Convergence of Yang-Mills-Higgs flow for twist Higgs pairs on Riemann surfaces

We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle(E,H)over Riemann surface X.It is already known the gradient flow with initial data(A0,φ0)converges to a critical point(A∞,φ∞).Using a modified Chern-Weil type inequality,we prove that the limiting twist Higgs bundle(E,d′′A∞,φ∞)coincides with the graded twist Higgs bundle defined by the HarderNarasimhan-Seshadri filtration of the initial twist Higgs bundle(E,d′′A0,φ0),generalizing Wilkin’s results for untwist Higgs bundle.     

LIMIT CYCLES BIFURCATION FOR A CLASS OF DEGENERATE SINGULARITY

In this paper, bifurcation of limit cycles for the degenerate equilibrium to a three- dimensional system is investigated. Firstly, we use formal series to calculate the focal values at the high-order critical point on center manifold. Then an example is studied, and the existence of 3 limit cycles on the center manifold is proved. In terms of high- order singularities in high-dimensional systems, our results are new.     

Yetter–Drinfeld Modules over Weak Braided Hopf Monoids and Center Categories

In this paper,we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter–Drinfeld modules over a weak braided Hopf monoid.We apply the general result to the calculus of the center in module categories.     

Persistent centers of complex systems

On the basis of some works on persistent centers and weakly persistent centers, in this paper we discuss a generalized version of persistent center and weakly persistent center for complex planar differential systems, in which conjugacy of variables may not be required. We give some complex systems which have a persistent center or weakly persistent center at the origin. Then, we find all conditions of persistent center for cubic systems and all conditions of weakly persistent center for complex cubic Lotka–Volterra system. Relations between complex systems and real ones are given concerning persistent centers and weakly persistent centers.     

New lower bounds for the Hilbert number of polynomial systems of Liénard type

In this paper, we study the maximal number of limit cycles of some kinds of polynomial Liénard systems with arbitrary degree and obtain some new lower bounds for the Hilbert number of the systems, which improve truly the certain existing results.     

平面运动刚体加速度瞬心的确定及应用

给出在特殊情况下,确定刚体平面运动加速度瞬心的方法以实例说明加速度瞬心在运动学以及动力学中的应用,可使一些问题求解大为简化．     

Oscillations in three-reaction quadratic mass-action systems

It is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes but allow target complexes with higher molecularities. As our goal is to find oscillatory networks of minimal size, we focus on networks with three reactions, the minimum number that is required for oscillation. However, some of our intermediate results are valid in greater generality. One key finding is that an isolated periodic orbit cannot occur in a three-reaction, trimolecular, mass-action system with bimolecular sources. In fact, we characterize all networks in this class that admit a periodic orbit; in every case, all nearby orbits are periodic too. Apart from the well-known Lotka and Ivanova reactions, we identify another network in this class that admits a center. This new network exhibits a vertical Andronov–Hopf bifurcation. Furthermore, we characterize all two-species, three-reaction, bimolecular-sourced networks that admit an Andronov–Hopf bifurcation with mass-action kinetics. These include two families of networks that admit a supercritical Andronov–Hopf bifurcation and hence a stable limit cycle. These networks necessarily have a target complex with a molecularity of at least four, and it turns out that there are exactly four such networks that are tetramolecular.     

On the Twist-Boat Conformation of the Tetrahydropyran Cycle in the Trioxa-Bis-Spiroketal Series

INTRODUCTION

In the solid state the trioxa-bis-spiroketal 2 (fig. 1) has a twist-boat conformation (tetrahydropyran cycle) and its infrared absorption and nuclear magnetic resonance (¹H at 250 MHz, ¹³C at 15,06 MHz) spectra let forsee the same conformation in solution.¹.     

Laminar Heat Transfer Augmentation through A Square Duct and Circular Tube Fitted with Twisted Tapes

Experimental studies on friction factor and heat transfer characteristics for the laminar flow of ethylene glycol in a square duct fitted with twisted tapes of different twist ratios under nearly uniform wall temperature conditions are reported in this article. The Nusselt numbers were found to be 5.44–7.49 and 2.46–4.87 times that of plain square duct forced convection values based on constant flow rate and constant pumping power criteria, respectively, for y = 2.66. The augmented friction factor and Nusselt number for a square duct is about 1.9 and 2.10 times higher than that for an augmented circular tube.     

用类Li原子波函数对H52+团簇的正四面体中心结构与能量的研究

在单中心球模型近似下,选用类Li原子解析波函数,用变分法计算了H52 团簇正四面体中心结构与能量.结果表明当中心氢原子核到顶角氢原子核之间的距离R=1.93a0时,体系能量有一极小值E=-4.3792 Hartree(a0=0.529177×10-10m,1 Hartree=27.2 eV).这表明H52 团簇的正四面体中心结构是稳定的结构,H52 团簇是可能存在的.