Optimal partitions having disjoint convex and conic hulls

LetA ¹,,A ⁿ be distinctk-dimensional vectors. We consider the problem of partitioning these vectors intom sets so as to maximize an objective which is a quasi-convex function of the sum of vectors in each set. We show that there exists an optimal partition whose sets have (pairwise) disjoint conic hulls. We also show that if the number of vectors in each of the sets is constrained, then a weaker conclusion holds, namely, there exists an optimal partition whose sets have (pairwise) disjoint convex hulls. The results rely on deriving necessary and sufficient conditions for a point to be an extreme point of a corresponding polytope.Research of this author was partially supported by NSF Grant ECS-83-10213 and by a Grant for the Promotion of Research at the Technion.     

Photophysics of ruthenium(II) complexes with 2-(2′-pyridyl) pyrimidine and 2,2′-bipyridine ligands in fluid solution

The photophysics of three complexes of the form Ru(bpy)₃₋(pypm)²⁺ (where bpy2,2′-bipyridine, pypm 2-(2′-pyridyl)pyrimidine and P=1, 2 or 3) was examined in H₂O, propylene carbonate, CH₃CN and 4:1 (v/v) C₂H₅OH---CH₃OH; comparison was made with the well-known photophysical behavior of Ru(bpy)₃²⁺. The lifetimes of the luminescent metal-to-ligand charge transfer (MLCT) excited states were determined as a function of temperature (between −103 and 90 °C, depending on the solvent), from which were extracted the rate constants for radiative and non-radiative decay and ΔE, the energy gap between the MLCT and metal-centered (MC) excited states. The results indicate that ^*Ru(bpy)₂(pypm)²⁺ decays via a higher lying MLCT state, whereas ^*Ru(pypm)₃²⁺ and ^*Ru(pypm)₂(bpy)²⁺ decay predominantly via the MC state.     

Electrostatic influence on rotational mobilities of sol-gel-encapsulated solutes by NMR and EPR spectroscopies

The rotational mobilities of small solute molecules encapsulated in tetramethyl orthosilicate (TMOS) sol-gels have been investigated by EPR spectroscopy of encapsulated nitroxide probes and by high-resolution NMR spectroscopic measurements of transferred NOE's (trNOE's), of T(1)'s, and of T(1)'s in the rotating frame (T(1)rho). The two spectroscopic methods are sensitive to motions on different time scales and hence, are nicely complementary. Suites of neutral, positively, and negatively charged nitroxide probes (EPR) and of simple diamagnetic small molecules (NMR) were selected to disclose influences of electrostatic interactions with the sol-gel walls and to probe the presence of multiple populations of molecules in distinct regions of the sol-gel pores. For neutral and negatively charged solute probes, both techniques disclose a single population with a significantly increased average rotational correlation time, which we interpret at least in part as resulting from exchange between free-volume and transiently immobilized surface populations. The electrostatic attraction between cationic probes and the negatively charged sol-gel walls causes the positively charged probes to be more effectively immobilized and/or causes a greater percentage of probes to undergo this transient immobilization. The EPR spectra directly disclose a population of cationic probes which are immobilized on the X-band EPR time scale: tau(c) greater than or approximately equal 10(-7) s. However, NMR measurements of trNOE's and of T(1)rho demonstrate that this population does exchange with the free-volume probes on the slower time scale of NMR. This approach is equally applicable to the study of solutes within other types of confined spaces, as well.     

Residual‐based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods

In this paper, we present a finite element method with a residual‐based artificial viscosity for simulation of turbulent compressible flow, with adaptive mesh refinement based on a posteriori error estimation with sensitivity information from an associated dual problem. The artificial viscosity acts as a numerical stabilization, as shock capturing, and as turbulence capturing for large eddy simulation of turbulent flow. The adaptive method resolves parts of the flow indicated by the a posteriori error estimates but leaves shocks and turbulence under‐resolved in a large eddy simulation. The method is tested for examples in 2D and 3D and is validated against experimental data. Copyright © 2012 John Wiley & Sons, Ltd.     

Development of a prototype high-current low-energy ion implanter

A high current-low energy implant system for the processing of semiconductor devices at medium-high dopant levels is described. Criteria for selection and design of ion beam components such as ion beam optics, vacuum requirements and reliability are discussed. Variations in wafer uniformities for within wafer, wafer-to-wafer and run-to-run are presented.     

Optimizing the monomer structure of polyhedral oligomeric silsesquioxane for ion transport in hybrid organic–inorganic block copolymers

Poly(ethylene oxide)-b-polyhedral oligomeric silsesquioxane (PEO–POSS) mixed with lithium bis(trifluoromethanesulfonyl)imide salt is a nanostructured hybrid organic–inorganic block copolymer electrolyte that may enable lithium metal batteries. The synthesis and characteristics of three PEO–POSS block copolymer electrolytes which only differ by their POSS silica cage substituents (ethyl, isobutyl, and isooctyl) is reported. Changing the POSS monomer structure results in differences in both thermodynamics and ion transport. All three neat polymers exhibit lamellar morphologies. Adding salt results in the formation of a disordered window which closes and gives way to lamellae at higher salt concentrations. The width of disordered window decreases with increasing length of the POSS alkyl chain substituent from ethyl to isobutyl and is absent in the isooctyl sample. Rheological measurements demonstrate good mechanical rigidity when compared with similar all-organic block copolymers. While salt diffusion coefficient and current ratio are unaffected by substituent length, ionic conductivity increases as the length of the alkyl chain substituent decreases: the ethyl substituent is optimal for ion transport. This is surprising because conventional wisdom suggests that ion transport occurs primarily in the PEO-rich domains, that is, ion transport should be unaffected by substituent length after accounting for the minor change in conducting phase volume fraction. © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 363–371