On U(n)-invariant strongly convex complex Finsler metrics

Science China Mathematics - In this paper, we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in ?n to be strongly convex, which also...     

A note on weakly-supplemented subgroups of finite groups

A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = HK. In the paper, we extend one main result of Kong and Liu (2014).     

A Note about Multi-Hilbert Transform on D(ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>)

In this paper, we first prove that, for a non-zero function f∈D(? ⁿ ), its multi-Hilbert transform Hnf is bounded and does not have compact support. In addition, a new distribution space D' _H (? ⁿ ) is constructed and the definition of the multi-Hilbert transform is extended to it. It is shown that D' _H (? ⁿ ) is the biggest subspace of D'(? ⁿ ) on which the extended multi-Hilbert transform is a homeomorphism.     

Dual‐signal amplification strategy for ultrasensitive chemiluminescence detection of PDGF–BB in capillary electrophoresis

Many efforts have been made toward the achievement of high sensitivity in capillary electrophoresis coupled with chemiluminescence detection (CE‐CL). This work describes a novel dual‐signal amplification strategy for highly specific and ultrasensitive CL detection of human platelet‐derived growth factor–BB (PDGF–BB) using both aptamer and horseradish peroxidase (HRP) modified gold nanoparticles (HRP–AuNPs–aptamer) as nanoprobes in CE. Both AuNPs and HRP in the nanoprobes could amplify the CL signals in the luminol–H₂O₂ CL system, owing to the excellent catalytic behavior of AuNPs and HRP in the CL system. Meanwhile, the high affinity of aptamer modified on the AuNPs allows detection with high specificity. As proof‐of‐concept, the proposed method was employed to quantify the concentration of PDGF–BB from 0.50 to 250 fm with a detection limit of 0.21 fm. The applicability of the assay was further demonstrated in the analysis of PDGF–BB in human serum samples with acceptable accuracy and reliability. The result of this study exhibits distinct advantages, such as high sensitivity, good specificity, simplicity, and very small sample consumption. The good performances of the proposed strategy provide a powerful avenue for ultrasensitive detection of rare proteins in biological sample, showing great promise in biochemical analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

CuO nanoparticles supported on carbon microspheres as electrode material for supercapacitors

Ionics - C/CuO nanocomposites were prepared by hydrothermal treatment of copper nitrate with starch, followed by H2O2 oxidation and calcination. Structure characterizations show that high...     

锡苯和铅苯二聚反应的理论研究

采用密度泛函理论B3LYP方法,研究了锡苯和铅苯的[2+2],[4+2]及[4+4]二聚反应的微观机理和势能剖面,考察了Sn(Pb)原子上的2,4,6-三甲基苯基(Mes)取代基对反应势能剖面的影响.研究结果表明,所有反应均为协同过程,且大多数情况下,2个C—Sn(Pb)键同步形成.[2+2]和[4+2]反应在热力学和动力学上均比相应的[4+4]反应容易进行,而[4+2]反应在动力学上比相应的[2+2]反应有利.Sn(Pb)原子上的Mes取代基在热力学和动力学上均不利于反应的进行.铅苯的动力学稳定性与锡苯相当,但其热力学稳定性高于锡苯.     

A fractional order optimal 4D chaotic financial model with Mittag-Leffler law

In this paper, a fractional 4D chaotic financial model with optimal control is investigated. The fractional derivative used in this financial model is Atangana–Baleanu derivative. The existence and uniqueness conditions of solutions for the proposed model are derived based on Mittag-Leffler law. Optimal control is incorporated into the model to maximize output. The Adams–Moulton scheme of the Atangana–Baleanu derivative is utilized to obtain the numerical results which produce new attractors. Euler-Lagrange optimality conditions are determined for the fractional 4D chaotic financial model. The numerical results show that the memory factor has a great influences on the dynamics of the model.     

Lyapunov criteria for the Feller–Dynkin property of martingale problems

We give necessary and sufficient criteria for the Feller–Dynkin property of solutions to martingale problems in terms of Lyapunov functions. Moreover, we derive a Khasminskii-type integral test for the Feller–Dynkin property of multidimensional diffusions with random switching. For one dimensional switching diffusions with state-independent switching, we provide an integral-test for the Feller–Dynkin property.     

Levenberg-Marquardt method with a general LM parameter and a nonmonotone trust region technique

We propose a new Levenberg-Marquardt (LM) method for solving the nonlinear equations. The new LM method takes a general LM parameter \lambda_k=\mu_k[(1-\theta)\|F_k\|^\delta+\theta\|J_k^TF_k\|^\delta] where \theta\in[0,1] and \delta\in(0,3) and adopts a nonmonotone trust region technique to ensure the global convergence. Under the local error bound condition, we prove that the new LM method has at least superlinear convergence rate with the order \min\{1+\delta,4-\delta,2\}. We also apply the new LM method to solve the nonlinear equations arising from the weighted linear complementarity problem. Numerical experiments indicate that the new LM method is efficient and promising.