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51.
Frederick?M.?KronzEmail author Tracy?A.?Lupher 《International Journal of Theoretical Physics》2005,44(8):1239-1258
It has been maintained that the physical content of a model of a system is completely contained in the C∗-algebra of quasi-local observables
that is associated with the system. The reason given for this is that the unitarily inequivalent representations of
are physically equivalent. But, this view is dubious for at least two reasons. First, it is not clear why the physical content
does not extend to the elements of the von Neumann algebras that are generated by representations of
. It is shown here that although the unitarily inequivalent representations of
are physically equivalent, the extended representations are not. Second, this view detracts from special global features
of physical systems such as temperature and chemical potential by effectively relegating them to the status of fixed parameters.
It is desirable to characterize such observables theoretically as elements of the algebra that is associated with a system
rather than as parameters, and thereby give a uniform treatment to all observables. This can be accomplished by going to larger
algebras. One such algebra is the universal enveloping von Neumann algebra, which is generated by the universal representation
of
; another is the direct integral of factor representations that are associated with the set of values of the global features.
Placing interpretive significance on the von Neumann algebras mentioned earlier sheds light on the significance of unitarily
inequivalent representations of
, and it serves to show the limitations of the notion of physical equivalence. 相似文献
52.
冯国 《纯粹数学与应用数学》2007,23(2):221-225,230
利用加权Ditzin-Totik 光滑模ω2φλ(f;t)w,借助Peetre K-泛函研究了Meyer-K(o)nig-Zeller算子,给出其特征刻画. 相似文献
53.
文中证明了在Bayes框架下,当漂移参数7服从有信息先验时,在相当广泛的统计模型中,数据删除模型(CDM)和均值漂移模型(MSOM)的参数估计不相等,几个数值例子验证了相应的结论. 相似文献
54.
B. Z. Shavarovskii 《Mathematical Notes》1998,64(5):663-673
The structure of polynomial matrices in connection with their reducibility by semiscalar-equivalent transformations and similarity
transformations to simpler forms is considered. In particular, the canonical form of polynomial matrices without multiple
characteristic roots with respect to the above transformations is indicated. This allows one to establish a canonical form
with respect to similarity for a certain type of finite collections of numerical matrices.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 769–782, November, 1998. 相似文献
55.
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 grΛ 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. 相似文献
56.
57.
《代数通讯》2013,41(5):1383-1407
ABSTRACT On calcule une base explicite de l'espace des dérivations modulo les dérivations intérieures des algèbres de Weyl quantiques et de certaines de leurs localisations simples. On applique les résultats obtenus à des questions de séparation à équivalence de Morita près de ces algèbres. We compute an explicit basis of the space of derivations modulo inner derivations for quantum Weyl algebras and some of their simple localizations. We apply these results to separate these algebras up to Morita equivalence. 相似文献
58.
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. 相似文献
59.
A. Tsurkov 《代数通讯》2013,41(8):3147-3154
In this article, we consider the problem of classification of the nilpotent class 2 finitely generated torsion free groups up to geometric equivalence. By a very easy technique it is proved that this problem is equivalent to the problem of classification of the complete in the Maltsev sense nilpotent torsion free finite rank groups up to isomorphism. This result leads to better understanding of the complexity of the problem of the classification of the quasi-varieties of the nilpotent class 2 groups. It is well known that the variety of the nilpotent class s groups is Noetherian for every s ∈ ?. So the problem of the classification of the quasi-varieties generated even by a single nilpotent class 2 finitely generated torsion free group is equivalent to the problem of classification of the complete in the Maltsev sense nilpotent torsion free finite rank groups up to isomorphism. 相似文献
60.
《Journal of separation science》2017,40(14):2895-2905
Bioactive equivalent combinatorial components play a critical role in herbal medicines. However, how to discover and enrich them efficiently is a question for herbal pharmaceuticals researchers. In our work, a novel two‐dimensional reversed‐phase/hydrophilic interaction high‐performance liquid chromatography method was established to perform real‐time components trapping and combining for preparation and isolation of coeluting components. Arenaria kansuensis was taken as an example, and solid‐phase extraction coupled with liquid–liquid extraction as a simple and efficient method for enriching trace components, reversed phase column coupled with hydrophilic interaction liquid chromatography XAmide column as two‐dimensional chromatography technology for isolation and preparation of coeluting constituents, enzyme‐linked immune‐sorbent assay as bio‐guided assay, and anti‐inflammatory bioactivity evaluation for bioactive constituents. A combination of 12 β‐carboline alkaloids was identified as anti‐inflammatory bioactive equivalent combinatorial components from A. kansuensis , which accounts for 1.9% w/w of original A. kansuensis . This work answers the key question of which are real anti‐inflammatory components from A. kansuensis and provides a fast and efficient approach for discovering and enriching trace β‐carboline alkaloids from herbal medicines for the first time. More importantly, the discovery of bioactive equivalent combinatorial components could improve the quality control of herbal products and inspire a herbal medicine based on combinatorial therapeutics. 相似文献