scholarly journals ON THE CLASSIFICATION OF NUCLEAR C*-ALGEBRAS

2002 ◽  
Vol 85 (1) ◽  
pp. 168-210 ◽  
Author(s):  
MARIUS DADARLAT ◽  
SØREN EILERS
Keyword(s):  
Subject Classification ◽  
Unified Approach ◽  
C Algebras ◽  
Starting Point ◽  
K Theory

We employ results from KK-theory, along with quasidiagonality techniques, to obtain wide-ranging classification results for nuclear C*-algebras. Using a new realization of the Cuntz picture of the Kasparov groups we show that two morphisms inducing equal KK-elements are approximately stably unitarily equivalent. Using K-theory with coefficients to associate a partial KK-element to an approximate morphism, our result is generalized to cover such maps. Conversely, we study the problem of lifting a (positive) partial KK-element to an approximate morphism. These results are employed to obtain classification results for certain classes of quasidiagonal C*-algebras introduced by H. Lin, and to reprove the classification of purely infinite simple nuclear C*-algebras of Kirchberg and Phillips. It is our hope that this work can be the starting point of a unified approach to the classification of nuclear C*-algebras.2000 Mathematical Subject Classification: primary 46L35; secondary 19K14, 19K35, 46L80.

scholarly journals MORPHISMS OF SIMPLE TRACIALLY AF ALGEBRAS

2004 ◽  
Vol 15 (09) ◽  
pp. 919-957 ◽  
Author(s):  
MARIUS DADARLAT
Keyword(s):  
Existence And Uniqueness ◽  
Residually Finite ◽  
C Algebras ◽  
Finite Dimensional ◽  
K Theory ◽  
Inner Automorphisms ◽  
Af Algebras ◽  
Universal Coefficient Theorem

Let A, B be separable simple unital tracially AF C*-algebras. Assuming that A is exact and satisfies the Universal Coefficient Theorem (UCT) in KK-theory, we prove the existence, and uniqueness modulo approximately inner automorphisms, of nuclear *-homomorphisms from A to B with prescribed K-theory data. This implies the AF-embeddability of separable exact residually finite-dimensional C*-algebras satisfying the UCT and reproves Huaxin Lin's theorem on the classification of nuclear tracially AF C*-algebras.

scholarly journals On the Classification of Simple Stably Projectionless C*-Algebras

2002 ◽  
Vol 54 (1) ◽  
pp. 138-224 ◽  
Author(s):  
Shaloub Razak
Keyword(s):  
Building Blocks ◽  
Isomorphism Theorem ◽  
Inductive Limits ◽  
C Algebras ◽  
Distinguished Subset ◽  
K Theory

AbstractIt is shown that simple stably projectionless C*-algebras which are inductive limits of certain specified building blocks with trivial K-theory are classified by their cone of positive traces with distinguished subset. This is the first example of an isomorphism theorem verifying the conjecture of Elliott for a subclass of the stably projectionless algebras.

scholarly journals FILTRATED K-THEORY FOR REAL RANK ZERO C*-ALGEBRAS

2012 ◽  
Vol 23 (08) ◽  
pp. 1250078 ◽  
Author(s):  
SARA ARKLINT ◽  
GUNNAR RESTORFF ◽  
EFREN RUIZ
Keyword(s):  
Primitive Ideal ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras ◽  
K Theory

The smallest primitive ideal spaces for which there exist counterexamples to the classification of non-simple, purely infinite, nuclear, separable C*-algebras using filtrated K-theory, are four-point spaces. In this article, we therefore restrict to real rank zero C*-algebras with four-point primitive ideal spaces. Up to homeomorphism, there are ten different connected T0-spaces with exactly four points. We show that filtrated K-theory classifies real rank zero, tight, stable, purely infinite, nuclear, separable C*-algebras that satisfy that all simple subquotients are in the bootstrap class for eight out of ten of these spaces.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory

FEATURES OF OPHTHALMIC CARE FOR PATIENTS WITH COMPLICATED CATARACTS

2020 ◽  
pp. 84-89
Author(s):  
Inna Ivanovna Lapkina
Keyword(s):  
Health Care ◽  
Surgical Treatment ◽  
Postoperative Complications ◽  
Key Words ◽  
Outpatient Treatment ◽  
Practical Application ◽  
Unified Approach ◽  
Case Histories ◽  
High Prevalence

Today, around 50 million people worldwide suffer from cataracts, more than a half of them need surgical treatment. High prevalence of this pathology in Ukraine, the need to improve the provision of ophthalmic care to patients, and the reform of the health care system have made the research relevant. Concomitant diseases and special conditions of the eye increase the risk of intra− and postoperative complications, worsen the functional parameters of patients after surgery. In order to develop a unified approach to the treatment of complicated cataracts based on diagnostically related groups of patients, a retrospective analysis of case histories of patients with different variants of complications related to the condition of the lens itself, its ligament apparatus and other structures of the eye was conducted. In each case, the surgeon has to choose the appropriate modification of cataract phacoemulsification surgery. The study proposed the classification of cataract phacoemulsification modifications on the basis of the techniques and the sequence of operation stages, taking into account the classification of the degrees of turbidity of the lens, proposed by L. Buratto. It has been noted that in complicated cases, according to the indications of the patient, surgery may be performed on several modifications of cataract phacoemulsification. The developed classification made it possible to generalize the various variants of pathology and greatly facilitate the choice of tactics of surgical treatment in complicated cataracts. It can be used not only for practical application, but also for improving the qualification of trained professionals. The prospect of further research is to identify contraindications for outpatient treatment of the patients with complicated cataracts. Key words: cataract complication, classification of phacoemulsification modifications, diagnostically related groups.

Chemometric Analysis for the Classification of some Groups of Drugs with Divergent Pharmacological Activity on the Basis of some Chromatographic and Molecular Modeling Parameters

2018 ◽  
Vol 21 (2) ◽  
pp. 125-137
Author(s):  
Jolanta Stasiak ◽  
Marcin Koba ◽  
Marcin Gackowski ◽  
Tomasz Baczek
Keyword(s):  
Correlation Analysis ◽  
Pharmacological Activity ◽  
Correlation Coefficients ◽  
Principal Component ◽  
Cardiovascular Drugs ◽  
New Drugs ◽  
Analgesic Drugs ◽  
Starting Point ◽  
Chromatographic Parameters

Aim and Objective: In this study, chemometric methods as correlation analysis, cluster analysis (CA), principal component analysis (PCA), and factor analysis (FA) have been used to reduce the number of chromatographic parameters (logk/logkw) and various (e.g., 0D, 1D, 2D, 3D) structural descriptors for three different groups of drugs, such as 12 analgesic drugs, 11 cardiovascular drugs and 36 “other” compounds and especially to choose the most important data of them. Material and Methods: All chemometric analyses have been carried out, graphically presented and also discussed for each group of drugs. At first, compounds’ structural and chromatographic parameters were correlated. The best results of correlation analysis were as follows: correlation coefficients like R = 0.93, R = 0.88, R = 0.91 for cardiac medications, analgesic drugs, and 36 “other” compounds, respectively. Next, part of molecular and HPLC experimental data from each group of drugs were submitted to FA/PCA and CA techniques. Results: Almost all results obtained by FA or PCA, and total data variance, from all analyzed parameters (experimental and calculated) were explained by first two/three factors: 84.28%, 76.38 %, 69.71% for cardiovascular drugs, for analgesic drugs and for 36 “other” compounds, respectively. Compounds clustering by CA method had similar characteristic as those obtained by FA/PCA. In our paper, statistical classification of mentioned drugs performed has been widely characterized and discussed in case of their molecular structure and pharmacological activity. Conclusion: Proposed QSAR strategy of reduced number of parameters could be useful starting point for further statistical analysis as well as support for designing new drugs and predicting their possible activity.

scholarly journals Exceptional nonrelativistic effective field theories with enhanced symmetries

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Tomáš Brauner
Keyword(s):  
Effective Field Theories ◽  
Explicit Construction ◽  
Effective Field ◽  
Field Theories ◽  
Relativistic Case ◽  
Starting Point ◽  
Higher Power ◽  
Mere Presence ◽  
Spatial Rotations

Abstract We initiate the classification of nonrelativistic effective field theories (EFTs) for Nambu-Goldstone (NG) bosons, possessing a set of redundant, coordinate-dependent symmetries. Similarly to the relativistic case, such EFTs are natural candidates for “exceptional” theories, whose scattering amplitudes feature an enhanced soft limit, that is, scale with a higher power of momentum at long wavelengths than expected based on the mere presence of Adler’s zero. The starting point of our framework is the assumption of invariance under spacetime translations and spatial rotations. The setup is nevertheless general enough to accommodate a variety of nontrivial kinematical algebras, including the Poincaré, Galilei (or Bargmann) and Carroll algebras. Our main result is an explicit construction of the nonrelativistic versions of two infinite classes of exceptional theories: the multi-Galileon and the multi-flavor Dirac-Born-Infeld (DBI) theories. In both cases, we uncover novel Wess-Zumino terms, not present in their relativistic counterparts, realizing nontrivially the shift symmetries acting on the NG fields. We demonstrate how the symmetries of the Galileon and DBI theories can be made compatible with a nonrelativistic, quadratic dispersion relation of (some of) the NG modes.

scholarly journals A CONTROL LIST FOR THE SYSTEMATIC IDENTIFICATION OF DISTURBANCE FACTORS

2021 ◽  
Vol 1 ◽  
pp. 51-60
Author(s):  
Peter Welzbacher ◽  
Gunnar Vorwerk-Handing ◽  
Eckhard Kirchner
Keyword(s):  
Literature Review ◽  
Product Development ◽  
Model Theory ◽  
Development Process ◽  
Product Development Process ◽  
Key Factors ◽  
Starting Point ◽  
Disturbance Factor ◽  
Systematic Identification

AbstractThe importance of considering disturbance factors in the product development process is often emphasized as one of the key factors to a functional and secure product. However, there is only a small number of tools to support the developer in the identification of disturbance factors and none of them yet ensures that the majority of occurring disturbance factors is considered. Thus, it is the aim of this contribution to provide a tool in form of a control list for the systematic identification of disturbance factors. At the beginning of this contribution, the terms “disturbance factor” and “uncertainty” are defined based on a literature review and different approaches for the classification of uncertainty are presented. Subsequently, the fundamentals of multipole based model theory are outlined. Moreover, a first approach in terms of a control list for a systematic identification of disturbance factors is discussed. Based on the discussed approach and taking the identified weaknesses as a starting point, a control list is presented that combines the existing basic concept of the control list with the fundamentals of multipole based model theory.

scholarly journals Graded K-theory and K-homology of relative Cuntz–Pimsner algebras and graph C⁎-algebras

2021 ◽  
Vol 496 (2) ◽  
pp. 124822
Author(s):  
Quinn Patterson ◽  
Adam Sierakowski ◽  
Aidan Sims ◽  
Jonathan Taylor
Keyword(s):  
C Algebras ◽  
K Theory
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