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11.
By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.  相似文献   
12.
The eigenvalue and the stability of singular differential systems with delay are considered. Firstly we investigate some properties of the eigenvalue, then give the exact exponential estimation for the fundamental solution, and finally discuss the necessary and sufficient condition of uniform asymptotic stability.  相似文献   
13.
We study factorisation in the ring of exponential polynomials and provide a proof of Ritt's factorisation theorem in modern notation and so generalised as to deal with polynomial coefficients as well as with several variables. We do this in the more general context of a group ring of a divisible torsion-free ordered abelian group over a unique factorisation domain.

  相似文献   

14.
The existence of global smooth solutions to the multi-dimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics.  相似文献   
15.
We consider quasi-isometric mappings of domains in multidimensional Euclidean spaces. We establish that a mapping depends continuously in the sense of the topology of Sobolev classes on its metric tensor to within isometry of the space. In the space of metric tensors we take the topology determined by means of almost everywhere convergence. We show that if the metric tensor of a mapping is continuous then the length of the image of a rectifiable curve is determined by the same formula as in the case of mappings with continuous derivatives. (Continuity of the metric tensor of a mapping does not imply continuity of its derivatives.)  相似文献   
16.
For exponential weights, a necessary condition of weighted mean convergence for Lagrange interpolation is given.  相似文献   
17.
We present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields. Our method is based on coupling and does not use information inequalities. In case one has a uniform control on the coupling, one obtains exponential concentration inequalities. If such a uniform control is no more possible, then one obtains polynomial or stretched-exponential concentration inequalities. Our abstract results apply to Gibbs random fields, both at high and low temperatures and in particular to the low-temperature Ising model which is a concrete example of non-uniformity of the coupling.   相似文献   
18.
二元域上n数组空间上的非线性置换在分组码,杂凑函数与流密码等密码学领域中有重要应用.域GF(2n)上的幂函数提供了二元域上n数组空间上的一类非线性置换.本文着重研究幂函数的强完全性、完全性与非线性度等密码学性质.作为结果,本文证明了幂函数具有完全性;证明了具有强完全性的函数必有较高的拓扑非线性度;木文找到一类具有强完全性的幂函数;周时也定出了幂函数的代数非线性度.  相似文献   
19.
A method has been developed to determine the boiling point distribution of sulfur compounds in light cycle oils (LCO'S). The method chosen for this analysis was GC with a flame photometric detector (FPD) and pyrolyzer. Tests were carried out to evaluate the recovery efficiency, repeatability, and accuracy of the method. Repeatabilities within 2% were obtained. The recovery of benzothiophenes and dibenzothiophenes was close to 100%; this was important because these are the major sulfur components in LCO's. No hydrocarbon or solvent interferences were observed with the use of the pyrolyzer, even for a 95% solvent level. Comparison with results from other techniques showed that the method accurately determined the levels of sulfur compounds in the LCO boiling point range.  相似文献   
20.
LetK be a quadratic Geld, and letR(N) be the number of integer ideals inK with norm at most AT. Letx with conductork be the quadratic character associated withK. Then |R(N)−NL(1,x)|⩽Bk 50/73 N 23/73(logN)461/146 forNAk, whereA andB are constants. ForNAk c,C sufficiently large, the factork 50/73 may be replaced by (d(k))4/73 k 46/73. Dedicated to the memory of Professor K G Ramanathan  相似文献   
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