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71.
Mikhail Katz 《Israel Journal of Mathematics》2008,164(1):381-395
We show that the existence of a nontrivial Massey product in the cohomology ring H* (X) imposes global constraints upon the Riemannian geometry of a manifold X. Namely, we exhibit a suitable systolic inequality, associated to such a product. This generalizes an inequality proved in
collaboration with Y. Rudyak, in the case when X has unit Betti numbers, and realizes the next step in M. Gromov’s program for obtaining geometric inequalities associated
with nontrivial Massey products. The inequality is a volume lower bound, and depends on the metric via a suitable isoperimetric
quotient. The proof relies upon W. Banaszczyk’s upper bound for the successive minima of a pair of dual lattices. Such an
upper bound is applied to the integral lattices in homology and cohomology of X. The possibility of applying such upper bounds to obtain volume lower bounds was first exploited in joint work with V. Bangert.
The latter work deduced systolic inequalities from nontrivial cup-product relations, whose role here is played by Massey products.
Supported by the Israel Science Foundation (grants no. 620/00, 84/03, and 1294/06) 相似文献
72.
73.
We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in
or
. Our planar structures are actually fitted for a more general class of objects – (β,δ)-covered objects – which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems: (i) finding a perfect containment matching between a set of points and a set of convex fat objects, and (ii) finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor. 相似文献
74.
75.
We determine the smallest number f(n,k) such that every (0,1)-matrix of order n what zero main diagonal which has at least f(n,k) 1's contains an irreducible, principal submatrix of order K. We characterize those matrices with f(n,k)-1 l's having no irreducible, principal submatrix of order k 相似文献
76.
Lateral translocation of electrocatalyst-modified magnetic particles was achieved upon application of an external magnetic field. Programmed electrocatalytic reactions at different electrodes or different areas of an electrode were performed. The spatially controlled electrocatalytic reactions were exemplified with NADH electrocatalytic oxidation and with bioelectrocatalytic electrode patterning. The method will be particularly useful for programmed electrochemical reactions at interdigitated electrodes. 相似文献
77.
78.
J. Katz 《Analytical and bioanalytical chemistry》1907,46(6-7):459-460
79.
We investigated an influence of hydrogen plasma treatment on electrical properties of shaped silicon polycrystals. Hydrogen penetration into polycrystalline silicon is demonstrated to depend on the state of the crystal (as-grown or annealed) and type of grain boundary (general or weakly deviated from special orientations). It is found that interaction of atomic hydrogen with grain boundaries can result not only in decrease of their electrical activity, but also in increase of potential barrier height at relatively high (more than 2 × 1018 cm–2) doses of incorporated hydrogen. This phenomenon is explained by a phenomenological model which takes into account passivation of grain boundary dangling bonds and boron atoms in the bulk as two main mechanisms controlling hydrogenation effect. 相似文献
80.
Alan R. Katz 《Letters in Mathematical Physics》1986,12(4):329-342
The semi-classical superspace pseudomechanics of Casalbuoni and others is shown to be the classical limit of a scalar superfield theory by a WKB type of approximation. By avoiding second class constraints, the relationship between the mechanics and the field theory is clarified. The spin1/2sector is then examined to find the (semiclassical) WKB limit of the Dirac equation. 相似文献