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61.
《Discrete Mathematics》2022,345(9):112891
We calculate moments of the so-called Kesten distribution by means of the expansion of the denominator of the density of this distribution and then integrate all summands with respect to the semicircle distribution. By comparing this expression with the formulae for the moments of Kesten's distribution obtained by other means, we find identities involving polynomials whose power coefficients are closely related to Catalan numbers, Catalan triangles, binomial coefficients. Finally, as applications of these identities we obtain various interesting relations between the aforementioned numbers, also concerning Lucas, Fibonacci and Fine numbers. 相似文献
62.
Vladimir Dobrić 《Journal of Theoretical Probability》1994,7(1):129-134
IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f
1+f
2, wheref
1 is Bochner -integrable andf
2 is Pettis -integrable with Pettis norm 0. The decomposition is unique. 相似文献
63.
Continuing the recent work of the second author, we prove that the diophantine equation
for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .
64.
刘文 《应用数学学报(英文版)》1996,12(3):328-331
ASTRONGLIMITTHEOREMFORGENERALIZEDCANTOR-LIKE RANDOM SEQUENCESLIUWEN(刘文)(DepartmentofMathematicsandPhysics,HebeiUniversityofTe... 相似文献
65.
Bjorn Poonen 《Journal of the American Mathematical Society》1996,9(3):783-812
Let be an algebraically closed field containing which is complete with respect to an absolute value . We prove that under suitable constraints on the coefficients, the series converges to a surjective, open, continuous -linear homomorphism whose kernel is locally compact. We characterize the locally compact sub--vector spaces of which occur as kernels of such series, and describe the extent to which determines the series. We develop a theory of Newton polygons for these series which lets us compute the Haar measure of the set of zeros of of a given valuation, given the valuations of the coefficients. The ``adjoint' series converges everywhere if and only if does, and in this case there is a natural bilinear pairing
which exhibits as the Pontryagin dual of . Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.
66.
Samuel S. Wagstaff Jr.. 《Mathematics of Computation》1996,65(213):383-391
We show that the minimum period modulo of the Bell exponential integers is for all primes and several larger . Our proof of this result requires the prime factorization of these periods. For some primes the factoring is aided by an algebraic formula called an Aurifeuillian factorization. We explain how the coefficients of the factors in these formulas may be computed.
67.
Michael Weiss 《Proceedings of the American Mathematical Society》1996,124(2):615-622
Upper bounds obtained by Gromov on the Betti numbers of certain closed Riemannian manifolds are shown to be upper bounds on the minimum number of cells in --spaces dominating such manifolds.
68.
Ionic mobility data for multicomponent electrolyte systems at low concentrations are scarce due to experimental difficulties and are actually restricted to aqueous solutions of alkali chlorides. Some new results are presented which have been obtained by using a radiotracer method valid even if one of the ionic species is present at very low concentrations (tracer ion). The following electrolyte systems (two electrolytes with a common ion in a solvent) have been investigated at a 0.5N total ionic strength: NaNO3–AgNO3, KNO3–AgNO3, LiNO3–AgNO3 either in pure water or in water-rich (acetonitrile or dimethylsulfoxide) mixed solvents. Since ionic conductivity data processing by an extended law generalized to mixtures, such as that proposed by Quint and Viallard, has proved to be delicate to handle, our experimental results have been compared with the qualitative predictions of the classical Onsager-Fuoss limiting law. The main conclusion of this work is to give clear experimental evidence of the inability of any continuum theory to predict the ionic mobilities when solvent structural effect have to be taken into account. Consequently, the ionic behavior, particularly that of the Ag+ ion, has been interpreted in terms of preferential solvation and solvent microscopic structure. The trace mobility measurements reflect the maximum structural effect on the ionic transport properties. 相似文献
69.
L. A. Dunyushkina A. V. Kuz’min V. B. Balakireva V. P. Gorelov 《Russian Journal of Electrochemistry》2006,42(4):375-380
Transport numbers for oxygen ions and protons are measured by an emf method in the system CaTi1?x FexO3?δ (x = 0.1–0.5) in the oxidizing and reducing atmospheres in the temperature interval 973–1173 K. It is shown that the compounds under study are mixed ion-electron conductors at small iron concentrations and electron conductors, at large iron contents. The proton conductivity in the compounds is very poor and does not exceed 0.5% in air. On the basis of the temperature dependences of transport numbers for ions and linear expansion, it is established that the CaTi0.9Fe0.1O3?δ system has a phase transition of a second order in a reducing environment at 1020–1050 K. The total and partial electron conductivities of CaTi0.9Fe0.1O3?δ are studied as a function of the partial pressure of oxygen at 1173 K. The nature of electroconduction in CaTi1?x FexO3?δ is discussed. 相似文献
70.
We implemented ab initio self‐consistent field (SCF) fractional occupation numbers (FON) calculation with Dunlap's interpolation scheme for the twisted ethylene, which is a prototype molecule of a σ–π biradical system. The calculational results are compared with those of complete‐active‐space (CAS) SCF and spin‐unrestricted Kohn–Sham (UKS) calculations on potential surfaces, occupation numbers of natural orbitals, and correlation entropies. It was found that the UKS methods gave similar results to CASSCF, while the FON solutions appeared in only the nearly complete degenerate region. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 317–323, 2003 相似文献