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71.
Synthesis and Crystal Structure of 18-Tungstotetranickel(II) diphosphate Na_(10){(PW_9O_(34))_2Ni_4(H_2O)_2}·26H_2O 总被引:1,自引:1,他引:0
CUI Chuan-Peng DAI Jing-Cao DU Wen-Xin WU Li-Ming FU Zhi-Yong HU Sheng-Min WU Xin-Tao② 《结构化学》2001,(4)
1 INTRODUCTIONThe inorganic chemistry concentrating on polyoxometallates, is in a position to connect elementary building blocks and their derivatives in different ways, enabling people to synthesize a large variety of remarkable substances, especially those in the "nanoworld". Of particular importance is the anionic-type which has {MOx}-type building-block units, where M stands for the d block elements in high oxidation states.[1] In 1973 Weakley, Evans and Showell isolated[2] K10P2W1… 相似文献
72.
Varghese Mathai 《Geometriae Dedicata》2003,99(1):1-15
We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C*
r
(, )-bundle and connection, which can be used to construct a C*
r
(, )-index that lies in the Grothendieck group of C*
r
(, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem. 相似文献
73.
We study the action of translation operators on wavelet subspaces. This action gives rise to an equivalence relation on the
set of all wavelets. We show by explicit construction that each of the associated equivalence classes is non-empty. 相似文献
74.
75.
We present a detailed proof of the existence-theorem for noncommutative spectral sections (see the noncommutative spectral flow, unpublished preprint, 1997). We apply this result to various index-theoretic situations, extending to the noncommutative context results of Booss–Wojciechowski, Melrose–Piazza and Dai–Zhang. In particular, we prove a variational formula, in K*(Cr*(Γ)), for the index classes associated to 1-parameter family of Dirac operators on a Γ-covering with boundary; this formula involves a noncommutative spectral flow for the boundary family. Next, we establish an additivity result, in K*(Cr*(Γ)), for the index class defined by a Dirac-type operator associated to a closed manifold M and a map r:M→BΓ when we assume that M is the union along a hypersurface F of two manifolds with boundary M=M+ F M−. Finally, we prove a defect formula for the signature-index classes of two cut-and-paste equivalent pairs (M1,r1:M1→BΓ) and (M2,r2:M2→BΓ), whereand φjDiff(F). The formula involves the noncommutative spectral flow of a suitable 1-parameter family of twisted signature operators on F. We give applications to the problem of cut-and-paste invariance of Novikov's higher signatures on closed oriented manifolds. 相似文献
M1=M+ (F,φ1) M−, M2=M+ (F,φ2) M−
76.
Thomas Schick 《Transactions of the American Mathematical Society》2001,353(8):3247-3265
A standing conjecture in -cohomology says that every finite -complex is of -determinant class. In this paper, we prove this whenever the fundamental group belongs to a large class of groups containing, e.g., all extensions of residually finite groups with amenable quotients, all residually amenable groups, and free products of these. If, in addition, is -acyclic, we also show that the -determinant is a homotopy invariant -- giving a short and easy proof independent of and encompassing all known cases. Under suitable conditions we give new approximation formulas for -Betti numbers.
77.
More on P-Stable Convex Sets in Banach Spaces 总被引:2,自引:0,他引:2
We study the asymptotic behavior and limit distributions for sums S
n =bn
-1 i=1
n i,where
i, i 1, are i.i.d. random convex compact (cc) sets in a given separable Banach space B and summation is defined in a sense of Minkowski. The following results are obtained: (i) Series (LePage type) and Poisson integral representations of random stable cc sets in B are established; (ii) The invariance principle for processes S
n(t) =bn
-1 i=1
[nt] i, t[0, 1], and the existence of p-stable cc Levy motion are proved; (iii) In the case, where
i are segments, the limit of S
n is proved to be countable zonotope. Furthermore, if B = R
d
, the singularity of distributions of two countable zonotopes Yp
1, 1,Yp
2, 2, corresponding to values of exponents p
1, p
2 and spectral measures
1,
2, is proved if either p
1 p
2 or
1
2; (iv) Some new simple estimates of parameters of stable laws in R
d
, based on these results are suggested. 相似文献
78.
The aim of this paper is to combine two ways for representing uncertainty through stochastic differential inclusions: a 'stochastic uncertainty", driven by a Wiener process, and a 'contingent uncertainty", driven by a set-valued map. The paper is also devoted to the invariance of closed under stochastic differential inclusions with a Lipschitz right-hand side, characterized in terms of stochastic tangent sets to closed subsets. 相似文献
79.
Nous présentons un cadre unificateur pour un certain nombre de résultats connus de convergence en loi pour des processus admettant une représentation linéaire par rapport à un bruit blanc faible pour lequel il existe un principe dinvariance faible. Nous montrons que ce principe dinvariance est équivalent à la convergence dune suite de mesures aléatoires spectrales. Ceci permet daffaiblir les hypothèses usuelles et donc dobtenir des résultats nouveaux de convergence en loi, notamment pour des processus à longue portée. 相似文献
80.
Marco Castrillón López Jaime Muñz Masquó 《International Journal of Theoretical Physics》2007,46(4):1020-1026
It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing
in the Lie algebra. Moreover, the Hamilton-Cartan equations of these Lagrangians are obtained and proved to be also independent
with respect to the pairing.
PACS Numbers 2003: 02.20.Qs, 02.20.Sv, 02.20.Tw, 02.40.Ma, 02.40.Vh, 11.10.Ef, 11.15.Kc
Mathematics Subject Classification 2000: Primary 70S15, Secondary 58A20, 58E15, 58E30, 70S05, 70S10, 81T13 相似文献