Search results for "algebra"

*-Representations of Partial *-Algebras

2002

This chapter is devoted to *-representations of partial *-algebras. We introduce in Section 7.1 the notions of closed, fully closed, self-adjoint and integrable *-representations. In Section 7.2, the intertwining spaces of two *-representations of a partial *-algebra are defined and investigated, and using them we define the induced extensions of a *-representation. Section 7.3 deals with vector representations for a *-representation of a partial *-algebra, which are the appropriate generalization to a *-representation of the notion of generalized vectors described in Chapter 5. Regular and singular vector representations are defined and characterized by the properties of the commutant, and…

Assessment of drainage network analysis methods to rank sediment yield hotspots

2021

This paper aims to test different methods used for assessing sediment yield indices to identify hotspots and rank sediment yield hotspots. This process includes the assessment of the entropy weight...

Time-Frequency Filtering for Seismic Waves Clustering

2014

This paper introduces a new technique for clustering seismic events based on processing, in time-frequency domain, the waveforms recorded by seismographs. The detection of clusters of waveforms is performed by a k-means like algorithm which analyzes, at each iteration, the time-frequency content of the signals in order to optimally remove the non discriminant components which should compromise the grouping of waveforms. This step is followed by the allocation and by the computation of the cluster centroids on the basis of the filtered signals. The effectiveness of the method is shown on a real dataset of seismic waveforms.

Computer simulation of the glass transition of polymer melts

2007

Bond fluctuation models on square and simple cubic lattices at melt densities are simulated, using potentials depending on the length of the (effective) bond (and also on the bond angle, in d=3 dimensions). Various relaxation functions have the Kohlrausch-Williams-Watts (KWW) form; the associated relaxation time diverges as exp (const/T 2) in d=2 and as exp [const/T−T 0)] in d=3. For d=3 the self-diffusion constant also follows the Vogel-Fulcher law, with T 0=250 K for chain lengths N=20 and potentials adapted to bisphenol-A-polycarbonate [BPA-PC].

Module categories of finite Hopf algebroids, and self-duality

2017

International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.

Using SOM and PCA for analysing and interpreting data from a P-removal SBR

2008

This paper focuses on the application of Kohonen self-organizing maps (SOM) and principal component analysis (PCA) to thoroughly analyse and interpret multidimensional data from a biological process. The process is aimed at enhanced biological phosphorus removal (EBPR) from wastewater. In this work, SOM and PCA are firstly applied to the data set in order to identify and analyse the relationships among the variables in the process. Afterwards, K-means algorithm is used to find out how the observations can be grouped, on the basis of their similarity, in different classes. Finally, the information obtained using these intelligent tools is used for process interpretation and diagnosis. In the…

Tree Structured Self-Organizing Maps

1999

Publisher Summary This chapter provides an overview of the tree structured self-organizing maps (TS-SOM). It was originally intended as a fast implementation of the self-organizing map (SOM). The chapter explains that TS-SOM is a constructive smoother for a class of dimension reduction problems. There is a well known relation between self-organizing maps and principal curves. Unfortunately in most presentations it is derived by simple reasoning, avoiding the mathematical statement of the problem, which is essential to understand how efficient SOM implementations can be constructed. In this chapter, SOM is derived as a numerical solution of a generic model in a continuous domain, which diffe…

On essential maximality of linear pseudo-differential operators

1989

Partial {$*$}-algebras of closable operators. I. The basic theory and the abelian case

1990

This paper, the first of two, is devoted to a systematic study of partial *-algebras of closable operators in a Hilbert space (partial Op*-algebras). After setting up the basic definitions, we describe canonical extensions of partial Op*-algebras by closure and introduce a new bounded commutant, called quasi-weak. We initiate a theory of abelian partial *-algebras. As an application, we analyze thoroughly the partial Op*-algebras generated by a single closed symmetric operator.

Split extensions, semidirect product and holomorph of categorical groups

2006

Working in the context of categorical groups, we show that the semidirect product provides a biequivalence between actions and points. From this biequivalence, we deduce a two-dimensional classification of split extensions of categorical groups, as well as the universal property of the holomorph of a categorical group. We also discuss the link between the holomorph and inner autoequivalences.