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101.
The Wigner's Theorem states that a bijective transformation of the set of all one-dimensional linear subspaces of a complex
Hilbert space which preserves orthogonality is induced by either a unitary or an anti-unitary operator. There exist many Wigner-type
theorems, in particular in indefinite metric spaces, von Neumanns algebras and Banach spaces and we try to find a common origin
of all these results by using properties of the lattice subspaces of certain topological vector spaces. We prove a Wigner-type
theorem for a pair of dual spaces which allows us to obtain, as particular cases, the usual Wigner's Theorem and some of its
generalizations.
PACS: 02.40.Dr, 03.65.Fd,03.65.Ta
AMS Subject Classification (1991): 06C15, 46A20, 81P10. 相似文献
102.
In a Hilbert space, there exists a natural correspondence between continuous projections and particular pairs of closed subspaces.
In this paper, we generalize this situation and associate to a symmetric lattice L a subset P(L) of L× L, called its projection poset. If L is the lattice of closed subspaces of a topological vector space then elements of P(L) correspond to continuous projections and we prove that automorphisms of P(L) are determined by automorphisms of the lattice L when this lattice satisfies some basic properties of lattices of closed subspaces.
Primary: 06C15, Secondary: 03G12 81P10. 相似文献
103.
O. N. Karpenkov 《Functional Analysis and Its Applications》2004,38(2):102-110
The notion of equivalence of multidimensional continued fractions is introduced. We consider some properties and state some conjectures related to the structure of the family of equivalence classes of two-dimensional periodic continued fractions. Our approach to the study of the family of equivalence classes of two-dimensional periodic continued fractions leads to revealing special subfamilies of continued fractions for which the triangulations of the torus (i.e., the combinatorics of their fundamental domains) are subjected to clear rules. Some of these subfamilies are studied in detail; the way to construct other similar subfamilies is indicated. 相似文献
104.
In an earlier paper (see Proc. London Math. Soc. (3) 84 (2002)257288) we showed that an irreducible integral binarycubic form f(x, y) attains infinitely many prime values, providingthat it has no fixed prime divisor. We now extend this resultby showing that f(m, n) still attains infinitely many primevalues if m and n are restricted by arbitrary congruence conditions,providing that there is still no fixed prime divisor. Two immediate consequences for the solvability of diagonal cubicDiophantine equations are given. 2000 Mathematics Subject Classification11N32 (primary), 11N36, 11R44 (secondary). 相似文献
105.
Antonio Ros 《Journal of the American Mathematical Society》2004,17(2):373-388
Given a cubic space group (viewed as a finite group of isometries of the torus ), we obtain sharp isoperimetric inequalities for -invariant regions. These inequalities depend on the minimum number of points in an orbit of and on the largest Euler characteristic among nonspherical -symmetric surfaces minimizing the area under volume constraint (we also give explicit estimates of this second invariant for the various crystallographic cubic groups ). As an example, we prove that any surface dividing into two equal volumes with the same (orientation-preserving) symmetries as the A. Schoen minimal Gyroid has area at least (the conjectured minimizing surface in this case is the Gyroid itself whose area is ).
106.
论略萨小说的“零件组合与立体叙事”艺术 总被引:2,自引:0,他引:2
略萨是结构现实主义小说的代表作家,主张"立体"地反映多样化的现实生活.为此,他在创作中积极引进了立体绘画艺术中的"粘贴"、"并置"等技巧,把多个故事的多个片段打乱并置在一起,既像色彩斑斓的粘贴画,又像细碎零件的有机组合,在时空交叉、跳跃中,多层面、多维度、多棱体地反映了现实生活的原生态.这样,小说的叙事就成为"立体"的,而读者的阅读随之也成为"立体"的了. 相似文献
107.
C. Boldrighini L. A. Bunimovich G. Cosimi S. Frigio A. Pellegrinotti 《Journal of statistical physics》2001,102(5-6):1271-1283
We consider a one-dimensional lattice of expanding antisymmetric maps [–1, 1][–1, 1] with nearest neighbor diffusive coupling. For such systems it is known that if the coupling parameter is small there is unique stationary (in time) state, which is chaotic in space-time. A disputed question is whether such systems can exhibit Ising-type phase transitions as grows beyond some critical value c. We present results from computer experiments which give definite indication that such a transition takes place: the mean square magnetization appears to diverge as approaches some critical value, with a critical exponent around 0.9. We also study other properties of the coupled map system. 相似文献
108.
Rafael Herná ndez Marí a J. Vá zquez-Gallo 《Transactions of the American Mathematical Society》2001,353(1):95-115
We determine the degree of some strata of singular cubic surfaces in the projective space . These strata are subvarieties of the parametrizing all cubic surfaces in . It is known what their dimension is and that they are irreducible. In 1986, D. F. Coray and I. Vainsencher computed the degree of the 4 strata consisting on cubic surfaces with a double line. To work out the case of isolated singularities we relate the problem with (stationary) multiple-point theory.
109.
We compute the subdirectly irreducible factors of the free Hermitean (semi)lattice generated by a single element a subject to the relation aa
; we also compute the factors of its induced distributive presentation. 相似文献
110.
We establish that an ordered Banach space is order-isomorphic to c0 if and only if it is a -Dedekind complete vector lattice and its norm dual is order-isomorphic to 1. 相似文献