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.
Vector fields, invariant varieties and linear systems
Nous etudions les relations entre les varietes invariantes des champs de vecteurs et le lieu d'inflexion des systemes lineaires par rapport aux champs de vecteurs. Parmi les consequences de cette investigation nous obtenons un critere pour l'existence d'integrales premieres rationnelles d'un degre donne, une borne pour le nombre d'integrales premieres dans les familles de champs vecteurs et une generalisation du critere de Darboux. Nous donnons aussi une nouvelle preuve du resultat de Gomez-Mont sur les feuilletages dont toutes les feuilles sont algebriques.
Mechanical behaviour and durability of high volume fly ash cementitious composites
The purpose of this research is to separate different morphological particles of ASTM class F fly ash, and study their effect on mechanical behaviour and durability of high volume cementitious mixtures. In this research wet separation of raw fly ash is carried out, which resulted in three layers of different morphological particles. The first layer of particles float, comprise of about 1-5% of fly ash, is identified as cenospheres or hollow spheres. The second layer of particles is measured to be 55-60% of raw fly ash and consisting of porous spherical and rounded particles rich in Si and Al. The third layer particles is measured to be about 35-40% of raw fly ash. High volume fly ash cementitious composites containing second or third layer particles are tested under compression and bending, highlighting a higher strength and ductility in comparison to cementitious ones containing raw fly ash particles. KEYWORDS. Cementitious matrix; Raw fly ash; Second layer particles; Third layer particles.