Speeding up Cylindrical Algebraic Decomposition by Gr\"obner Bases

Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a mixed system of equalities and inequalities, it is possible to apply Gr\"obner bases to the (conjoined) equalities before invoking CAD. We see that this is, quite often but not always, a beneficial preconditioning of the CAD problem. It is also possible to precondition the (conjoined) inequalities with respect to the equalities, and this can also be useful in many cases.Comment: To appear in Proc. CICM 2012, LNCS 736

Terpenylic acid and related compounds: precursors for dimers in secondary organic aerosol from the ozonolysis of α- and β-pinene

In the present study, we have characterized the structure of a higher-molecular weight (MW) 358 α- and β-pinene dimeric secondary organic aerosol (SOA) product that received ample attention in previous molecular characterization studies and has been elusive. Based on mass spectrometric evidence for deprotonated molecules formed by electrospray ionization in the negative ion mode and chemical considerations, it is suggested that diaterpenylic acid is a key monomeric intermediate for dimers of the ester type. It is proposed that cis-pinic acid is esterified with the hydroxyl-containing diaterpenylic acid, which can be explained through acid-catalyzed hydrolysis of the recently elucidated lactone-containing terpenylic acid and/or diaterpenylic acid acetate, both first-generation oxidation products. To a minor extent, higher-MW 358 and 344 diester products are formed containing other terpenoic acids as monomeric units, i.e., diaterpenylic acid instead of cis-pinic acid, and diaterebic acid instead of diaterpenylic acid. It is shown that the MW 358 diester and related MW 344 compounds, which can be regarded as processed SOA products, also occur in ambient fine (PM2.5) rural aerosol collected at night during the warm period of the 2006 summer field campaign conducted at K-puszta, Hungary, a rural site with coniferous vegetation. This indicates that, under ambient conditions, the higher-MW diesters are formed in the particle phase over a longer time-scale than that required for gas-to-particle partitioning of their monomeric precursors in laboratory α-/β-pinene ozonolysis experiments

Terpenylic Acid and Related Compounds from the Oxidation of α-Pinene: Implications for New Particle Formation and Growth above Forests

Novel secondary organic aerosol (SOA) products from the monoterpene α-pinene with unique dimer-forming properties have been identified as lactone-containing terpenoic acids, i.e., terpenylic and 2-hydroxyterpenylic acid, and diaterpenylic acid acetate. The structural characterizations were based on the synthesis of reference compounds and detailed interpretation of mass spectral data. Terpenylic acid and diaterpenylic acid acetate are early oxidation products generated upon both photooxidation and ozonolysis, while 2-hydroxyterpenylic acid is an abundant SOA tracer in ambient fine aerosol that can be explained by further oxidation of terpenylic acid. Quantum chemical calculations support that noncovalent dimer formation involving double hydrogen bonding interactions between carboxyl groups of the monomers is energetically favorable. The molecular properties allow us to explain initial particle formation in laboratory chamber experiments and are suggested to play a role in new particle formation and growth above forests, a natural phenomenon that has fascinated scientists for more than a century

Effect of varying experimental conditions on the viscosity of α-pinene derived secondary organic material

Knowledge of the viscosity of particles containing secondary organic material (SOM) is useful for predicting reaction rates and diffusion in SOM particles. In this study we investigate the viscosity of SOM particles as a function of relative humidity and SOM particle mass concentration, during SOM synthesis. The SOM was generated via the ozonolysis of α-pinene at < 5 % relative humidity (RH). Experiments were carried out using the poke-and-flow technique, which measures the experimental flow time (τexp, flow) of SOM after poking the material with a needle. In the first set of experiments, we show that τexp, flow increased by a factor of 3600 as the RH increased from < 0.5 RH to 50 % RH, for SOM with a production mass concentration of 121 µg m−3. Based on simulations, the viscosities of the particles were between 6  ×  105 and 5  ×  107 Pa s at < 0.5 % RH and between 3  ×  102 and 9  ×  103 Pa s at 50 % RH. In the second set of experiments we show that under dry conditions τexp, flow decreased by a factor of 45 as the production mass concentration increased from 121 to 14 000 µg m−3. From simulations of the poke-and-flow experiments, the viscosity of SOM with a production mass concentration of 14 000 µg m−3 was determined to be between 4  ×  104 and 1.5  ×  106 Pa s compared to between 6  ×  105 and 5  ×  107 Pa s for SOM with a production mass concentration of 121 µg m−3. The results can be rationalized by a dependence of the chemical composition of SOM on production conditions. These results emphasize the shifting characteristics of SOM, not just with RH and precursor type, but also with the production conditions, and suggest that production mass concentration and the RH at which the viscosity was determined should be considered both when comparing laboratory results and when extrapolating these results to the atmosphere

Calibration of centre-of-mass energies at LEP1 for precise measurements of Z properties

The determination of the centre-of-mass energies from the LEP1 data for 1993, 1994 and 1995 is presented. Accurate knowledge of these energies is crucial in the measurement of the Z resonance param eters. The improved understanding of the LEP energy behaviour accumulated during the 1995 energy scan is detailed, while the 1993 and 1994 measurements are revised. For 1993 these supersede the pr eviously published values. Additional instrumentation has allowed the detection of an unexpectedly large energy rise during physics fills. This new effect is accommodated in the modelling of the beam-energy in 1995 and propagated to the 1993 and 1994 energies. New results are reported on the magnet temperature behaviour which constitutes one of the major corrections to the average LEP ene rgy. The 1995 energy scan took place in conditions very different from the previous years. In particular the interaction-point specific corrections to the centre-of-mass energy in 1995 are more complicated than previously: these arise from the modified radiofrequency-system configuration and from opposite-sign vertical dispersion induced by the bunch-train mode of LEP operation. Finall y an improved evaluation of the LEP centre-of-mass energy spread is presented. This significantly improves the precision on the Z width

Learn-merge invariance of priors: A characterization of the Dirichlet distributions and processes

AbstractLearn-merge invariance is a property of prior distributions (related to postulates introduced by the philosophers W. E. Johnson and R. Carnap) which is defined and discussed within the Bayesian learning model. It is shown that this property in its strong formulation characterizes the Dirichlet distributions and processes. Generalizations towards weaker formulations are outlined

Learn-merge invariance of priors: A characterization of the Dirichlet distributions and processes

Learn-merge invariance is a property of prior distributions (related to postulates introduced by the philosophers W. E. Johnson and R. Carnap) which is defined and discussed within the Bayesian learning model. It is shown that this property in its strong formulation characterizes the Dirichlet distributions and processes. Generalizations towards weaker formulations are outlined.prior Dirichlet distribution multinomial situation symmetric measures inductive learning