Polynomial differential equations with many real ovals in the same algebraic complex solution
Let FolR(2, d) be the space of real algebraic foliations of degree d in RP(2). For fixed d, let IntR(2, d) = {F 2 FolR(2, d) | F has a non-constant rational first integral}. Given F 2 IntR(2, d), with primitive first integral G, set O(F) = number of real ovals of the generic level (G = c). Let O(d) = sup{O(F) | F 2 IntR(2, d)}. The main purpose of this paper is to prove that O(d) = +1 for all d _ 5.
On compact analytic surfaces II
THEOREM 11.1. The family 9(,{, G) consists of all analytic fibre spaces Bi, '2C H'(A, f2(B#)). The notion of fibre spaces and their equivalences depends on the sheaf of structure groups.' By a (63-fibre space we mean a fibre space with a sheaf (3 of structure groups, and we say that two fibre spaces are (X-equivalent if they are equivalent as (63-fibre spaces. The fibre space Bi may be considered as an analytic fibre space, as an f2(BO)-fibre space, or as an f2(Bl)-fibre space. The cohomology class C) C H'(Ay, f(BO)) represents the f2(Bl)-equivalence class of Be. Let C& denote the fibre of BI over u c A. It is clear that
A New Vacuum Pressure Infiltration CFRP Method and Preparation Experimental Study of Composite
In order to prepare a carbon-fiber-reinforced polymer composite (CFRP) with ideal microstructure and properties, a new vacuum pressure infiltration CFRP method is proposed based on an analysis of existing CFRP preparation process methods. Research on composite material preparation systems was carried out by using this new method principle. The system mainly includes a fiber pre-forming module, a vacuum heating infiltration module, a hot-press curing molding module, and a data acquisition control module. Under the conditions of natural curing at 0 MPa + 6 h + 25 °C, vacuum heating curing at –0.05 MPa + 30 min + 80 °C, and hot-press curing at 0.7 MPa + 5 min + 50 °C, a two-dimensional (2D) CFRP with excellent microstructure and properties was successfully prepared. Observing the microstructure of the prepared composite material, it can be found that the inside of the composite material was sufficiently and uniformly infiltrated, and common preparation defects such as holes and delamination were effectively controlled. Through the performance test, the bending strength of the material reached 790 MPa.