A note on iterative roots of PM functions

In this paper we study iterative roots of PM functions, a special class of non-monotone functions. Problem 2 in [W. Zhang, PM functions, their characteristic intervals and iterative roots, Ann. Polon. Math. LXV (1997) 119-128] is solved partly and Theorem 4 in that paper is generalized.     

A weak Kantorovich existence theorem for the solution of nonlinear equations

The Kantorovich theorem is a fundamental tool in nonlinear analysis for proving the existence and uniqueness of solutions of nonlinear equations arising in various fields. This theorem was weakened recently by Argyros who used a combination of Lipschitz and center-Lipschitz conditions in place of the Lipschitz conditions of the Kantorovich theorem. In the present paper we prove a weak Kantorovich-type theorem that gives the same conclusions as the previous two results under weaker conditions. Illustrative examples are provided in the paper.     

Monotonicity properties of operations on generalized topologies

Summary In the paper [5], several operations on generalized topologies are considered. They are not monotone in general, but an old result on monotonicity may be sharpened.     

企业声誉在电子商务消费者信任建立过程的作用机制

声誉是企业的一项重要无形资产,能够增进企业对消费者的吸引力。本文从消费者视野探索企业声誉在电子商务消费者信任建立过程的作用机制。将感知的安全性引入技术接受模型,建立了理论模型及假设,并应用结构方程模型分析软件进行了检验。结果表明,企业声誉通过消费者感知的安全性、有用性和易用性正向影响消费者信任,消费者感知的安全性、易用性也通过感知的有用性影响消费者信任。     

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.      

Corrigendum to “Discrepancy principle for the dynamical systems method” [Communications in Nonlinear Science and Numerical Simulation 10 (2005) 95–101]

Consider an operator equation B(u) − f = 0 in a real Hilbert space. Let us call this equation ill-posed if the operator B′(u) is not boundedly invertible, and well-posed otherwise. The dynamical systems method (DSM) for solving this equation consists of a construction of a Cauchy problem, which has the following properties: (1) it has a global solution for an arbitrary initial data, (2) this solution tends to a limit as time tends to infinity, (3) the limit is the minimal-norm solution to the equation B(u) = f. A global convergence theorem is proved for DSM for equation B(u) − f = 0 with monotone operators B.     

Design of Cavities for a Short Pulse Powerful Large Orbit Gyrotron

Designs of cavities for fundamental and high harmonic operation in Large Orbit Gyrotron (LOG) are discussed. The fundamental operation allows one to use beam currents in the range from 200 A to 300 A achieve output power of the order of 9–10 MW at frequency 143.6 GHz. Mode competition calculations show that stable oscillations in the TE^1,4 mode using high beam currents are possible even with the pitch factor 1.3 which is significantly lower than the design value 1.55. For the second harmonic operation, the maximum current used for excitation of the TE^2,4 mode is 60 A and the optimum magnetic field is 7.6 T. A cavity design for fourth harmonic operation using the TE^4,4 mode is also presented.     

Iteration 2-theories

The axioms of iteration 2-theories capture, up to isomorphism, the equational properties of iteration in conjunction with horizontal and vertical composition in all algebraically complete categories. We give a concrete representation of the free iteration 2-theory generated by a 2-signature.     

A study of the practical limitations of principal components analysis and the labelling of unresolved HPLC peaks

Summary The method of iterative target transformation factor analysis (ITTFA) used in conjunction with second derivative peak finding has shown to be a practical method for the peak deconvolution and reconstruction of HPLC chromatograms and spectra. The second derivative method of peak finding is acceptable for resolutions above 0.5 for peaks of similar heights. Above 0.5 resolution the labelling gives correct results where the spectra are substantially different and also when reasonably similar. Below this value the peak labelling was still accurate where the spectra were different. Solvent effects on the spectra of the compounds studied are small and do not hinder the peak labelling process. Thus small “local” libraries are feasible. Presented at the 17th International Symposium on Chromatography, September 25–30, 1988. Vienna, Austria.