Filtrations, mixed complexes, and cyclic homology in mixed characteristic

We examine the cyclic homology of the monoidal category of modules over a finite dimensional Hopf algebra, motivated by the need to demonstrate that there is a difference between the recently introduced mixed anti-Yetter-Drinfeld contramodules and the usual stable anti-Yetter-Drinfeld contramodules. Namely, we show that Sweedler's Hopf algebra provides an example where mixed complexes in the category of stable anti-Yetter-Drinfeld contramodules (previously studied) are not equivalent, as differential graded categories to the category of mixed anti-Yetter-Drinfeld contramodules (recently introduced).

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Extraction of hafnium(IV) with organophosphorus reagents from solutions of mineral acids mixtures

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19793656 ◽

1979 ◽

Vol 44 (12) ◽

pp. 3656-3664

Author(s):

Oldřich Navrátil ◽

Jiří Smola ◽

Rostislav Kolouch

Keyword(s):

Ionic Strength ◽

Aqueous Phase ◽

Organic Phase ◽

Perchloric Acid ◽

Synergic Effect ◽

Salting Out ◽

Initial Concentration ◽

Mixed Complexes ◽

Synergic Extraction ◽

Mineral Acids

Extraction of hafnium(IV) was studied from solutions of mixtures of perchloric and nitric acids and of perchloric and hydrochloric acids for constant ionic strength, I = 2, 4, 6, or 8, and for cHf 4 . 10-4 mol l-1. The organic phase was constituted by solutions of some acidic or neutral organophosphorus reagents or of 2-thenoyltrifluoroacetone, 1-phenyl-3-methyl-4-benzoyl-5-pyrazolone, or N-benzoyl-N-phenylhydroxylamine in benzene, chloroform, or n-octane. A pronounced synergic extraction of hafnium proceeds only on applying organophosphorus reagents from an aqueous phase whose acidity is not lower than 3M-(HClO4 + HNO3) or 5M-(HClO4 + HCl). The synergic effect was not affected markedly by a variation of the initial concentration of hafnium in the range 1 . 10-8 -4 .10-4 mol l-1, it lowered with increasing initial concentration of the organophosphorus reagent and decreasing concentration of the H+ ions. It is suggested that the hafnium passes into the organic phase in the form of mixed complexes, the salting-out effect of perchloric acid playing an appreciable part.

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Cyclic-Homology Chern–Weil Theory for Families of Principal Coactions

Communications in Mathematical Physics ◽

10.1007/s00220-020-03804-2 ◽

2020 ◽

Author(s):

Piotr M. Hajac ◽

Tomasz Maszczyk

Keyword(s):

Cyclic Homology ◽

Quantum Deformation ◽

Homotopy Formula ◽

Standard Quantum ◽

Unital Algebra ◽

Hopf Fibrations ◽

Chain Homotopy ◽

Cartan Model ◽

Extension Algebra ◽

Hochschild Complex

AbstractViewing the space of cotraces in the structural coalgebra of a principal coaction as a noncommutative counterpart of the classical Cartan model, we construct the cyclic-homology Chern–Weil homomorphism. To realize the thus constructed Chern–Weil homomorphism as a Cartan model of the homomorphism tautologically induced by the classifying map on cohomology, we replace the unital subalgebra of coaction-invariants by its natural H-unital nilpotent extension (row extension). Although the row-extension algebra provides a drastically different model of the cyclic object, we prove that, for any row extension of any unital algebra over a commutative ring, the row-extension Hochschild complex and the usual Hochschild complex are chain homotopy equivalent. It is the discovery of an explicit homotopy formula that allows us to improve the homological quasi-isomorphism arguments of Loday and Wodzicki. We work with families of principal coactions, and instantiate our noncommutative Chern–Weil theory by computing the cotrace space and analyzing a dimension-drop-like effect in the spirit of Feng and Tsygan for the quantum-deformation family of the standard quantum Hopf fibrations.

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A Spectrophotometric Study of the Saturated Mixed Complexes of Mercury(II)-Bromide-Iodide

Inorganic Chemistry ◽

10.1021/ic50006a025 ◽

1963 ◽

Vol 2 (2) ◽

pp. 340-345 ◽

Cited By ~ 6

Author(s):

Thomas G. Spiro ◽

David N. Hume

Keyword(s):

Spectrophotometric Study ◽

Mixed Complexes

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A pathological case of the C1 conjecture in mixed characteristic

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004118000178 ◽

2018 ◽

Vol 167 (01) ◽

pp. 61-64 ◽

Cited By ~ 1

Author(s):

INDER KAUR

Keyword(s):

Line Bundle ◽

Moduli Space ◽

Projective Curve ◽

Free Sheaf ◽

Smooth Projective Curve ◽

Mixed Characteristic ◽

Locally Free Sheaf ◽

Fixed Rank ◽

Pathological Case

AbstractLet K be a field of characteristic 0. Fix integers r, d coprime with r ⩾ 2. Let XK be a smooth, projective, geometrically connected curve of genus g ⩾ 2 defined over K. Assume there exists a line bundle ${\cal L}_K$ on XK of degree d. In this paper we prove the existence of a stable locally free sheaf on XK with rank r and determinant ${\cal L}_K$. This trivially proves the C1 conjecture in mixed characteristic for the moduli space of stable locally free sheaves of fixed rank and determinant over a smooth, projective curve.

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Study on Cavity Growth in Uniaxial Tension of ZK60 Magnesium Alloy

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.353-358.687 ◽

2007 ◽

Vol 353-358 ◽

pp. 687-690

Author(s):

Yan Dong Yu ◽

De Liang Yin ◽

Bao You Zhang

Keyword(s):

Volume Fraction ◽

Cavity Growth ◽

Experimental Studies ◽

Superplastic Forming ◽

Cavity Radius ◽

Analysis Software ◽

Mixed Characteristic ◽

Substantial Growth ◽

Zk60 Magnesium Alloy ◽

Electronic Microscope

Cavity growth is a typical microstructure feature in superplastic forming (SPF) of materials. Substantial growth and interlink of cavities in superplastic deformation usually lead to reduction in elongation, even to failure. Consequently, it is necessary to investigate the mechanism and model of cavity growth. In this paper, experimental studies on cavity growth were carried out by means of superplastic tension of ZK60 magnesium alloys. Scanning electronic microscope (SEM) was employed for observation of fractography. Experimental cavity radius and volume fraction were determined by optical microscopy and corresponding picture-based analysis software. It is found that, the fractured surfaces after a superplastic elongation have a mixed characteristic of intergranular cavities and dimples. Further, the cavity growth is identified to follow a exponentially increasing mode.

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