Stable equivalences of graded algebras

We extend the notion of stable equivalence to the class of locally finite graded algebras. For such an algebra Λ, we focus on the Krull–Schmidt category gr_Λ of finitely generated -graded Λ-modules with degree 0 maps, and the stable category obtained by factoring out those maps that factor through a graded projective module. We say that Λ and Γ are graded stably equivalent if there is an equivalence that commutes with the grading shift. Adapting arguments of Auslander and Reiten involving functor categories, we show that a graded stable equivalence α commutes with the syzygy operator (where defined) and preserves finitely presented modules. As a result, we see that if Λ is right noetherian (resp. right graded coherent), then so is any graded stably equivalent algebra. Furthermore, if Λ is right noetherian or k is artinian, we use almost split sequences to show that a graded stable equivalence preserves finite length modules. Of particular interest in the nonartinian case, we prove that any graded stable equivalence involving an algebra Λ with socΛ=0 must be a graded Morita equivalence.     

Stable categories of higher preprojective algebras

We introduce (n+1)$(n+1)$-preprojective algebras of algebras of global dimension n$n$. We show that if an algebra is n$n$-representation-finite then its (n+1)$(n+1)$-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)$(n+1)$-preprojective algebra is (n+1)$(n+1)$-Calabi–Yau, and, more precisely, it is the (n+1)$(n+1)$-Amiot cluster category of the stable n$n$-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)$(n+1)$-cluster tilting object. We show that even if the (n+1)$(n+1)$-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for n∈{1,2}$n\in \{1,2\}$) the results above still hold for the stable category of Cohen–Macaulay modules.     

Finiteness conditions in the stable module category

We study groups whose cohomology functors commute with filtered colimits in high dimensions. We relate this condition to the existence of projective resolutions which exhibit some finiteness properties in high dimensions, and to the existence of Eilenberg–Mac Lane spaces with finitely many n-cells for all sufficiently large n. To that end, we determine the structure of completely finitary Gorenstein projective modules over group rings. The methods are inspired by representation theory and make use of the stable module category, in which morphisms are defined through complete cohomology. In order to carry out these methods, we need to restrict ourselves to certain classes of hierarchically decomposable groups.     

Uniqueness and Sharp Estimates on Solutions to Hyperbolic Systems with Dissipative Source

Global weak solutions of a strictly hyperbolic system of balance laws in one-space dimension were constructed (cf. Christoforou, 2006 Christoforou , C. ( 2006 ). Hyperbolic systems of balance laws via vanishing viscosity . J. Diff. Eq. 221 ( 2 ): 470 – 541 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) via the vanishing viscosity method under the assumption that the source term g is dissipative. In this article, we establish sharp estimates on the uniformly Lipschitz semigroup 𝒫 generated by the vanishing viscosity limit in the general case which includes also nonconservative systems. Furthermore, we prove uniqueness of solutions by means of local integral estimates and show that every “viscosity solution” can be constructed as a limit of vanishing viscosity approximations.     

Derived Equivalence Classification of Nonstandard Selfinjective Algebras of Domestic Type

We give a complete derived equivalence classification of all nonstandard representation-infinite domestic selfinjective algebras over an algebraically closed field. As a consequence, a complete stable equivalence classification of these algebras is obtained.     

In vitro translation with [<Superscript>34</Superscript>S]-labeled methionine,selenomethionine, and telluromethionine

Heteroisotope and heteroatom tagging with [³⁴S]-enriched methionine (Met), selenomethionine (SeMet), and telluromethionine (TeMet) was applied to in vitro translation. Green fluorescent protein (GFP) and JNK stimulatory phosphatase-1 (JSP-1) genes were translated with wheat germ extract (WGE) in the presence of Met derivatives. GFPs containing Met derivatives were subjected to HPLC coupled with treble detection, i.e., a photodiode array detector, a fluorescence detector, and an inductively coupled plasma mass spectrometer (ICP-MS). The activities of JSP-1-containing Met derivatives were also measured. GFP and JSP-1 containing [³⁴S]-Met and SeMet showed comparable fluorescence intensities and enzyme activities to those containing naturally occurring Met. TeMet was unstable and decomposed in WGE, whereas SeMet was stable throughout the experimental period. Thus, although Te was the most sensitive to ICP-MS detection among S, Se, and Te, TeMet was less incorporated into the proteins than Met and SeMet. Finally, the potential of heteroisotope and heteroatom tagging of desired proteins in in vitro translation followed by ICP-MS detection was discussed. Figure TeMet was less incorporated into GFP than Met and SeMet due to its instability in WGE     

Electron paramagnetic resonance (EPR) and stable isotope records of paleoenvironmental conditions during peat formation

EPR spectroscopy was performed on four peat cores (1-2.5 m depth) collected from Yellowstone National Park (USA), Scotland (UK) and Lower Silesia (Poland) to study peat formation process. The stable free radicals identified in all investigated samples are semiquinone type and g-parameters range from 2.0030 to 2.0048. The highest g-values are characteristic of upper well-aerated peat layers and gradually decrease with depth. The lowest g-values are typical of relatively old fens and bogs where anaerobic conditions are expected and carbonization processes are advanced. The decrease in g-parameter value is connected with conjugation of semiquinone units with gradually augmented polyaromatic units in the peat substance. Generally the radical concentration increases with depth (0.05-5x10(17) spins/gram). However the g-values, line width parameters, and spin concentrations exhibit strong variations in some peat layers. Variation of these parameters observed for certain peat horizons correlate with the variation of carbon stable isotopic composition. For the old well-conserved peat deposits (e.g. Scotland/UK, approximately 5600 BP), variation of EPR parameters may be used to study paleo redox conditions.     

六六六异构体稳定碳同位素组成分析

采用GC-C-IRMS、EA-IRMS和Dual-inlet IRMS 3种稳定同位素比值质谱仪分别对六六六的α、β和γ3种异构体的稳定碳同位素组成进行了分析。对比3种分析系统测定的碳同位素组成数据表明GC-C-IRMS系统能够准确和精确地测定六六六碳同位素组成。应用GC-C-IRMS技术分析了水样品中α-和γ-六六六的碳同位素组成,结果表明六六六在溶解、稀释、萃取、挥发等过程碳同位素组成没有分馏现象。采用GC-C-IRMS技术分析环境样品中持久性有机氯农药稳定碳同位素组成可能得到广泛应用。     

Features of stable radical generation in lignin on exposure to nitrogen dioxide

The mechanism of stable radical generation in lignin under the action of nitrogen dioxide and NO₂ - air mixture is considered. The formation of phenoxyl, iminoxyl and acylaminoxyl radicals has been detected by EPR. The proposed mechanism involves a primary oxidative reaction of phenol groups with dimers of NO₂ (nitrosyl nitrate) resulting in the formation of phenoxyl radicals and nitric oxide. In the subsequent recombination of phenoxyl radicals and nitric oxide, nitroso compounds and oximes are formed. By reaction of oximes with radicals NO₂, stable iminoxyl radicals are formed. This mechanism is confirmed by kinetic dependencies obtained over a wide range of NO₂ concentrations. From IR spectroscopy measurements it follows that hydroxyl groups of non-phenolic structures of lignin are oxidised to aldehydes producing acylaminoxyl radicals by reaction with NO₂. The kinetic data show that the adsorption of NO₂ on the lignin surface is the rate-determining factor in stable radical formation.