On new third-order convergent iterative formulas

In this paper, we present new iteration methods with cubic convergence for solving nonlinear equations. The main advantage of the new methods are free from second derivatives and it permit that the first derivative is zero in some points. Analysis of efficiency shows that the new methods can compete with Newton’s method and the classical third-order methods. Numerical results indicate that the new methods are effective and have definite practical utility.      

Reverse Mathematics and Grundy colorings of graphs

The relationship of Grundy and chromatic numbers of graphs in the context of Reverse Mathematics is investi‐gated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Further examples of integrable systems in two dimensions

The construction of the second constant of motion of second order for two-dimensional classical systems is carried out in terms ofz=q ₁ +iq ₂ andq=q ₁ −iq ₂. As a result a class of Toda-type potentials admitting second order invariants is explored.     

Non-collision periodic solutions of second order singular dynamical systems

We study the existence of non-collision periodic solutions for second order singular dynamical systems. The repulsive case and the attractive case are dealt with using a unified topological approach. The proof is based on a well-known fixed point theorem for completely continuous operators, involving a new type of cone. We do not need to consider so-called strong force conditions. Moreover, for the repulsive case, the critical case can be covered. Recent results in the literature, even in the scalar case, are complemented, generalized and improved.     

利率相依的离散时间保险风险模型的破产问题

本文对利率具有一阶自回归的离散时间风险模型进行了研究,得到了破产前最大盈余的分布,破产前盈余、破产后赤字与破产前最大盈余的联合分布以及首达某一水平x的时间分布的递推公式.     

A complexity approach to sustainability – Stafford Beer revisited

There is wide acceptance of the need for a more holistic approach to sustainability. However, practical solutions remain elusive and tend to exhibit underlying conflicts between different paradigms and their associated methodologies. This paper argues the need to wield analytical tools that themselves embody the principles of systemic, ecological thinking. We present here a theoretical framework based on complexity science – focused on organisational and second order cybernetics – that highlights our understanding of the concept of sustainability. The paper goes on to reflect upon how current practice would benefit from such an approach.     

Quantitative determination of acyclovir in plasma by near infrared spectroscopy

The aim of this study was to assess the feasibility of near infrared spectroscopy (NIRS) for analysis of acyclovir in plasma. This methodology was based on the direct measurement of the transmission spectra of liquid samples and a multivariate calibration model (partial least squares, PLS) to determine the acyclovir concentration in plasma sample. The PLS calibration set was built on using the spiked samples by mixing different amounts of acyclovir. Concentration of acyclovir in the plasma samples was calculated employing a 6-factors PLS calibration using the spectral information in the range of 6102-5450 cm^− 1. The root mean square errors of prediction (RMSEP) found was 1.21 for acyclovir. The developed PLS-NIRS procedure allows the determination of 120 samples/h does not require any sample pretreatment and avoids waste generation.     

Order selection and pricing methods using flexible quantity and fuzzy approach for buyer evaluation

This paper presents the methods for order selection and pricing of manufacturer (supplier) with make-to-order basis when orders exceed production capacity. By quoting the concepts of triangular fuzzy numbers and linguistic variables, a fuzzy approach to evaluating buyers by taking into account both positive and negative criteria is proposed. According to the classified results of buyers, the orders will be produced with priority, declined, or determined by MIP model. The fixed quantity MIP model and flexible quantity MIP model are employed to determine the produced orders along with the production quantity and the reference amount for price reduction. By applying the concept of TOPSIS, the closeness coefficients for satisfaction grades of orders and for ranking values of buyers are used as the adjusting rates in the final pricing MIP model to set segmented price.     

A note on the second problem of Stokes for Maxwell fluids

New exact solutions corresponding to the second problem of Stokes for Maxwell fluids have been established by means of Laplace transforms. For large times, these solutions reduce to the well-known steady-state solutions which are periodic in time and independent of the initial conditions. Furthermore, the transient solutions are in accordance with the previous solutions obtained using the Fourier sine transform. The required time to get the steady-state is determined by graphical illustrations. This time decreases if the frequency of the velocity increases. The effects of the material parameters on the decay of the transients in time are also investigated by graphs.     

On the Growth and Fixed Points of Solutions of Second Order Differential Equations with Meromorphic Coefficients

In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain that the exponents of convergence of these fixed points are all equal to the order of growth.