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241.
Generators of some Ramanujan formulas 总被引:2,自引:0,他引:2
Jesús Guillera 《The Ramanujan Journal》2006,11(1):41-48
In this paper we prove some Ramanujan type formulas for 1/π but without using the theory of modular forms. Instead we use
the WZ—method created by H. Wilf and D. Zeilberger and find some hypergeometric functions in two variables which are second
components of WZ—pairs than can be certified using Zeilberger's EKHAD package. These certificates have an additional property
which allows us to get generalized Ramanujan's type series which are routinely proven by computer. We call these second hypergeometric
components of the WZ—pairs generators. Finding generators seems a hard task but using a kind of experimental research (explained
below), we have succeeded in finding some of them. Unfortunately we have not found yet generators for the most impressive
Ramanujan's formulas. We also prove some interesting binomial sums for the constant 1/π2. Finally we rewrite many of the obtained series using pochhammer symbols and study the rate of convergence.
2000 Mathematics Subject Classification Primary—33C20 相似文献
242.
A palladium‐TPPTS catalyst heterogenized on KF/alumina has been shown to be effective and recyclable for the selective formation of monooctadienylxylopyranosides via the telomerization of butadiene with D ‐xylose. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
243.
带干扰的Erlang(2)风险模型的不破产概率 总被引:1,自引:0,他引:1
本文讨论了带干扰的Erlang(2)风险模型,通过构造一个延迟更新过程,我们得到了不破产概率满足的积分-微分方程,进而得到了不破产概率的明确表达式. 相似文献
244.
Teruyuki Yorioka 《Mathematical Logic Quarterly》2006,52(2):203-216
We prove the iteration lemmata, which are the key lemmata to show that extensions by Pmax variations satisfy absoluteness for Π2-statements in the structure 〈H (ω 2), ∈, NSω 1, R 〉 for some set R of reals in L (ℝ), for the following statements: (1) The cofinality of the null ideal is ℵ1. (2) There exists a good basis of the strong measure zero ideal. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
245.
T. Rajagopalan J.A. Lubguban S. Gangopadhyay J. Sun S.L. Simon R. Butler 《Applied Surface Science》2006,252(18):6323-6331
Hexamethyldisilazane (HMDS) vapor treatment of plasma-damaged nanoporous organosilicate thin films has been studied as a function of treatment temperature in this work. Although, the HMDS vapor treatment facilitated incorporation of methyl (CH3) groups subsequent to the removal of free hydroxyl (OH) groups in the damaged films at treatment temperature as low as 55 °C, the bonded OH groups were not removed. More significantly, detailed analysis of the results reveals that HMDS vapor modified only the surface of the plasma-damaged samples and not the entire film as expected. This is attributed to the formation of a thin solid layer on the surface, which effectively prevents penetration of HMDS vapors into the bulk. The Fourier transform-infrared (FT-IR) absorption and dielectric constant measurements confirm that the vapor treatment assists only partial curing of the plasma-damaged films. Alternative processes of curing the films with HMDS dissolved in supercritical carbon dioxide (SCCO2) as a medium of reaction in static and pulsed modes were also attempted and the results are presented in this paper. 相似文献
246.
V. V. Panić A. B. Dekanski S. K. Milonjić V. B. Mišković-Stanković B. Ž. Nikolić 《Russian Journal of Electrochemistry》2006,42(10):1055-1060
Electrocatalytic properties of RuO2/Ti anode with different coating masses, which are prepared by the alkoxide sol-gel procedure, are investigated in chlorine
and oxygen evolution reactions by polarization measurements and electrochemical impedance spectroscopy in H2SO4 and NaCl electrolytes. According to polarization measurements, the activity of anodes at overpotentials below 100 mV is independent
of coating mass. However, impedance measurements above 100 mV reveal changes in the activity of anodes in chlorine evolution
reaction for different coating masses. The diffusion limitations related to the evolved chlorine are registered in low-frequency
domain at 1.10 V (SCE), diminishing with the increase in potential to the 1.15 V (SCE). The observed impedance behavior is
discussed with respect to the activity model for activated titanium anodes in chlorine evolution reaction involving formation
of gas channels within porous coating structure. Gas channels enhance the mass transfer rate similarly to the forced convection,
which also increases the activity of anode. This is more pronounced for the anode of greater coating mass due to its more
compact surface structure. The more compact structure appears to be beneficial for gas channels formation.
Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 10, pp. 1173–1179.
The text was submitted by the authors in English. 相似文献
247.
Chenghang Wang 《Applied Surface Science》2006,253(4):2282-2288
In this paper, thin films of titanium oxide imprinted with O,O-dimethyl-(2,4-dichlorophenoxyacetoxyl)(3′-nitrobenyl) methinephosphonate (Phi-NO2) were prepared via liquid phase deposition (LPD) method on a glassy carbon electrode. The imprinted molecular in the films was removed by treatment with immersion in CH2Cl2. X-ray diffraction (XRD) and electrochemical methods were introduced to show the evidence of the molecular imprinting phenomenon. It was also found that the recognition ability of the sensor depended on the substituents associated with tridimensional structures of the nitro-compounds. Under the optimized condition, the sensor showed better sensitivity, selectivity and reproducibility to the imprinted molecule and the linear relationship between the current and the concentration of analyte in the range of 0.1-50 μM was obtained. LPD proved to be a powerful method for imprinting titanium oxide thin sense films. 相似文献
248.
采用溶胶-凝胶工艺与原位生长技术,制备了ZnSe/SiO2复合薄膜.X射线衍射分 析表明薄膜中ZnSe晶体呈立方闪锌矿结构.X射线荧光分析结果显示薄膜中Zn与Se摩尔比为1 ∶1.01—1∶1.19.利用场发射扫描电子显微镜观察了复合薄膜的表面形貌,结果表明复合薄 膜表面既存在尺寸约为400nm的ZnSe晶粒,也存在尺寸小于100nm的ZnSe晶粒.利用椭偏仪测 量了薄膜椭偏角Ψ,Δ与波长λ的关系,采用Maxwell-Garnett有效介质理论对薄膜的光学 常数、厚度、气孔率、ZnS
关键词:
2复合薄膜')" href="#">ZnSe/SiO2复合薄膜
光学性质
椭偏光度法
荧光光谱 相似文献
249.
250.
In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from l 2, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors. 相似文献