Numerical application of Euler's series transformation and its generalizations

Summary A nonlinear generalizationÊ _z of Euler's series transformation is compared with the (linear) Euler-Knopp transformationE _z and a twoparametric methodE . It is shown how to applyE orE _, to compute the valuef(z_o) of a functionf from the power series at 0 iff is holomorphic in a half plane or in the cut plane. BothE andE _, are superior toÊ _z . A compact recursive algorithm is given for computingE andE _,.     

Effective computation of periodic orbits and bifurcation diagrams in delay equations

Summary By employing a numerical method which uses only rather classical tools of Numerical Analysis such as Newton's method and routines for ordinary differential equations, unstable periodic solutions of differential-difference equations can be computed. The method is applied to determine bifurcation diagrams with backward bifurcation.Dedicated to Professor Lothar Collatz on the occasion of his 70th birthdayThis paper has been read at the Conference of Numerical Mathematicians, Zeist, The Netherlands, October 12–15, 1979     

1-(2-吡啶偶氮)-2-萘酚薄膜的非线性光学特性研究

运用Ｚ扫描方法研究了１－（２－吡啶偶氮）－２－萘酚薄膜的非线性光学特性。用皮秒脉冲激光测得在５３２ ｎｍ 处、光强较低时χ（３）Ｒ ＝ １．２９×１０－ ９ ｅｓｕ, β＝ ４２ ｃｍ ／ＧＷ; 同时研究了不同光脉冲能量时的非线性吸收特性, 发现其非线性吸收随着光强的增大由反饱和吸收转为饱和吸收     

Commutator representations of differential calculi on the quantum group SUq(2)

Let (Γ, d) be the 3D-calculus or the 4D_±-calculus on the quantum group SU_q (2). We describe all pairs (π, F) of a ^*-representation π of (SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF, π(x)] for x ε (SU_q (2)). As an application commutator representations of the two-dimensional left-covariant calculus on Podles quantum 2-sphere S_qc² with c = 0 are given.     

Effect of parametric modulation on pattern formation in reaction diffusion systems

Reaction diffusion systems can exhibite both spatial and temporal patterns. We show that the effect of spatial variation of the removal rate can have significant effect on the stability boundaries. In particular there can be a case of parametric resonance. Received 11 March 1998     

Stochastic resonance and transient bimodality

Summary The phenomenon of stochastic resonance is predicted in a monostable system displaying transient bimodality during the evolution. The signal-to-noise ratio as a function of the noise intensity calculated within the rate equation theory with many simplifying assumptions exhibits a promising peak. The numerical simulations are also reported. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

Non-dynamical stochastic resonance: Theory and experiments with white and various coloured noises

Summary We describe the simplest system which shows stochastic resonance. A linear(ized) theory for white and (almost) arbitrarily coloured noise is presented. The presented new system has new, unique properties which originate from itsnon-dynamical character; for example, the strength and phase shift of periodic response of the system is independent of the frequency. Experiments have been carried out with the following noise processes: (physical) white noise, (physical) Lorentzian noise and (physical) 1/f noise. With a small extension of the system, its linear-response regime can be significantly increased. As the system is similar to some simple models of neurones, the new results might have not only physical but also biological importance. Paper presented at the International Workshop “Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena”, Elba, 5–10 June 1994.     

Discrete Green's Function for Lattice Random Walk

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U(1) symmetry in the current algebra and N-fermionic massless Thirring model

Local U(1) symmetry in current algebra constructed by fermions has been found. The symmetry is related to the simplest q-deformation of N-fermions. We give the physical interpretation through the N-fermionic massless Thirring model. The Bethe ansatz wavefunction is also given.     

Synthesizing 0.9PZN–0.1BT by mechanically activating mixed oxides

0.9Pb(Zn_1/3Nb_2/3)–0.1BaTiO₃ (0.9PZN–0.1BT) of perovskite structure has been successfully prepared by mechanically activating mixed oxides of PbO, ZnO, Nb₂O₅, BaO and TiO₂. The novel mechanochemical technique skips the phase-forming calcination step at an intermediate temperature that is always required in both the conventional solid state reaction and chemistry-based precursor routes. Ultrafine 0.9PZN–0.1BT particles of perovskite structure were formed when the constituent oxides were mechanically activated for more than 10 h. The powder was sintered to a density of 96% theoretical density at 1100°C for 1 h. The sintered 0.9PZN–0.1BT exhibits perovskite structure and a peak dielectric constant of 8800 at the Curie temperature of 60°C when measured at a frequency of 100 Hz.