An Index Theory For Quantum Dynamical Semigroups

W. Arveson showed a way of associating continuous tensor product systems of Hilbert spaces with endomorphism semigroups of type I factors. We do the same for general quantum dynamical semigroups through a dilation procedure. The product system so obtained is the index and its dimension is a numerical invariant for the original semigroup.

     

An algorithm for then×n optimum assignment problem

In this paper we present an algorithm for finding an optimum assignment for ann×n matrixM inn iterations. The method uses systematic permutations on the rows ofM and is based on the properties of optimum assignments. The implementation presented in the paper requires at mostO(n ³) in time andn ²+6n memory locations for solving a densen×n problem.This work was supported by the National Science Foundation Grant NSF ENG 74-19788.     

A new method of producing local enhancement of buoyancy in liquid flows

We describe here a novel method of generating large volumetric heating in a liquid. The method uses the principle of ohmic heating of the liquid, rendered electrically conducting by suitable additives if necessary. Electrolysis is prevented by the use of high frequency alternating voltage and chemically treated electrodes. The technique is demonstrated by producing substantial heating in an initially neutral jet of water. Simple flow visualisation studies, made by adding dye to the jet, show marked changes in the growth and development of the jet with heat addition.Also with National Aeronautical Laboratory, Bangalore 560 017, India     

Spectrophotometric studies of copper (II)—bis-2-pyridyl glycol complex

An aqueous solution ofbis-2-pyridyl glycol forms a deep blue water-soluble complex with an aqueous solution of copper (II) salts. The complex has an absorption maximum at 600–650 mµ between pH range 3·0–8·7. The complex is stable for four days and obeys Lambert-Beer’s law in the concentration range of 5·08–50·80 ppm. of copper (II) in solution. The optical density of the complex remains constant between pH 3·8–5·9. The molar composition as determined by the method of continuous variation and by the slope ratio method has been found to be 1:1. The limits of interference due to some foreign ions during the estimation of copper (II) have been determined.     

Bose-Einstein condensates in rotating lattices

Strongly interacting bosons in a two-dimensional rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Such a system corresponds to a rotating lattice potential imprinted on a trapped Bose-Einstein condensate. Second-order quantum phase transitions between states of different symmetries are observed at discrete rotation rates. For the square lattice we study, there are four possible ground-state symmetries.     

Search for ZH → l+ l- bb production in 4.2 fb(-1) of pp collisions at sqrt[s] =1 .96 TeV

We present a search for the standard model Higgs boson produced in association with a Z boson in 4.2 fb(-1) of pp collisions, collected with the D0 detector at the Fermilab Tevatron at sqrt[s] =1 .96 TeV. Selected events contain one reconstructed Z → e+ e- or Z → μ+ μ- candidate and at least two jets, including at least one b-tagged jet. In the absence of an excess over the background expected from other standard model processes, limits on the ZH cross section multiplied by the branching ratios are set. The limit at M(H) = 115 GeV is a factor of 5.9 larger than the standard model prediction.     

Indentation of transversely isotropic power-law hardening materials: computational modelling of the forward and reverse problems

Using a combination of dimensional analysis and large deformation finite element simulations of triple indentations of 120 materials, a framework for capturing the indentation response of transversely isotropic materials is developed. By considering 4800 combinations of material properties within the bounds of the original set of 120 materials, forward algorithms that predict the indentation response of materials and reverse algorithms that predict the materials’ elastic and plastic properties from experimentally measured indentation responses are formulated for both longitudinal and transverse indentations. Issues of accuracy, reversibility, uniqueness and sensitivity within the context of the indentation of transversely isotropic materials are addressed carefully. Using 1400 combinations of material properties, it is demonstrated that there is perfect reversibility between the material properties and their indentation responses as predicted by the forward and reverse algorithms. On average, the differences between the results of the finite element analysis and those predicted by the forward algorithms for longitudinal or transverse indentations are less than 1%, thus demonstrating the high accuracy and uniqueness of the forward analysis. For longitudinal and transverse indentations, the reverse algorithms provide accurate results in most cases with an average error of 3 and 6%, respectively. A sensitivity analysis with a ±2% variation in the material properties in the forward algorithm and ±2% variation in the indentation responses in the reverse algorithms demonstrated the robustness of the algorithms developed in the present study, with the longitudinal indentations providing relatively less sensitivity to variability in indentation responses as compared to the transverse indentations.     

Transformation of a [4+6] Salicylbisimine Cage to Chemically Robust Amide Cages

In recent years, interest in shape‐persistent organic cage compounds has steadily increased, not least because dynamic covalent bond formation enables such structures to be made in high to excellent yields. One often used type of dynamic bond formation is the generation of an imine bond from an aldehyde and an amine. Although the reversibility of the imine bond formation is advantageous for high yields, it is disadvantageous for the chemical stability of the compounds. Amide bonds are, in contrast to imine bonds much more robust. Shape‐persistent amide cages have so far been made by irreversible amide bond formations in multiple steps, very often accompanied by low yields. Here, we present an approach to shape‐persistent amide cages by exploiting a high‐yielding reversible cage formation in the first step, and a Pinnick oxidation as a key step to access the amide cages in just three steps. These chemically robust amide cages can be further transformed by bromination or nitration to allow post‐functionalization in high yields. The impact of the substituents on the gas sorption behavior was also investigated.