On the third gap for proper holomorphic maps between balls

Let $F$ be a proper rational map from the complex ball $\mathbb B ^n$ into $\mathbb B ^N$ with $n>7$ and $3n+1 \le N\le 4n-7$ . Then $F$ is equivalent to a map $(G, 0, \dots , 0)$ where $G$ is a proper holomorphic map from $\mathbb B ^n$ into $\mathbb B ^{3n}$ .     

Universal prediction-based adaptive fault estimator applied to secure communication

In this paper, a communication scheme that could use a nonlinear dynamical system to create encrypted keys with an additional dimension is proposed, and the scheme could keep encrypted keys not to diverge. Since the divergence of encrypted keys (nonlinear signals) easily happens in non-linear systems coupled with other systems, the adaptive control approach, proposed in this paper, uses the universal state-space adaptive observer-based fault diagnosis/estimator and the high-performance tracker to eliminate the divergence of encrypted keys. At the same time, the receiver of communication retrieves informal messages by the universal state-space adaptive observer-based fault diagnosis/estimator and the high-performance tracker. Thus, this paper takes advantage of the merit of digital redesign methodology for a practical implementation of secure-communication, and the estimator solves the problem of secure communication. Thus developed a new approach could add more dimensions into nonlinear secure-communication systems without having the problem of divergence of encrypted keys.     

Tetragonal tungsten oxide nanobelts synthesized by chemical vapor deposition

Tungsten trioxide (WO₃) nanobelts in tetragonal structure were grown on Si substrates by a hot-wall chemical vapor deposition (CVD) method without using catalysts. The products were characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), transmission electron microscopy (TEM), Raman spectroscopy, and photoluminescence (PL) spectrum. The width of the nanobelts is in the range of 50–100 nm with width-to-thickness ratios of 5–10 and lengths of up to tens of micrometers. These nanobelts grew along the [0 0 1] direction and can be identified as the tetragonal WO₃ structures. Raman and PL measurements indicate the high quality of the nanobelts. The vapor–solid growth mechanism could be applicable in our experiment.     

Streakline visualization of the structures in the near wake of a circular cylinder in sinusoidally oscillating flow

A numerical investigation of three-dimensional sinusoidally oscillating flow around a circular cylinder was conducted to examine mushroom-type structures in the near wake that are manifestations of the Honji instability. The focus of this paper is to examine the flow structure through the analysis of the streaklines in the flow. Through the use of streakline visualizations and their correlation with vorticity in the flow field, the onset and development of the mushroom-type structures is followed. The parameter value range is 0.1<KC<2.0 and β=1035, 6815, and 9956. The streakline patterns in several axial planes are examined and used to describe the various mechanisms that sustain the mushroom-type structure during the oscillatory cycle.     

Electron transfer versus nucleophilic pathways in the ion-pair annihilation of organoborate anions by carbonylmanganese(I) cations

Substituted carbonylmanganese cations [Mn(CO)₅L]⁺, where L=py, PPh₃ and PPh₂Me, readily react with various organoborate anions (tetramethylborate, methyltriphenylborate and tetraphenylborate) in THF solution to afford a mixture of dimanganese carbonyls, hydridomanganese carbonyls and alkylmanganese carbonyls. The formation of the dimanganese carbonyl dimers as well as the hydridomanganese carbonyls suggests the involvement of 19-electron carbonylmanganese radicals that stem from an initial electron transfer. On the other hand, the acetonitrile-substituted analogue [Mn(CO)₅(CH₃CN)]⁺ reacts with the same borate anions to afford the alkylated RMn(CO)₅, where R=CH₃ and C₆H₅, as the sole carbonylmanganese product. As such, this alkylative annihilation is best formulated as a direct attack on the carbonyl carbon by the borate nucleophile. The two different pathways can be understood in terms of the balance between the electrophilicity of the carbonyl ligand and the electron affinity of the carbonylmanganese cation.     

Implementing and using high-order finite element methods

We present theoretical analyses of and detailed timings for two programs which use high-order finite element methods to solve the Navier- Strokes equations in two and three dimensions. The analyses show that algorithms popular in low-order finite element implementations are not always appropriate for high-order methods. The timings show that with the proper algorithms high-order finite element methods are viable for solving the Navier-Stokes equations. We show that it is more efficient, both in time and storage, not to precompute element matrices as the degree of approximating functions increases. We also study the cost of assembling the stiffness matrix versus directly evaluating bilinear forms in two and three dimensions. We show that it is more efficient not to assemble the full stiffness matrix for high-order methods in some cases. We consider the computational issues with regard to both Euclidean and isoparametric elements. We show that isoparametric elements may be used with higher-order elements without increasing the order of computational complexity.     

Model conversions of uncertain linear system using the improved block-pulse function approach

This paper presents an improved block-pulse function approach to convert a continuous-time (respectively, discrete-time) structured uncertain linear system into an equivalent discrete-time (respectively, continuous-time) structured uncertain linear model. The concept of the principle of equivalent areas is utilized for the uncertain model conversions. This allows the use of well-established theorems and algorithms in the discrete-time (respectively, continuous-time) domain to indirectly solve the continuous-time (respectively, discrete-time) domain problems. A numerical example is given to demonstrate the effectiveness of the proposed method.     

On Randers spaces of constant flag curvature

This paper concerns a ubiquitous class of Finsler metrics on smooth manifolds of dimension n. These are the Randers metrics. They figure prominently in both the theory and the applications of Finsler geometry. For n ≥ 3, we consider only those with constant flag curvature. For n = 2, we focus on those whose flag curvature is a (possibly constant) function of position only. We characterize such metrics by three efficient conditions. With the help of examples in 2 and 3 dimensions, we deduce that the Yasuda-Shimada classification of Randers space forms actually addresses only a special case. The corrected classification for that special case is sharp, holds for n ≥ 2, and follows readily from our three necessary and sufficient conditions.