硅和锗纳米线的原子排布和电荷分布的密度泛函紧束缚方法研究

低维硅锗材料是制备纳米电子器件的重要候选材料，是研发高效率、低能耗和超高速新一代纳米电子器件的基础材料之一，有着潜在的应用价值。采用密度泛函紧束缚方法分别对厚度相同、宽度在0.272 nm~0.554 nm之间的硅纳米线和宽度在0.283 nm~0.567 nm之间的锗纳米线的原子排布和电荷分布进行了计算研究。硅、锗纳米线宽度的改变使原子排布，纳米线的原子间键长和键角发生明显改变。纳米线表层结构的改变对各层内的电荷分布产生重要影响。纳米线中各原子的电荷转移量与该原子在表层内的位置相关。纳米线的尺寸和表层内原子排列结构对体系的稳定性产生重要影响。     

Structure dependent sampling in compressed sensing: Theoretical guarantees for tight frames

Many of the applications of compressed sensing have been based on variable density sampling, where certain sections of the sampling coefficients are sampled more densely. Furthermore, it has been observed that these sampling schemes are dependent not only on sparsity but also on the sparsity structure of the underlying signal. This paper extends the result of Adcock, Hansen, Poon and Roman (arXiv:1302.0561, 2013) [2] to the case where the sparsifying system forms a tight frame. By dividing the sampling coefficients into levels, our main result will describe how the amount of subsampling in each level is determined by the local coherences between the sampling and sparsifying operators and the localized level sparsities – the sparsity in each level under the sparsifying operator.     

Electronic properties of α-graphyne nanoribbons under the electric field effect

In this paper, we investigate the electronic structure of both armchair and zigzag α-graphyne nanoribbons. We use a simple tight binding model to study the variation of the electronic band gap in α-graphyne nanoribbon. The effects of ribbon width, transverse electric field and edge shape on the electronic structure have been studied. Our results show that in the absence of external electric field, zigzag α-graphyne nanoribbons are semimetal and the electronic band gap in armchair α-graphyne nanoribbon oscillates and decreases with ribbon's width. By applying an external electric field the band gap in the electronic structure of zigzag α-graphyne nanoribbon opens and oscillates with ribbon width and electric field magnitude. Also the band gap of armchair α-graphyne nanoribbon decreases in low electric field, but it has an oscillatory growth behavior for high strength of external electric field.     

On tight 6-cycle decompositions of complete 3-uniform hypergraphs

The complete 3-uniform hypergraph of order v has a vertex set V of size v and the set of all 3-element subsets of V as its edge set. A tight 6-cycle is a hypergraph with vertex set $\{a,b,c,d,e,f\}$ and edge set $\{\{a,b,c\},\{b,c,d\},\{c,d,e\},\{d,e,f\},\{e,f,a\},\{f,a,b\}\}$. We show that there exists a decomposition of the complete 3-uniform hypergraph of order v into isomorphic copies of a tight 6-cycle if and only if $v\equiv 1$, 2, 10, 20, 28, or $29(\mathrm{mod}36)$.     

A variant of Boneh-Franklin IBE with a tight reduction in the random oracle model

The first practical identity based encryption (IBE) scheme was published by Boneh and Franklin at Crypto 2001, based on the elliptic curve pairing. Since that time, many other IBE schemes have been published. In this paper, we describe a variant of Boneh-Franklin with a tight reduction in the random oracle model. Our new scheme is quite efficient compared to existing schemes; moreover, upgrading from Boneh-Franklin to our new scheme is straightforward.      

Optical absorption of zigzag single walled boron nitride nanotubes in axial magnetic field

We have investigated the effect of axial magnetic field on the band structure, dipole matrix elements and absorption spectrum in different energy ranges, using tight binding approximation. It is found that magnetic field breaks the degeneracy in the band structure and creates new allowed transitions in the dipole matrix which leads to creation of new peaks in the absorption spectrum. It is found that, unlike to CNTs which show metallic–semiconductor transition, the BNNTs remain semiconductor in any magnetic field strength. By calculation the diameter dependence of peak positions, we found that the positions of three first peaks in the lower energy region (E <5.3 eV) are proportional to n⁻². In the middle energy region (7 < E < 7.5 eV) all (n, 0) zigzag BNNTs, with even and odd nanotube index, have two distinct peaks in the absence of magnetic field which these peaks may be used to identify zigzag BNNTs from other tube chiralities. For odd (even) tubes, in the middle energy region, applying the magnetic field leads to splitting of these two peaks into three (five) distinct peaks.     

An interdependency index for the outputs of uncertain systems

The study of mechanical systems with uncertain parameters is gaining increasing interest in the field of system analysis to provide an expedient model for the prediction of the system behavior. Making use of the Transformation Method, the uncertain parameters of the system are modeled by fuzzy numbers in contrast to random numbers used in stochastic approaches. As a result of this analysis, a quantification of the overall uncertainty of the system outputs, including a worst-case scenario, is obtained. The inputs of the resulting fuzzy-valued model are a priori uncorrelated but after the uncertainties are propagated through the model, interdependency (or interaction) between the outputs may arise. If such interdependency is neglected, a misinterpretation of the results may occur. For example, in the case of applying uncertainty analysis in the early design phase of a product to determine the relevant design-parameter space, the interdependency between the design variables may reduce significantly the available part of the design space. This paper proposes a measure of interdependency between the uncertain system outputs. The interdependency index can be derived by a postprocessing of the data gained by the analysis with the Transformation Method. Such information can be obtained by a negligible amount of extra computation time.     

Stabilizing the monodromy of an open book decomposition

We prove that any mapping class on a compact oriented surface with non-empty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.