Noncommutative ball maps

In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free. These types of functions have recently been used in the study of dimension-free linear system engineering problems. In this paper we characterize NC analytic maps that send dimension-free matrix balls to dimension-free matrix balls and carry the boundary to the boundary; such maps we call “NC ball maps”. We find that up to normalization, an NC ball map is the direct sum of the identity map with an NC analytic map of the ball into the ball. That is, “NC ball maps” are very simple, in contrast to the classical result of D'Angelo on such analytic maps in C. Another mathematically natural class of maps carries a variant of the noncommutative distinguished boundary to the boundary, but on these our results are limited. We shall be interested in several types of noncommutative balls, conventional ones, but also balls defined by constraints called Linear Matrix Inequalities (LMI). What we do here is a small piece of the bigger puzzle of understanding how LMIs behave with respect to noncommutative change of variables.     

The failure of rational dilation on a triply connected domain

For a bounded triply connected domain with boundary consisting of disjoint analytic curves there exists an operator on a complex Hilbert space so that the closure of is a spectral set for , but does not dilate to a normal operator with spectrum in , the boundary of . There is considerable overlap with the construction of an example on such a domain recently obtained by Agler, Harland and Raphael using numerical computations and work of Agler and Harland.

     

Desorption of small ionic fragments from oligonucleotides induced by low energy carbon ions

The degradation of oligonucleotide films containing differing base sequences induced by 4 keV C⁺ ions has been studied experimentally. The oligonucleotides were deposited onto a gold coated stainless steel substrate and the anions and cations released from the films were analyzed by a quadrupole mass spectrometer. The total ion desorption yield was recorded as a function of time using a constant C⁺ ion flux of 6 × 10¹⁴ ions cm^-2 s^-1. At low fluences the formation of small ionic fragments was observed, whilst for fluences greater than 1.2 × 10¹⁸ ions cm^-2 molecules were sputtered from the substrate. In addition to studies of the influence of a particular base to the total cation desorption yield, the effect of base substitution with bromine was measured for negative ion desorption. These results showed a strong degradation of oligonucleotide films during ion bombardment.     

Target structure induced suppression of the ionization cross section for very low energy antiproton-hydrogen collisions

Low energy antiprotons have been used previously to give benchmark data for theories of atomic collisions. Here we present measurements of the cross section for single, nondissociative ionization of molecular hydrogen for impact of antiprotons with kinetic energies in the range 2-11 keV, i.e., in the velocity interval of 0.3-0.65 a.u. We find a cross section which is proportional to the projectile velocity, which is quite unlike the behavior of corresponding atomic cross sections, and which has never previously been observed experimentally.     

On-line Monitoring of Continuous Flow Chemical Synthesis Using a Portable,Small Footprint Mass Spectrometer

For on-line monitoring of chemical reactions (batch or continuous flow), mass spectrometry (MS) can provide data to (1) determine the fate of starting materials and reagents, (2) confirm the presence of the desired product, (3) identify intermediates and impurities, (4) determine steady state conditions and point of completion, and (5) speed up process optimization. Recent developments in small footprint atmospheric pressure ionization portable mass spectrometers further enable this coupling, as the mass spectrometer can be easily positioned with the reaction system to be studied. A major issue for this combination is the transfer of a sample that is representative of the reaction and also compatible with the mass spectrometer. This is particularly challenging as high concentrations of reagents and products can be encountered in organic synthesis. The application of a portable mass spectrometer for on-line characterization of flow chemical synthesis has been evaluated by coupling a Microsaic 4000 MiD to the Future Chemistry Flow Start EVO chemistry system. Specifically, the Hofmann rearrangement has been studied using the on-line mass spectrometry approach. Sample transfer from the flow reactor is achieved using a mass rate attenuator (MRA) and a sampling make-up flow from a high pressure pump. This enables the appropriate sample dilution, transfer, and preparation for electrospray ionization. The capability of this approach to provide process understanding is described using an industrial pharmaceutical process that is currently under development. The effect of a number of key experimental parameters, such as the composition of the sampling make-up flow and the dilution factor on the mass spectrometry data, is also discussed. Figure

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Classification of all noncommutative polynomials whose Hessian has negative signature one and a noncommutative second fundamental form

Every symmetric polynomial p = p(x) = p(x ₁,..., x _g ) (with real coefficients) in g noncommuting variables x ₁,..., x _g can be written as a sum and difference of squares of noncommutative polynomials:

Isometric representations of some quotients ofH ∞ of an annulus

Let denote an annulus,E a finite subset of with at least three elements, and the ideal of functions in which vanish at the points ofE. The quotient does not have a completely isometric representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representation on a Hilbert space of dimension twice the cardinality ofE.     

Deformation mechanisms of constrained polymer chains. II. Deformation energetics of tie molecules

Energy-deformation characteristics for the primary T, S, and U conformational units of tie molecules were obtained from the analysis of data generated from a constrained minimization algorithm. Energy-deformation profiles (covering the range from compact equilibrium defect structures to the fully extended chain) are reported for the S₀ and S₁ members of the S_λ family and for the U₀₀ member of the U_mn family. Estimates of the energy content V⁰ and the elastic modulus E were obtained from the computed energy-deformation data in the vicinity of the equilibrium Structure—S₀ → {60°, 180°, ?60°}, V = 1.7 kcal/mole, E = 60 kcal/cm³ [250 × 10¹⁰ dyn/cm²];S₁ → {60°, 180°, 180°, 180°, ?60°}: V = 1.7 kcal/mole, E = 25 kcal/cm³ [100 × 10¹⁰ dyn/cm²]; and U₀₀ → {60°, 180°, 60°, 180°, 60°}: V = 2.7 kcal/mole, E = 80 kcal/cm³ [340 × 10¹⁰ dyn/cm²]. Although the elastic modulus of the U₀₀ unit is comparable to the elastic modulus of the fully extended chain, the highenergy content of this unit (V₀ = 2.7 Kcal/mole) prohibits a significant population and thereby mitigates an appreciable reinforcing effect from this rigid unit. A model for a surrogate force constant is introduced to generalize the results from this study to any member of the S_λ or U_mn family as well as any combination of S_λ and U_mn units. This generalization provides a basis for estimating the deformation characteristics of tie molecules comprised of various populations of these primary conformational building blocks.