Recent experimental work in lung morphogenesis has described an elegant pattern of branching phenomena. Two primary forms of branching have been identified: side branching and tip splitting. In our previous study of lung branching morphogenesis, we used a 4 variable partial differential equation (PDE), due to Meinhardt, as our mathematical model to describe the reaction and diffusion of morphog...

We analyze three-body decays of and . Under the factorization approach, there are tree level diagrams for these decay modes and the transition matrix element of decay is factorized into a form factor multiplied by decay constant and form factor multiplied into weak vertices form factor. The transition matrix element of decay is also factorized into a form factor multiplied into weak vertic...

Herein a quenched-flow kinetic technique was applied to calculate the rate constants of 1-hexene and 1-octene oligomerization catalyzed by the Cp2ZrCl2 and Cp2HfCl2/MAO catalyst systems, and subsequently a mechanism for the higher α-olefin oligomerization reaction was proposed. The oligomerization results showed that Zr-based catalyst in the oligomerization of 1-octene had the highest activity ...

In this study, the compatibility of the blends of polypropylene (PP) and polybutene-1(PB-1) homopolymer before and after long chain branching process were studied. The blends were prepared and long-chain branched directly via reactive extrusion process in presence of free radical initiator and trimethylolpropane tri methacrylate (TMPTMA) poly functional monomer. The optimum percentage of TMPTMA...

Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. In the present paper we establish some properties of integrating factors subjected to morphisms, and we...

internal iliac artery (iia) shows frequent variations in its branching pattern. we saw variations in the branching pattern of right iia in a male cadaver. the iia divided into anterior and posterior divisions. the branches of the anterior division included umbilical artery, inferior vesical artery, obturator artery. the other branches arose from posterior trunk such as iliolumbar, lateral sacra...

For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...