An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

A new joint model for longitudinal and survival data with a cure fraction

We develop a new joint cure rate model for longitudinal and survival data. The model allows for multiple longitudinal markers as well as a cure structure for the survival component based on the promotion time cure rate model, as described in Ibrahim et al. (Bayesian Survival Analysis, Springer, New York, 2001). Several characteristics and properties of the new model are discussed and examined. A real dataset from a melanoma clinical trial is given to demonstrate the methodology.     

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     

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.