Relation among C-curve characterization diagrams

As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane can, therefore, be partitioned into regions labelled according to the characterization of the curve when the fourth point is in each region. This partitioned plane is called a "characterization diagram". By moving one of the control points but fixing the rest, one can induce different characterization diagrams. In this paper, we investigate the relation among all different characterization diagrams of cubic C-curves based on the singularity conditions proposed by Yang and Wang (2004). We conclude that, no matter what the C-curve type is or which control point varies, the characterization diagrams can be obtained by cutting a common 3D characterization space with a corresponding plane.

Original New Theory Abbreviation of Metals

The electrons of metallic iron atoms all have wave-particle duality.The electrons of each iron atom are particles in the liquid state,the solid state is fluctuating.The wave-particle duality parameters of each iron atom electron are different,there is a small difference,the same is gathered into one,become a single grain.The parameters of wave-particle duality are different.The crystallization temperature of liquid state is different from that of solid。

Uniform trigonometric polynomial B-spline curves

This paper presents a new kind of uniform spline curve, named trigonometric polynomial B-splines, over space Ω = span{sini,cost, tk-3,tk-4, …,t, 1} of which k is an arbitrary integer larger than or equal to 3. We show that trigonometric polynomial B-spline curves have many similar properties to traditional B-splines. Based on the explicit representation of the curve we have also presented the subdivision formulae for this new kind of curve. Since the new spline can include both polynomial curves and trigonometric curves as special cases without rational form, it can be used as an efficient new model for geometric design in the fields of CAD/CAM.

Bainite isothermal transformation of Si–Mn–Mo alloy by phase structure factor calculation under different rare earth contents

The effect of rare earth （RE） on bainite trans- formation mechanism is not yet unified in the academia. Therefore, further studying the effect of RE on bainite transformation mechanism will have important guiding significance for the development of bainite steels. In this paper, using differential dilatometer （DIL805A/D）, heat treatment was performed and C-curve was drawn. The effect of phase structure factor on bainite transformation under two different fractions of RE in Si-Mn-Mo bainite steels was investigated by the empirical electron theory （EET） of solids, molecules, dilatometry, and metallogra- phy. Experimental results show that RE makes Fe-C- RE segregation structural unit of Si-Mn-Mo bainite steels increase, i.e., the values of phase structure factor （na, FDC） increase, and delay bainite transformation due to the drag effect resulting from the segregation of RE ferrite island interphase and the retardation of RE to carbon diffusion in Si-Mn-Mo bainite steels. Beside this, C-curve is shifted to right and down, and microstructures of bainite ferrite and substructures are finer.