A geometric technique to generate lower estimates for the constants in the Bohnenblust--Hille inequalities

The Bohnenblust--Hille (polynomial and multilinear) inequalities were proved in 1931 in order to solve Bohr's absolute convergence problem on Dirichlet series. Since then these inequalities have found applications in various fields of analysis and analytic number theory. The control of the constants involved is crucial for applications, as it became evident in a recent outstanding paper of Defant, Frerick, Ortega-Cerd\'{a}, Ouna\"{\i}es and Seip published in 2011. The present work is devoted to obtain lower estimates for the constants appearing in the Bohnenblust--Hille polynomial inequality and some of its variants. The technique that we introduce for this task is a combination of the Krein--Milman Theorem with a description of the geometry of the unit ball of polynomial spaces on $\ell^2_\infty$.Comment: This preprint does no longer exist as a single manuscript. It is now part of the preprint entitled "The optimal asymptotic hypercontractivity constant of the real polynomial Bohnenblust-Hille inequality is 2" (arXiv reference 1209.4632

Dissection, in vivo imaging and analysis of the mouse epitrochleoanconeus muscle

Analysis of rodent muscles affords an opportunity to glean key insights into neuromuscular development and the detrimental impact of disease-causing genetic mutations. Muscles of the distal leg, for instance the gastrocnemius and tibialis anterior, are commonly used in such studies with mice and rats. However, thin and flat muscles, which can be dissected, processed and imaged without major disruption to muscle fibres and nerve-muscle contacts, are more suitable for accurate and detailed analyses of the peripheral motor nervous system. One such wholemount muscle is the predominantly fast twitch epitrochleoanconeus (ETA), which is located in the upper forelimb, innervated by the radial nerve, and contains relatively large and uniformly flat neuromuscular junctions (NMJs). To facilitate incorporation of the ETA into the experimental toolkit of the neuromuscular disease field, here, we describe a simple method for its rapid isolation (<5 min), supported by high-resolution videos and step-by-step images. Furthermore, we outline how the ETA can be imaged in live, anaesthetised mice, to enable examination of dynamic cellular processes occurring at the NMJ and within intramuscular axons, including transport of organelles, such as mitochondria and signalling endosomes. Finally, we present reference data on wild-type ETA fibre-type composition in young adult, male C57BL6/J mice. Comparative neuroanatomical studies of different muscles in rodent models of disease can generate critical insights into pathogenesis and pathology; dissection of the wholemount ETA provides the possibility to diversify the repertoire of muscles analysed for this endeavour

Coalescence and Anti-Coalescence Interference of Two-Photon Wavepacket in a Beam Splitter

We study a general theory on the interference of two-photon wavepacket in a beam splitter (BS). We find that the perfect coalescence interference requires a symmetric spectrum of two-photon wavepacket which can be entangled or un-entangled. Furthermore, we introduce a two-photon wavepacket with anti-symmetric spectrum, which is related with photon entanglement and shows a perfect anti-coalescence effect. The theory present uniform and complete explanation to two-photon interference.Comment: 5 pages, 2 figure

Ten systemic steps for sustainable energy savings in small and medium enterprises

Energy savings are a priority in the different industrial sectors including Small and Medium Enterprises (SMEs). They have a conceptual perception of energy savings by replacing their service and production technologies with more efficient one. However, this technological change requires large-scale investment. There is another approach that can be used to reduce energy costs that has less impact on company production costs and does not require investments in technology. This approach considers planning and control procedures, which are considered in the present study. This study proposes a new method consisting of 10 systematic steps to achieve energy savings in SMEs. This method initially evaluates when, how, and where the energy is used, then identifies opportunities to achieve sustainable energy savings. The method involves various activities including an assessment of energy efficiency based on final energy consumption, adjusting production plans with low energy consumption and costs, and monitoring the energy budget. Application of this methodology in SMEs can save energy around 5 − 20% over a period of 1 to 3 y with some very low payback periods of less than a year. Operational controls implementation in Significant Energy Uses (SEU) can save energy around 2 − 5% of the consumption, without requiring investment in technology

Efeitos de extratos pirolenhosos utilizados como tratamento de sementes sobre doenças da fase Inicial e crescimento de plântulas de Soja.

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