Higher composition

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  • Two centuries ago, in his celebrated work Disquisitiones Arithmeticae of 1801, Gauss laid down the beautiful law of composition of integral binary quadratic forms which would play such a critical role in number theory in the decades to follow. Even today, two centuries later, this law of composition still remains one of the primary tools for understanding and computing with the class groups of quadratic orders. It is hence only natural to ask whether higher analogues of this composition law exist that could shed light on the structure of other algebraic number rings and fields. ...

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  • Annals of Mathematics In our first article [2] we developed a new view of Gauss composition of binary quadratic forms which led to several new laws of composition on various other spaces of forms. Moreover, we showed that the groups arising from these composition laws were closely related to the class groups of orders in quadratic number fields, while the spaces underlying those composition laws were closely related to certain exceptional Lie groups.

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  • In the first three parts of this series, we considered quadratic, cubic and quartic rings (i.e., rings free of ranks 2, 3, and 4 over Z) respectively, and found that various algebraic structures involving these rings could be completely parametrized by the integer orbits of an appropriate group representation on a vector space. These orbit results are summarized in Table 1.

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  • In the first two articles of this series, we investigated various higher analogues of Gauss composition, and showed how several algebraic objects involving orders in quadratic and cubic fields could be explicitly parametrized. In particular, a central role in the theory was played by the parametrizations of the quadratic and cubic rings themselves. These parametrizations are beautiful and easy to state.

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  • Polysaccharide fractions isolated from Lentinula edodes fruitbodies and mycelium demonstrate strong immunomodulating, antioxidant and anticancer activity. We hypothesized, that polysaccharide fractions enriched in selenium would possess higher biological activity than non-enriched fractions, currently used to treat cancer. The first goal of this study was to isolate selenium (Se)-enriched polysaccharide fractions of different molecular weight from L. edodes mycelium cultivated under the submerged conditions in Se-enriched medium, and to investigate their monosaccharide composition....

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  • This paper describes a compositional semantics for temporal expressions as part of the meaning representation language (MRL) of the JANUS system, a natural language understanding and generation system under joint development by BBN Laboratoires and the Information Sciences Institute. 1 The analysis is based on a higher order intansional logic described in detail in Hinrichs, Ayuso and Scha (1987). Temporal expressions of English are translated into this language as quantifiers over times which bind temporal indices on predicates.

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  • Eight students in this study achieved an increase in their Overall score from Test 1 to Test 2 of one whole band and a further 14 achieved a half band increase. In other words, just over half of this sample of 40 students were able to achieve a better result in the IELTS Test when taken again after two or three years of higher education in Australia. A total of 12 students achieved the same Overall score in Test 2 as in Test 1, and six students actually regressed, dropping a half band. Of course, this is not to say...

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  • Steel–Concrete Composite Box Girder Bridges 13.1 13.2 13.3 13.4 13.5 13.6 Introduction Typical Sections General Design Principles Flexural Resistance Shear Resistance Stiffeners, Bracings, and Diaphragms Stiffeners • Top Lateral Bracings • Internal Diaphragms and Cross Frames Yusuf Saleh California Department of Transportation Lian Duan California Department of Transportation 13.7 Other Considerations Fatigue and Fracture • Torsion • Constructability • Serviceability 13.8 Design Example 13.

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  • With the adoption of these English–language arts content standards in 1997, California set forth for the first time a uniform and specific vision of what students should know and be able to do in this subject area. Reflecting a strong consensus among educators, these standards establish high expectations for all students.

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  • Preparations derived from Lentinula edodes (Berk.) Pegl. mycelium are worldwide used as dietary supplements containing compounds active as immune system enhancers, demonstrating chemopreventive and anticancer activity. L. edodes mycelium enriched with organic forms of selenium like selenized yeast possess putative, higher cancer preventive properties. The objective of this study was to test the effect of enrichment in selenium on antioxidant, reducing and free radical scavenging activity of water and alcohol extracts from mycelium of L. edodes (Berk.).

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  • Market and banking supervisors and regulators are in the process of stepping up their monitoring of the ETF market. Work is underway nationally and internationally on assessing how recent innovations in this area can add to financial system risks, what incentives underpin them, and what potential flaws there might be in current risk practices. The interaction of ETF regulatory frameworks with recent innovations as well as the scope for regulatory arbitrage across regions and markets is also being examined.

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  • In 2008 food prices surged plunging millions back into hunger and triggering riots from Egypt to Haiti and Cameroon to Bangladesh. Whereas fuel prices, which also surged, have fallen back sharply food prices remain problematic with wheat, corn and soya still higher than they were 12-18 months ago. In order to understand the factors underpinning the food crisis and to assess trends, UNEP commissioned a Rapid Response team of internal and international experts. Their conclusions are presented in this report launched during UNEP’s 25th Governing Council/Global Ministerial Environment Forum.

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  • Cigarette smokers were 2.7 times more likely to have respiratory diseases than those of non-smokers. Similarly consumption of alcohol and use of non-smoked tobacco were found to be risk factors of hypertension. BMI more than 25 was risk factor for hypertension and diabetes. On the other hand risk of respiratory diseases and cataract increased below a BMI of 18.5. Risk for musculoskeletal problems was found to be higher in both extremes of physical status. The higher risk of diseases to the both extremes of BMI suggests a U- shaped relationship of diseases with BMI. BMI less 18.

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  • Overall, our analysis can be understood as one of the first cross-country empirical studies on the determinants of bank fees and as a contribution to the literature testing the contradictory empirical predictions of the SCP and ES hypotheses regarding the influence of concentration on prices in the banking industry.

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  • Indian culture promotes universal marriage. Of importance to ARH is the traditional young marriage age of girls—referred to as early marriage. The national average age at marriage for women in India is 16.4 years, although there are vast regional variations. Most northern and north-eastern states, as well as Tamil Nadu and Kerala in the south and Goa in the west, have a higher age at marriage, ranging from ages 18–22. The majority of the states in the western, central, and eastern parts of India reported an average age at marriage similar to...

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  • Together, the empirical facts established in this paper suggest that capital regulation and buffers may only be of second order importance in determining the capital structure of most banks. Hence, our paper sheds new light on the debate whether regulation or market forces determine banks’ capital structures. Barth et al. (2005), Berger et al. (2008) and Brewer et al. (2008) observe that the levels of bank capital are much higher than the regulatory minimum. This could be explained by banks holding capital buffers in excess of the regulatory minimum.

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  • There is growing recognition of the large health and productivity costs imposed by poor indoor environmental quality (IEQ) in commercial buildings—estimated variously at up to hundreds of billions of dollars per year. This is not surprising as people spend 90% of their time indoors, and the concentration of pollutants indoors is typically higher than outdoors, sometimes by as much as 10 or even 100 times. 6 The relationship between worker comfort/pro- ductivity and building design/operation is com- plicated.

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  • Digital cinema resolution is measured in units of “K,” which stands for 1024 horizontal pixels. In the early years of the DCI Specification, the dominant resolution was 2048 pixels horizontal x 1080 vertical, known as 2K. But 2K represents only 7% more pixels than 1920 x 1080 HDTV. Fortunately, a more future-oriented, higher-resolution option was also written into the DCI Specification: 4K. At 4096 pixels horizontal x 2160 vertical, this is exactly four times as many pixels as 2K, and greater than four times the pixel count of HDTV. ...

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  • Our empirical analysis uses two different data sources: the RobertWood Johnson Foundation’s 1997 Employer Health Insurance Survey (EHIS) and MEDSTAT MarketScan commercially insured health claims and eligibility information for 1998–1999. We first use the EHIS data to examine turnover patterns and their relationship to firm and employee characteristics. The EHIS data reveal that small firms are very heterogeneous; the heterogeneity concerns workers’ turnover rates, besides workers’ age distribution and other health-related demographic variables.

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  • Therefore, the integration of the sensors in the furniture is one of the ways to implement an invisible ubiquitous computing environment. The second advantage is that for Ambient Assisted Living solutions, elderly people prefer not to be aware of the existence of the sensors, since this presence is understood as a reminder that they need this support, and it is highly important not to make these deployments highly impacting in people, in order to achieve a higher acceptance.

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