The matrix rate of return

In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous analysis of evolution of baskets parameterized by complex variables in both continuous and discrete time models.     

Widely tunable, high-repetition-rate, dual signal-wave optical parametric oscillator by using two periodically poled crystals

This paper reports on a high-repetition-rate dual signal-wave (DSW) optical parametric oscillator (OPO) operating at the 1.5 μm band with tunable wavelength intervals from 2.5 nm to 69.1 nm. Two periodically poled crystals, a periodically poled lithium niobate (PPLN) with multiple gratings and a single grating MgO-doped PPLN (PPMgOLN), are cascaded in the same OPO cavity to generate dual signal-waves by using quasi-phase-matched (QPM) technique. The pump source was a Q-switched diode-pumped Nd:YVO₄ laser operating at 50 kHz. At an incident pump power of 3 W, an average output power of 169.6 mW at 1489.2 nm and 1558.3 nm has been achieved.     

TEM investigation of the formation mechanism of deformation twins in Fe–Mn–Si–Al TWIP steels

The microstructure of a Fe–Mn–Si–Al twinning-induced plasticity (TWIP) steel exhibiting remarkable work hardening rate under uniaxial tensile deformation was investigated using transmission electron microscopy to uncover the mechanism(s) controlling the nucleation and growth of the mechanically induced twins. The results show that the stair-rod cross-slip deviation mechanism is necessary for the formation of the twins, while large extrinsic stacking faults homogenously distributed within the grains could act as preferential sources for the activation of the deviation process. The influence of such features on the thickness and strength of the twins and the resulting mechanical behaviour is discussed and compared to similar works recently performed on Fe–Mn–C TWIP steels.     

Cation and anion substitution effects on the ultrafast dynamics of interionic interaction in imidazolium based ionic liquids

Room-temperature Ionic Liquids(ILs) have numerous unique properties that differ from those of conventional molecular solvents.Although the unique properties of ILs have been suggested to origin from their microscopic interionic interaction,detailed dynamics of interionic interaction of ILs has not been fully understood.Here,with the Femtosecond Optical Heterodyne-Detected Raman Induced Kerr Effect Spectroscopy(fs-OHD-RIKES),we measured the ultrafast dynamics of the interionic interaction of three typical im...     

Non-linear dynamics of a mechanical system with a frictional unilateral constraint

We analyze the dynamics of a two-dimensional system constituted by two masses subjected to elastic, gravitational and viscous forces and constrained by a moving frictional mono-lateral surface. The model exhibits a time-varying dynamics capable of reproducing the hopping phenomenon, an unwanted phenomenon observed in many applications such as the motion of a robotic arm on a surface or that of a wiper on a windscreen. The system dynamics, besides being affected by geometrical non-linearities, has a non-smooth nature due to the impact and friction laws involved in the model. The complexity of the resulting equations and of the transition conditions require the problem to be solved numerically. Various periodic motions are found and the effect of varying the system parameters, in particular the friction coefficient, is investigated. Finally, simulations are used to gain some insight the behavior of the windscreen wiper.     

Long‐range analysis of density fitting in extended systems

Density fitting scheme is analyzed for the Coulomb problem in extended systems from the correctness of long‐range behavior point of view. We show that for the correct cancellation of divergent long‐range Coulomb terms it is crucial for the density fitting scheme to reproduce the overlap matrix exactly. It is demonstrated that from all possible fitting metric choices the Coulomb metric is the only one which inherently preserves the overlap matrix for infinite systems with translational periodicity. Moreover, we show that by a small additional effort any non‐Coulomb metric fit can be made overlap‐preserving as well. The problem is analyzed for both ordinary and Poisson basis set choices. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

一个新的高维向量Lie代数及其应用

构造了一个新的8维向量Lie代数,通过适当设计等谱问题,利用屠格式和扩展的迹恒等式得到了AKNS族的可积耦合及Hamilton结构.     

Chern-simons theory in the SO(5)/U(2) harmonic superspace

We consider the superspace of D=3, N=5 supersymmetry using SO(5)/U(2) harmonic coordinates. Three analytic N=5 gauge superfields depend on three vector and six harmonic bosonic coordinates and also on six Grassmann coordinates. Decomposing these superfields in Grassmann and harmonic coordinates yields infinite-dimensional supermultiplets including a three-dimensional gauge Chern-Simons field and auxiliary bosonic and fermionic fields carrying SO(5) vector indices. The superfield action of this theory is invariant with respect to the D=3, N=6 conformal supersymmetry realized on N=5 superfields. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 2, pp. 217–234, November, 2008.     

Extended Bose-Hubbard model with pair hopping on triangular lattice

We study systematically an extended Bose-Hubbard model on the triangular lattice by means of a meanfield method based on the Gutzwiller ansatz. Pair hopping terms are explicitly included and a three-body constraint is applied. The zero-temperature phase diagram and a variety of quantum phase transitions are investigated in great detail. In particular, we show the existence and the stability of the pair supersolid phase.