Box-threshold graphs

A graph is called box-threshold when all pairs of vertices with incomparable neighborhoods have the same degree. Several properties of box-threshold graphs, generalizing properties of threshold graphs, are proved. A transportation model with priority constraints is used to characterize their degree sequences. Further characterizations are given using the concept of the frame of a graph.     

Universal radius of injectivity for locally quasiconformal mappings

Ifn>2 and iff is a locally quasiconformal mapping from the ballB ⁿ= {x∈R ⁿ:⋎x⋎<1} intoR ⁿ ∪ {∞} thenf is injective inB ⁿ (r)={x∈R ⁿ:⋎x⋎ <r} wherer>0 depends only onn and the maximal dilatation off. Supported in part by the Samuel Neaman Fund, Special Year in Complex Analysis, Technion, I.I.T., Haifa, Israel, 1975/76.     

Damage models for multi-component systems

A series system of n components is subject to a damage process. The damage to each component is cumulative and when it exceeds a certain threshold the component, and hence the device, fails. For various optimality criteria related to system lifetime and system reliability, we find the optimal allocation of resources among the components where the total resources are limited and the allocation of the resources determines the threshold level of each component. Various inventory-type applications are noted.     

Analytical study of diffusive relativistic shock acceleration

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. The particle spectral index s is found to be sensitive to D, particularly downstream and at certain angles. The analysis, confirmed numerically, justifies and generalizes previous results for isotropic diffusion. It can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by gamma-ray burst afterglow observations.     

Interaction of scanning probes with semiconductor nanocrystals; physical mechanism and basis for near-field optical imaging

We investigate the modification of photoluminescence (PL) from single semiconductor nanocrystal quantum dots (NCs) in the proximity of metal and semiconducting atomic force microscope (AFM) tips. The presence of the tip alters the radiative decay rate of an emitter via interference and opens efficient nonradiative decay channels via energy transfer to the tip material. These effects cause quenching (or enhancement) of the emitter's PL intensity as a function of its distance from the interacting tip. We take advantage of this highly distance-dependent effect to realize a contrast mechanism for high-resolution optical imaging. AFM tips are optimized as energy acceptors by chemical functionalization with InAs NCs to achieve optical resolution down to 30 nm. The presented experimental scheme offers high-resolution optical information while maintaining the benefits of traditional AFM imaging. We directly measure the PL intensity of single NCs as a function of the tip distance. Our results are in good agreement with calculations made by a classical theoretical model describing an oscillating dipole interacting with a planar mirror.