Dynamic stability of a class of fractional-order nonlinear systems via fixed point theory

In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in $\left(\frac{1}{2},1\right)$. However, the case of the fractional-order belonging to $(0,\frac{1}{2})$ has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective.     

A Generalization of Lappan’s Theorem to Higher Dimensional Complex Projective Space

In this paper, the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result: Let f be a holomorphic mapping of ? into Pⁿ(C), and let H₁, · · · , H_q be hyperplanes in general position in Pⁿ(C).Assume that sup {(1 ? |z|²)f^?(z) : z ∈ q[ j=1 f^?1(H_j )o < ∞,if q ≥ 2n² + 3, then f is normal.     

Investigation of Intrachain Exciton Diffusion of MEH-PPV in Solution with Different Polarity

Femtosecond time-resolved transient grating technique was adopted to insight into the intra-chain exciton diffusion of MEH-PPV in solution with different polarity. Broadband white-light continuum was introduced as the probe to observe the transient absorption and the femtosecond time-resolved transient grating information simultaneously. The vibrational dephasing behaviors, single exciton relaxation, and population relaxation dynamics of MEH-PPV were systematically investigated. The result shows that the relaxation processes of the sample solution will be accelerated in the solvent with larger polarity.     

A dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.     

Roles of N?→NN and πN→? Reactions in Heavy-Ion Collisions at Intermediate Energies

Within the framework of the isospin-dependent transport model, the roles of the reactions N? → NN and πN→ ? are investigated through simulating heavy-ion collisions at 1000 MeV/nucleon. The absorption process N? → NN plays an important role for heavy impact systems and small impact parameters than for light impact systems and large impact parameters. The resorption process πN→ ? is of importance for heavy impact systems and large impact parameters than for light impact systems and small impact parameters. Thus the influences of the reaction N? → N N(πN→ ?) on pion production dynamics can be neglected in heavy-ion collisions for smaller(larger) impact parameters and light systems. It is the reaction πN→ ? that causes the anti-correlation of pions and nucleons in the rapidity dependence of the directed flow.     

Rhodium-catalysed synthesis of fused pyrimidine derivatives employing N-sulfonyl-1,2,3-triazoles as a 1-aza-[4C] synthon

A new synthetic application of N-sulfonyl-1,2,3-triazoles acting as a 1-aza-[4C] synthon via the 1,2-shift reaction of an α-imine rhodium carbene was developed for the synthesis of fused pyrimidine derivatives. The high reactivity of the strained three-membered 2H-azirine ring facilitated the unusual cyclization of electron-deficient dienes with electron-deficient dienophiles. The compatibility was good with common functionalities tolerated. Excellent chemoselectivity was observed, and no reactions occurred between the rhodium carbene and 2H-azirine. The products could be converted into seven-membered multi-functionalized 1H-1,4-diazepine derivatives, illustrating the potential application of the protocol in medium-sized N-heterocycle synthesis.     

In(OTf)3 catalyzed reductive etherification of 2-aryloxybenzaldehydes and 2-(arylthio)benzaldehydes

2-Aryloxybenzaldehydes and 2-(arylthio)benzaldehydes undergo reductive etherification in presence of 5 mol% In(OTf)₃ and stoichiometric amount of Et₃SiH under solvent free conditions to generate novel symmetrical dibenzyl ethers and thioethers in excellent yields. In(OTf)₃ is found to be superior in terms of catalytic activity over the other metal triflates tested for the reaction. Xanthenes and thioxanthenes, as anticipated, could not be obtained under these conditions.     

非同类机极小化最大完工时间的保密排序问题

提出并研究了一类非同类机的极小化最大完工时间的保密排序问题Rm||Cmax.该问题的模型参数分为若干组,每个组都由一个不愿意共享或公开自己数据的单位所拥有.基于随机矩阵变换构造了一个不泄露私有数据且与原问题等价的安全规划模型,求解该安全模型可以获得问题的最优解,而且各单位的隐私数据仍然保持不被泄露.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

汽配件颜色喷涂顺序问题的TSP转化与建模

汽配件颜色喷涂顺序问题通常以生产线上相邻汽配件颜色切换次数少为最优目标,以进一步降低生产成本.该类问题具有所有汽配件都必须喷涂一次且只喷涂一次的特点,为此提出了TSP转化与建模的方法.将待喷涂汽配件定义为TSP顶点,任意两个待喷涂汽配件的颜色切换定义为顶点的距离,仿照TSP问题构建0-1规划模型;类似于顶点距离,将某些汽配件的颜色或类别不相邻要求定义为0-1矩阵,巧妙地构造了喷涂生产的约束条件.该建模方法简单快速,通用性高,适用于具有类似特点的各类生产实践问题.