A cubically convergent Newton-type method under weak conditions

Under weak conditions, we present an iteration formula to improve Newton's method for solving nonlinear equations. The method is free from second derivatives, permitting f^′(x)=0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative. Analysis of convergence demonstrates that the new method is cubically convergent. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newton's method.     

A new smoothing Newton-type method for second-order cone programming problems

A new smoothing function of the well-known Fischer–Burmeister function is given. Based on this new function, a smoothing Newton-type method is proposed for solving second-order cone programming. At each iteration, the proposed algorithm solves only one system of linear equations and performs only one line search. This algorithm can start from an arbitrary point and it is Q-quadratically convergent under a mild assumption. Numerical results demonstrate the effectiveness of the algorithm.     

High sensitivity chemiluminescence enzyme immunoassay for detecting staphylococcal enterotoxin A in multi-matrices

In this study, detection of staphylococcal enterotoxin A (SEA) in multi-matrices using a highly sensitive and specific microplate chemiluminescence enzyme immunoassay (CLEIA) has been established. A pair of monoclonal antibodies (mAbs) was selected from 37 anti-SEA mAbs by pairwise analysis, and the experimental conditions of the CLEIA were optimized. This CLEIA exhibited high performance with a wide dynamic range from 6.4 pg mL⁻¹ to 1600 pg mL⁻¹, and the measured low limit of detection (LOD) was 3.2 pg mL⁻¹. No cross-reactivity was observed when this method was applied to test SEB, SEC1, and SED. It has also been successfully applied for analyzing SEA in a variety of environmental, biological, and clinical matrices, such as sewage, tap water, river water, roast beef, peanut butter, cured ham, 10% nonfat dry milk, milk, orange juice, human urine, and serum. Thus, the highly sensitive and SEA-specific CLEIA should make it attractive for quantifying SEA in public health and diagnosis in near future.     

Perturbation analysis for the positive definite solution of the nonlinear matrix equation X-\sum_{i=1}^{m} A_{i}^{*}X^{-1}A_{i}=Q

Consider the perturbation analysis for positive definite solution of the nonlinear matrix equation $X-\sum_{i=1}^{m}A_{i}^{*}X^{-1}A_{i}=Q$ which arises in an optimal interpolation problem. Two perturbation bounds for the unique positive definite solution are obtained, and an explicit expression of the condition number for the unique positive definite solution is derived. The theoretical results are illustrated by several numerical examples.     

The convergence of a modified smoothing-type algorithm for the symmetric cone complementarity problem

The symmetric cone complementarity problem (denoted by SCCP) is a broad class of optimization problems, which contains the semidefinite complementarity problem, the second-order cone complementarity problem, and the nonlinear complementarity problem. In this paper we first extend the smoothing function proposed by Huang et al. (Sci. China 44:1107–1114, 2001) for the nonlinear complementarity problem to the context of symmetric cones and show that it is coercive under suitable assumptions. Based on this smoothing function, a smoothing-type algorithm, which is a modified version of the Qi-Sun-Zhou method (Qi et al. in Math. Program. 87:1–35, 2000), is proposed for solving the SCCP. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. Preliminary numerical results for some second-order cone complementarity problems are reported which indicate that the proposed algorithm is effective.     

High-temperature impedance spectroscopy of BaFe0.5Nb0.5O3 ceramics doped with Bi0.5Na0.5TiO3

Bi_0.5Na_0.5TiO₃ (BNT)-doped BaFe_0.5Nb_0.5O₃ (BFN) ceramics were synthesized by a two-step solid-state reaction. Temperature dependence of dielectric properties measured at different frequencies was investigated over broad temperature and frequency ranges. Impedance spectroscopy and universal dielectric response were employed to study the relaxation behavior and conductivity mechanism of the ceramics in a frequency range from 40 Hz to 100 MHz and a temperature range from 300 K to 800 K. The complex plane impedance data revealed the bulk and grain boundary contributions toward conductivity processes in the form of semicircular arcs. The high-temperature conductivity of ceramics is attributable to thermally activated second ionized oxygen vacancy.     

接枝改性PVDF基含氟聚合物

聚偏氟乙烯(PVDF基)含氟聚合物由于其独特的性能受到了广泛的关注。将功能化链段引入PVDF基含氟聚合物可以进一步提升其性能并拓展其应用领域。相较于物理共混法和直接共聚改性法,通过接枝改性法将功能化单体引入含氟聚合物的侧链具有更显著的优势,可便捷、高效地得到组成精确,结构可控的接枝共聚物。本文综述了通过活性自由基聚合(包括ATRP、SET-LRP、有机催化原子转移自由基聚合(O-ATRP)、光诱导Cu(Ⅱ)介导RDRP)和高能射线辐射(γ射线,紫外,电子束)等对PVDF基含氟聚合物功能化接枝改性的方法,并对其发展趋势以及改性聚合物的应用前景进行了展望。     

A new one‐step smoothing newton method for the second‐order cone complementarity problem

In this paper, we present a new one‐step smoothing Newton method for solving the second‐order cone complementarity problem (SOCCP). Based on a new smoothing function, the SOCCP is approximated by a family of parameterized smooth equations. At each iteration, the proposed algorithm only need to solve one system of linear equations and perform only one Armijo‐type line search. The algorithm is proved to be convergent globally and superlinearly without requiring strict complementarity at the SOCCP solution. Moreover, the algorithm has locally quadratic convergence under mild conditions. Numerical experiments demonstrate the feasibility and efficiency of the new algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

A smoothing Newton method for the second-order cone complementarity problem

In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore, we prove that the generated sequence is bounded if the solution set of the SOCCP is nonempty and bounded. Under the assumption of nonsingularity, we establish the local quadratic convergence of the algorithm without the strict complementarity condition. Numerical results indicate that the proposed algorithm is promising.     

Influence of programming strain rates on the shape‐memory performance of semicrystalline multiblock copolymers

Multiblock copolymers named PCL‐PIBMD consisting of crystallizable poly(ε‐caprolactone) segments and crystallizable poly[oligo(3S‐iso‐butylmorpholine‐2,5‐dione)] segments coupled by trimethyl hexamethylene diisocyanate provide a versatile molecular architecture for achieving shape‐memory effects (SMEs) in polymers. The mechanical properties as well as the SME performance of PCL‐PIBMD can be tailored by the variation of physical parameters during programming such as deformation strain or applied temperature protocols. In this study, we explored the influence of applying different strain rates during programming on the resulting nanostructure of PCL‐PIBMD. Programming was conducted at 50 °C by elongation to ε_m = 50% with strain rates of 1 or 10 or 50 mm min^?1. The nanostructural changes were visualized by atomic force microscopy (AFM) measurements and investigated by in situ wide and small angle X‐ray scattering experiments. With increasing the strain rate, a higher degree of orientation was observed in the amorphous domains. Simultaneously the strain‐induced formation of new PIBMD crystals as well as the fragmentation of existing large PIBMD crystals occurred. The observed differences in shape fixity ratio and recovery stress of samples deformed with various strain rates can be attributed to their different nanostructures. The achieved findings can be relevant parameters for programming the shape‐memory polymers with designed recovery forces. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1935–1943