Polar Varieties, Real Equation Solving and Data-Structures: The hypersurface case

In this paper we apply for the first time a new method for multivariate equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for complex root determination to the {\em real} case. Our main result concerns the problem of finding at least one representative point for each connected component of a real compact and smooth hypersurface. The basic algorithm of \cite{gh1}, \cite{gh2}, \cite{gh3} yields a new method for symbolically solving zero-dimensional polynomial equation systems over the complex numbers. One feature of central importance of this algorithm is the use of a problem--adapted data type represented by the data structures arithmetic network and straight-line program (arithmetic circuit). The algorithm finds the complex solutions of any affine zero-dimensional equation system in non-uniform sequential time that is {\em polynomial} in the length of the input (given in straight--line program representation) and an adequately defined {\em geometric degree of the equation system}. Replacing the notion of geometric degree of the given polynomial equation system by a suitably defined {\em real (or complex) degree} of certain polar varieties associated to the input equation of the real hypersurface under consideration, we are able to find for each connected component of the hypersurface a representative point (this point will be given in a suitable encoding). The input equation is supposed to be given by a straight-line program and the (sequential time) complexity of the algorithm is polynomial in the input length and the degree of the polar varieties mentioned above.Comment: Late

Polar Varieties and Efficient Real Elimination

Let $S_0$ be a smooth and compact real variety given by a reduced regular sequence of polynomials $f_1, ..., f_p$. This paper is devoted to the algorithmic problem of finding {\em efficiently} a representative point for each connected component of $S_0$ . For this purpose we exhibit explicit polynomial equations that describe the generic polar varieties of $S_0$. This leads to a procedure which solves our algorithmic problem in time that is polynomial in the (extrinsic) description length of the input equations $f_1, >..., f_p$ and in a suitably introduced, intrinsic geometric parameter, called the {\em degree} of the real interpretation of the given equation system $f_1, >..., f_p$.Comment: 32 page

Can Corrective Ad Statements Based on \u3cem\u3eU.S. v. Philip Morris USA Inc.\u3c/em\u3e Affect Consumer Beliefs about Smoking?

To comply with the court\u27s ruling in U.S. v. Philip Morris USA Inc., tobacco companies must fund a large advertising campaign to \u27correct\u27 smoking beliefs about which consumers may have been misled as a result of past deceptive practices of tobacco companies. The authors use an ad copy experiment to examine (1) the effects of different versions of corrective ad statements that plaintiff intervenors submitted to the court on multi-item belief measures and (2) the impact of the ad versions and beliefs on general attitudes toward smoking across current adult smokers and nonsmokers. The tested ad versions include a copy-only control condition, a copy-with-graphic-visual condition, and a version with a potentially distracting visual. The results indicate that the corrective statements in advertisements can have a positive effect on antismoking beliefs of focal interest in the case and that the test advertisements affect some beliefs more strongly than others. The authors discuss potential policy implications and limitations and provide suggestions for further research

Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case

The objective of this paper is to show how the recently proposed method by Giusti, Heintz, Morais, Morgenstern, Pardo \cite{gihemorpar} can be applied to a case of real polynomial equation solving. Our main result concerns the problem of finding one representative point for each connected component of a real bounded smooth hypersurface. The algorithm in \cite{gihemorpar} yields a method for symbolically solving a zero-dimensional polynomial equation system in the affine (and toric) case. Its main feature is the use of adapted data structure: Arithmetical networks and straight-line programs. The algorithm solves any affine zero-dimensional equation system in non-uniform sequential time that is polynomial in the length of the input description and an adequately defined {\em affine degree} of the equation system. Replacing the affine degree of the equation system by a suitably defined {\em real degree} of certain polar varieties associated to the input equation, which describes the hypersurface under consideration, and using straight-line program codification of the input and intermediate results, we obtain a method for the problem introduced above that is polynomial in the input length and the real degree.Comment: Late

How Do Antitobacco Campaign Advertising and Smoking Status Affect Beliefs and Intentions? Some Similarities and Differences Between Adults and Adolescents

This article presents two studies that examine similarities and differences with respect to how adults and adolescents process and respond to information in an antitobacco ad campaign. Study 1 examines (1) the effects of antitobacco advertising campaign measures (e.g., campaign advertisement integration, perceived strength of ad-based messages, attitude toward the ad campaign) on four key adult antismoking beliefs and (2) the influence of these campaign evaluations and beliefs on smokers’ intentions to quit smoking. Hierarchical regression results show that antismoking ad campaign reactions explain substantial additional variance in beliefs about tobacco industry deceptiveness, smoking addictiveness, harmfulness of secondhand smoke, and restrictions on smoking at different public venues. The findings also show that the campaign variables as a whole are positively related to intentions to quit smoking, beyond the variance that is explained by demographics. In Study 2, the authors replicate and extend these findings for the campaign using similar measures and procedures for a sample of more than 900 adolescents. They draw comparisons between these adult and adolescent findings and offer some implications for potential corrective advertising for consumers’ beliefs about smoking that may be required of tobacco companies based on U.S. v. Philip Morris USA, Inc

Real root finding for equivariant semi-algebraic systems

Let $R$ be a real closed field. We consider basic semi-algebraic sets defined by $n$-variate equations/inequalities of $s$ symmetric polynomials and an equivariant family of polynomials, all of them of degree bounded by $2d < n$. Such a semi-algebraic set is invariant by the action of the symmetric group. We show that such a set is either empty or it contains a point with at most $2d-1$ distinct coordinates. Combining this geometric result with efficient algorithms for real root finding (based on the critical point method), one can decide the emptiness of basic semi-algebraic sets defined by $s$ polynomials of degree $d$ in time $(sn)^{O(d)}$. This improves the state-of-the-art which is exponential in $n$. When the variables $x_1, \ldots, x_n$ are quantified and the coefficients of the input system depend on parameters $y_1, \ldots, y_t$, one also demonstrates that the corresponding one-block quantifier elimination problem can be solved in time $(sn)^{O(dt)}$

Carbon Dioxide Capture from Fuel Gas Streams under Elevated Pressures and Temperatures Using Novel Physical Solvents

The conventional processes for acid gas removal (AGR), including CO2 in the Integrated Gasification Combined Cycle (IGCC) power generation facilities are: a chemical process, using methyl-diethanolamine (MDEA); a physical process, using chilled methanol (Rectisol) or a physical process, using mixtures of dimethylethers of polyetheleneglycol (Selexol). These conventional processes require cooling of the fuel gas streams for CO2 capture and subsequent reheating before sending to turbines, which decreases the plant thermal efficiency and increases the overall cost. Thus, there is a pressing need for developing an economical process which can capture CO2 from the hot fuel gas stream without significant cooling. The overall objective of this study is to investigate the potential use of physical solvents for selective capture of CO2 from post water-gas-shift streams under relatively elevated pressures and temperatures. In order to achieve this objective, a comprehensive literature review was conducted to define an “ideal solvent” for CO2 capture and to identify six different physical solvents which should obey such a definition. The first physical solvents identified were perfluorocarbons (PFCs), which are known to have low reactivity, high chemical stability and relatively low vapor pressures. Three different PFCs, known as PP10, PP11, and PP25, were selected as potential candidates for CO2 capture. The equilibrium solubilities of CO2 and N2 were measured in these PFCs under different operating conditions up to 30 bar and 500 K. These PFCs have relatively low viscosity at 500 K, very good thermal and chemical stabilities and showed high CO2 solubilities; hence they were considered as “ideal solvents.” The CO2 solubilities in PP25 were found to be greater than in the other two PFCs. Due to its superior behavior, PP25 was selected for the development of a conceptual process for CO2 capture form Pittsburgh No. 8 shifted fuel gas mixture using Aspen Plus simulator. Unfortunately, during the pressure-swing option for solvent regeneration, the solvent loss was significant due to the fact that the boiling point of PP25 is 533 K which is close to the absorber temperature (500 K). Also, other drawbacks of PFCs include, high cost, and absorption of other gases (light hydrocarbons) along with CO2. It was then decided to seek different physical solvents, which have negligible vapor pressure, in addition to the other attractive properties of the “ideal solvent” in order to use in the Aspen Plus simulator. Extensive literature search led to Ionic Liquids (ILs), which are known to have unique properties in addition to extremely low vapor pressures, and therefore they were considered excellent candidates for the CO2 capture from fuel gas streams under elevated pressures and temperatures. Three ILs, namely TEGO IL K5, TEGO IL P9 and TEGO IL P51P, manufactured by Evonik Goldschmidt Chemical Corporation, were selected as potential solvents for CO2 capture. The solubilities of CO2, H2, H2S and N2 were measured in the TEGO IL K5 and the solubilities of CO2 and H2 were measured in the TEGO IL K5 at pressures up to 30 bar and temperatures from 300 to 500 K. Also, the density and viscosity of these three ILs were measured within the same pressure and temperature ranges, and the surface tension for TEGO IL K5 and TEGO IL P51P were measured from 296 to 369 K. Due to their superior performance for CO2 capture, the TEGO IL K5 and the TEGO IL P51P were selected to be used in the Aspen simulator for the conceptual process development. The density and surface tension data for the TEGO IL K5 and the TEGO IL P51P were used in Aspen Plus, employing the Peng-Robinson Equation of state (P-R EOS) to obtain the critical properties of the two ILs; and the measured solubility data were also used to obtain the binary interaction parameters between the shifted gas constituents and two ILs. The Aspen Plus simulator was employed to develop a conceptual process for CO2 capture from a shifted fuel gas stream (102.52 kg/s) generated using Pittsburgh # 8 coal for a 400 MWe power plant. The conceptual process developed consisted mainly of 4 adiabatic absorbers (2.4 m ID) arranged in parallel and packed with Plastic Pall Rings of 0.025 m for CO2 capture; 3 flash drums arranged in series for solvent regeneration using the pressure-swing option; and 2 pressure-intercooling systems for separating and pumping CO2 to the sequestration sites. The compositions of all process steams, CO2 capture efficiency, and net power were calculated using Aspen Plus for each solvent. The results indicated that, based on the composition of the inlet gas stream to the absorbers, 87.6 and 81.42 mol% of CO2 were captured and sent to sequestration sites; and 97.69 and 97. 86 mol% of H2 were separated and sent to turbines using the TEGO IL K5 and the TEGO IL P51P, respectively. Also, the two solvents exhibited minimum loss of 0.06 and 0.17 wt% with a net power balance of -26.44 and -14.72 MW for the TEGO IL K5 and the TEGO IL P51P, respectively. Thus, the TEGO IL K5 could be selected as a physical solvent for CO2 capture from shifted hot fuel gas streams since large quantities of CO2 are absorbed

Studies on the generative reproduction of grapevine powdery mildew (Uncinula necator BERK.)

Morphology and factors influencing the development of Uncinula necator fruit bodies were studied.The resistance levels of hostplants and the amount of cleistothecia on their leaves were significantly correlated under field conditions.The number of cleistothecia was about 80 % lower on greenhouse plants than on field-grown vines with similar susceptibility.An UV irradiation (2 h) did not induce the opening of the cleistothecia after cold storage, neither did light or darkness. A longer UV treatment (5 h), however, decreased the percentage of open cleistothecia.Liquid water was essential for the opening process. An atmosphere with a 100 % relative humidity was not sufficient.The fruit bodies opened readily at +22 °C, but not at +5 °C and below.Cleistothecia contained up to 6 asci with an average content of 6 ascospores. About 50 % of the ascospores had still their full vitality after 6-weeks cold storage