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51.
52.
We analyze the critical length for design purposes of six-dimensional spaces invariant under translations and reflections
containing the functions 1, cos t and sin t. These spaces also contain the first degree polynomials as well as trigonometric and/or hyperbolic functions. We identify
the spaces whose critical length for design purposes is greater than 2π and find its maximum 4π. By a change of variables,
two biparametric families of spaces arise. We call shape preservation region to the set of admissible parameters in order
that the space has shape preserving representations for curves. We describe the shape preserving regions for both families.
To our friend Mariano Gasca on occasion of his 60th birthday
Research partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo. 相似文献
53.
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
54.
M. Abbad R. El. Azouzi M. El. Kamili 《Mathematical Methods of Operations Research》2006,63(3):461-471
In this paper we consider some properties on prices under flow control in a network that is to be shared by noncooperative users. Each user is faced with an optimization problem which is formulated as the minimization of its own criterion subject to constraint on the flows of the other users. The operating points of the network are the Nash equilibria of the underlying routing game. Our objective is to study the behavior of prices of all users when the network designer needs to allocate capacities to network links. For parallel links topologies, we show that degradation of the performances such as prices will not take place, as well as the users may find it beneficial to improve their requests 相似文献
55.
We show that the algorithm presented in an earlier paper by Studniarski (Numer. Math., 55:685–693, 1989) can be applied, after only a small modification, to approximate numerically Clarke’s subgradients of semismooth functions
of two variables. Results of computational testing of this modified algorithm are also reported.
相似文献
56.
57.
Materials from the Mn(0.5−x)CaxTi2(PO4)3 (0≤x≤0.50) solid solution were obtained by solid-state reaction in air at 1000 °C. Selected compositions were investigated by powder X-ray diffraction analysis, 31P nuclear magnetic resonance (NMR) spectroscopy and electrochemical lithium intercalation. The structure of all samples determined by Rietveld analysis is of the Nasicon type with the R
space group. Mn2+/Ca2+ ions occupy only the M1 sites in the Ti2(PO4)3 framework. The divalent cations are ordered in one of two M1 sites, except for the Mn0.50Ti2(PO4)3 phase, where a small departure from the ideal order is observed by XRD and 31P MAS NMR. The electrochemical behaviour of Mn0.50Ti2(PO4)3 and Mn(0.5−x)CaxTi2(PO4)3 phases was characterised in Li cells. Two Li ions can be inserted without altering the Ti2(PO4)3 framework. In the 0≤y≤2 range, the OCV curves of Li//LiyMn0.50Ti2(PO4)3 cells show two main potential plateaus at 2.90 and 2.50–2.30 V. Comparison between the OCV curves of Li//Li(1+y)Ti2(PO4)3 and Li//LiyMn0.50Ti2(PO4)3 shows that the intercalation occurs first in the unoccupied M1 site of Mn0.50Ti2(PO4)3 at 2.90 V and then, for compositions y>0.50, at the M2 site (2.50–2.30 V voltage range). The effect of calcium substitution in Mn0.50Ti2(PO4)3 on the lithium intercalation is also discussed from a structural and kinetic viewpoint. In all systems, the lithium intercalation is associated with a redistribution of the divalent cation over all M1 sites. In the case of Mn0.50Ti2(PO4)3, the stability of Mn2+ either in an octahedral or tetrahedral environment facilitates cationic migration. 相似文献
58.
Christian Erich Zybill Mahmoud Abdel-Hafiez Sami Allam Tharwat El Sherbini 《Progress in Solid State Chemistry》2007,35(2-4):469-480
Ferroelectric thin films form an equilibrium domain structure compatible with their respective crystallographic symmetry. In tetragonal (111) PZT, 90° domains prevail; in (pseudo-tetragonal) (100) SBT both 90° and 180° domains are present. The size of 90° domains has been measured for e.g., PZT as slabs of 15 nm width. Domain size is a result of stress minimization in the film during the paraelectric (PE) → ferroelectric (FE) transition. A precise and regular domain pattern for (111) PZT and (100) SBT films has been investigated in detail by TMSFM. Single domains can be addressed mechanically with the tip of an AFM. Such single domain switching corresponds to a data storage density of 200 Gbit/inch2. Applications of ferroelectric and high- paraelectric materials for e.g., non-volatile data storage replacing DRAM devices or as sensors in infrared cameras are increasingly becoming popular. 相似文献
59.
M. T. Crespo J. M. Los Arcos C. E. Granados M. L. Aceña 《Journal of Radioanalytical and Nuclear Chemistry》1989,130(1):99-110
A new method of analysis of the efficiency of four filters of MnO2 in series which takes into account the reactions induced in plutonium by the sorbent is described. The system of differential equations describing the behaviour of plutonium in water as it passes through the filters is solved and the parameters of the filters are determined for a best fitting of the solutions corresponding to the experimental uncertainties. The method is checked by numerical simulation and then applied to water solutions with a known plutonium concentration and to some experimental results given by other authors. In all occassions the results are consistent with the possibility of determining the contents of plutonium in sea and continental waters with uncertainties of the order of 10%. 相似文献
60.
R. López-Martens J. Mauritsson P. Johnsson K. Varjú A. L’Huillier W. Kornelis J. Biegert U. Keller M. Gaarde K. Schafer 《Applied physics. B, Lasers and optics》2004,78(7-8):835-840
We characterize the temporal structure of high-order harmonic radiation on both the femtosecond and attosecond time scales. The harmonic emission is characterized by mixed-color two-photon ionization with an infrared femtosecond laser using a Mach–Zehnder interferometer where both pump and probe arms travel completely separate paths. In a first experiment, we measure the duration and chirp of individual harmonics. In a second experiment, we resolve, for the first time with this type of setup, the attosecond beating of several harmonics generated under conditions similar to the first experiment. We suggest that the results of both measurements can be combined to determine the full attosecond time structure of the harmonic emission. PACS 32.80.Rm; 42.65.Ky 相似文献