University of Rennes

About: University of Rennes is a education organization based out in Rennes, France. It is known for research contribution in the topics: Population & Crystal structure. The organization has 18404 authors who have published 40374 publications receiving 995327 citations.

Time after time: flowering phenology and biotic interactions

Abstract: The role of biotic interactions in shaping plant flowering phenology has long been controversial; plastic responses to the abiotic environment, limited precision of biological clocks and inconsistency of selection pressures have generally been emphasized to explain phenological variation. However, part of this variation is heritable and selection analyses show that biotic interactions can modulate selection on flowering phenology. Our review of the literature indicates that pollinators tend to favour peak or earlier flowering, whereas pre-dispersal seed predators tend to favour off-peak or later flowering. However, effects strongly vary among study systems. To understand such variation, future studies should address the impact of mutualist and antagonist dispersal ability, ecological specialization, and habitat and plant population characteristics. Here, we outline future directions to study how such interactions shape flowering phenology.

Mathematical Scattering Theory: Analytic Theory

Abstract: The main subject of this book is applications of methods of scattering theory to differential operators, primarily the Schrodinger operator There are two different trends in scattering theory for differential operators The first one relies on the abstract scattering theory The second one is almost independent of it In this approach the abstract theory is replaced by a concrete investigation of the corresponding differential equation In this book both of these trends are presented The first half of this book begins with the summary of the main results of the general scattering theory of the previous book by the author, ""Mathematical Scattering Theory: General Theory"", American Mathematical Society, 1992 The next three chapters illustrate basic theorems of abstract scattering theory, presenting, in particular their applications to scattering theory of perturbations of differential operators with constant coefficients and to the analysis of the trace class method In the second half of the book direct methods of scattering theory for differential operators are presented After considering the one-dimensional case, the author returns to the multi-dimensional problem and discusses various analytical methods and tools appropriate for the analysis of differential operators, including, among others, high- and low-energy asymptotics of the Green function, the scattering matrix, ray and eikonal explansions The book is based on graduate courses taught by the author at Saint-Petersburg (Russia) and Rennes (France) Universities and is oriented towards a reader interested in studying deep aspects of scattering theory (for example, a graduate student in mathematical physics)