Strichartz estimates for the metaplectic representation

We provide new estimates for the matrix coefficients of the metaplectic representation, inspired by a formal analogy with the Strichartz estimates which hold for several classes of evolution propagators U(t). The one parameter group of unitary operators U(t) is replaced by a unitary representation of a non-compact Lie group, the group element playing the role of time; the case of the metaplectic or oscillatory representation is of special interest in this connection, because the Schroedinger group is a subgroup of the metaplectic group. We prove uniform weak-type sharp estimates for matrix coefficients and Strichartz-type estimates for that representation. The crucial point is the choice of function spaces able to detect such a decay, which in general will depend on the given group action. The relevant function spaces here turn out to be the so-called modulation spaces from Time-frequency Analysis in Euclidean space, and Lebesgue spaces with respect to Haar measure on the metaplectic group. The proofs make use in an essential way of the covariance of the Wigner distribution with respect to the metaplectic representation

Analysis on Trees with Nondoubling Flow Measures

We consider trees with root at infinity endowed with flow measures, which are nondoubling measures of at least exponential growth and which do not satisfy the isoperimetric inequality. In this setting, we develop a Calderón–Zygmund theory and we define BMO and Hardy spaces, proving a number of desired results extending the corresponding theory as known in more classical settings

ESTIMATES FOR MATRIX COEFFICIENTS OF REPRESENTATIONS

Estimates for matrix coefficients of unitary representations of semisimple Lie groups have been studied for a long time, starting with the seminal work by Bargmann, by Ehrenpreis and Mautner, and by Kunze and Stein. Two types of estimates have been established: on the one hand, Lp estimates, which are a dual formulation of the Kunze-Stein phenomenon, and which hold for all matrix coef-ficients, and on the other pointwise estimates related to asymptotic expansions at infinity, which are more precise but only hold for a restricted class of matrix coefficients. In this paper we prove a new type of estimate for the irreducibile unitary representations of SL(2, R) and for the so-called meta-plectic representation, which we believe has the best features of, and implies, both forms of estimate described above. As an application outside representation theory, we prove a new L2 estimate of dispersive type for the free Schro center dot dinger equation in Rn

How Online Solutions Help Beat the Lockdown in Higher Education: A Central Asia Case Study

This chapter is aimed at summarizing the recent initiatives put in action for solving the problems in delivering the educational services in the Turin Polytechnic University in Tashkent, TTPU, after the lockdown, and the stringent measures taken by the Uzbek government in March 2020, for the pandemic explosion of the COVID-19 virus. The long-lasting connection between Politecnico di Torino, a European University, and this Central Asia Institution has been proven to be extremely effective, maximizing the benefits of TTPU in promptly offering online solutions for remote lectures, and the preparation of the technical substrate for both the exams and admission test which will be delivered after the completion of the second semester lectures. A summary of the IT tools adopted, with compact highlights of their features, as well as the qualitative feedback collected from the first courses offered with a reshaped structure suitable for online classes are thoroughly discussed in this work

Effect of inoculation with Lentilactobacillus buchneri and Lacticaseibacillus paracasei on the maize silage volatilome: the advantages of advanced 2d-chromatographic fingerprinting approaches

[Image: see text] In this study, the complex volatilome of maize silage samples conserved for 229 d, inoculated with Lentilactobacillus buchneri (Lbuc) and Lacticaseibacillus paracasei (Lpar), is explored by means of advanced fingerprinting methodologies based on comprehensive two-dimensional gas chromatography and time-of-flight mass spectrometry. The combined untargeted and targeted (UT) fingerprinting strategy covers 452 features, 269 of which were putatively identified and assigned within their characteristic classes. The high amounts of short-chain free fatty acids and alcohols were produced by fermentation and led to a large number of esters. The impact of Lbuc fermentation was not clearly distinguishable from the control samples; however, Lpar had a strong and distinctive signature that was dominated by propionic acid and 1-propanol characteristic volatiles. The approach provides a better understanding of silage stabilization mechanisms against the degradative action of yeasts and molds during the exposure of silage to air

Evaluation of the environmental impacts of suckler calf-to-beef mixedcrop-livestock farms in northern Italy: A farm-based study

The issue of the environmental impacts of beef production has been extensively debated in recent years. However, the research on this theme has mainly been based on farm-model studies with limited attention to contribution analysis of impact categories and aspects linked to cropping systems and feed self-sufficiency in mixed crop-livestock farms. This study evaluated the cradle-tofarm gate environmental impacts of mixed-crop livestock farms rearing the Piedmontese beef breed and suckler calf-to-beef operations in Northwest Italy. Data have been collected from detailed on-farm questionnaires, field books, and invoices of 11 farms over two years (2017-2018). The environmental impacts have been evaluated in terms of land occupation (LO, m2/year), global warming potential (GWP, kg CO2-eq), acidification potential (AP, g SO2-eq) and non-renewable cumulative energy demand (CED, MJ), using life cycle assessment methodology. The functional unit considered was one kilogram of live weight produced at the farm gate. The Piedmontese beef production system showed comparable average environmental impacts with those found in other studies, even though high variability was observed in the studied farms. The GWP averaged 15.7 kg of CO2 eq/kg LW and ranged from 12.1 to 17.6 kg of CO2 eq/kg LW. The CED, LO and AP were on average 62.4 MJ/kg LW, 18.5 m2/y/kg LW and 305 g SO2 eq/kg LW, respectively. Differences in environmental impacts and GWP contribution analysis were mainly due to differences in cropping system management strategies and the consequent levels of feed self-sufficiency. A positive effect of high fertility and animal productivity was observed on the GWP (r=0.62; P<0.01), highlighting the importance of improving efficiency of these aspects for the reduction of emissions. From the contribution analysis of impact categories, the high cost of purchased feeds (in particular protein feeds), transport, and mineral fertilizers for feed production were highly relevant. However further research is needed to confirm these findings. Highlights - Study of 11 farms for two years. - High relevance of purchased feeds on environmental impacts. - Productive and reproductive performances are key points in reducing environmental impacts. - Importance of the valorisation of farm crop surfaces to satisfy animals' needs