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A theorem of Arens and Calderon states that if A is a commutative Banach algebra with Jacobson radical Rad(A), and if a0,..., an ∈ A with a0 2 Rad(A) and a1 an invertible element of A, then there exists y ∈ Rad(A) such that ... n this paper, we give extensions of this result to commutative non-normed topological algebras, as this is vital for extending an embedding theorem of Allan in [2] regarding the embedding of the formal power series algebra C[[X]] into a commutative Banach algebra. [ABSTRACT FROM AUTHOR]

We present a general survey on formal power series over topological algebras, along with some perspectives which are not easily found in the literature. [ABSTRACT FROM AUTHOR]

The present study examines the effect of mangrove vegetation and different seasons on organic carbon pools, distributions, and source compositions under the stressed hydro-climatological settings of the Iranian coast (Persian Gulf). Significant seasonal and spatial differences were detected only for the δ 13 POC (particulate organic carbon) owing to the fluctuation of its sources. Five end-member particulate organic carbon sources (POC) (mangrove leaf, planktonic particles, zooplankton, microphytobenthos (MPB), and sediment) contributed to the POC pool at different levels depending on their seasonal and site-specific abundance. Variations in topographic features such as, the elevations of mangrove and non-mangrove creeks, appeared to play an important role in regulating POC concentrations but not DOC concentrations. Planktonic particles contributed to the POC pool (maximum 10–65%) at the mangrove sites mostly in the summer whereas the contributions of sediment and MPB (5–35%) increased in winter. Iranian mangroves are weak exporters of carbon to the Persian Gulf where mangrove plant materials (leaf, litter) had little contributions to the POC and DOC pool (5–25% and 8–15%, respectively). It is most likely that OC export in these arid regions are limited by low rainfall and river input. Finally, seasonality and site-specific activity largely control OC dynamics in these relatively understudied arid mangroves. [ABSTRACT FROM AUTHOR]

It is an open question whether every derivation of a Fréchet GB$^{\ast }$-algebra $A[{\it\tau}]$ is continuous. We give an affirmative answer for the case where $A[{\it\tau}]$ is a smooth Fréchet nuclear GB$^{\ast }$-algebra. Motivated by this result, we give examples of smooth Fréchet nuclear GB$^{\ast }$-algebras which are not pro-C$^{\ast }$-algebras. [ABSTRACT FROM AUTHOR]

Soft-constraint affinity propagation (SCAP) is a new statistical-physics based clustering technique [M. Leone, Sumedha, M. Weigt, Bioinformatics 23, 2708 (2007)]. First we give the derivation of a simplified version of the algorithm and discuss possibilities of time- and memory-efficient implementations. Later we give a detailed analysis of the performance of SCAP on artificial data, showing that the algorithm efficiently unveils clustered and hierarchical data structures. We generalize the algorithm to the problem of semi-supervised clustering, where data are already partially labeled, and clustering assigns labels to previously unlabeled points. SCAP uses both the geometrical organization of the data and the available labels assigned to few points in a computationally efficient way, as is shown on artificial and biological benchmark data. [ABSTRACT FROM AUTHOR]

Boolean networks and their dynamics are of great interest as abstract modeling schemes in various disciplines, ranging from biology to computer science. Whereas parallel update schemes have been studied extensively in past years, the level of understanding of asynchronous updates schemes is still very poor. In this paper we study the propagation of external information given by regulatory input variables into a random Boolean network. We compute both analytically and numerically the time evolution and the asymptotic behavior of this propagation of external regulation (PER). In particular, this allows us to identify variables that are completely determined by this external information. All those variables in the network that are not directly fixed by PER form a core which contains, in particular, all nontrivial feedback loops. We design a message-passing approach allowing to characterize the statistical properties of these cores in dependence of the Boolean network and the external condition. At the end we establish a link between PER dynamics and the full random asynchronous dynamics of a Boolean network. [ABSTRACT FROM AUTHOR]