When Ramification points meet

Summary This paper contains three applications of the technique of limit series (our [1986]) to the theory of ramification of linear series on smooth curves, and curves of compact type, overC.Let {L _t t|<}, be a family of linear series on a smooth family of smooth curves {C _t }, and letp ₁(t),p ₂(t)C _t be sections of the family which coincide (only) att=0. Setp=p ₁())=p ₂(0)C ₀.We first give a condition related to the Schubert calculus which must be satisfied by the ramification series and the . We then take up the converse problem: In what ways can a given ramification point arise as a limit? We show that if the ramification point isdimensionally proper in the sense of our [1986], then families of every kind allowed by the Schubert calculus condition can actually be constructed. Finally, we prove that dimensional propriety is in a strong sense an open condition, so that ramification points constructed as above are again dimensionally proper.In the body of the paper we work not with pairs of points, as above, but with arbitrary finite collections of points approaching (possibly) several points of the limit curve. Further, by their nature, the results are valid for families of curves of compact type.     

Sharpness of the phase transition in percolation models

The equality of two critical points — the percolation thresholdp _H and the pointp _T where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP — at the bond densityp=1–e ^– in the single parameter case. These are: (1)MhM/h+M ²+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a ³ structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that . An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department     

Further evidence for magnetic charge from meson spectroscopy

Recently evidence was presented for the existence of magnetic charge from Zeeman splitting in meson states. The model by Akers predicted the existence of a new meson at 1814 MeV withI ^G(J ^PC )=0⁺(0^–+). Experimental evidence for this new meson is cited and discussed.     

A new method for the direct calculation of resonance parameters with application to the quasibound states of the H2X1Σ g + system

A new method for the direct calculation of resonance parameters is presented. It is based upon searching for poles of the scattering matrix at complex energies. This search is expedited by the use of analytic derivatives of the scattering matrix with respect to the total energy. This procedure is applied initially to a single channel problem, but is generalizable to more complicated systems. Using the most accurate available potential energy data, we calculate resonance parameters for all of the physically important quasibound states of the ground electronic state of the hydrogen molecule. Corrections to the Born-Oppenheimer potential are included and assessed. The new method has no difficulty locating resonances with widths greater than about 1×10^–7 cm^–1. It is easier to find narrow resonances by monitoring the dependence of the imaginary part of the reactance matrix on the real part of a complex energy than to monitor the dependence of the eigenphase sum on energy at real energies.     

Spectrophotometric determination of hydrazines withperi-naphthindan-2,3,4-trione hydrate

Summary A new micromethod for spectrophotometric determination of hydrazine compounds is described. It is based on a reaction withperi-naphthindan-2,3,4-trione hydrate at pH 2.5 to give a red precipitate of dihydroxy-peri-naphthindenone which is dissolved in methanol and measured at 460 nm. The results obtained show an average recovery of 99.8 %, the precision being ± 1 %.

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Zusammenfassung Eine neue Mikromethode zur spektrophotometrischen Bestimmung von Hydrazinverbindungen wurde beschrieben. Sie beruht auf der Reaktion mit peri-Naphthindan-2,3,4-trion-hydrat bei pH 2,5, wobei ein roter Niederschlag von Dihydroxy-peri-naphthindenon entsteht, der in Methanol gelöst und bei 460 nm gemessen wird. 99,8% Substanz werden wiedergefunden, die Genauigkeit beträgt ±1%.

     

Interaction of dextran sulfates with positively and negatively charged silver bromide hydrosols

Summary The effects of dextran sulfates of different molecular weights and charge densities on the stability of positively and negatively charged silver bromide solsin statu nascendi have been studied by means of light scattering.The plots of scattering intensities of a positively charged sol against the concentration of the added dextran sulfates show one pronounced maximum, the position which is independent on the molecular weight of the polyelectrolyte used. The maximum shifts to lower polyion concentrations with dilution of the sol.The effect of polyanions on the stability of silver bromide sols of the same sign of charge were investigated as a function of molecular weight of the polymers, the sol concentration, the charge and the concentration of counterions, and the addition of methanol. Destabilization only occurred if sufficient amount of indifferent electrolyte was present in the system. However, the concentration of counterions necessary to produce a flocculation maximum was lower in the presence of the polyelectrolytes than in their absence. The results obtained were compared with the data on sols containing nonionic dextrans reported earlier.

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Zusammenfassung Der Einfluß der Dextransulfate von verschiedenen Molekulargewichten und Ladungsdichten auf die Stabilität der positiv und negativ geladenen Silberbromid-Solein statu nascendi wurden durch Lichtstreuung untersucht. Wenn die Intensitäten der Lichtstreuung eines positiv geladenen Silberbromid-Sols gegen die Konzentration der zugesetzten DextranSulfate aufgetragen werden, tritt ein ausgeprägtes Maximum auf, dessen Lage von dem Molekulargewicht des angewandten Polyelektrolyten unabhängig ist. Bei Verdünnung des Sols wird das Maximum zur niedrigeren Konzentration des Polyanions verschoben.Der Einfluß der Polyanionen auf die Stabilität der Silberbromid-Sole mit gleichem Ladungsvorzeichen wurde in Abhängigkeit von dem Molekulargewicht des zugesetzten Dextransulfats, der Solkonzentration, der Ladung und Konzentration der Gegenionen und dem Zusatz von Methylalkohol untersucht. Destabilisierung wird nur in Anwesenheit einer genügenden Menge von Neutralelektrolyten in den untersuchten Systemen beobachtet. Die Konzentration der Gegenionen, die ein Flockungsmaximum verursachen, ist immer niedriger als die kritische Koagulationsmenge derselben Ionen für das gleiche Sol in Abwesenheit von Makroionen. Die Resultate wurden mit den Wechselwirkungen der Silberbromid-Sole mit nichtionogenen Dextranen verglichen, und der Mechanismus der Flockung durch Polyelektrolyte wurde diskutiert.

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5 figures and 1 table

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Supported by the NSF Grant GP 42331 X.

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A part of the Ph.D. Thesis by David Lindsay.     

Effect of ionic additives on the elution of sodium aryl sulfonates in supercritical fluid chromatography

Addition of a small amount of polar solvent (i.e., modifier) to CO2 in packed column supercritical fluid chromatography (SFC) has shown major improvements in both polar analyte solubility and interaction of the polar analyte with the stationary phase. Recently, the addition of an ionic component (i.e., additive) to the primary modifier by one of us has been shown to extend even further the application of SFC to polar analytes. In this work, the effect of various ionic additives on the elution of ionic compounds, such as sodium 4-dodecylbenzene sulfonate and sodium 4-octylbenene sulfonate, has been studied. The additives were lithium acetate, ammonium acetate, tetramethylammonium acetate, tetrabutylammonium acetate, and ammonium chloride dissolved in methanol. Three stationary phases with different degrees of deactivation were considered: conventional cyanopropyl, deltabond cyanopropyl, and bare silica. The effect of additive concentration and additive functionality on analyte retention was investigated. Sodium 4-dodecylbenzene sulfonate was successfully eluted using all the additives with good peak shape under isocratic/isobaric/isothermal conditions. Different additives, however, yielded different retention times and in some cases different peak shapes.     

Copolymerization of styrene. V. Copolymerization with α-cyanocinnamamide

Copolymers of styrene with α-cyanocinnamamide were prepared by free radical initiation in bulk and in DMF solution and also by thermal initiation in bulk. The copolymerization parameters were determined by the conventional scheme of copolymerization and by an improved scheme taking into account the penultimate unit. Different values of the copolymerization parameters were obtained at the above mentioned different polymerization conditions, indicating the existence of a solvent effect. The influence of the comonomer on some of the basic properties, like intrinsic viscosity, solubility, melting range, and glass transition temperature and on some mechanical and behavior properties of the copolymers was studied in comparison with homopolystyrene.