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.     

Latrunculin,a new 2-thiazolidinone macrolide from the marine sponge latrunculia magnifica

Three new toxins were isolated from the Red Sea sponge $\text{Latrunculia magnifica}$ A full structure determination of these toxins, by spectroscopic methods, was aided by an X-ray diffraction analysis of a crystalline derivative ($\text{1}$b) of latrunculin-A. The Latrunculins exhibit a new class of 14 and 16 membered macrolides to which the rare 2-thiazolidinone moiety is attached. A biogenesis of these biologically active compounds is put forward.     

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.