Numerical Schemes for Rough Parabolic Equations

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H \textgreater{} 1/3.Comment: Applied Mathematics and Optimization, 201

Cytomegalovirus Infection of the Cervix Detected By Cytology and Histology: A Report of Five Cases

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72846/1/j.1365-2303.1993.tb00094.x.pd

Country Perspectives on Hay-Making Landscapes as Part of the European Agricultural Heritage

This paper provides an overview of traditional hay-making structures and the related agricultural landscapes in Europe. The information was collected using a standardised questionnaire that was completed by experts from different countries. What all countries had in common was that hay production with its corresponding structures was widespread. However, the scope and importance differed among the countries today. We found differences in type and extent, in degree of awareness, and in the cultural meaning of hay-making structures. The differences were connected with built structures, as well as with other tangible and intangible aspects of cultural heritage. The distribution of the broad variety of hay-making-related structures, especially semipermanent ones, has changed throughout history, as well as the hay-making techniques, as a result of agrarian specialisation, land reclamation, and consolidation. Today, in some countries, the relevance of hay-making was mainly connected to horse keeping and landscape management (like in Germany and Hungary), while in others (like Slovakia and Slovenia), it was still predominantly used for cattle and sheep

Basic and extensible post-processing of eddy covariance flux data with REddyProc

With the eddy covariance (EC) technique, net fluxes of carbon dioxide (CO2) and other trace gases as well as water and energy fluxes can be measured at the ecosystem level. These flux measurements are a main source for understanding biosphere–atmosphere interactions and feedbacks through cross-site analysis, model–data integration, and upscaling. The raw fluxes measured with the EC technique require extensive and laborious data processing. While there are standard tools1 available in an open-source environment for processing high-frequency (10 or 20&thinsp;Hz) data into half-hourly quality-checked fluxes, there is a need for more usable and extensible tools for the subsequent post-processing steps. We tackled this need by developing the REddyProc package in the cross-platform language R that provides standard CO2-focused post-processing routines for reading (half-)hourly data from different formats, estimating the u* threshold, as well as gap-filling, flux-partitioning, and visualizing the results. In addition to basic processing, the functions are extensible and allow easier integration in extended analysis than current tools. New features include cross-year processing and a better treatment of uncertainties. A comparison of REddyProc routines with other state-of-the-art tools resulted in no significant differences in monthly and annual fluxes across sites. Lower uncertainty estimates of both u* and resulting gap-filled fluxes by 50&thinsp;% with the presented tool were achieved by an improved treatment of seasons during the bootstrap analysis. Higher estimates of uncertainty in daytime partitioning (about twice as high) resulted from a better accounting for the uncertainty in estimates of temperature sensitivity of respiration. The provided routines can be easily installed, configured, and used. Hence, the eddy covariance community will benefit from the REddyProc package, allowing easier integration of standard post-processing with extended analysis. 1http://fluxnet.fluxdata.org/2017/10/10/toolbox-a-rolling-list-of-softwarepackages-for-flux-related-data-processing/, last access: 17 August 2018</p

Variable exponent Besov-Morrey spaces

In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.publishe

An integrative environmental pollen diversity assessment and its importance for the Sustainable Development Goals

Pollen is at once intimately part of the reproductive cycle of seed plants and simultaneously highly relevant for the environment (pollinators, vector for nutrients, or organisms), people (food safety and health), and climate (cloud condensation nuclei and climate reconstruction). We provide an interdisciplinary perspective on the many and connected roles of pollen to foster a better integration of the currently disparate fields of pollen research, which would benefit from the sharing of general knowledge, technical advancements, or data processing solutions. We propose a more interdisciplinary and holistic research approach that encompasses total environmental pollen diversity (ePD) (wind and animal and occasionally water distributed pollen) at multiple levels of diversity (genotypic, phenotypic, physiological, chemical, and functional) across space and time. This interdisciplinary approach holds the potential to contribute to pressing human issues, including addressing United Nations Sustainable Development Goals, fostering social and political awareness of these tiny yet important and fascinating particles

Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of Rn. We investigate the extent to which the properties of these spaces, and the relations between them, that hold in the well-studied case of a Lipschitz open set, generalise to non-Lipschitz cases. Our motivation is to develop the functional analytic framework in which to formulate and analyse integral equations on non-Lipschitz sets. In particular we consider an application to boundary integral equations for wave scattering by planar screens that are non-Lipschitz, including cases where the screen is fractal or has fractal boundary