Hybrid fluorescent nanoparticles from quantum dots coupled to cellulose nanocrystals

Carboxylated cellulose nanocrystals (CNCs) were decorated with CdSe/ZnS quantum dots (QDs) using a carbodiimide chemistry coupling approach. The one-step covalent modification was supported by nanoscale imaging, which showed QDs clustered on and around the CNCs after coupling. The QD–CNC hybrid nanoparticles remained colloidally stable in aqueous suspension and were fluorescent, exhibiting the broad excitation and narrow emission profile characteristic of the QDs. QD–CNCs in nanocomposite films imparted strong fluorescence within CNC-compatible matrices at relatively low loadings (0.15 nmol QDs/g of dry film), without altering the overall physical properties or self-assembly of the CNCs. The hybrid QD–CNCs may find applications in nanoparticle tracking, bio-imaging, optical/sensing devices, and anti-counterfeit technologies.     

Studies related to the synthesis of maytansinoids.

Two approaches to the partial synthesis of C₁–C₅ of a bis-nor maytansinoid $\text{1}$ have been investigated starting on the one hand with (S)-(?)-malic acid and on the other, with D-(+)-ribonolactone.     

The synthesis of N-substituted ketimines from oxazirdines

N-Unsubstituted diaryl, alkyl aryl and dialkyl ketimines are prepared in good yield at ambient temperature by the reaction of KOBu^t on oxaziridines having an α-hydrogen atom on the N-alkyl substituent; the mechanism and stereochemistry of the reaction are discussed.     

Conjugacy languages in groups

We study the regularity of several languages derived from conjugacy classes in a finitely generated group G for a variety of examples including word hyperbolic, virtually abelian, Artin, and Garside groups. We also determine the rationality of the growth series of the shortlex conjugacy language in virtually cyclic groups, proving one direction of a conjecture of Rivin.     

On second-order periodic elliptic operators in divergence form

We consider second-order, strongly elliptic, operators with complex coefficients in divergence form on . We assume that the coefficients are all periodic with a common period. If the coefficients are continuous we derive Gaussian bounds, with the correct small and large time asymptotic behaviour, on the heat kernel and all its H?lder derivatives. Moreover, we show that the first-order Riesz transforms are bounded on the -spaces with . Secondly if the coefficients are H?lder continuous we prove that the first-order derivatives of the kernel satisfy good Gaussian bounds. Then we establish that the second-order derivatives exist and satisfy good bounds if, and only if, the coefficients are divergence-free or if, and only if, the second-order Riesz transforms are bounded. Finally if the third-order derivatives exist with good bounds then the coefficients must be constant. Received in final form: 28 February 2000 / Published online: 17 May 2001     

Weyl's theorem and tensor products: A counterexample

Approximately fifty percent of Weyl's theorem fails to transfer from Hilbert space operators to their tensor product. As a biproduct we find that the product of circles in the complex plane is a limaçon.     

Completeness for intersection classes

An intersection representation of a graph is a function gf mapping vertices to sets such that for any u ≠ v, u is adjacent to v iff gf(u) ∩ gf(v) ≠ . The intersection class defined by a set of sets ∑ is the set of all graphs having an intersection representation using sets from ∑. Interval graphs and chordal graphs are well-studied examples of intersection classes.

This paper introduces the notion of completeness for intersection classes. That is, determining precisely what restrictions can be made on the allowable sets without losing the power to represent any graph in the intersection class. The solution to this problem is presented for the chordal graphs.     

Local Lower Bounds on Heat Kernels

We analyze convolution semigroups on a regular measure space which satisfies the local doubling property. We assume the kernels are bounded and symmetric with the characteristic small-time, volume-dependent, singularity. Then, using a weak conservation property, we deduce local lower bounds with a comparable singularity.Applications are given to a wide range of subelliptic and strongly elliptic self-adjoint, or near self-adjoint, operators on Lie groups.