Smooth wavelet approximations of truncated Legendre polynomials via the Jacobi theta function

The family of nth order q-Legendre polynomials are introduced. They are shown to be obtainable from the Jacobi theta function and to satisfy recursion relations and multiplicatively advanced differential equations (MADEs) that are analogues of the recursion relations and ODEs satisfied by the nth degree Legendre polynomials. The nth order q-Legendre polynomials are shown to have vanishing kth moments for 0...4;k<n , as does the nth degree truncated Legendre polynomial. Convergence results are obtained, approximations are given, a reciprocal symmetry is shown, and nearly orthonormal frames are constructed. Conditions are given under which a MADE remains a MADE under inverse Fourier transform. This is used to construct new wavelets as solutions of MADEs

Q-advanced models for tsunami and rogue waves

A wavelet [subscript] Kq[/subscript] (t ) , that satisfies the q-advanced differential equation [superscript] K q [variant prime][/superscript] ( t ) =[subscript] K q[/subscript] (qt ) for q >1 , is used to model N-wave oscillations observed in tsunamis. Although q-advanced ODEs may seem nonphysical, we present an application that model tsunamis, in particular the Japanese tsunami of March 11, 2011, by utilizing a one-dimensional wave equation that is forced by [subscript] Fq[/subscript] ( t ,x ) =[subscript] Kq[/subscript] [subscript] (t )q[/subscript] Sin (x ) . The profile [subscript] F q[/subscript] is similar to tsunami models in present use. The function Sin [superscript] ( t ) [/superscript] q is a wavelet that satisfies a q-advanced harmonic oscillator equation. It is also shown that another wavelet, Cos [superscript] ( t ) [/superscript] q , matches a rogue-wave profile. This is explained in terms of a resonance wherein two small amplitude forcing waves eventually lead to a large amplitude rogue. Since wavelets are used in the detection of tsunamis and rogues, the signal-analysis performance of [subscript] K q[/subscript] and [superscript] Cos q [/superscript] is examined on actual data

Solutions of a Class of Multiplicatively Advanced Differential Equations II: Fourier Transforms

For a wide class of solutions to multiplicatively advanced differential equations (MADEs), a comprehensive set of relations is established between their Fourier transforms and Jacobi theta functions. In demonstrating this set of relations, the current study forges a systematic connection between the theory of MADEs and that of special functions. In a large subset of the general case, we introduce a new family of Schwartz wavelet MADE solutions Wμ,λðtÞ for μ and λ rational with λ > 0. These Wμ,λðtÞ have all moments vanishing and have a Fourier transform related to theta functions. For low parameter values derived from λ, the connection of the Wμ,λðtÞ to the theory of wavelet frames is begun. For a second set of low parameter values derived from λ, the notion of a canonical extension is introduced. A number of examples are discussed. The study of convergence of the MADE solution to the solution of its analogous ODE is begun via an in depth analysis of a normalized example W−4/3,1/3ðtÞ/W−4/3,1/3ð0Þ. A useful set of generalized q-Wallis formulas are developed that play a key role in this study of convergence.ECU Libraries Open Access Publishing Support Fun

X-Ray Microanalysis of Hollow Heart Potatoes

Electron microprobe and X-ray fluorescence techniques were used to study elemental gradients associated with the physiological disorder hollow heart i n potato tubers. Gradients were found along the length and across the width of mature tubers. These were not rela ted to the disorder, however . Tubers with advanced symptoms of the disorder had elemental levels and gradients similar to those in healthy, control tubers. The results suggest that if the disorder is initially caused by an elemental deficiency, as has sometimes been proposed , the deficiency is temporary and no longer exists in mature tubers with advanced hollow heart. Radial gradients were associated rnd inly with two contrasting tissues . the centra 1 pith and the surrounding perimedullary zone. Tissue differences are critical in microprobe studies involving small samples Microprobe studies of developing tubers containing incipient stages of hollow heart. employing strip samples restricted to the central pith where the disorder originates and taken so as to traverse the small lesions, showed a dramatic increase in Mg in lesion areas. It is suggested that a nutrient imbalance may trigger the onset of the cell necrosis that characterizes the initiation of hollow heart in potato . A localized Mg toxicity or Ca deficiency due to high Mg:Ca ratio is implicated

New small molecule inhibitors of histone methyl transferase DOT1L with a nitrile as a non-traditional replacement for heavy halogen atoms

A number of new nucleoside derivatives are disclosed as inhibitors of DOT1L activity. SARs established that DOT1L inhibition could be achieved through incorporation of polar groups and small heterocycles at the 5-position (5, 6, 12) or by the application of alternative nitrogenous bases (18). Based on these results, CN-SAH (19) was identified as a potent and selective inhibitor of DOT1L activity where the polar 5-nitrile group was shown by crystallography to bind in the hydrophobic pocket of DOT1L. In addition, we show that a polar nitrile group can be used as a non-traditional replacement for heavy halogen atoms

Biodegradation of thiocyanate by a native groundwater microbial consortium

Gold ore processing typically generates large amounts of thiocyanate (SCN−)-contaminated effluent. When this effluent is stored in unlined tailings dams, contamination of the underlying aquifer can occur. The potential for bioremediation of SCN−-contaminated groundwater, either in situ or ex situ, remains largely unexplored. This study aimed to enrich and characterise SCN−-degrading microorganisms from mining-contaminated groundwater under a range of culturing conditions. Mildly acidic and suboxic groundwater, containing ∼135 mg L−1 SCN−, was collected from an aquifer below an unlined tailings dam. An SCN−-degrading consortium was enriched from contaminated groundwater using combinatory amendments of air, glucose and phosphate. Biodegradation occurred in all oxic cultures, except with the sole addition of glucose, but was inhibited by NH4+ and did not occur under anoxic conditions. The SCN−-degrading consortium was characterised using 16S and 18S rRNA gene sequencing, identifying a variety of heterotrophic taxa in addition to sulphur-oxidising bacteria. Interestingly, few recognised SCN−-degrading taxa were identified in significant abundance. These results provide both proof-of-concept and the required conditions for biostimulation of SCN− degradation in groundwater by native aquifer microorganisms

Modelling of amorphous polymer surfaces in computer simulation

We study surface effects in amorphous polymer systems by means of computer simulation. In the framework of molecular dynamics, we present two different methods to prepare such surfaces. {\em Free} surfaces are stabilized solely by van--der--Waals interactions whereas {\em confined} surfaces emerge in the presence of repelling plates. The two models are compared in various computer simulations. For free surfaces, we analyze the migration of end--monomers to the surface. The buildup of density and pressure profiles from zero to their bulk values depends on the surface preparation method. In the case of confined surfaces, we find density and pressure oszillations next to the repelling plates. We investigate the influence of surfaces on the coordination number, on the orientation of single bonds, and on polymer end--to--end vectors. Furthermore, different statistical methods to determine location and width of the surface region for systems of various chain lengths are discussed and applied. We introduce a ``height function'' and show that this method allows to determine average surface profiles only by scanning the outermost layer of monomers.Comment: 23 pages, 12 figure

A three dimensional model of the photosynthetic membranes of Ectothiorhodospira halochloris

The three dimensional organization of the complete photosynthetic apparatus of the extremely halophilic, bacteriochlorophyll b containing Ectothiorhodospira halochloris has been elaborated by several techniques of electron microscopy. Essentially all thylakoidal sacs are disc shaped and connected to the cytoplasmic membrane by small membraneous ldquobridgesrdquo. In sum, the lumina of all thylakoids (intrathylakoidal space) form one common periplasmic space. Thin sections confirm a paracrystalline arrangement of the photosynthetic complexes in situ. The ontogenic development of the photosynthetic apparatus is discussed based on a structural model derived from serial thin sections

Geophysical validation and long-term consistency between GOME-2/MetOp-A total ozone column and measurements from the sensors GOME/ERS-2, SCIAMACHY/ENVISAT and OMI/Aura

The main aim of the paper is to assess the consistency of five years of Global Ozone Monitoring Experiment-2/Metop-A [GOME-2] total ozone columns and the long-term total ozone satellite monitoring database already in existence through an extensive inter-comparison and validation exercise using as reference Brewer and Dobson ground-based measurements. The behaviour of the GOME-2 measurements is being weighed against that of GOME (1995–2011), Ozone Monitoring Experiment [OMI] (since 2004) and the Scanning Imaging Absorption spectroMeter for Atmospheric CartograpHY [SCIAMACHY] (since 2002) total ozone column products. Over the background truth of the ground-based measurements, the total ozone columns are inter-evaluated using a suite of established validation techniques; the GOME-2 time series follow the same patterns as those observed by the other satellite sensors. In particular, on average, GOME-2 data underestimate GOME data by about 0.80%, and underestimate SCIAMACHY data by 0.37% with no seasonal dependence of the differences between GOME-2, GOME and SCIAMACHY. The latter is expected since the three datasets are based on similar DOAS algorithms. This underestimation of GOME-2 is within the uncertainty of the reference data used in the comparisons. Compared to the OMI sensor, on average GOME-2 data underestimate OMI_DOAS (collection 3) data by 1.28%, without any significant seasonal dependence of the differences between them. The lack of seasonality might be expected since both the GOME data processor [GDP] 4.4 and OMI_DOAS are DOAS-type algorithms and both consider the variability of the stratospheric temperatures in their retrievals. Compared to the OMI_TOMS (collection 3) data, no bias was found. We hence conclude that the GOME-2 total ozone columns are well suitable to continue the long-term global total ozone record with the accuracy needed for climate monitoring studies