Positivstellens?tze for real function algebras

We look for algebraic certificates of positivity for functions which are not necessarily polynomial functions. Similar questions were examined earlier by Lasserre and Putinar [Positivity and optimization for semi-algebraic functions (to appear), Proposition 1] and by Putinar [A Striktpositivestellensatz for measurable functions (corrected version) (to appear), Theorem 2.1]. We explain how these results can be understood as results on hidden positivity: The required positivity of the functions implies their positivity when considered as polynomials on the real variety of the respective algebra of functions. This variety is however not directly visible in general. We show how algebras and quadratic modules with this hidden positivity property can be constructed. We can then use known results, for example Jacobi’s representation theorem (Jacobi in Math Z 237:259–273, 2001, Theorem 4), or the Krivine-Stengle Positivstellensatz (Marshall in Positive polynomials and sums of squares. Mathematical Surveys and Monographs 146, 2008, page 25), to obtain certificates of positivity relative to a quadratic module of an algebra of real-valued functions. Our results go beyond the results of Lasserre and Putinar, for example when dealing with non-continuous functions. The conditions are also easier to check. We explain the application of our result to various sorts of real finitely generated algebras of semialgebraic functions. The emphasis is on the case where the quadratic module is also finitely generated. Our results also have application to optimization of real-valued functions, using the semidefinite programming relaxation methods pioneered by Lasserre [SIAM J Optim 11(3): 796–817, 2001; Lasserre in Moments, positive polynomials and their applications. Imperial College Press, London, 2009; Lasserre and Putinar in Positivity and optimization for semi-algebraic functions (to appear); Marshall in Positive polynomials and sums of squares. Mathematical Surveys and Monographs 146, 2008, page 25].     

Can we get deeper inside the pion at the LHC?

We propose a measurement of leading neutrons spectra at LHC in order to extract inclusive π ⁺ p and π ⁺ π ⁺ cross-sections with high p _T jets production. The cross-sections for these processes are simulated with the use of parton distributions in hadrons. In this work we estimate the possibility to extract parton distributions in the pion from the data on these cross-sections and also search for signatures of fundamental differences in the pion and proton structure.     

Cladobotric acids A-F: new cytotoxic polyketides from a New Zealand Cladobotryum sp

[reaction: see text] Cladobotric acids A-F (1-6), fungal-derived polyketides, were isolated from the fermentation broth of a New Zealand Cladobotryum species. Structures were determined by extensive spectral analysis and X-ray crystallography, and the polyketide origin of 1-6 was concluded from feeding experiments with (13)C-labeled precursors. The observed folding pattern for the polyketide chain is unusual for fungi. Cladobotric acids A-F (1-6) exhibited notable cytotoxicity against the murine P388 leukemia cell line and were also active against Bacillus subtilis and Candida albicans.     

Optimized measurement temperature gives access to the solution structure of a 49 kDa homohexameric β-propeller

Ph1500 is a homohexameric, two-domain protein of unknown function from the hyperthermophilic archaeon Pyrococcus horikoshii. The C-terminal hexamerization domain (Ph1500C) is of particular interest, as it lacks sequence homology to proteins of known structure. However, it resisted crystallization for X-ray analysis, and proteins of this size (49 kDa) present a considerable challenge to NMR structure determination in solution. We solved the high-resolution structure of Ph1500C, exploiting the hyperthermophilic nature of the protein to minimize unfavorable relaxation properties by high-temperature measurement. Thus, the side chain assignment (97%) and structure determination became possible at full proton density. To our knowledge, Ph1500C is the largest protein for which this has been achieved. To minimize detrimental fast water exchange of amide protons at increased temperature, we employed a strategy where the temperature was optimized separately for backbone and side chain experiments.     

Glossary of terms for separations coupled to mass spectrometry

This document is a glossary of terms for separations coupled to mass spectrometry. It covers gas chromatography/mass spectrometry, liquid chromatography/mass spectrometry, and supercritical fluid chromatography/mass spectrometry and the sample introduction, ionization, and data analysis methods used with these combined techniques.     

Effect of high salt concentrations on the stabilization of bubbles by silica particles

The stabilization of air bubbles by hydrophobically modified silica particles has been investigated in detail. The silica particles used had a nominal primary particle size of 20 nm and were made hydrophobic by treatment with dichlorodimethylsilane to yield particles with varying percent grafting of alkyl chains ("% SiOR"). Contact-angle (theta) measurements of pure water droplets on flats made from compressed samples of the particles showed a steep increase in theta above ca. 20% SiOR. Other measurements also showed a significant increase in theta when the salt concentration was raised to 1-3 mol dm(-3). Bubbles were formed in a sonicated dispersion of particles by suddenly lowering the pressure. Maximum stability was obtained with 33% SiOR particles and 2-3 mol dm(-3) NaCl. Under these conditions, theta was around 40 degrees. Above a threshold size of around 70 microm, bubbles were extremely stable to disproportionation and coalescence and bubble stability increased significantly with an increase in the NaCl concentration from 0.5 to 3 mol dm(-3). Furthermore, rheological measurements showed that at NaCl concentrations in this range weak particle gels were formed with a finite yield stress. The strength of these gels increased with an increasing NaCl concentration between 0.5 and 3 mol dm(-3) and with an increasing time of aging the dispersions, implicating this as part of the mechanism leading to an increased bubble stability in these systems. Dispersions in the absence of NaCl showed little or no foamability at all. Use of CaCl2 and Al(NO)3 at similar ionic strengths showed that equivalent stability could not be obtained with these salts. Atomic force microscopy (AFM) measurements of the adhesion between a pure (0% SiOR) silica sphere and flat showed a significant increase in the adhesion between 0.5 and 3 mol dm(-3) NaCl, even though in this concentration range no significant change in the electrostatic repulsion might be expected. It is concluded that the increased particle-particle adhesion, effective hydrophobicity, and bubble-stabilization properties of the particles at high NaCl concentrations are probably due to the collapse of protruding polysilicic acid chains on the surface of the silica.     

Particle formation by infrared laser ablation of glycerol: implications for ion formation

The quantity and size distribution of micrometer-sized particles ejected from thin films of glycerol were measured using light scattering particle sizing. Thin glycerol films were irradiated at atmospheric pressure with an infrared optical parametric oscillator at wavelengths between 2.95 and 3.1 microm. Particulate material resulting from the ablation was sampled directly into a particle-sizing instrument and particles with diameters greater than 500 nm were detected and sized by light scattering. The fluence threshold for particle formation was between 2000 and 3000 J/m2 for all laser wavelengths. At threshold, fewer than 100 particles/cm3 were detected and this value increased to several thousand particles/cm3 at twice the threshold fluence. The average size of the coarse particles ranged from 900 nm to 1.6 microm at threshold and decreased by 10-20% at twice the threshold fluence. The coarse particle formation observations were compared with ion formation behavior in matrix-assisted laser desorption ionization and interpreted in terms of a photomechanical mechanism for material ablation and ion formation.     

Age-dependent survival, reproduction and photorepair activity in Daphnia magna (Straus, 1820) after exposure to artificial ultraviolet radiation

We examined age-related vulnerability of Daphnia magna to UV-B (ultraviolet-B radiation, 280-320 nm), the age-related relationships between UV-B dosage and reproduction, and the effects of duration of PRR (photorecovery radiation) on survival and fecundity. Animals were exposed to 0, 6, 9 or 12 h UV-B (peak emission 312 nm) at 1, 2, 3 or 4 days of age and followed to 12 days. Survival decreased with increasing exposure to UV-B, but increased with age at exposure. Duration of UV-B, but not age at exposure, decreased offspring production. Survival increased with an increase in duration of PRR for animals of all ages; however, the effect was not age related. Three-day-old animals were exposed to 6 h of UV-B followed by 0-600 min of PRR. Survival was greatest in controls, lowest in the group that received no PRR and similar for all other groups. Most mortality occurred within the first 72 h postirradiation. Offspring production was highest in light controls, lowest in the UV-B-exposed group that received no PRR and not significantly different among other groups. This study demonstrates the need to consider age when examining the effects of UV-B on zooplankton and the need to monitor responses over a sufficient length of time.