Spectrality of certain self‐affine measures on the generalized spatial Sierpinski gasket

The self‐affine measure corresponding to a upper or lower triangle expanding matrix M and the digit set in the space is supported on the generalized spatial Sierpinski gasket, where are the standard basis of unit column vectors in . We consider in this paper the existence of orthogonal exponentials on the Hilbert space , i.e., the spectrality of . Such a property is directly connected with the entries of M and is not completely determined. For this generalized spatial Sierpinski gasket, we present a method to deal with the spectrality or non‐spectrality of . As an application, the spectral property of a class of such self‐affine measures are clarified. The results here generalize the corresponding results in a simple manner.     

Stability prediction for milling process with multiple delays using an improved semi‐discretization method

Milling chatter leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Thus, it is desirable to predict and avoid the onset of this instability. Considering that the stability of milling with variable pitch cutter or tool runout case is characterized by multiple delays, in this paper, an improved semi‐discretization method is proposed to predict the stability lobes for milling processes with multiple delays. Taking the variable pitch milling, for example, a comparisonwith prior methods is conducted to verify the accuracy and efficiency of the proposed approach for the stability prediction both in low and high radial immersion ratios. In addition, the rate of convergence of the proposed method is also evaluated. The results show that the proposed method has high computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.     

Positive solutions for multi‐point boundary value problems of fractional differential equations with p‐Laplacian

This paper investigates the existence of solutions for multi‐point boundary value problems of higher‐order nonlinear Caputo fractional differential equations with p‐Laplacian. Using the five functionals fixed‐point theorem, the existence of multiple positive solutions is proved. An example is also given to illustrate the effectiveness of ourmain result. Copyright © 2015 John Wiley & Sons, Ltd.     

Several transitive properties and Devaney’s chaos

The relation among transitivity, indecomposability and Z-transitivity is discussed. It is shown that for a non-wandering system (each point is non-wandering), indecomposability is equivalent to transitivity, and for the dynamical systems without isolated points, Z-transitivity and transitivity are equivalent. Besides, a new transitive level as weak transitivity is introduced and some equivalent conditions of Devaney's chaos are given by weak transitivity. Moreover, it is proved that both d-shadowing property and d-shadowing property imply weak transitivity.     

On superlinear convergence of quasi-Newton methods for nonsmooth equations

We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.     

水热法制备Sb2S3纳米棒有序阵列

以Sb(S₂CNEt₂)₃为单源前驱体，通过改变时间、温度、表面活性剂等反应条件，用水热法成功合成了各种尺寸的Sb₂S₃纳米棒及其有序阵列。X-射线衍射(XRD)、能量分散光谱(EDS)以及选区电子衍射(SAED)研究表明纳米棒由正交晶系Sb₂S₃单晶构成。扫描电子显微镜(SEM)和透射电子显微镜(TEM)研究显示Sb₂S     

咔咯锰(Ⅴ)氧配合物与苯乙烯的氧原子转移反应机理

采用密度泛函理论B3LYP方法研究了咔咯锰(Ⅴ)氧配合物(MnVO corrole)与苯乙烯氧原子转移(oxygen atom transfer,OAT)反应途径和吸电子取代基的影响.计算结果发现氧原子进攻苯乙烯中双键的β碳原子形成过渡态,结合内禀反应坐标法(intrinsic reaction coordinate ...     

On meromorphic functions that share three values of finite weights

A uniqueness theorem for two distinct non-constant meromorphic functions that share three values of finite weights is proved, which generalizes two previous results by H.X. Yi, and X.M. Li and H.X. Yi. As applications of it, many known results by H.X. Yi and P. Li, etc. could be improved. Furthermore, with the concept of finite-weight sharing, extensions on Osgood-Yang's conjecture and Mues' conjecture, and a generalization of some prevenient results by M. Ozawa and H. Ueda, ect. could be obtained.     

Bounded positive entire solutions of singular quasilinear elliptic equations

Suppose that β?0 is a constant and that is a continuous function with R₊:=(0,∞). This paper investigates N-dimensional singular, quasilinear elliptic equations of the form