Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach.Comment: 20 pages. Some changes, the most important being on Conjecture 3.2, three references added ([Mas75], [MB90] and [Yu94]) and one reference updated [BS12]. Accepted in Bull. Brazil. Mat. So

The GH51 α-l-arabinofuranosidase from Paenibacillus sp. THS1 is multifunctional, hydrolyzing main-chain and side-chain glycosidic bonds in heteroxylans.

Background: Conceptually, multi functional enzymes are attractive because in the case of complex polymer hydrolysis having two or more activities defined by a single enzyme offers the possibility of synergy and reduced enzyme cocktail complexity. Nevertheless, multi functional enzymes are quite rare and are generally multi domain assemblies with each activity being defined by a separate protein module. However, a recent report described a GH51 arabinofuranosidase from Alicyclobacillus sp. A4 that displays both α l arabinofuranosidase and β d xylanase activities, which are defined by a single active site. Following on from this, we describe in detail another multi functional GH51 arabinofuranosidase and discuss the molecular basis of multifunctionality. Results: THSAbf is a GH51 α l arabinofuranosidase. Characterization revealed that THSAbf is active up to 75 °C, stable at 60 °C and active over a broad pH range (4–7). THSAbf preferentially releases para nitrophenyl from the l arabino furanoside ( k cat / K M = 1050 s − 1 mM − 1 ) and to some extent from d galactofuranoside and d xyloside. THSAbf is active on 4 O methylglucuronoxylans from birch and beechwood (10.8 and 14.4 U mg − 1 , respectively) and on sugar beet branched and linear arabinans (1.1 ± 0.24 and 1.8 ± 0.1 U mg − 1 ). Further investigation revealed that like the Alicyclo - bacillus sp. A4 α l arabinofuranosidase, THSAbf also displays endo xylanase activity, cleaving β 1,4 bonds in heteroxy lans. The optimum pH for THASAbf activity is substrate dependent, but ablation of the catalytic nucleophile caused a general loss of activity, indicating the involvement of a single active center. Combining the α l arabinofuranosidase with a GH11 endoxylanase did not procure synergy. The molecular modeling of THSAbf revealed a wide active site cleft and clues to explain multi functionality

The Frenchness of Marcel Lefebvre and the Society of St Pius X:a new reading

The case of Marcel Lefebvre and the Society of St Pius X (SSPX) deserves fresh perspectives. The current historiography is too franco-centric, focused on selective aspects of Lefebvre’s biography and the actions of isolated individuals, rather than with the life of the SSPX itself. After evaluating the current state of the historiography, this article proposes a new analysis of the SSPX’s political discourses in France and internationally and undertakes to reframe the relationship between Lefebvre’s life and his congregation by re-examining his African missionary experiences. Such new perspectives will be helpful as the SSPX moves towards regularisation under the pontificate of Pope Francis

Recycling oriented vertical vibratory separation of copper and polypropylene particles

Vibration has been employed in various engineering processes for material handling. The famous Brazil nut effect, large particles tend to rise to the top under vibration, initiates various research about vibration induced particle segregation. Particle size and density are two determining factors for their behaviour under vibration. Previous research in University of Nottingham proves vertical vibratory separation to be a promising environmental friendly mechanical separation method for recycling metallic fraction from shredded Waste Electric and Electronic Equipment (WEEE) stream. A pilot scale thin cell vibratory separator has been developed to investigate the potential for WEEE recycling applications. Shredded copper and polypropylene particles have been chosen to mimic metallic and non-metallic fractions in WEEE. Vibratory separation experiment with controlled environment and addition of solid lubricant are presented in this paper. The result demonstrates the effect of relative humidity and solid lubricant on improving flowability of granular system hence successful vibratory separation. The proposed mechanisms for the presence of moisture and solid lubricant are lubricant effect and elimination of static electricity

Leadership and style in the French Fifth Republic:Nicolas Sarkozy’s presidency in historical and cultural perspective

This article contributes to the body of the developing theoretical research in leadership and presidential studies by adding analysis of what I have termed ‘comportmental style’ as a factor in leader/follower relations. Within institutionalism and the wider structure/agency debate in political science, one of the challenges as regards the study of leadership is to identify factors that offer scope to or else militate against leaders’ performance. The comportmental style of Nicolas Sarkozy (President of the French Republic 2007–2012), deployed in the context of the – changing – institution of the presidency, was a major factor in his extreme unpopularity, and contributed to his defeat in 2012. What this tells us about the nature of the changing French presidency and the role of style will be discussed in the conclusion