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.

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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X-Ray Structure Of A Ternary Metal-Complex - Copper(Ii) Inosine 5'-Monophosphate Imidazole - Metal-Binding To The N(7) Atom Of The Nucleotide In A Mixed-Ligand System Containing An Aromatic Amine

A ternary metal-nucleotide complex, Na2[Cu(5’-IMP)2(im)o,8(H20)l,2(H20)2h]as~ 1be2e.n4 pHr2ep0a,r ed and its structure analyzed by X-ray diffraction (5’-IMP = inosine 5’-monophos hate; im = imidazole). The complex crystallizes in space group C222, with a = 8.733 (4) A, b = 23.213 (5) A, c = 21.489 (6) 1, and Z = 4. The structure was solved by the heavy-atom method and refined by full-matrix least-squares technique on the basis of 2008 observed reflections to a final R value of 0.087. Symmetry-related 5’-IMP anions coordinate in cis geometry through the N(7) atoms of the bases. The other cis positions of the coordination plane are statistically occupied by nitrogen atoms of disordered im groups and water oxygens with occupancies 0.4 and 0.6, respectively. Water oxygens in axial positions complete the octahedral coordination of Cu(I1). The complex is isostructural with C~S-[P~(S’-IMP),(NH~)~a] m”,o del proposed for Pt(I1) binding to DNA. The base binding observed in the present case is different from the typical ”phosphate only” binding shown from earlier studies on metal-nucleotide complexes containing various other ?r-aromatic amines.

Synthesis and physico-chemical properties of diruthenium(III, II) tetra-aryl carboxylato compounds

Monochloro-tetra-μ-aryl-carboxylatodiruthenium(III, II) compounds Ru2Cl (O2CAr)4 (Ar = -C6H5; -C6H4-p-OCH3), are prepared and characterized. The compounds have magnetic moments that correspond to three unpaired spins per dimer. The Rusingle bondRu bond order is 2.5 and the ground electronic configuration is σ2π4δ2(δ*π*)3. The visible spectral band is observed at ca 450 nm along with a shoulder near 580 nm in DMF solution. The compounds undergo a one-electron Ru(III)Ru(II) → Ru(II)Ru(II) quasi-reversible reduction in DMF near 0.0 V vs sce.

Cervical headgear in Class II division 1 correction in children : Academic Dissertation

Class II division 1 malocclusion occurs in 3.5 to 13 percent of 7 12 year-old children. It is the most common reason for orthodontic treatment in Finland. Correction is most commonly performed using headgear treatment. The aim of this study was to investigate the effects of cervical headgear treatment on dentition, facial skeletal and soft tissue growth, and upper airway structure, in children. 65 schoolchildren, 36 boys and 29 girls were studied. At the onset of treatment a mean age was 9.3 (range 6.6 12.4) years. All the children were consequently referred to an orthodontist because of Class II division 1 malocclusion. The included children had protrusive maxilla and an overjet of more than 2mm (3 to 11 mm). The children were treated with a Kloehn-type cervical headgear as the only appliance until Class I first molar relationships were achieved. The essential features of the headgear were cervical strong pulling forces, a long upward bent outer bow, and an expanded inner bow. Dental casts and lateral and posteroanterior cephalograms were taken before and after the treatment. The results were compared to a historical, cross-sectional Finnish cohort or to historical, age- and sex-matched normal Class I controls. The Class I first molar relationships were achieved in all the treated children. The mean treatment time was 1.7 (range 0.3-3.1) years. Phase 2 treatments were needed in 52% of the children, most often because of excess overjet or overbite. The treatment decreased maxillary protrusion by inhibiting alveolar forward growth, while the rest of the maxilla and mandible followed normal growth. The palate rotated anteriorly downward. The expansion of the inner bow of the headgear induced widening of the maxilla, nasal cavity, and the upper and lower dental arches. Class II malocclusion was associated with narrower oro- and hypopharyngeal space than in the Class I normal controls. The treatment increased the retropalatal airway space, while the rest of the airway remained unaffected. The facial profile improved esthetically, while the facial convexity decreased. Facial soft tissues masked the facial skeletal convexity, and the soft tissue changes were smaller than skeletal changes. In conclusion, the headgear treatment with the expanded inner bow may be used as an easy and simple method for Class II correction in growing children.