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.

Assignments of non-retail commercial leases: Some contentious issues

Assignment clauses in non-retail commercial leases are as infinitely varied as the circumstances in which disputes arise. Each clause must be individually interpreted as part of the lease in which it is embedded. Whilst the assignment of a lease is one of the most commonplace transactions between lessor and lessee, the case law reveals few unifying principles. This article seeks to cautiously identify a set of principles which should be in the mind of any lawyer when a dispute relating to an assignment arises. It concludes with a short checklist of matters which must be considered by such a person to encourage the application of principles in the first instance towards a resolution of the dispute.

Structural studies of analgesics and their interactions. Part 4. Crystal structures of phenylbutazone and a 2 : 1 complex between phenylbutazone and piperazine

The X-ray crystal structures of 4-butyl-1,2-diphenylpyrazolidine-3,5-dione (phenylbutazone)(I). and its 2 : 1 complex (II) with piperazine have been determined by direct methods and the structures refined to R 0.096 (2 300 observed reflections measured by diffractometer) and 0.074 (2 494 observed reflections visuallyestimated). Crystals are monoclinic, space group P21/c; for (I)a= 21.695(4), b= 5.823(2), c= 27.881(4)Å, = 108.06 (10)°, Z= 8, and for (II)a= 8.048(4), b= 15.081(4), c= 15.583(7)Å, = 95.9(3)°, Z= 2. The two crystallographically independant molecules in the structure of (I) are similar except for the conformation of the butyl group, which is disordered in one of the molecules. In the pyrazolidinedione group, the two C–C bonds are single and the two C–O bonds double. The two nitrogen atoms in the five-membered ring are pyramidal with the attached phenyl groups lying on the opposite sides of the mean plane of the ring. The phenylbutazone molecule in (II) exists as a negative ion owing to deprotonation of C-4. C-4 is therefore trigonal and the orientation of the Bu group with respect to the pyrazolidinedione group is considerably different from that in (I); there is also considerable electron delocalization along the C–O and C–C bonds. These changes in geometry and electronic structure may relate to biological activity. The doubly charged cationic piperazine molecule exists in the chair form with the nitrogen atoms at the apices. The crystal structure of (II) is stabilized by ionic interactions and N–H O hydrogen bonds.

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.

Non-linear response of soil N2O emissions to nitrogen fertiliser in a cotton-fallow rotation in sub-tropical Australia

Nitrogen fertiliser is a major source of atmospheric N2O and over recent years there is growing evidence for a non-linear, exponential relationship between N fertiliser application rate and N2O emissions. However, there is still high uncertainty around the relationship of N fertiliser rate and N2O emissions for many cropping systems. We conducted year-round measurements of N2O emission and lint yield in four N rate treatments (0, 90, 180 and 270 kg N ha-1) in a cotton-fallow rotation on a black vertosol in Australia. We observed a nonlinear exponential response of N2O emissions to increasing N fertiliser rates with cumulative annual N2O emissions of 0.55 kg N ha-1, 0.67kg N ha-1, 1.07 kg N ha-1 and 1.89 kg N ha-1 for the four respective N fertiliser rates while no N response to yield occurred above 180N. The N fertiliser induced annual N2O EF factors increased from 0.13% to 0.29% and 0.50% for the 90N, 180N and 270N treatments respectively, significantly lower than the IPCC Tier 1 default value (1.0 %). This non-linear response suggests that an exponential N2O emissions model may be more appropriate for use in estimating emission of N2O from soils cultivated to cotton in Australia. It also demonstrates that improved agricultural N management practices can be adopted in cotton to substantially reduce N2O emissions without affecting yield potential.

Identification of IDUA and WNT16 phosphorylation-related non-synonymous polymorphisms for bone mineral density in meta-analyses of genome-wide association studies

Protein phosphorylation regulates a wide variety of cellular processes. Thus, we hypothesize that single-nucleotide polymorphisms (SNPs) that may modulate protein phosphorylation could affect osteoporosis risk. Based on a previous conventional genome-wide association (GWA) study, we conducted a three-stage meta-analysis targeting phosphorylation-related SNPs (phosSNPs) for femoral neck (FN)-bone mineral density (BMD), total hip (HIP)-BMD, and lumbar spine (LS)-BMD phenotypes. In stage 1, 9593 phosSNPs were meta-analyzed in 11,140 individuals of various ancestries. Genome-wide significance (GWS) and suggestive significance were defined by α = 5.21 × 10–6 (0.05/9593) and 1.00 × 10–4, respectively. In stage 2, nine stage 1–discovered phosSNPs (based on α = 1.00 × 10–4) were in silico meta-analyzed in Dutch, Korean, and Australian cohorts. In stage 3, four phosSNPs that replicated in stage 2 (based on α = 5.56 × 10–3, 0.05/9) were de novo genotyped in two independent cohorts. IDUA rs3755955 and rs6831280, and WNT16 rs2707466 were associated with BMD phenotypes in each respective stage, and in three stages combined, achieving GWS for both FN-BMD (p = 8.36 × 10–10, p = 5.26 × 10–10, and p = 3.01 × 10–10, respectively) and HIP-BMD (p = 3.26 × 10–6, p = 1.97 × 10–6, and p = 1.63 × 10–12, respectively). Although in vitro studies demonstrated no differences in expressions of wild-type and mutant forms of IDUA and WNT16B proteins, in silico analyses predicts that WNT16 rs2707466 directly abolishes a phosphorylation site, which could cause a deleterious effect on WNT16 protein, and that IDUA phosSNPs rs3755955 and rs6831280 could exert indirect effects on nearby phosphorylation sites. Further studies will be required to determine the detailed and specific molecular effects of these BMD-associated non-synonymous variants. © 2015 American Society for Bone and Mineral Research.

Non-preferential trading clubs

This paper examines the welfare implications of non-discriminatory tariff reforms by a subset of countries, which we term a non-preferential trading club. We show that there exist coordinated tariff reforms, accompanied by appropriate income transfers between the member countries, that unambiguously increase the welfare of these countries while leaving the welfare of non-members unaltered. In terms of economic policy implications, our results show that there exist regional, MFN-consistent arrangements that lead to Pareto improvements in world welfare.

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.

Characterization of the restriction enzyme-like endonuclease encoded by the Entamoeba histolytica non-long terminal repeat retrotransposon EhLINE1

The genome of the human pathogen Entamoeba histolytica, a primitive protist, contains non-long terminal repeat retrotransposable elements called EhLINEs. These encode reverse transcriptase and endonuclease required for retrotransposition. The endonuclease shows sequence similarity with bacterial restriction endonucleases. Here we report the salient enzymatic features of one such endonuclease. The kinetics of an EhLINE1-encoded endonuclease catalyzed reaction, determined under steady-state and single-turnover conditions, revealed a significant burst phase followed by a slower steady-state phase, indicating that release of product could be the slower step in this reaction. For circular supercoiled DNA the K-m was 2.6 x 10-8 m and the k(cat) was 1.6 x 10-2 sec-1. For linear E. histolytica DNA substrate the K-m and k(cat) values were 1.3 x 10-8 m and 2.2 x 10-4 sec-1 respectively. Single-turnover reaction kinetics suggested a noncooperative mode of hydrolysis. The enzyme behaved as a monomer. While Mg2+ was required for activity, 60% activity was seen with Mn2+ and none with other divalent metal ions. Substitution of PDX12-14D (a metal-binding motif) with PAX(12-14)D caused local conformational change in the protein tertiary structure, which could contribute to reduced enzyme activity in the mutated protein. The protein underwent conformational change upon the addition of DNA, which is consistent with the known behavior of restriction endonucleases. The similarities with bacterial restriction endonucleases suggest that the EhLINE1-encoded endonuclease was possibly acquired from bacteria through horizontal gene transfer. The loss of strict sequence specificity for nicking may have been subsequently selected to facilitate spread of the retrotransposon to intergenic regions of the E. histolytica genome.

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.