A note on local unitary equivalence of isotropic-like states

We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition.

Energetical Theories on Fatigue Life Prediction

Current developments on fatigue life prediction methods have been systematically reviewed.In con- sideration of the irreversibility of energy dissipation during fatigue damage process,the main contents for fatigue damage estimation and localized equivalence as well as simulation models have been established.A frame of energy-based fatigue life prediction method has been proposed,meanwhile, the procedure in application to a practical structure component has been described.

Local symmetries of finite type hypersurfaces in C^2 Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v = |z|k, local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.

Combustion enhancement in rearward step based scramjet combustor by air injection at step base

Numerical simulations were performed to model the non-reacting and reacting flow behind a rearward step flameholder in Mach 1.6 supersonic flow with fuel injection at the step base.The combustor geometry was based on the University of Florida scramjet experimental facility.Turbulence was modeled using k-u shear stress transport(SST),laminar flamelet was used for combustion modeling.Wall static pressure showed good agreement with experimental data for non-reacting and reacting flow.For non-reacting flow,dummy fuel helium mole fraction distribution in the recirculation region behind the step was validated with planar laser induced fluorescence(PLIF)images in experiments.To improve the combustion characteristics,air was injected in tandem with hydrogen at step base using various configurations.With all fuel injection as baseline,the case with 2 air jets around each fuel jet and air injected at 2 times the stagnation pressure of fuel showed the most improvement compared to other cases.It was most effective in reducing the local fuel richness,shortening the flame length and increasing combustion efficiency.

Flame Propagation Through Concentration Gradient

The experiment was carried out in homogeneous propane-air mixture and in several concentration gradient of mixture. Igniter is put on the upper side of the combustion chamber In concentration gradient experiment, fixture was ignited from lean side. An experimental study was conducted in a combustion chamber. The combustion chamber has glass windows for optical measurements at any side. For the measurement of distribution of fuel concentration, infrared absorption method using 3.39μm He-Ne laser was used, and for the observation of propagating flame, Schlieren method was employed. As a measurement result of flame propagation velocity and flammable limit, for a mixture of an identical local equivalence ratio, flame propagation velocity in concentration gradient is faster than that in homogeneous mixture, and rich flammable limit in concentration gradient shows a tendency to be higher than that in homogeneous mixture.

THE QUALITATIVE CLASSIFICATION OF A SPECIAL TYPE OF HIGHER ORDER ORDINARY DIFFERENTIAL SYSTEM

In this paper, a theorem of the local qualitative classification of equllibrium of a special type of higher order ordinary differential system is provided for establishing the theoretical bases to extend the planer. qualitative nomgraphy in [1] to the special geometricaljy qualitative method in 3-dimensions.

Constructing unextendible product bases from multiqubit ones

The construction of multipartite unextendible product bases(UPBs)is a basic problem in quantum information.We respectively construct two families of 2×2×4 and 2×2×2×4 UPBs of size eight by using the existing four-qubit and five-qubit UPBs.As an application,we construct novel families of multipartite positive-partial-transpose entangled states,as well as their entanglement properties in terms of the geometric measure of entanglement.