Search results for "Functional analysis"
showing 10 items of 1059 documents
The transition state and cognate concepts
2019
Abstract This review aims firstly to clarify the meanings of key terms and concepts associated with the idea of the transition state, as developed by theoreticians and applied by experimentalist, and secondly to provide an update to the meaning and significance of the transition state in an era when computational simulation, in which complexity is being increasingly incorporated, is commonly employed as a means by which to bridge the realms of theory and experiment. The relationship between the transition state and the potential-energy surface for an elementary reaction is explored, with discussion of the following terms: saddle point, minimum-energy reaction path, reaction coordinate, acti…
Two-dimensional Banach spaces with polynomial numerical index zero
2009
We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.
Vertical versus horizontal Sobolev spaces
2020
Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi f$ belongs to the Euclidean Sobolev space $S^{p}_{\alpha}(\mathbb{R}^{2n + 1})$ for any test function $\varphi$. In short, $S^{p}_{2\alpha}(\mathbb{H}^{n}) \subset S^{p}_{\alpha,\mathrm{loc}}(\mathbb{R}^{2n + 1})$. We show that the localisation can be omitted if one only cares for Sobolev regularity in the vertical direction: the horizontal Sobolev space $S_{2\alpha}^{p}(\mathbb{H}^{n})$ is continuously contained in the vertical Sobolev sp…
Theoretical Investigation of the Low-Energy States of CpMoCl(PMe 3 ) 2 and Their Role in the Spin-Forbidden Addition of N 2 and CO
2003
International audience; A recent computational investigation of Jahn−Teller effects in unsaturated 16-electron d4d6 [CpMLn] complexes (Abu-Hasanayn, F.; Cheong, P.; Oliff, M. Angew. Chem.2002, 41, 2120) highlighted the typical presence of two spin-triplet and two singlet states of competing stability in these complexes and pointed out the necessity to account for more than one electronic state in studies thereof. Consequently, we have reinvestigated the addition of N2 to all the four low-energy states of CpMoCl(PH3)2, a reaction for which previously only one singlet and one triplet state have been considered (Keogh, D. W.; Poli, R. J. Am. Chem. Soc.1997, 119, 2516). The present study was pe…
Open data and digital morphology
2017
International audience; Over the past two decades, the development of methods for visualizing and analysing specimens digitally, in three and even four dimensions, has transformed the study of living and fossil organisms. However, the initial promise that the widespread application of such methods would facilitate access to the underlying digital data has not been fully achieved. The underlying datasets for many published studies are not readily or freely available, introducing a barrier to verification and reproducibility, and the reuse of data. There is no current agreement or policy on the amount and type of data that should be made available alongside studies that use, and in some cases…
Functional rearrangement of the light-harvesting antenna upon state transitions in a green alga
2014
AbstractState transitions in the green alga Chlamydomonas reinhardtii serve to balance excitation energy transfer to photosystem I (PSI) and to photosystem II (PSII) and possibly play a role as a photoprotective mechanism. Thus, light-harvesting complex II (LHCII) can switch between the photosystems consequently transferring more excitation energy to PSII (state 1) or to PSI (state 2) or can end up in LHCII-only domains. In this study, low-temperature (77 K) steady-state and time-resolved fluorescence measured on intact cells of Chlamydomonas reinhardtii shows that independently of the state excitation energy transfer from LHCII to PSI or to PSII occurs on two main timescales of <15 ps and …
Optimality Conditions for Non-Qualified Parabolic Control Problems
1994
We consider parabolic state constrained optimal control problems where the usual Slater condition is not necessarily satisfied. Instead, a weaker interiority property is assumed. Optimality conditions with a Lagrange multiplier are given. As an application we present an augmented Lagrangian algorithm. Numerical test results are included.
Opinion dynamics in social networks through mean field games
2016
Emulation, mimicry, and herding behaviors are phenomena that are observed when multiple social groups interact. To study such phenomena, we consider in this paper a large population of homogeneous social networks. Each such network is characterized by a vector state, a vector-valued controlled input, and a vector-valued exogenous disturbance. The controlled input of each network aims to align its state to the mean distribution of other networks' states in spite of the actions of the disturbance. One of the contributions of this paper is a detailed analysis of the resulting mean-field game for the cases of both polytopic and $mathcal L_2$ bounds on controls and disturbances. A second contrib…
Obstacles and opportunities in the functional analysis of extracellular vesicle RNA - an ISEV position paper
2017
The release of RNA-containing extracellular vesicles (EV) into the extracellular milieu has been demonstrated in a multitude of different in vitro cell systems and in a variety of body fluids. RNA-containing EV are in the limelight for their capacity to communicate genetically encoded messages to other cells, their suitability as candidate biomarkers for diseases, and their use as therapeutic agents. Although EV-RNA has attracted enormous interest from basic researchers, clinicians, and industry, we currently have limited knowledge on which mechanisms drive and regulate RNA incorporation into EV and on how RNA-encoded messages affect signalling processes in EV-targeted cells. Moreover, EV-R…
Evidence of Absorptive Function in vivo in a Neo-Formed Bio-Artificial Intestinal Segment Using a Rodent Model.
2015
A promising therapeutic approach for intestinal failure consists in elongating the intestine with a bio-engineered segment of neo-formed autologous intestine. Using an acellular biologic scaffold (ABS), we, and others, have previously developed an autologous bio-artificial intestinal segment (BIS) that is morphologically similar to normal bowel in rodents. This neo-formed BIS is constructed with the intervention of naïve stem cells that repopulate the scaffold in vivo, and over a period of time, are transformed in different cell populations typical of normal intestinal mucosa. However, no studies are available to demonstrate that such BIS possesses functional absorptive characteristics nece…