Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Disabled Veteran's Benefits, SSI/Title II Benefits, and Wages

This Just the Facts Series addresses the disability financial compensation and disability-related pension programs that may affect many benefits analysis clients. The interface between these programs and SSI/Title II is explained, as well as the effect of wages on these benefits.

The limit to wheat water-use efficiency in eastern Australia. II. Influence of rainfall patterns

We investigated the influence of rainfall patterns on the water-use efficiency of wheat in a transect between Horsham (36°S) and Emerald (23°S) in eastern Australia. Water-use efficiency was defined in terms of biomass and transpiration, WUEB/T, and grain yield and evapotranspiration, WUEY/ET. Our working hypothesis is that latitudinal trends in WUEY/ET of water-limited crops are the complex result of southward increasing WUEB/T and soil evaporation, and season-dependent trends in harvest index. Our approach included: (a) analysis of long-term records to establish latitudinal gradients of amount, seasonality, and size-structure of rainfall; and (b) modelling wheat development, growth, yield, water budget components, and derived variables including WUEB/T and WUEY/ET. Annual median rainfall declined from around 600 mm in northern locations to 380 mm in the south. Median seasonal rain (from sowing to harvest) doubled between Emerald and Horsham, whereas median off-season rainfall (harvest to sowing) ranged from 460 mm at Emerald to 156 mm at Horsham. The contribution of small events (≤ 5 mm) to seasonal rainfall was negligible at Emerald (median 15 mm) and substantial at Horsham (105 mm). Power law coefficients (τ), i.e. the slopes of the regression between size and number of events in a log-log scale, captured the latitudinal gradient characterised by an increasing dominance of small events from north to south during the growing season. Median modelled WUEB/T increased from 46 kg/ha.mm at Emerald to 73 kg/ha.mm at Horsham, in response to decreasing atmospheric demand. Median modelled soil evaporation during the growing season increased from 70 mm at Emerald to 172 mm at Horsham. This was explained by the size-structure of rainfall characterised with parameter τ, rather than by the total amount of rainfall. Median modelled harvest index ranged from 0.25 to 0.34 across locations, and had a season-dependent latitudinal pattern, i.e. it was greater in northern locations in dry seasons in association with wetter soil profiles at sowing. There was a season-dependent latitudinal pattern in modelled WUEY/ET. In drier seasons, high soil evaporation driven by a very strong dominance of small events, and lower harvest index override the putative advantage of low atmospheric demand and associated higher WUEB/T in southern locations, hence the significant southwards decrease in WUEY/ET. In wetter seasons, when large events contribute a significant proportion of seasonal rain, higher WUEB/T in southern locations may translate into high WUEY/ET. Linear boundary functions (French-Schultz type models) accounting for latitudinal gradients in its parameters, slope, and x-intercept, were fitted to scatter-plots of modelled yield v. evapotranspiration. The x-intercept of the model is re-interpreted in terms of rainfall size structure, and the slope or efficiency multiplier is described in terms of the radiation, temperature, and air humidity properties of the environment. Implications for crop management and breeding are discussed.

Type II beta-turn conformation of pivaloyl-L-prolyl-alpha-aminoisobutyryl-N-methylamide: Theoretical, spectroscopic, and X-ray studies

Pivaloyl-L-Pro-Aib-N-methylamide has been shown to possess one intramolecular hydrogen bond in (CD3)2SO solution, by 1H-nmr methods, suggesting the existence of beta -turns, with Pro-Aib as the corner residues. Theoretical conformational analysis suggests that Type II beta-turn conformations are about 2 kcal mol-1 more stable than Type III structures. A crystallographic study has established the Type II beta-turn in the solid state. The molecule crystallizes in the space group P21 with a = 5.865 Å, b = 11.421 Å, c = 12.966 Å, beta = 97.55°, and Z = 2. The structure has been refined to a final R value of 0.061. The Type II -turn conformation is stabilized by an intramolecular 4 1 hydrogen bond between the methylamide NH and the pivaloyl CO group. The conformational angles are Pro = -57.8°, Pro = 139.3°, Aib = 61.4°, and Aib = 25.1°. The Type II beta-turn conformation for Pro-Aib in this peptide is compared with the Type III structures observed for the same segment in larger peptides.

Functional dynamics of the nitrogen balance of sorghum. II. Grain filling period.

Maintenance of green leaf area during grain filling can increase grain yield of sorghum grown under terminal water limitation. This 'stay-green' trait has been related to the nitrogen (N) supply-demand balance during grain filling. This study quantifies the N demand of grain and N translocation rates from leaves and stem and explores effects of genotype and N stress on onset and rate of leaf senescence during the grain filling period. Three hybrids differing in potential height were grown at three levels of N supply under well-watered conditions. Vertical profiles of biomass, leaf area, and N% of leaves, stem and grain were measured at regular intervals. Weekly SPAD chlorophyll readings on main shoot leaves were correlated with observed specific leaf nitrogen (SLN) to derive seasonal patterns of leaf N content. For all hybrids, individual grain N demand was sink determined and was initially met through N translocation from the stem and rachis. Only if this was insufficient did leaf N translocation occur. Maximum N translocation rates from leaves and stem were dependent on their N status. However, the supply of N at canopy scale was also related to the amount of leaf area senescing at any one time. This supply-demand framework for N dynamics explained effects of N stress and genotype on the onset and rate of leaf senescence.

Interaction of manganese(II) with valinomycin: Observation of mixed complexes

The interaction of antibiotic valinomycin with manganese (II) has been studied using circular dichroism, electron spin resonance and infrared techniques. Results show that Mn(II) forms complexes with valinomycin in both 2:1 (valinomycin-ion-valinomycin sandwich) and 1:1 (equimolar) stoichiometries. The 1:1 type observed here is very different from the well known K+-valinomycin bracelet conformation.

The role of catechol-O-methyltransferase (COMT) and the effects of COMT inhibition in brain and in cardiovascular and renal pathophysiology

Catechol-O-methyltransferase (COMT) metabolizes catecholamines such as dopamine (DA), noradrenaline (NA) and adrenaline, which are vital neurotransmitters and hormones that play important roles in the regulation of physiological processes. COMT enzyme has a functional Val158Met polymorphism in humans, which affects the subjects COMT activity. Increasing evidence suggests that this functional polymorphism may play a role in the etiology of various diseases from schizophrenia to cancers. The aim of this project was to provide novel biochemical information on the physiological and especially pathophysiological roles of COMT enzyme as well as the effects of COMT inhibition in the brain and in the cardiovascular and renal system. To assess the roles of COMT and COMT inhibition in pathophysiology, we used four different study designs. The possible beneficial effects of COMT inhibition were studied in double-transgenic rats (dTGRs) harbouring human angiotensinogen and renin genes. Due to angiotensin II (Ang II) overexpression, these animals exhibit severe hypetension, cardiovascular and renal end-organ damage and mortality of approximately 25-40% at the age of 7-weeks. The dTGRs and their Sprague-Dawley controls tissue samples were assessed with light microscopy, immunohistochemistry, reverse transcriptase-polymerase chain reaction (RT-PCR) and high-pressure liquid chromatography (HPLC) to evaluate the tissue damages and the possible protective effects pharmacological intervention with COMT inhibitors. In a second study, the consequence of genetic and pharmacological COMT blockade in blood pressure regulation during normal and high-sodium was elucidated using COMT-deficient mice. The blood pressure and the heart rate were measured using direct radiotelemetric blood pressure surveillance. In a third study, the effects of acute and subchronic COMT inhibition during combined levodopa (L-DOPA) + dopa decarboxylase inhibitor treatment in homocysteine formation was evaluated. Finally, we assessed the COMT enzyme expression, activity and cellular localization in the CNS during inflammation-induced neurodegeneration using Western blotting, HPLC and various enzymatic assays. The effects of pharmacological COMT inhibition on neurodegeneration were also studied. The COMT inhibitor entacapone protected against the Ang II-induced perivascular inflammation, renal damage and cardiovascular mortality in dTGRs. COMT inhibitors reduced the albuminuria by 85% and prevented the cardiovascular mortality completely. Entacapone treatment was shown to ameliorate oxidative stress and inflammation. Furthermore, we established that the genetic and pharmacological COMT enzyme blockade protects against the blood pressure-elevating effects of high sodium intake in mice. These effects were mediated via enhanced renal dopaminergic tone and suggest an important role of COMT enzyme, especially in salt-sensitive hypertension. Entacapone also ameliorated the L-DOPA-induced hyperhomocysteinemia in rats. This is important, since decreased homocysteine levels may decrease the risk of cardiovascular diseases in Parkinson´s disease (PD) patients using L-DOPA. The Lipopolysaccharide (LPS)-induced inflammation and subsequent delayed dopaminergic neurodegeneration were accompanied by up-regulation of COMT expression and activity in microglial cells as well as in perivascular cells. Interestingly, similar perivascular up-regulation of COMT expression in inflamed renal tissue was previously noted in dTGRs. These results suggest that inflammation reactions may up-regulate COMT expression. Furthermore, this increased glial and perivascular COMT activity in the central nervous system (CNS) may decrease the bioavailability of L-DOPA and be related to the motor fluctuation noted during L-DOPA therapy in PD patients.

Androgen receptor in transcriptional regulation and carcinogenesis

Androgens control a variety of developmental processes that create the male phenotype and are important for maintaining male fertility and normal functions of tissues and organs that are not directly involved in procreation. Androgen receptor (AR) that mediates the biological actions of androgens is a member of the nuclear receptor superfamily of ligand-inducible transcription factors. Although AR was cloned over 15 years ago, the mechanisms by which it regulates gene expression are not well understood. A growing body of in vitro experimental evidence suggests that a complex network of proteins is involved in the androgen-dependent transcriptional regulation. However, the process of AR-dependent transcriptional regulation under physiological conditions is largely elusive. In the present study, a series of experiments were performed, including quantitative chromatin immunoprecipitation (ChIP) assays, to investigate AR-mediated transcription process using living prostate cancer cells. Our results show that the loading of AR and recruitment of coactivators and RNA polymerase II (Pol II) to both the promoter and enhancer of AR target genes are a transient and cyclic event that in addition to hyperacetylation, also involves dynamic changes in methylation, phosphorylation of core histone H3 in androgen-treated LNCaP cells. The dynamics of testosterone (T)-induced loading of AR onto the proximal promoters of the genes clearly differed from that loaded onto the distal enhancers. Significantly, more holo-AR was loaded onto the enhancers than the promoters, but the principal Pol II transcription complex was assembled on the promoters. By contrast, the pure antiandrogen bicalutamide (CDX) complexed to AR elicited occupancy of the PSA promoter, but was unable to load onto the PSA enhancer and was incapable of recruiting Pol II, coactivators and following changes of covalent histone modifications. The partial antagonist cyproterone acetate (CPA) and mifepristone (RU486) were capable of promoting AR loading onto both the PSA promoter and enhancer at a comparable efficiency with androgen in LNCaP cells expressing mutant AR. However, CPA- and RU486-bound AR not only recruited Pol II and coactivator p300 and GRIP1 onto the promoter and enhancer, but also recruited the corepressor NCoR onto the promoter as efficiently as CDX. In addition, we demonstrate that both proteasome and protein kinases are implicated in AR-mediated transcription. Even though proteasome inhibitor MG132 and protein kinase inhibitor DRB (5, 6-Dichlorobenzimidazole riboside) can block ligand-dependent accumulation of PSA mRNA with same efficiency, their use results in different molecular profiles in terms of the formation of AR-mediated transcriptional complex. Collectively, these results indicate that transcriptional activation by AR is a complicated process, which includes transient loading of holo-AR and recruitment of Pol II and coregulators accompanied by a cascade of distinct covalent histone modifications; This process involves both the promoter and enhancer elements, as well as other general components of the cell machineries e.g. proteasome and protein kinase; The pure antiandrogen CDX and the partial antagonist CPA and RU486 exhibit clearly different profiles in terms of their ability to induce the formation of AR-dependent transcriptional complexes and the histone modifications associated with the target genes in human prostate cancer cells. Finally, by using quantitative RT-PCR to compare the expression of sixteen AR co-regulators in prostate cancer cell lines, xenografts, and clinical prostate cancer specimens we suggest that AR co-regulators protein inhibitor of activated STAT1 (PIAS1) and steroid receptor coactivator 1(SRC1) could be involved in the progression of prostate cancer.

Model of Strangriede Cemetery during World War II when it was a holding area for Jews to be deported; Hannover Cemeteries

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Metal chelates in vinyl polymerization: Kinetics and mechanism of acrylonitrile polymerization initiated by Cu(II) imine complexes

The free radical polymerization of acrylonitrile (AN) initiated by Cu(II) 4-anilino 2-one [Cu(II) ANIPO] Cu(II), 4-p-toluedeno 3-pentene 2-one [Cu(II) TPO], and Cu(II) 4-p-nitroanilino 3-pentene 2-one [Cu(II) NAPO] was studied in benzene at 50 and 60°C and in carbon tetrachloride (CCl4), dimethyl sulfoxide (DMSO), and methanol (MeOH) at 60°C. Although the polymerization proceeded in a heterogeneous phase, it followed the kinetics of a homogeneous process. The monomer exponents were 2 at two different temperatures and in different solvents. The square-root dependence of Rp on initiator concentration and higher monomer exponents accounted for a 1:2 complex formation between the chelate and monomer. The complex formation was shown by ultraviolet (UV) study. The activation energies, kinetics, and chain transfer constants were also evaluated.

Electrochemical phase formation (ECPF) and macrogrowth Part II. Two-rate models

A general theory is evolved for a class of macrogrowth models which possess two independent growth-rates. Relations connecting growth-rates to growth geometry are established and some new growth forms are shown to result for models with passivation or diffusion-controlled rates. The corresponding potentiostatic responses, their small and large time behaviours and peak characteristics are obtained. Numerical transients are also presented. An empirical equation is derived as a special case and an earlier equation is corrected. An interesting stochastic result pertaining to nucleation events in the successive layers is proved.

Coalescence of rigid droplets in a stirred dispersion-II. Band-limited force fluctuations

The coalescence of nearly rigid liquid droplets in a turbulent flow field is viewed as the drainage of a thin film of liquid under the action of a stochastic force representing the effect of turbulence. The force squeezing the drop pair is modelled as a correlated random function of time. The drops are assumed to coalesce once the film thickness becomes smaller than a critical thickness while they are regarded as separated if their distance of separation is larger than a prescribed distance. A semi-analytical solution is derived to determine the coalescence efficiency. The veracity of the solution procedure is established via a Monte-Carlo solution scheme. The model predicts a reversing trend of the dependence of the coalescence efficiency on the drop radii, the film liquid viscosity and the turbulence energy dissipation per unit mass, as the relative fluctuation increases. However, the dependence on physical parameters is weak (especially at high relative fluctuation) so that for the smallest droplets (which are nearly rigid) the coalescence efficiency may be treated as an empirical constant. The predictions of this model are compared with those of a white-noise force model. The results of this paper and those in Muralidhar and Ramkrishna (1986, Ind. Engng Chem. Fundam. 25, 554-56) suggest that dynamic drop deformation is the key factor that influences the coalescence efficiency.

Interior of Aenny Catzenstein nee Gottschalk's cottage during WW II; Ascona, Switzerland Architecture Residences Interiors

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