships of tymoviral coat proteins

The 3prime terminal 1255nt sequence of Physalis mottle virus (PhMV) genomic RNA has been determined from a set of overlapping cDNA clones. The open reading frame (ORF) at the 3prime terminus corresponds to the amino acid sequence of the coat protein (CP) determined earlier except for the absence of the dipeptide, Lys-Leu, at position 110-111. In addition, the sequence upstream of the CP gene contains the message coding for 178 amino acid residues of the C-terminus of the putative replicase protein (RP). The sequence downstream of the CP gene contains an untranslated region whose terminal 80 nucleotides can be folded into a characteristic tRNA-like structure. A phylogenetic tree constructed after aligning separately the sequence of the CP, the replicase protein (RP) and the tRNA-like structure determined in this study with the corresponding sequences of other tymoviruses shows that PhMV wrongly named belladonna mottle virus [BDMV(I)] is a separate tymovirus and not another strain of BDMV(E) as originally envisaged. The phylogenetic tree in all the three cases is identical showing that any subset of genomic sequence of sufficient length can be used for establishing evolutionary relationships among tymoviruses.

Non-bonded interactions in cyclobutane-thiones

Using UVPES and electronic spectral data the presence of an interaction between thd 1,3-thiocarbonyl groups in Image has been identified. EHT calculations also predict such an interaction. Presence of weak interaction between 1,3-carbonyl and thiocarbonyl groups in Image has been inferred from electronic absorption and emission spectra.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

The C-terminal domain is sufficient for endonuclease activity of Neisseria gonorrhoeae MutL

The mutL gene of Neisseria gonorrhoeae has been cloned and the gene product purified. We have found that the homodimeric N. gonorrhoeae MutL (NgoL) protein displays an endonuclease activity that incises covalently closed circular DNA in the presence of Mn2+, Mg2+ or Ca2+ ions, unlike human MutL alpha which shows endonuclease activity only in the presence of Mn2+. We report in the present paper that the C-terminal domain of N. gonorrhoeae MutL (NgoL-CTD) consisting of amino acids 460-658 exhibits Mn2+-dependent endonuclease activity. Sedimentation velocity, sedimentation equilibrium and dynamic light scattering experiments show NgoL-CTD to be a dimer. The probable endonucleolytic active site is localized to a metal-binding motif, DMHAX(2)EX(4)E, and the nicking endonuclease activity is dependent on the integrity of this motif. By in vitro comparison of wild-type and it mutant NgoL-CTD protein, we show that the latter protein exhibits highly reduced endonuclease activity. We therefore suggest that the mode of excision initiation in DNA mismatch repair may be different in organisms that lack MutH protein, but have MutL proteins that harbour the D[M/Q]HAX(2)EX(4)E motif.

The trishanku gene and terminal morphogenesis in Dictyostelium discoideum

P>Multicellular development in the social amoeba Dictyostelium discoideum is triggered by starvation. It involves a series of morphogenetic movements, among them being the rising of the spore mass to the tip of the stalk. The process requires precise coordination between two distinct cell types-presumptive (pre-) spore cells and presumptive (pre-) stalk cells. Trishanku (triA) is a gene expressed in prespore cells that is required for normal morphogenesis. The triA- mutant shows pleiotropic effects that include an inability of the spore mass to go all the way to the top. We have examined the cellular behavior required for the normal ascent of the spore mass. Grafting and mixing experiments carried out with tissue fragments and cells show that the upper cup, a tissue that derives from prestalk cells and anterior-like cells (ALCs), does not develop properly in a triA- background. A mutant upper cup is unable to lift the spore mass to the top of the fruiting body, likely due to defective intercellular adhesion. If wild-type upper cup function is provided by prestalk and ALCs, trishanku spores ascend all the way. Conversely, Ax2 spores fail to do so in chimeras in which the upper cup is largely made up of mutant cells. Besides proving that under these conditions the wild-type phenotype of the upper cup is necessary and sufficient for terminal morphogenesis in D. discoideum, this study provides novel insights into developmental and evolutionary aspects of morphogenesis in general. Genes that are active exclusively in one cell type can elicit behavior in a second cell type that enhances the reproductive fitness of the first cell type, thereby showing that morphogenesis is a cooperative process.

Role of Bacillus subtilis BacB in the Synthesis of Bacilysin

Bacilysin is a non-ribosomally synthesized dipeptide antibiotic that is active against a wide range of bacteria and some fungi. Synthesis of bacilysin (L-alanine-[2,3-epoxycyclohexano-4]-L-alanine) is achieved by proteins in the bac operon, also referred to as the bacABCDE (ywfBCDEF) gene cluster in B. subtilis. Extensive genetic analysis from several strains of B. subtilis suggests that the bacABC gene cluster encodes all the proteins that synthesize the epoxyhexanone ring of L-anticapsin. These data, however, were not consistent with the putative functional annotation for these proteins whereby BacA, a prephenate dehydratase along with a potential isomerase/guanylyl transferase, BacB and an oxidoreductase, BacC, could synthesize L-anticapsin. Here we demonstrate that BacA is a decarboxylase that acts on prephenate. Further, based on the biochemical characterization and the crystal structure of BacB, we show that BacB is an oxidase that catalyzes the synthesis of 2-oxo-3-(4-oxocyclohexa-2,5-dienyl)propanoic acid, a precursor to L-anticapsin. This protein is a bi-cupin, with two putative active sites each containing a bound metal ion. Additional electron density at the active site of the C-terminal domain of BacB could be interpreted as a bound phenylpyruvic acid. A significant decrease in the catalytic activity of a point variant of BacB with a mutation at the N-terminal domain suggests that the N-terminal cupin domain is involved in catalysis.

CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal non-equilibrium model

High frequency, miniature, pulse tube cryocoolers are extensively used in space applications because of their simplicity. Parametric studies of inertance type pulse tube cooler are performed with different length-to-diameter ratios of the pulse tube with the help of the FLUENT (R) package. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of porous zones, in addition to the wall thickness of the components. Dynamic characteristics and the actual mechanism of energy transfer in pulse are examined with the help of the pulse tube wall time constant. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the performance of the pulse tube refrigerator. The thermal non-equilibrium predicts a higher cold heat exchanger temperature compared to thermal equilibrium. The pressure drop through the porous medium has a strong non-linear effect due to the dominating influence of Forchheimer term over that of the linear Darcy term at high operating frequencies. The phase angle relationships among the pressure, temperature and the mass flow rate in the porous zones are also important in determining the performance of pulse tuberefrigerator.

Crystallization kinetics of SrBi2B2O7 glasses by non-isothermal methods

Transparent glasses of SrBi2B2O7 (SBBO) were fabricated via the conventional melt-quenching technique. The amorphous and the glassy nature of the as-quenched samples were, respectively, confirmed by X-ray powder diffraction (XRD) and differential scanning calorimetry (DSC). The glass transition (T (g)) and the crystallization parameters [crystallization activation energy (E (cr)) and Avrami exponent (n)] were evaluated under non-isothermal conditions using DSC. There was a close agreement between the activation energies for the crystallization process determined by Augis and Bennet and Kissinger methods. The variation of local activation energy [E (c)(x)] that was determined by Ozawa method, decreased with the fraction of crystallization (x). The Avrami exponent (n(x)) increased with the increase in fraction of crystallization (x) suggesting that there was a change over in the crystallization process from the surface to the bulk.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.