Noncommutative localisation in algebraic K-theory II

In [Amnon Neeman, Andrew Ranicki, Noncommutative localisation in algebraic K-theory I, Geom. Topol. 8 (2004) 1385-1425] we proved a localisation theorem in the algebraic K-theory of noncommutative rings. The main purpose of the current article is to express the general theorem of the previous paper in a more user-friendly fashion, in a way more suitable for applications. In the process we compare our result to the existing theorems in the literature, showing how the previous paper improves all the existing results.It should be pointed out that there have been two very interesting recent preprints on related topics. The reader is referred to the beautiful papers of Krause [Henning Krause, Cohomological quotients and smashing localizations, http://wwwmath.upb.de/~hkrause/publications.html. [8]] and Dwyer [William G. Dwyer, Noncommutative localization in homotopy theory, preprint, http://www.nd.edu/~wgd/. [4]]. Krause studies the lifting of chain complexes and the relation with the telescope conjecture, and Dwyer generalises to the homotopy theoretic framework.     

Breathers in ferrimagnetic systems

Breathers in discrete nonlinear ferrimagnetic spin lattices are investigated for both easy-axis and easy-plane configurations. The region in frequency space of the formation of breathers is determined and the anticontinuum limit discussed. The monochromatic and the coloured breathers are found out numerically for different parameters and different conditions of excitations.     

Guided Antitumoural Drugs: (Imidazol-2-ylidene)(L)gold(I) Complexes Seeking Cellular Targets Controlled by the Nature of Ligand L

Three [1,3-diethyl-4-(p-methoxyphenyl)-5-(3,4,5-trimethoxyphenyl)imidazol-2-ylidene](L)gold(I) complexes, 4 a (L=Cl), 5 a (L=PPh₃), and 6 a (L=same N-heterocyclic carbene (NHC)), and their fluorescent [4-(anthracen-9-yl)-1,3-diethyl-5-phenylimidazol-2-ylidene](L)gold(I) analogues, 4 b , 5 b , and 6 b , respectively, were studied for their localisation and effects in cancer cells. Despite their identical NHC ligands, the last three accumulated in different compartments of melanoma cells, namely, the nucleus ( 4 b ), mitochondria ( 5 b ), or lysosomes ( 6 b ). Ligand L was also more decisive for the site of accumulation than the NHC ligand because the couples 4 a / 4 b , 5 a / 5 b , and 6 a / 6 b , carrying different NHC ligands, afforded similar results in cytotoxicity tests, and tests on targets typically found at their sites of accumulation, such as DNA in nuclei, reactive oxygen species and thioredoxin reductase in mitochondria, and lysosomal membranes. Regardless of the site of accumulation, cancer cell apoptosis was eventually induced. The concept of guiding a bioactive complex fragment to a particular subcellular target by secondary ligand L could reduce unwanted side effects.     

Light-Activated Carbon Monoxide Prodrugs Based on Bipyridyl Dicarbonyl Ruthenium(II) Complexes

Two photoactivatable dicarbonyl ruthenium(II) complexes based on an amide-functionalised bipyridine scaffold (4-position) equipped with an alkyne functionality or a green-fluorescent BODIPY (boron-dipyrromethene) dye have been prepared and used to investigate their light-induced decarbonylation. UV/Vis, FTIR and ¹³C NMR spectroscopies as well as gas chromatography and multivariate curve resolution alternating least-squares analysis (MCR-ALS) were used to elucidate the mechanism of the decarbonylation process. Release of the first CO molecule occurs very quickly, while release of the second CO molecule proceeds more slowly. In vitro studies using two cell lines A431 (human squamous carcinoma) and HEK293 (human embryonic kidney cells) have been carried out in order to characterise the anti-proliferative and anti-apoptotic activities. The BODIPY-labelled compound allows for monitoring the cellular uptake, showing fast internalisation kinetics and accumulation at the endoplasmic reticulum and mitochondria.     

Dual energy time reversed elastic wave propagation and nonlinear signal processing for localisation and depth-profiling of near-surface defects: a simulation study

Nonlinear Elastic Wave Spectroscopy (NEWS) relies on the activation of defects by wave energy that propagates through the medium. In general, the response of activated defects will not scale linearly with the excitation amplitude, and the resulting nonlinear signatures can be identified and used for quality inspection. The efficiency of NEWS based inspection methods is therefore intrinsically linked to the locally deposited activation energy at the defect zone and the ability to generate nonlinear signatures that exceed the noise level of acquisition. Time Reversal techniques allow focusing of high levels of energy in small areas, and are consequently very useful for the local activation of defected zones. In this report, numerical simulations are reported showing the potential of a combination consisting of dual energy reciprocal Time Reversal and nonlinearity filtering using the Scaling Subtraction Method. The method is applied to the detection of planar near-surface defects parallel to the surface in a 2D domain. The results are evaluated for sweep excitation at different frequency ranges; for point-like receiver as well as extended transducers, and for in-plane as well as out-of-plane focusing. The observable nonlinear response at the surface is linked to an effective nonlinearity within the medium based on the defect geometry and the distribution of the local stresses.     

Quasi-static versus dynamic failure instabilities in fluid-saturated porous mediaModes de rupture sous conditions quasi-statiques et dynamiques dans les milieux poreux saturés

Using a linear perturbation approach, we show that under quasi-static conditions, unbounded growth of perturbations coincides with localization under drained or undrained conditions. Under dynamic loadings, unbounded growth is related either to the emergence of stationary discontinuities (and these are set by drained conditions) or to the appearance of the flutter phenomenon (acceleration waves). For associative behaviour the inception of unbounded growth is always set (under both static and dynamic conditions) by the singularity of the drained acoustic tensor. It is only for non-associative flow that unbounded growth may correspond to undrained localization in quasi-static conditions and to flutter under dynamic conditions. To cite this article: A. Benallal, C. Comi, C. R. Mecanique 330 (2002) 339–345.     

Multidimensional bisection: The performance and the context

Two aspects of the multidimensional bisection algorithms for the global optimisation of Lipschitz continuous functions are investigated. Firstly, for several test functions we examine the numerical performance of the deepest point algorithm and two acceleration procedures. Secondly, we phrase the branch and bound framework of Horst and Tuy in terms of covers, and show the algorithms to be included in this framework. A result of Basso on the convergence of localisations is extended to higher dimensions.The paper was presented at the II. IIASA-Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

Covering Coalgebras and Dual Non-singularity

Localisation is an important technique in ring theory and yields the construction of various rings of quotients. Colocalisation in comodule categories has been investigated by some authors (see Jara et al., Commun. Algebra, 34(8):2843–2856, 2006 and Nastasescu and Torrecillas, J. Algebra, 185:203–220, 1994). Here we look at possible coalgebra covers π : D → C that could play the rôle of a coalgebra colocalisation. Codense covers will dualise dense (or rational) extensions; a maximal codense cover construction for coalgebras with projective covers is proposed. We also look at a dual non-singularity concept for modules which turns out to be the comodule-theoretic property that turns the dual algebra of a coalgebra into a non-singular ring. As a corollary we deduce that hereditary coalgebras and hence path coalgebras are non-singular in the above sense. We also look at coprime coalgebras and Hopf algebras which are non-singular as coalgebras.