On multistep interval methods for solving the initial value problem

In this paper we shortly complete our previous considerations on interval versions of Adams multistep methods [M. Jankowska, A. Marciniak, Implicit interval multistep methods for solving the initial value problem, Comput. Meth. Sci. Technol. 8(1) (2002) 17–30; M. Jankowska, A. Marciniak, On explicit interval methods of Adams–Bashforth type, Comput. Meth. Sci. Technol. 8(2) (2002) 46–57; A. Marciniak, Implicit interval methods for solving the initial value problem, Numerical Algorithms 37 (2004) 241–251]. It appears that there exist two families of implicit interval methods of this kind. More considerations are dealt with two new kinds of interval multistep methods based on conventional well-known Nyström and Milne–Simpson methods. For these new interval methods we prove that the exact solution of the initial value problem belongs to the intervals obtained. Moreover, we present some estimations of the widths of interval solutions. Some conclusions bring this paper to the end.     

An analysis of the order of Runge-Kutta methods that use an iterative scheme to compute their internal stage values

We employ B-series to analyze the order of Runge-Kutta (RK) methods that use simple iteration, modified Newton iteration or full Newton iteration to compute their internal stage values. Our assumptions about the initial guess for the internal stage values cover a wide range of practical schemes. Moreover, the analytical techniques developed in this paper can be applied in many other similar contexts.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, the Information Technology Research Centre of Ontario, and the Norwegian Research Council for Science and Humanities.     

The Connectedness of Space Curve Invariants

In this paper we will give necessary conditions for a Borel-fixed monomial ideal to be the generic initial ideal of a reduced, irreducible, non-degenerate curve in P³.     

小型可变坡水槽的结构及其特点

可变坡水槽作为研究水流及泥沙运动特性和水力学实验的一种设备已被广泛应用，本文论述了作者所研制的小型可变坡水槽的结构及其特点。     

Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations

We introduce the notion of signature for relations in mapping class groups and show that the signature of a Lefschetz fibration over the 2-sphere is the sum of the signatures for basic relations contained in its monodromy. Combining explicit calculations of the signature cocycle with a technique of substituting positive relations, we give some new examples of non-holomorphic Lefschetz fibrations of genus and which violate slope bounds for non-hyperelliptic fibrations on algebraic surfaces of general type.

     

基于自适应斜坡补偿的双环电流模DC/DC混沌控制

提出了一种自适应斜坡补偿方法,将该方法引入到双环电流模buck DC/DC的混沌控制中,并给出实现该方法的电路结构.建立了双环电流模DC/DC系统稳定性分析的离散模型,理论分析了自适应斜坡补偿在双环控制下系统的稳定性条件,推导出了自适应因子k与系统工作的最大占空比的关系式.仿真结果表明该方法可有效控制系统的分岔和混沌现象,提高系统的工作范围和动态响应速度.     

Design considerations of depressed clad W-shaped single mode dispersion compensating fibers

Dispersion compensating fibers (DCFs) are being widely used as dispersion compensation techniques because of its superior characteristics. This work reports the theoretical modelling of a single mode DCF having W-shaped shallow as well as deeply depressed clad profile. The DCFs have been designed and optimized by suitable adjusting different fiber parameters such as, central relative index difference (Δ⁺), inner core radius (a), depression depth parameter (ρ), normalized end position of the depressed clad (p), etc. at a given spot size . The figure of merit (FOM) characteristics including the bend loss as well as other losses associated with fiber manufacturing technique have been thoroughly investigated. Performances of these DCFs for recent wavelength division multiplexing (WDM) transmission system have also been discussed. By adjusting different fiber parameters, the effective core area (A_eff) of the above DCFs can be controlled to minimize the effect of non-linearities on them.     

BABAR measurement of baryon time-like form factors via initial state radiation

BABAR has measured with unprecedented accuracy the e^＋e^- → pp and e^＋e^- →∧∧ cross sections by means of the initial state radiation technique, which has the advantages of good efficiency, good energy resolution and full angular acceptance, even exactly at threshold. A peculiar feature of these cross sections is their non-vanishing values at threshold. In the case of charged baryons, this phenomenon is expected according to the Coulomb interaction between the outgoing baryon and antibaryon. Once this Coulomb enhancement factor is taken into account, the striking result is achieved that the proton form factor at threshold is ｜GP（4Mp^2）｜ = 1, that is what is expected for pointlike fermion pairs, in spite of the proton structure. However a Coulomb enhancement factor is not expected for neutral fermions, likely in contradiction with the BABAR data. Qualitatively this behaviour is consistent with Coulomb interactions at the valence quark level.     

ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra

This case study investigates the impact of the integration of information and communications technology (ICT) in mathematics visualization skills and initial teacher education programmes. It reports on the influence GeoGebra dynamic software use has on promoting mathematical learning at secondary school and on its impact on teachers’ conceptions about teaching and learning mathematics. This paper describes how GeoGebra-based dynamic applets – designed and used in an exploratory manner – promote mathematical processes such as conjectures. It also refers to the changes prospective teachers experience regarding the relevance visual dynamic representations acquire in teaching mathematics. This study observes a shift in school routines when incorporating technology into the mathematics classroom. Visualization appears as a basic competence associated to key mathematical processes. Implications of an early integration of ICT in mathematics initial teacher training and its impact on developing technological pedagogical content knowledge (TPCK) are drawn.