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41.
On the Validations of the Asymptotic Matching Conjectures 总被引:1,自引:0,他引:1
In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies,
which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p∈[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs. 相似文献
42.
The excitation function of the reaction7Li(d, α)5He has been measured between 0.6 and 2.0 MeV in steps of 50 keV. The two resonances at 0.75 and 1.00 MeV corresponding to the levels at 17.28 and 17.48 of the compound nucleus9Be were resolved. Angular distribution measurements were performed at 14 different energies mainly near the 1.00 MeV resonance. From the analysis of the data the 17.28 MeV level seems to be a positive parity state (3/2+ → 7/2+) whilst a negative parity (7/2? or 9/2?) is indicated for the 17.48 MeV level. This is contrary to the order of parities as given in the literature. 相似文献
43.
44.
This note contains two types of small ball estimates for random vectors in finite-dimensional spaces equipped with a quasi-norm. In the first part, we obtain bounds for the small ball probability of random vectors under some smoothness assumptions on their density function. In the second part, we obtain Littlewood–Offord type estimates for quasi-norms. This generalizes results which were previously obtained in Friedland and Sodin (C R Math Acad Sci Paris 345(9):513–518, 2007), and Rudelson and Vershynin (Commun Pure Appl Math 62(12):1707–1739, 2009). 相似文献
45.
Shmuel Friedland 《Israel Journal of Mathematics》1980,35(1-2):89-108
LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈
p
B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a
B(ε) ifB(ε)=T(ε)A(ε)T
−1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈
a
B(ε) provided thatA(ε)≈
p
B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the
origin and was first stated by Wasow.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 相似文献
46.
47.
Shmuel Friedland 《Proceedings of the American Mathematical Society》1997,125(12):3519-3526
We give a relatively simple proof that the orthogonal group over the integers is the unique finite subgroup (up to a conjugation) in of the maximal order for .
48.
Shmuel Friedland 《Linear algebra and its applications》1975,12(2):127-137
Let A be an n×n complex-valued matrix, all of whose principal minors are distinct from zero. Then there exists a complex diagonal matrix D, such that the spectrum of AD is a given set σ = {λ1,…,λn} in C. The number of different matrices D is at most n!. 相似文献
49.
M. Asche K. J. Friedland P. Kleinert H. Kostial J. Herzog R. Hey 《Superlattices and Microstructures》1991,10(4)
The phase coherence length of the electrons is determined by magnetoconductivity for a wide range of sheet concentrations of Si-donors and free electrons. For diffusive carrier motion a comparison of the experimental and theoretical results for weak fields shows that the weak localisation is limited by inelastic electron-electron-scattering as expected for disturbed systems. For higher magnetic fields the role of mutual electron-electron interaction is also significant. 相似文献
50.
Let λ
d
(p) be the p monomer-dimer entropy on the d-dimensional integer lattice ℤ
d
, where p∈[0,1] is the dimer density. We give upper and lower bounds for λ
d
(p) in terms of expressions involving λ
d−1(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of ℤ
d
is bounded above by λ
d
(p). We compute the first three terms in the formal asymptotic expansion of λ
d
(p) in powers of
\frac1d\frac{1}{d}. We prove that the lower asymptotic matching conjecture is satisfied for λ
d
(p). Converted to a power series in p, our “formal” expansion shows remarkable validity in low dimensions, d=1,2,3, in which dimensions we give some numerical studies. 相似文献