On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

The K–nucleus cross sections in relativistic non-linear models

The K⁺−nucleus cross sections have been calculated in relativistic non-linear models taking into account the in-medium modifications of nucleons and mesons properties. More precisely, we have taken into account both the dressing of the nucleon effective mass by the scalar nuclear field in the target and the coupling of the mesons exchanged between the K⁺ and the nucleons to the polarization of the medium. First, using the most recent relativistic non-linear models, the in-medium σ, ω and ρ meson masses have been obtained in the nuclear matter rest frame. The influence of the non-linear contributions on the K⁺−nucleus cross sections has then been studied. Finally, we have compared our results with the experimental data.     

An “Instrumental Approach” to Study the Integration of a Computer Tool Into Mathematics Teaching: the Case of Spreadsheets

This article reports on research focused on the integration of a specific computer tool, the spreadsheet, into mathematics teaching. After presenting some important results obtained by research in this area, we revisit these in the light of an instrumental approach, which we perceive as essential to analyse the construction of mathematical meanings in spreadsheet environments and to understand better the questions of technological integration. Then, these theoretical elements are used in order to design an exploratory experiment with grade 7 pupils and analyse its results.     

Approximation of a laminated microstructure for a rotationally invariant,double well energy density

Summary. We give error estimates for the approximation of a laminated microstructure which minimizes the energy for a rotationally invariant, double well energy density . We present error estimates for the convergence of the deformation in the convergence of directional derivatives of the deformation in the “twin planes,” the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient. Received July 25, 1995 / Revised version received November 20, 1995     

Lower bounds for the discrepancy of triples of inversive congruential pseudorandom numbers with power of two modulus

This paper deals with the inversive congruential method with power of two modulusm for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences are studied based on the distribution of triples of successive pseudorandom numbers. It is shown that there exist parameters in the inversive congruential method such that the discrepancy of the corresponding point sets in the unit cube is of an order of magnitude at leastm ^–1/3. The method of proof relies on a detailed analysis of certain rational exponential sums.     

Ab initio study of the electronic structures and conduction properties of some novel low band-gap donor-acceptor polymers

The results of the electronic structures and conduction properties of four novel donor-acceptor polymers based on polysilole, obtained on the basis of ab initio Hartree-Fock crystal orbital method using their optimized geometries, are reported. The repeat unit of these polymers consists of bicyclopentadisilole unit bridged by an electron-accepting group Y(Y=CCH₂ in PSICH, CO in PSICF, CCF₂ and CC(CN)₂ in PSICN). All the polymers on the basis of their geometries and π-bond order values are found to have benzenoid-type electronic structures. Comparison of the important electronic properties such as ionization potential, electron affinity and band-gap of these polymers indicates PSICN to be the best candidate for intrinsic conductivity and reductive (n-) doping while PSICH is predicted to be the best candidate for oxidative (p-) doping. All these polymers are estimated to have band-gap values ranging between 1 and 2 eV. The low band-gap values of these polymers are rationalised on the basis of the patterns of their frontier orbitals.     

Conservation Laws of K(m, n) and mK(m, n) Equations

Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2, n) equations and mnK(m, n) equations are found by using of this approach and some new results have been obtained.     

MEASUREMENTS OF Fe AND Cu K-Shell IONIZATION CROSS SECTIONS BY SLOW ELECTRON IMPACT

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Modeling film flows down inclined planes

A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations. Received: 16 April 1998 / Revised: 29 June 1998 / Accepted: 2 July 1998