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11.
Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σn≥1 an/(qn ? 1) ? K for non-zero periodic sequences (an) in K of period length ≤ 2. As a corollary, we get a quantitative version of the linear independence over K of 1, the q-harmonic series, and a q-analogue of log 2. A similar result on 1, the q-harmonic series, and a q-analogue of ζ(2) is also proved. Mathematics Subject Classification (2000): 11J72, 11J82 相似文献
12.
This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of
this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical
solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions
are provided. 相似文献
13.
Leif Schrder Christian Schmitz Peter Bachert 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2004,171(2):87
Proton NMR resonances of the endogenous metabolites creatine and phosphocreatine ((P)Cr), taurine (Tau), and carnosine (Cs, β-alanyl-l-histidine) were studied with regard to residual dipolar couplings and molecular mobility. We present an analysis of the direct 1H–1H interaction that provides information on motional reorientation of subgroups in these molecules in vivo. For this purpose, localized 1H NMR experiments were performed on m. gastrocnemius of healthy volunteers using a 1.5-T clinical whole-body MR scanner. We evaluated the observable dipolar coupling strength SD0 (S = order parameter) of the (P)Cr-methyl triplet and the Tau-methylene doublet by means of the apparent line splitting. These were compared to the dipolar coupling strength of the (P)Cr-methylene doublet. In contrast to the aliphatic protons of (P)Cr and Tau, the aromatic H2 (δ = 8 ppm) and H4 (δ = 7 ppm) protons of the imidazole ring of Cs exhibit second-order spectra at 1.5 T. This effect is the consequence of incomplete transition from Zeeman to Paschen-Back regime and allows a determination of SD0 from H2 and H4 of Cs as an alternative to evaluating the multiplet splitting which can be measured directly in high-resolution 1H NMR spectra. Experimental data showed striking differences in the mobility of the metabolites when the dipolar coupling constant D0 (calculated with the internuclear distance known from molecular geometry in the case of complete absence of molecular dynamics and motion) is used for comparison. The aliphatic signals involve very small order parameters S ≈ (1.4 − 3) × 10−4 indicating rapid reorientation of the corresponding subgroups in these metabolites. In contrast, analysis of the Cs resonances yielded S ≈ (113 − 137) × 10−4. Thus, the immobilization of the Cs imidazole ring owing to an anisotropic cellular substructure in human m. gastrocnemius is much more effective than for (P)Cr and Tau subgroups. Furthermore, 1H NMR experiments on aqueous model solutions of histidine and N-acetyl-l-aspartate (NAA) enabled the assignment of an additional signal component at δ = 8 ppm of Cs in vivo to the amide group at the peptide bond. The visibility of this proton could result from hydrogen bonding which would agree with the anticipated stronger motional restriction of Cs. Referring to the observation that all dipolar-coupled multiplets resolved in localized in vivo 1H NMR spectra of human m. gastrocnemius collapse simultaneously when the fibre structure is tilted towards the magic angle (θ ≈ 55°), a common model for molecular confinement in muscle tissue is proposed on the basis of an interaction of the studied metabolites with myocellular membrane phospholipids. 相似文献
14.
Peter Nesvadba Lucienne Bugnon Rosemarie Sift 《Journal of polymer science. Part A, Polymer chemistry》2004,42(13):3332-3341
The synthesis of new 7‐membered diazepanone alkoxyamines [2,2,7,7‐tetramethyl‐1‐(1‐phenyl‐ethoxy)‐[1,4]diazepan‐5‐one ( 3 ) and 2,7‐diethyl‐2,3,7‐trimethyl‐1‐(1‐phenyl‐ethoxy)‐[1,4]diazepan‐5‐one ( 8 )] through the Beckmann rearrangement of piperidin‐4‐one alkoxyamines was developed. Both 3 and 8 were evaluated as initiators and regulators for the nitroxide‐mediated radical polymerization of styrene and n‐butyl acrylate. 8 , a sterically highly hindered alkoxyamine readily available as a crystalline solid, allowed the fast and controlled polymerization and preparation of polymers with low polydispersity indices (1.2–1.4) up to a degree of polymerization of about 100. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3332–3341, 2004 相似文献
15.
Hans‐Peter Brack Denise Ruegg Heinrich Bührer Michal Slaski Selmiye Alkan Günther G. Scherer 《Journal of Polymer Science.Polymer Physics》2004,42(13):2612-2624
The influence of irradiation and grafting on the crystallinity of three base polymers has been investigated with differential scanning calorimetry. Grafting has the largest effect on the base polymer crystallinity and results in a reduction of the crystallinity. The thermal degradation of the base polymers and grafted films has been investigated with thermogravimetric analysis. The extent of the fluorination of the base polymer, the irradiation method, and the graft level all influence the thermal degradation and its activation energy. It is proposed that the variation of the chain lengths of the grafted polystyrene chains is actually a primary underlying factor responsible for the influence of these various parameters on the degradation process. The first results of a comparative thermal analysis of some fuel‐cell membranes are also presented, and the promise and shortcomings of this method are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2612–2624, 2004 相似文献
16.
17.
Fabio A. C. C. Chalub Peter A. Markowich Benoît Perthame Christian Schmeiser 《Monatshefte für Mathematik》2004,142(1-2):123-141
Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal 相似文献
18.
We propose means for computing the Fourier expansions of periodic
functions appearing in higher moments of the sum-of-digits
function and in the solutions of some divide-and-conquer
recurrences. The expansions are shown to be absolutely
convergent. We also give a new approach to efficiently compute
numerically the coefficients involved to high precision. 相似文献
19.
Peter Naur 《BIT Numerical Mathematics》1986,26(2):175-187
The questions raised by A. M. Turing in his paper on thought and machines are discussed. Human thought is considered in turn as a concept of normal language usage, as a basic concept of psychology, and as the basis of intellectual activity. It is concluded that neither of these notions of thought identifies something specific that a human being can or cannot do. The imitation game proposed by Turing for deciding whether a machine can think is found to result from an arbitrary empoverishment of the channel of communication between the interrogator and the item under investigation. Turing's notions of thinking are shown to lead to logical difficulties. An alternative view of consciousness, that would place it beyond the reach of any finite test, is finally discussed. 相似文献
20.
This paper shows that the dimension of internal structure of a component can be measured remotely to a resolution better than 5 μm by use of the combination of high resolution optical microscopy and image processing.A specialised high resolution, long working distance and diffraction limited lens was used to image within the component. A series of digital images were made to map spatially the interior of the component. An edge detector was then used to localise the specific location of features in order that an accurate internal measurement could be made. A visualisation of the internal surface finish was also achieved. 相似文献