Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Low temperature crystal structures of two rhodanine derivatives, 3-amino rhodanine and 3-methyl rhodanine: geometry of the rhodanine ring

Rhodanines (2-thio-4-oxothiazolidines) are synthetic small molecular weight organic molecules with diverse applications in biochemistry, medicinal chemistry, photochemistry, coordination chemistry and industry. The X-ray crystal structure determination of two rhodanine derivatives, namely (I), 3-aminorhodanine [3-amino-2-thio-4-oxothiazolidine], C3H4N2OS2, and (II) 3-methylrhodanine [3-methyl-2-thio-4-oxothiazolidine], C4H5NOS2, have been conducted at 100 K. I crystallizes in the monoclinic space group P2(1)/n with unit cell parameters a = 9.662(2), b = 9.234(2), c = 13.384(2) angstrom, beta = 105.425(3)degrees, V = 1151.1(3) angstrom(3), Z = 8 (2 independent molecules per asymmetric unit), density (calculated) = 1.710 mg/m(3), absorption coefficient = 0.815 mm(-1). II crystallizes in the orthorhombic space group Iba2 with unit cell a = 20.117(4), b = 23.449(5), c = 7.852(2) angstrom, V = 3703.9(12) angstrom(3), Z = 24 (three independent molecules per asymmetric unit), density (calculated) = 1.584 mg/m(3), absorption coefficient 0.755 mm(-1). For I in the final refinement cycle the data/restraints/parameter ratios were 2639/0/161, goodness-of-fit on F-2 = 0.934, final R indices [I > 2sigma(I)] were R1 = 0.0299, wR2 = 0.0545 and R indices (all data) R1 = 0.0399, wR2 = 0.0568. The largest difference peak and hole were 0.402 and -0.259 e angstrom(-3). For II in the final refinement cycle the data/restraints/parameter ratios were 3372/1/221, goodness-of-fit on F(2) = 0.950, final R indices [I > 2sigma(I)] were R1 = 0.0407, wR2 = 0.1048 and R indices (all data) R1 = 0.0450, wR2 = 0.1088. The absolute structure parameter = 0.19(9) and largest difference peak and hole 0.934 and -0.301 e angstrom(-3). Details of the geometry of the five molecules (two for I and three for II) and the crystal structures are fully discussed. Corresponding features of the molecular geometry are highly consistent and firmly establish the geometry of the rhodanine

A conceptual framework for designing pharmaceutical reverse logistics networks in China

Over latest decade, Reverse Logistics (RL) has gained more and more attention from both industry and academia. In the past, most research on RL has been focused on automobile, electronic waste, computer, paper, package and package material. There is very little research and practice on drug recycling. Nevertheless, it is vital important to properly dispose expired drug because of hazardous contain which may harm to people and environment. In China, public awareness of the harmfulness of expired drugs is still very low and very few efforts have been made to recycle drugs. Therefore, this research aims to build up a conceptual framework to indentify factors of influencing drug recycling in China, from scratch borrowing from existing literature and industry practices in other recycling areas. This framework helps in designing reverse logistic (RL) network and also can provide a useful reference tool for policymakers at the local and national level. Furthermore, a primary research is planed to validate the framework and RL network.

Multiple environmental controls on phytoplankton growth strategies determine adaptive responses of the N : P ratio

The controls on the 'Redfield' N:P stoichiometry of marine phytoplankton and hence the N:P ratio of the deep ocean remain incompletely understood. Here, we use a model for phytoplankton ecophysiology and growth, based on functional traits and resource-allocation trade-offs, to show how environmental filtering, biotic interactions, and element cycling in a global ecosystem model determine phytoplankton biogeography, growth strategies and macromolecular composition. Emergent growth strategies capture major observed patterns in marine biomes. Using a new synthesis of experimental RNA and protein measurements to constrain per-ribosome translation rates, we determine a spatially variable lower limit on adaptive rRNA:protein allocation and hence on the relationship between the largest cellular P and N pools. Comparison with the lowest observed phytoplankton N:P ratios and N:P export fluxes in the Southern Ocean suggests that additional contributions from phospholipid and phosphorus storage compounds play a fundamental role in determining the marine biogeochemical cycling of these elements.

Nomenclature and syntaxonomic notes on some high-rank syntaxa of the European grassland vegetation

We present descriptions of a new order (Ranunculo cortusifolii-Geranietalia reuteri and of a new alliance (Stachyo lusitanicae-Cheirolophion sempervirentis) for the herbaceous fringe communities of Macaronesia and of the southwestern Iberian Peninsula, respectively. A new alliance, the Polygalo mediterraneae-Bromion erecti (mesophilous post-cultural grasslands), was introduced for the Peninsular Italy. We further validate and typify the Armerietalia rumelicae (perennial grasslands supported by nutrient-poor on siliceous bedrocks at altitudes characterized by the submediterranean climate of central-southern Balkan Peninsula), the Securigero-Dasypyrion villosae (lawn and fallow-land tall-grass annual vegetation of Italy), and the Cirsio vallis-demoni-Nardion (acidophilous grasslands on siliceous substrates of the Southern Italy). Nomenclatural issues (validity, legitimacy, synonymy, formal corrections) have been discussed and clarified for the following names: Brachypodio-Brometalia, Bromo pannonici-Festucion csikhegyensis, Corynephoro-Plantaginion radicatae, Heleochloion, Hieracio-Plantaginion radicatae, Nardetea strictae, Nardetalia strictae, Nardo-Callunetea, Nardo-Galion saxatilis, Oligo-Bromion, Paspalo-Heleochloetalia, Plantagini-Corynephorion and Scorzoneret alia villosae.