CYCLE SPACES OF GRAPHS ON THE SPHERE AND THE PROJECTIVE PLANE

Cycle base theory of a graph has been well studied in abstract mathematical field such matroid theory as Whitney and Tutte did and found many applications in prat-ical uses such as electric circuit theory and structure analysis, etc. In this paper graph embedding theory is used to investigate cycle base structures of a 2-(edge)-connected graph on the sphere and the projective plane and it is shown that short cycles do generate the cycle spaces in the case of 'small face-embeddings'. As applications the authors find the exact formulae for the minimum lengthes of cycle bases of some types of graphs and present several known results. Infinite examples shows that the conditions in their main results are best possible and there are many 3-connected planar graphs whose minimum cycle bases can not be determined by the planar formulae but may be located by re-embedding them into the projective plane.

Unsteady flow characteristic analysis of turbine based combined cycle(TBCC)inlet mode transition10.1016/j.jppr.2015.07.006

A turbine based combined cycle(TBCC)propulsion system uses a turbine-based engine to accelerate the vehicle from takeoff to the mode transition flight condition,at which point,the propulsion system performs a“mode transition”from the turbine to ramjet engine.Smooth inlet mode transition is accomplished when flow is diverted from one flowpath to the other,without experiencing unstart or buzz.The smooth inlet mode transition is a complex unsteady process and it is one of the enabling technologies for combined cycle engine to become a functional reality.In order to unveil the unsteady process of inlet mode transition,the research of over/under TBCC inlet mode transition was conducted through a numerical simulation.It shows that during the mode transition the terminal shock oscillates in the inlet.During the process of inlet mode transition mass flow rate and Mach number of turbojet flowpath reduce with oscillation.While in ramjet flowpath the flow field is non-uniform at the beginning of inlet mode transition.The speed of mode transition and the operation states of the turbojet and ramjet engines will affect the motion of terminal shock.The result obtained in present paper can help us realize the unsteady flow characteristic during the mode transition and provide some suggestions for TBCC inlet mode transition based on the smooth transition of thrust.

Minor and Minimum Cycle Bases of a 3-connected Planar Graph

In this paper, we prove that if any set of ｜E（G）｜- ｜V（G）｜ ＋ 1 facial cycles of a 3-connected planar graph G embedded in the plane doesn＇t form a minimum cycle base of G, then any minimum cycle base of G contains a separating cycle, and G has a minor isomorphic to T6, where T6 is the graph obtained from the complete graph K6 by deleting a path with four edges.

3D shape measurement of larger complex objects based on fringe cycle correction

The grating fringe on the reference plane is broadened in the intersecting axis system because of oblique-angle projection. In order to solve this problem, we study the theoretical model of the temporal phase unwrapping method based on the fringe cycle correction. We also study the 3D shape measurement theoretical model of the larger complex objects after considering the coordinate deviation and lens distortion. Experimental results demonstrate that the fringe cycle on the reference plane can be corrected to a constant value, the lens distortion can be corrected, and 3D shape of larger complex objects can be accurately measured.

Short Cycle Structure of Graphs on Surfaces (1)-the Uniqueness Theorems

In this paper we investigate cycle base structures of a （weighted） graph and show that much information of short cycles is contained in a MCB （minimum cycle base）. After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be a MCB. Further more, we show that the structure of MCB in a （weighted） graph is unique. In the case of nonnegative weight, every pair of MCB have the same number of k-cycles for each integer k ≥ 3. The property is also true for those having longest length （although much work has been down in evaluating MCB, little is known for those having longest length）.