Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Pentapnictogen heterocyclic monoanions: Structure,stability, and aromaticity

Inorganic planar ring-shape molecules with 4n + 2 π electrons are always the focus of experimental synthesis and theoretical research due to their potential aromaticity and stability. In this work, the whole series of five-membered heterocycle monoanions X _nY_5-n⁻ (X, Y = group 15 elements; n = 1-4) were thoroughly investigated by means of density functional theory calculations. They all have large formation energies and HOMO-LUMO gap energies, suggesting the potential thermodynamic and kinetic stability. Their aromaticities are comparable to that of typical aromatic hydrocarbons. Their thermal stabilities were firmly established by the ab initio molecular dynamics simulations. As most of them are predicted for the first time, their various spectra were simulated for experimental characterization. Furthermore, we demonstrate that these five-membered cyclic anions can be employed as η⁵-ligand to construct novel all-inorganic metallocenes, which may serve as the building blocks of low-dimensional nanomaterials.     

Gas-phase 21Ne NMR studies and the nuclear magnetic dipole moment of neon-21

Gas-phase ²¹Ne nuclear magnetic resonance spectra were measured at the natural abundance of ²¹Ne isotope for samples consisting of pressurized neon up to 60 bar at room temperature and applying the magnetic field of the strength B₀ = 11.7574 T. It showed that the nuclear magnetic resonance frequency is linearly dependent on the density of gaseous neon. The resonance frequency was extrapolated to the zero-density point, and it permitted the determination of the ²¹Ne nuclear magnetic moment, μ(²¹Ne) = 0.6617774(10) μ_N. The present value of μ(²¹Ne) is not influenced by the bulk magnetic susceptibility of neon and interactions between neon atoms; therefore, it is more precise and reliable than the previous result obtained for μ(²¹Ne).     

变角度纤维复合材料层合斜板的颤振分析

假设纤维方向角沿层合板的长度方向线性变化，研究了变角度纤维复合材料层合斜板的颤振．通过坐标变换将斜板变换为正方形板，采用层合板表面连续变化的速度环量来模拟空气对其的作用，速度环量分布利用Cauchy积分公式计算．建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度．通过数值算例验证了本文模型和方法的正确性和收敛性，分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响．研究结果表明，通过纤维的变角度铺设，可有效地提高层合板的基频和颤振/不稳定性分离临界速度．经合理设计的变角度复合材料层合板具有抑制颤振的作用．     

The effects of resource limitation and consensual incentives on cooperation

Exploring the evolution of cooperation has been one of the most challenging topics and attracted increasing attention in various realms. Hereby, we institute an analytic model where the relationship between the common benefits and contributions is the typical saturation nonlinearity. We investigate the evolutionary dynamics of cooperation with and without consensual incentives respectively. The population always evolves to full defection when the incentives are absent. Cooperation, however, can be promoted by consensual incentives when the degree of cooperators' preferences for incentives is great. There exists an intermediate amount of resources at which the positive effect of consensual incentives on cooperation is minimized. Furthermore, there is a U-shape relationship between the degree of cooperators' preference for an incentive and the evolution of cooperation. A greater basin of full cooperation can be induced when the cooperators' preference for reward is more pronounced than that for punishment.     

Norbornene derivatives from a metal‐free,strain‐promoted cycloaddition reaction: New building blocks for ring‐opening metathesis polymerization reactions

The preparation of new ring opening metathesis polymerization (ROMP) monomers using a 1,3‐dipolar cycloaddition between aryl azides and norbornadiene is described. Various norbornenetriazolines, obtained through a solvent‐and catalyst‐free reaction, can subsequently be incorporated into polymer backbones through ROMP reactions. Furthermore, thermal decomposition of the triazoline moiety can allow for further polymer functionalization. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2357–2362