Polynomials on Banach spaces with unconditional bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.

Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

De novo generation of a non-segmented negative strand RNA virus with a bicistronic gene

Reverse genetics has facilitated the use of non-segmented negative strand RNA viruses (NNSV) as vectors. Currently, heterologous gene expression necessitates insertion of extra-numeral transcription units (ENTUs), which may alter the NNSV polar transcription gradient and attenuate growth relative to wildtype (Wt). We hypothesized that rescuing recombinant Sendai Virus (rSeV) with a bicistronic gene might circumvent this attenuation but still allow heterologous open reading frame (ORF) expression. Therefore, we used a 9-nucleotide sequence previously described with internal ribosome entry site (IRES) activity, which, when constructed as several repeats, synergistically increased the level of expression of the second cistron [Chappell, S.A., Edelman, G.M., Mauro, V.P., 2000. A 9-nt segment of a cellular mRNA can function as an internal ribosome entry site (IRES) and when present in linked multiple copies greatly enhances IRES activity. Proc. Natl. Acad. Sci. U.S.A. 97, 1536-1541]. We inserted the Renilla luciferase (rLuc) ORF, preceded by 1, 3 or 7 IRES copies, downstream of the SeV N ORF in an infectious clone. Corresponding rSeVs were successfully rescued. Interestingly, bicistronic rSeVs grew as fast as or faster than Wt rSeV. Furthermore, SeV gene transcription downstream of the N/rLuc gene was either equivalent to, or slightly enhanced, compared to Wt rSeV. Importantly, all rSeV/rLuc viruses efficiently expressed rLuc. IRES repetition increased rLuc expression at a multiplicity of infection of 0.1, although without evidence of synergistic enhancement. In conclusion, our approach provides a novel way of insertion and expression of foreign genes in NNSVs. (C) 2008 Elsevier B.V. All rights reserved.

Phase-Transfer Catalysis in Segmented Flow in a Microchannel: Fluidic Control of Selectivity and Productivity

Precise control over the interfacial area of aqueous and organic slugs in segmented flow in a microchannel reactor provides an attractive means to optimize the yield and productivity of a phase-transfer-catalyzed reaction. Herein, we report the selective alkylation of phenylacetonitrile to the monoalkylated product in a microchannel of 250-mu m internal diameter operated in a continuous and solvent-free manner in the slug-flow regime. The conversion of phenylacetonitrile increased from 40% to 99% as a result of a 97% larger slug surface-to-volume ratio when the volumetric aqueous-to-organic phase flow ratio was raised from 1.0 to 6.1 at the same residence time. The larger surface-to-volume ratio significantly promoted catalyst phase transfer but decreased selectivity because of the simultaneous increase of the rate of the consecutive reaction to the dialkylated product. There exists all Optimum flow ratio with a maximum productivity. Conversion and selectivity in the microchannel reactor were both found to be significantly larger than in a stirred reactor.

Algorithmic computation of knot polynomials of secondary structure elements of proteins

The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure-alpha-helix, antiparallel beta-sheet, and parallel beta-sheet-and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm-not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures.

Efficient and selective hydrogen peroxide-mediated oxidation of sulfides in batch and segmented and continuous flow using a peroxometalate-based polymer immobilised ionic liquid phase catalyst

The peroxometalate-based polymer immobilized ionic liquid phase catalyst [PO4{WO(O-2)(2)}(4)]@PIILP has been prepared by anion exchange of ring opening metathesis-derived pyrrolidinium-decorated norbornene/ cyclooctene copolymer and shown to be a remarkably efficient system for the selective oxidation of sulfides under mild conditions. A cartridge packed with a mixture of [PO4{WO(O-2)(2)}(4)]@PIILP and silica operated as a segmented or continuous flow process and gave good conversions and high selectivity for either sulfoxide (92% in methanol at 96% conversion for a residence time of 4 min) or sulfone (96% in acetonitrile at 96% conversion for a residence time of 15 min). The immobilized catalyst remained active for 8 h under continuous flow operation with a stable activity/selectivity profile that allowed 6.5 g of reactant to be processed (TON = 46 428) while a single catalyst cartridge could be used for the consecutive oxidation of multiple substrates giving activity-selectivity profiles that matched those obtained with fresh catalyst.

Polyploid measles virus with hexameric genome length

Particles of most virus species accurately package a single genome, but there are indications that the pleomorphic particles of parainfluenza viruses incorporate multiple genomes. We characterized a stable measles virus mutant that efficiently packages at least two genomes. The first genome is recombinant and codes for a defective attachment protein with an appended domain interfering with fusion-support function. The second has one adenosine insertion in a purine run that interrupts translation of the appended domain and restores function. In that genome, a one base deletion in a different purine run abolishes polymerase synthesis, but restores hexameric genome length, thus ensuring accurate RNA encapsidation, which is necessary for efficient replication. Thus, the two genomes are complementary. The infection kinetics of this mutant indicate that packaging of multiple genomes does not negatively affect growth. We also show that polyploid particles are produced in standard infections at no expense to infectivity. Our results illustrate how the particles of parainfluenza viruses efficiently accommodate cargoes of different volume, and suggest a mechanism by which segmented genomes may have evolved.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

The visual processing of motion-defined transparency

Our understanding of how the visual system processes motion transparency, the phenomenon by which multiple directions of motion are perceived to co-exist in the same spatial region, has grown considerably in the past decade. There is compelling evidence that the process is driven by global-motion mechanisms. Consequently, although transparently moving surfaces are readily segmented over an extended space, the visual system cannot separate two motion signals that co-exist in the same local region. A related issue is whether the visual system can detect transparently moving surfaces simultaneously, or whether the component signals encounter a serial â??bottleneckâ?? during their processing? Our initial results show that, at sufficiently short stimulus durations, observers cannot accurately detect two superimposed directions; yet they have no difficulty in detecting one pattern direction in noise, supporting the serial-bottleneck scenario. However, in a second experiment, the difference in performance between the two tasks disappears when the component patterns are segregated. This discrepancy between the processing of transparent and non-overlapping patterns may be a consequence of suppressed activity of global-motion mechanisms when the transparent surfaces are presented in the same depth plane. To test this explanation, we repeated our initial experiment while separating the motion components in depth. The marked improvement in performance leads us to conclude that transparent motion signals are represented simultaneously.

Transparency Proposals for European Sovereign Bond Markets

The debate over the possible extension of transparency regulation in Europe to include sovereign bonds has opened up a number of other issues in need of serious consideration. One such issue is the appropriateness of the entire infrastructure supporting the trading of European sovereign bonds. In recent years sovereign issuers have supported the development of an electronic inter-dealer market but have remained unconcerned with the opacity of dealer-to-customer trading. The degree of segmentation in this market is high relative to what exists in nearly all other financial markets. This paper explores why European sovereign bond markets have developed in such a segmented way and considers how this structure could be altered to improve transparency without adversely affecting liquidity, efficiency or the benefits enjoyed by primary dealers and issuers. It is suggested that the structure of the market could be improved greatly if the largest and most active investors were permitted access to the inter-dealer electronic trading platforms. This would solve a number of market imperfections and increase the proportion of market activity that is conducted in a transparent way. The paper argues that sovereign issuers in Europe have the means to provide incentives that would influence dealers to support reduced segmentation. Some practical examples of how this could be achieved are provided and the potential benefits are outlined.