纳米团簇B92的密度泛函理论研究

利用密度泛函理论(DFT)研究了一种新颖的准球形纳米团簇B92.经过结构优化和频率分析,这一准球形笼状团簇的直径为0.968 nm,其结构满足Eoustani提出的"Aufbau principle".团簇B92的平均结合能、能隙(HOMO-LUMO gap)、垂直电离势(VIP)及垂直电子亲和势(VEA)分别为5.28 eV,1.19 eV,5.47eV及2.45 eV.计算所得到的红外谱(IR)上有一个明显的峰在895 Cm-1处.此谱将有助于从实验上确定本文所提出的团簇B92的结构,团簇B92的电荷分布表明,其有望成为未来纳米电子学中的一种电容器,另外,作为比较,本文也给出了其他一些笼状硼团簇的性质.     

Free-Space QKD with Modulating Retroreflectors Based on the B92 Protocol

Free-space quantum key distribution (QKD) has attracted considerable attention due to its lower channel loss and link flexibility. It allows two participants share theoretical unconditional secure keys, and can potentially be applied to air-to-ground quantum communication to establish a global quantum network. Free-space QKD using modulating retro-reflectors (MRR-QKD) significantly reduces the pointing requirement and simplifies the structure of the mobile terminal, therefore making it suitable for lightweight aircraft such as unmanned aerial vehicle and Cubesat, etc. Based on intensity modulation of two non-orthogonal states and the B92 protocol, we proposed a scheme to improve the previous work (Optics Express 2018, 26, 11331). Our scheme simplifies the optical structure and shows more robustness in equipment imperfection. The analysis and simulation show that the number of multiple quantum well modulators needed in our scheme decreases from eight to three with similar performance. Additionally, while the previous scheme cannot work due to low modulator extinction ratio or high optical misalignment, our scheme can still operate.     

A system of partial differential equations modeling the competition for two complementary resources in flowing habitats

This paper examines a system of reaction-diffusion equations arising from a flowing water habitat. In this habitat, one or two microorganisms grow while consuming two growth-limiting, complementary (essential) resources. For the single population model, the existence and uniqueness of a positive steady-state solution is proved. Furthermore, the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values. Mathematical analysis for the two competing populations is carried out. More precisely, the long-time behavior is determined by using the monotone dynamical system theory when the semi-trivial solutions are both unstable. It is also shown that coexistence solutions exist by using the fixed point index theory when the semi-trivial solutions are both (asymptotically) stable.     

Ecoepidemic models with disease incubation and selective hunting

In this paper we consider ecoepidemic models in which the basic demographics is represented by predator-prey interactions, with the disease modeled by an SEI system. At first we consider a basic Lotka-Volterra type of interaction. Then we also introduce competition for resources among individuals of the prey population. Several variations of the model are presented, in which the prey intra-specific population pressure assumes different forms, depending on the virulence of the disease. Indeed, the latter may affect the exposed and infected individuals so much that they may not be able to compete with the sound ones for resources. A further distinguishing feature of this investigation lies in the way in which the predator actively selects the prey for hunting. For instance in some cases predators may discard the diseased ones, as less palatable, while in other situations they would instead search expressly for the infected, since these are weaker individuals and thus easier to hunt. The equilibria of the systems are analyzed, showing that in some cases bifurcations arise, contrary to what happens to similar classical Holling type I ecoepidemic models. These persistent oscillations seem to be triggered by the number of subpopulations present in the system, which is larger than those introduced in the former models, counting also the latent class. Furthermore, adding predation to an SEI epidemic model has profound effects on the stability of its equilibria. In particular, once the predators are introduced into an SEI epidemic at a stable endemic equilibrium, their presence destabilizes this equilibrium making the previous stable conditions unrecoverable.     

Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays

In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB.     

The combinatorics and extreme value statistics of protein threading

In protein threading, one is given a protein sequence, together with a database of protein core structures that may contain the natural structure of the sequence. The object of protein threading is to correctly identify the structure(s) corresponding to the sequence. Since the core structures are already associated with specific biological functions, threading has the potential to provide biologists with useful insights about the function of a newly discovered protein sequence. Statistical tests for threading results based on the theory of extreme values suggest several combinatorial problems. For example, what is the number of waysm′=# _t {L _i >x _i } _i ⁼⁰ⁿ of choosing a sequence {X _i } _i ⁼¹ⁿ from the set {1, 2, ...,t}, subject to the difference constraints {L _i =X _i+1?X _i >x _i } _i ⁼⁰ⁿ , whereX ₀=0,X _n+1=t+1, and {x _i } _i ⁼⁰ⁿ is an arbitrary sequence of integers? The quantitym′ has many attractive combinatorial interpretations and reduces in special continuous limits to a probabilistic formula discovered by the Finetti. Just as many important probabilities can be derived from de Finetti's formula, many interesting combinatorial quantities can be derived fromm′. Empirical results presented here show that the combinatorial approach to threading statistics appears promising, but that structural periodicities in proteins and energetically unimportant structure elements probably introduce statistical correlations that must be better understood.     

Nonmonotone travelling waves in a single species reaction-diffusion equation with delay

We prove the existence of a continuous family of positive and generally nonmonotone travelling fronts for delayed reaction-diffusion equations , when g∈C²(R₊,R₊) has exactly two fixed points: x₁=0 and x₂=K>0. Recently, nonmonotonic waves were observed in numerical simulations by various authors. Here, for a wide range of parameters, we explain why such waves appear naturally as the delay h increases. For the case of g with negative Schwarzian, our conditions are rather optimal; we observe that the well known Mackey-Glass-type equations with diffusion fall within this subclass of (∗). As an example, we consider the diffusive Nicholson's blowflies equation.     

On the complexity of some subgraph problems

We study the complexity of the problem of deciding the existence of a spanning subgraph of a given graph, and of that of finding a maximum (weight) such subgraph. We establish some general relations between these problems, and we use these relations to obtain new NP-completeness results for maximum (weight) spanning subgraph problems from analogous results for existence problems and from results in extremal graph theory. On the positive side, we provide a decomposition method for the maximum (weight) spanning chordal subgraph problem that can be used, e.g., to obtain a linear (or O(nlogn)) time algorithm for such problems in graphs with vertex degree bounded by 3.