Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity

Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.

Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Plant secondary compounds and soil microbial processes in carbon and nitrogen cycling in relation to tree species

The aim of this study was to explore soil microbial activities related to C and N cycling and the occurrence and concentrations of two important groups of plant secondary compounds, terpenes and phenolic compounds, under silver birch (Betula pendula Roth), Norway spruce (Picea abies (L.) Karst) and Scots pine (Pinus sylvestris L.) as well as to study the effects of volatile monoterpenes and tannins on soil microbial activities. The study site, located in Kivalo, northern Finland, included ca. 70-year-old adjacent stands dominated by silver birch, Norway spruce and Scots pine. Originally the soil was very probably similar in all three stands. All forest floor layers (litter (L), fermentation layer (F) and humified layer (H)) under birch and spruce showed higher rates of CO2 production, greater net mineralisation of nitrogen and higher amounts of carbon and nitrogen in microbial biomass than did the forest floor layers under pine. Concentrations of mono-, sesqui-, di- and triterpenes were higher under both conifers than under birch, while the concentration of total water-soluble phenolic compounds as well as the concentration of condensed tannins tended to be higher or at least as high under spruce as under birch or pine. In general, differences between tree species in soil microbial activities and in concentrations of secondary compounds were smaller in the H layer than in the upper layers. The rate of CO2 production and the amount of carbon in the microbial biomass correlated highly positively with the concentration of total water-soluble phenolic compounds and positively with the concentration of condensed tannins. Exposure of soil to volatile monoterpenes and tannins extracted and fractionated from spruce and pine needles affected carbon and nitrogen transformations in soil, but the effects were dependent on the compound and its molecular structure. Monoterpenes decreased net mineralisation of nitrogen and probably had a toxic effect on part of the microbial population in soil, while another part of the microbes seemed to be able to use monoterpenes as a carbon source. With tannins, low-molecular-weight compounds (also compounds other than tannins) increased soil CO2 production and nitrogen immobilisation by soil microbes while the higher-molecular-weight condensed tannins had inhibitory effects. In conclusion, plant secondary compounds may have a great potential in regulation of C and N transformations in forest soils, but the real magnitude of their significance in soil processes is impossible to estimate.

How weed control and fertilisation influence tree physiological processes and growth at early establishment in an exotic F1 hybrid pine plantation of subtropical Australia

Purpose This study investigated how nitrogen (N) nutrition and key physiological processes varied under changed water and nitrogen competition resulting from different weed control and fertilisation treatments in a 2-year-old F1 hybrid (Pinus elliottii Engelm var. elliottii × P. caribaea var. hondurensis Barr. ex Golf.) plantation on a grey podzolic soil type, in Southeast Queensland. Materials and methods The study integrated a range of measures including growth variables (diameter at ground level (DGL), diameter at breast height (DBH) and height (H)), foliar variables (including foliar N concentration, foliar δ13C and δ15N) and physiological variables (including photosynthesis (An), stomatal conductance (gs), transpiration (E), intrinsic water use efficiency (WUEi) (A/gs) and xylem pressure potential (ΨXPP)) to better understand the mechanisms influencing growth under different weed control and fertilisation treatments. Five levels of weed control were applied: standard (routine), luxury, intermediate, mechanical and nil weed control, all with routine fertilisation plus an additional treatment, routine weed control and luxury fertilisation. Relative weed cover was assessed at 0.8, 1.1 and 1.6 years after plantation establishment to monitor the effectiveness of weed control treatments. Soil investigation included soil ammonium (NH4 +-N), nitrate (NO3 −-N), potentially mineralizable N (PMN), gravimetric soil moisture content (MC), hot water extractable organic carbon (HWETC), hot water extractable total N (HWETN), total C, total N, stable C isotope composition (δ13C), stable N isotope composition (δ15N), total P and extractable K. Results and discussion There were significant relationships between foliar N concentrations and relative weed cover and between tree growth and foliar N concentration or foliar δ15N, but initial site preparation practices also increased soil N transformations in the planting rows reducing the observable effects of weed control on foliar δ15N. A positive relationship between foliar N concentration and foliar δ13C or photosynthesis indicated that increased N availability to trees positively influenced non-stomatal limitations to photosynthesis. However, trees with increased foliar N concentrations and photosynthesis were negatively related to xylem pressure potential in the afternoons which enhanced stomatal limitations to photosynthesis and WUEi. Conclusions Luxury and intermediate weed control and luxury fertilisation positively influenced growth at early establishment by reducing the competition for water and N resources. This influenced fundamental key physiological processes such as the relationships between foliar N concentration, A n, E, gs and ΨXPP. Results also confirmed that time from cultivation is an important factor influencing the effectiveness of using foliar δ15N as an indicator of soil N transformations.

Vibrational assignments of five-membered heterocyclic compounds. Normal vibrations of oxazolidine-2-one and -2-thione

Infrared spectra of oxazolidine-2-one (Oxo), -2-thione (Oxt) and their N-deuteriated derivatives have been measured over the range 4000-20 cm−1. The fundamental frequencies of these molecules have been assigned on the basis of normal coordinate calculations carried out using a Urey-Bradley potential function supplemented with valence type constants for the out-of-plane modes of the planar skeleton. The results of the vibrational analyses are discussed and correlated with the assignments available for the other related five membered heterocyclic molecules.

Photodimerization of olefins in solid state

Photochemical transformations of organic solids provide an exciting area of research with new synthetic possibilities. These reactions are generally governed by topochemical factors rather than the normal rules of chemical reactivity. Defects play a crucial role in some of the reactions. Some of the transformations such as the photodimerization of 4, 4'-dimethoxystilbene occur in a single crystal fashion.

Spectroscopic and Coordination Behavior of α-Cyanothioacetamide

α-Cyanothioacetamide (CTAM) complexes of cuprous chloride CuCl–2CTAM and cuprous bromide CuBr–2CTAM have been prepared. The infrared spectra of CTAM and its complexes, and the laser Raman spectrum of CTAM have been recorded. Assignment of the frequencies of the ligand has been made on the basis of a normal coordinate analysis using the Urey-Bradley force field. The copper (I) complexes are inferred to have thiocarbonyl sulfur and amide nitrogen bonded CTAM as evidenced from infrared and electronic spectra.

Infrared spectral assignments of methyl and ethyl xanthato complexes of nickel(II)

Assignments of the infrared frequencies of methyl and ethyl xanthato complexes of nickel(II) have been made with the aid of normal coordinate analyses. The assignments are discussed in relation to those in related molecules.

Use of Multiblade Coordinates for Helicopter Flap-Lag Stability with Dynamic Inflow

Rotor flap-lag stability in forward flight is studied with and without dynamic inflow feedback via a multiblade coordinate transformation (MCT). The algebra of MCT is found to be so involved that it requires checking the final equations by independent means. Accordingly, an assessment of three derivation methods is given. Numerical results are presented for three- and four-bladed rotors up to an advance ratio of 0.5. While the constant-coefficient approximation under trimmed conditions is satisfactory for low-frequency modes, it is not satisfactory for high-frequency modes or for untrimmed conditions. The advantages of multiblade coordinates are pronounced when the blades are coupled by dynamic inflow.

Molecular Modelling of Estrogen-Producing Enzymes CYP450 Aromatase and 17beta-Hydroxysteroid Dehydrogenase Type 1

Breast cancer is the most common cancer in women in the western countries. Approximately two-thirds of breast cancer tumours are hormone dependent, requiring estrogens to grow. Estrogens are formed in the human body via a multistep route starting from cholesterol. The final steps in the biosynthesis include the CYP450 aromatase enzyme, converting the male hormones androgens (preferred substrate androstenedione ASD) into estrogens(estrone E1), and the 17beta-HSD1 enzyme, converting the biologically less active E1 into the active hormone 17beta-hydroxyestradiol E2. E2 is bound to the nuclear estrogen receptors causing a cascade of biochemical reactions leading to cell proliferation in normal tissue, and to tumour growth in cancer tissue. Aromatase and 17beta-HSD1 are expressed in or near the breast tumour, locally providing the tissue with estrogens. One approach in treating hormone dependent breast tumours is to block the local estrogen production by inhibiting these two enzymes. Aromatase inhibitors are already on the market in treating breast cancer, despite the lack of an experimentally solved structure. The structure of 17beta-HSD1, on the other hand, has been solved, but no commercial drugs have emerged from the drug discovery projects reported in the literature. Computer-assisted molecular modelling is an invaluable tool in modern drug design projects. Modelling techniques can be used to generate a model of the target protein and to design novel inhibitors for them even if the target protein structure is unknown. Molecular modelling has applications in predicting the activities of theoretical inhibitors and in finding possible active inhibitors from a compound database. Inhibitor binding at atomic level can also be studied with molecular modelling. To clarify the interactions between the aromatase enzyme and its substrate and inhibitors, we generated a homology model based on a mammalian CYP450 enzyme, rabbit progesterone 21-hydroxylase CYP2C5. The model was carefully validated using molecular dynamics simulations (MDS) with and without the natural substrate ASD. Binding orientation of the inhibitors was based on the hypothesis that the inhibitors coordinate to the heme iron, and were studied using MDS. The inhibitors were dietary phytoestrogens, which have been shown to reduce the risk for breast cancer. To further validate the model, the interactions of a commercial breast cancer drug were studied with MDS and ligand–protein docking. In the case of 17beta-HSD1, a 3D QSAR model was generated on the basis of MDS of an enzyme complex with active inhibitor and ligand–protein docking, employing a compound library synthesised in our laboratory. Furthermore, four pharmacophore hypotheses with and without a bound substrate or an inhibitor were developed and used in screening a commercial database of drug-like compounds. The homology model of aromatase showed stable behaviour in MDS and was capable of explaining most of the results from mutagenesis studies. We were able to identify the active site residues contributing to the inhibitor binding, and explain differences in coordination geometry corresponding to the inhibitory activity. Interactions between the inhibitors and aromatase were in agreement with the mutagenesis studies reported for aromatase. Simulations of 17beta-HSD1 with inhibitors revealed an inhibitor binding mode with hydrogen bond interactions previously not reported, and a hydrophobic pocket capable of accommodating a bulky side chain. Pharmacophore hypothesis generation, followed by virtual screening, was able to identify several compounds that can be used in lead compound generation. The visualisation of the interaction fields from the QSAR model and the pharmacophores provided us with novel ideas for inhibitor development in our drug discovery project.

Infrared spectral assignments for transition metal thioxanthates

The i.r. frequencies of ethylthioxanthate complexes of some transition metals have been interpreted on the basis of normal coordinate treatments of the 1:1 molecular models. The band assignments are disscussed in comparison with those in closely related xanthate molecules.

North American Jewish Students Appeal records, undated, 1962, 1964-1996 (bulk 1971-1995)

The records of the North American Jewish Students Appeal (NAJSA or APPEAL) contains documents on two levels of concern: those documents dealing with the NAJSA as a student-run organization promoting Jewish identity among college-aged youth; and those documents dealing with the APPEAL as a fundraising organization for several well-known student constituent organizations. The Constituents were: the Jewish Student Press Service, Lights in Action, the North American Jewish Students Network, the Progressive Zionist Caucus, Response: A Contemporary Jewish Review, Yavneh Religious Students Organization, and Yugntruf Youth for Yiddish. Documents include correspondence, financial records, minutes, press releases, information on grants awarded to student organizations for programming and publishing, student journals, and newspapers, photographs, and ephemera.

Natural frequencies of polar orthotropic annular plates

The classical Rayleigh-Ritz method with simple polynomials as admissible functions has been used for obtaining natural frequencies of transversely vibrating polar orthotropic annular plates. The method in conjunction with transformations introduced in the analysis has been found to be quite effective, particularly for large hole sizes. Estimates of natural frequencies corresponding to modes with one as well as two nodal diameters are obtained for the nine combinations of clamped, simply supported and free edge conditions and for various values of rigidity ratio and hole sizes. Based on the variation of eigenvalue parameter with rigidity ratio, the frequencies of these modes as well as those of axisymmetric modes have been expressed by means of simple formulae in terms of rigidity ratio and the frequencies of corresponding modes in the isotropic case. These formulae have been used in determining the fundamental frequencies of orthotropic plates.

Natural frequencies of circumferentially truncated sector plates with simply supported straight edges

The classical Rayleigh-Ritz method in conjunction with suitable co-ordinate transformations is found to be effective for accurate estimation of natural frequencies of circumferentially truncated circular sector plates with simply supported straight edges. Numerical results are obtained for all the nine combinations of clamped, simply supported and free boundary conditions at the circular edges and presented in the form of graphs. The analysis confirms an earlier observation that the plate behaves like a long rectangular strip as the width of the plate in the radial direction becomes small.

Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.