Immersed essential surfaces and Dehn surgery

It is known that an embedded essential surface F in a hyperbolic manifold M remains essential in Dehn filling spaces M(γ) for most slopes γ on a torus boundary component T of M. The main theorem of this paper is to generalize this result to immersed surfaces. More explicitly, if an immersed essential surface F has coannular slopes β₁,…,β_n on T, then there is a constant K such that F remains essential in M(γ) when Δ(γ,β_i)>K for all i. It will also be shown that all but finitely many Freedman tubings of a geometrically finite surface in M are π₁-injective.     

Enumeration of one-nodal rational curves in projective spaces

We give a formula computing the number of one-nodal rational curves that pass through an appropriate collection of constraints in a complex projective space. The formula involves intersections of tautological classes on moduli spaces of stable rational maps. We combine the methods and results from three different papers.     

Assignment of chemical shifts in benzohydroxamic acid and structure of its silylated derivatives by 15N enrichment

¹⁵N isotopic enrichment was necessary for the unequivocal assignment of the ¹H NMR lines to the protons in the NH–OH fragment of benzohydroxamic acid, BHXA, C₆H₅CONHOH, in dry dimethyl sulfoxide solutions. The assignment [δ(NH) = 11.21, δ(OH) = 9.01, ¹J(¹⁵N,¹H) = 102.2 Hz, ²J(¹⁵N,¹H) <1.5 Hz], which is opposite to that used by other authors, confirms the assignment extended to BHXA by Brown and co‐workers from the spectra of acetohydroxamic acid. The enrichment allowed also assignment of the ²⁹Si lines in the spectra of disilylated benzohydroxamic acid, (Z)‐tert‐butyldimethylsilyl N‐tert‐butyldimethylsilyloxybenzoimidate (2) and (Z)‐tert‐butyldiphenylsilyl N‐tert‐butyldiphenylsilyloxybenzoimidate (3), and confirmed structure of the monosilylated products, N‐tert‐butyldiphenylsilyloxybenzamide (4) and N‐tert‐butyldiphenylsilyloxy benzoimidic acid (5). Copyright © 2003 John Wiley & Sons, Ltd.     

Dual Homogeneous Forms and Varieties of Power Sums

We review the classical definition of the dual homogeneous form of arbitrary even degree which generalizes the well-known notion of the dual quadratic form. Following the ideas of S. Mukai we apply this construction to the study of the varieties parametrizing representations of a homogeneous polynomial as a sum of powers of linear forms.Research supported in part by NSF Grant DMS 0245203.Lecture held in the Seminario Matematico e Fisico on October 15, 2003Received: April, 2004     

On essential extensions of reduced rings and domains

A ring is said to be a left essential extension of a reduced ring (domain) if it contains a left ideal which is a reduced ring (domain) and intersects nontrivially every nonzero twosided ideal of the ring. We prove that every ring which is a left essential extension of a reduced ring is a subdirect sum of rings which are essential extensions of domains, but the converse implication does not hold. We give some applications of this result and discuss several related questions.Received: 6 January 2003     

Bioengineering functional copolymers. III. Synthesis of biocompatible poly[(N‐isopropylacrylamide‐co‐maleic anhydride)‐g‐poly(ethylene oxide)]/poly(ethylene imine) macrocomplexes and their thermostabilization effect on the activity of the enzyme penicillin G acylase

Stimuli‐responsive poly[(N‐isopropylacrylamide‐co‐maleic anhydride)‐g‐poly(ethylene oxide)]/poly(ethylene imine) macrobranched macrocomplexes were synthesized by (1) the radical copolymerization of N‐isopropylacrylamide and maleic anhydride with α,α′‐azobisisobutyronitrile as an initiator in 1,4‐dioxane at 65 °C under a nitrogen atmosphere, (2) the polyesterification (grafting) of prepared poly(N‐isopropylacrylamide‐co‐maleic anhydride) containing less than 20 mol % anhydride units with α‐hydroxy‐ω‐methoxy‐poly(ethylene oxide)s having different number‐average molecular weights (M_n = 4000, 10,000, or 20,000), and (3) the incorporation of macrobranched copolymers with poly(ethylene imine) (M_n = 60,000). The composition and structure of the synthesized copolymer systems were determined by Fourier transform infrared, ¹H and ¹³C NMR spectroscopy, and chemical and elemental analyses. The important properties of the copolymer systems (e.g., the viscosity, thermal and pH sensitivities, and lower critical solution temperature behavior) changed with increases in the molecular weight, composition, and length of the macrobranched hydrophobic domains. These copolymers with reactive anhydride and carboxylic groups were used for the stabilization of penicillin G acylase (PGA). The conjugation of the enzyme with the copolymers significantly increased the thermal stability of PGA (three times at 45 °C and two times at 65 °C). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1580–1593, 2003     

N[a,b]类中边界Nevanlinna-Pick插值(I)

用所谓的Hankel向量方法求解N[a,b]函数类中带边界插值数据的Nevanlina-Pick插值(BNP(N[a,b]))问题,并建立BNP(N[a,b])问题与[a,b]上的某种带约束条件的Hausdorff矩量问题之间等价的可解条件以及解之间明确的一一对应关系.这使得当BNP(N[a,b])问题有多解时,能通过带约束条件的矩量问题的可解性准则和解获得BNP(N[a,b])问题的可解性准则和解的参数化描述,而在唯一解的情况下,通过BNP(N[a,b])问题解的存在唯一性准则和唯一解来获得带约束条件的     

Quantitative assessment of solid oxide electrochemical doping

Quantitative analysis of metal cation doping by solid oxide electrochemical doping (SOED) has been performed under galvanostatic doping conditions. A M–β″-Al₂O₃ (M=Ag, Na) microelectrode (contact radius: about 10 μm) was used as cation source to attain a homogeneous solid–solid contact between the β″-Al₂O₃ and doping target. In Ag doping into alkali borate glass, the measured dopant amount closely matched the theoretical value. High Faraday efficiencies of above 90% were obtained. This suggests that the dopant amount can be precisely controlled on a micromole scale by the electric charge during electrolysis. On the other hand, current efficiencies of Na doping into Bi₂Sr₂CaCu₂O_y (BSCCO) ceramics depended on the applied constant current. Efficiencies of above 80% were achieved at a constant current of 10 μA (1.6 A cm⁻²). The relatively low efficiencies were explained by the saturation of BSCCO grain boundaries with Na. By contrast, excess Na was detected on the anodic surface of ceramics at a constant current of 100 μA (16 A cm⁻²). In the present study, we demonstrate that SOED enables micromole-scale control over dopant amount.     

Configurational and conformational preferences in stereoselective acylations of <Emphasis Type="Italic">N</Emphasis>-methyl-1,3-diaminopropane with acyl chlorides

Evidence for a stereoinduction profile of the reaction of N-methyl-1,3-diaminopropane with acyl chlorides has been provided. A possibility to engage in intramolecular CH₂⋯HN and Cl⋯H-N interactions and the proton migration process to the methylamino group leads to the E secondary amides carrying the N⋯H⁺⋯N or N-H⋯N bridges, that show unusual spectroscopic images. Empirical relations between the Δδ _C chemical shift differences, the polarizability of the CO(S) groups and hydrogen bonding strength have been found. Both ¹H-¹⁵N-GHSQC and GHMBC experiments provide insight into the nature of hydrogen bonding and confirm the cyclic array of atoms.     

Approximation of a laminated microstructure for a rotationally invariant,double well energy density

Summary. We give error estimates for the approximation of a laminated microstructure which minimizes the energy for a rotationally invariant, double well energy density . We present error estimates for the convergence of the deformation in the convergence of directional derivatives of the deformation in the “twin planes,” the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient. Received July 25, 1995 / Revised version received November 20, 1995