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991.
A new sodium arsenate with layer structure has been synthesized and its crystal structure solved and refined by single-crystal X-ray diffraction. The crystal is trigonal, space group , a=11.199(3) Å, c=5.411(2) Å, V=587.80(3) Å3, Z=1; the refinement converged to R=0.0282 and wR=0.0751 for 590 reflections with (I)>2sigma(I). The structural model gives the formula Na7As11O32, which would be non-neutral; besides, the structural model is not validated by the charge distribution (CD) analysis, which gives an unsatisfactory agreement on the computed charges of the cations. The CD analysis suggest incomplete (5/6) occupation of the O5 site, which leads to the deficiency of an oxygen atom per unit cell and to formula Na7As11O31: this new structural model corresponds to a neutral compound, is validated by the CD analysis, and results in better displacement parameters for O5 than its non neutral counterpart. The (001) anionic layers are built up from corner and edge sharing of As1 and As2 distorted octahedra and As3 distorted tetrahedra, the sodium cations playing the role of interlayer cations. The effects of the oxygen deficiency on the crystal structure are discussed. 相似文献
992.
Humio Ichimura 《Archiv der Mathematik》2006,87(6):539-545
Let p be an odd prime number and
. Let
be the classical Stickelberger ideal of the group ring
. Iwasawa [6] proved that the index
equals the relative class number
of
. In [2], [4] we defined for each subgroup H of G a Stickelberger ideal
of
, and studied some of its properties. In this note, we prove that when
mod 4 and [G : H] = 2, the index
equals the quotient
.
Received: 13 January 2006 相似文献
993.
Qingxue Wang 《Advances in Mathematics》2006,206(2):329-357
In this paper, we give a natural construction of mixed Tate motives whose periods are a class of iterated integrals which include the multiple polylogarithm functions. Given such an iterated integral, we construct two divisors A and B in the moduli spaces of n-pointed stable curves of genus 0, and prove that the cohomology of the pair is a framed mixed Tate motive whose period is that integral. It generalizes the results of A. Goncharov and Yu. Manin for multiple ζ-values. Then we apply our construction to the dilogarithm and calculate the period matrix which turns out to be same with the canonical one of Deligne. 相似文献
994.
In this paper we extend Champernowne’s construction of a normal sequence in base b to the
case and obtain an explicit construction of the generic point of the
shift transformation of the set
. We prove that the intersection of the constructed configuration with an arbitrary polynomial curve in the plane is a normal
sequence in base b. 相似文献
995.
We prove that the explicit formula in a symmetric case for a triple (Z,
, Φ) in Jorgenson-Lang’s fundamental class of functions holds for a larger class of (not necessarily differentiable or even
continuous) test functions. As one of the most important applications, we show that the Selberg trace formula for a strictly
hyperbolic cocompact Fuchsian group Γ is valid for a larger class of test functions. Further applications to growth estimates
for the logarithmic derivative of the Selberg zeta function are considered. 相似文献
996.
We define 〈q, r〉-linear arithmetical functions attached to the 〈q, r〉-number systems and give a necessary and sufficient condition for their generating power series to be algebraically independent
over
. We also deduce algebraic independence of the functions values at a nonzero algebraic number in the circle of convergence. 相似文献
997.
We study the problem of best approximations of a vector
by rational vectors of a lattice
whose common denominator is bounded. To this end we introduce successive minima for a periodic lattice structure and extend
some classical results from geometry of numbers to this structure. This leads to bounds for the best approximation problem
which generalize and improve former results. 相似文献
998.
999.
We introduce a new class of adelic heights on the projective line. We estimate their essential minimum and prove a result
of equidistribution (at every place) for points of small height with estimates on the speed of convergence. To each rational
function R in one variable and defined over a number field K, is associated a normalized height on the algebraic closure of K. We show that these dynamically defined heights are adelic in our sense, and deduce from this equidistribution results for
preimages of points under R at every place of K. Our approach follows that of Bilu, and relies on potential theory in the complex plane, as well as in the Berkovich space
associated to the projective line over , for each prime p.
Le premier auteur tient à remercier chaleureusement le project MECESUP UCN0202, ainsi que l'ACI ``Systèmes Dynamiques Polynomiaux'
qui ont permis son séjour à l'Université Catholique d'Antofagasta. Le deuxième auteur est partiellement soutenu par le projet
FONDECYT N 1040683. Enfin, nous remercions le rapporteur pour sa lecture détaillée de l'article. 相似文献
1000.
For a number fieldF, we prove that any tame D4-extensionN/F has a normal integral basis (NIB) if and only if any tame (2, 2)-extensionK/F has a NIB. 相似文献