In this paper, a critical Galton-Watson branching process with immigration Zn is studied. We first obtain the convergence rate of harmonic moment Zn. Then large deviation $${S_{{Z_n}}}≔ \sum\nolimits_{i = 1}^{{Z_n}} {{X_i}} $$ obtained, where {Xi} sequence independent and identically distributed zero-mean random variables tail index α > 2. shall see that converging determined by mean, variance ...

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...

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...

In this article we prove that a semialgebraic map $$\pi :M\rightarrow N$$ is branched covering if and only its associated spectral covering. addition, such has neat behavior with respect to the branching locus, ramification set index. A crucial fact preceding result characterization of prime ideals whose fibers under previous are singletons.

The forgotten topological index of a (molecule) graph is the sum cubes all its vertex degrees, which plays significant role in measuring branching carbon atom skeleton. It meaningful and difficult to explore sufficient conditions for given keeping certain properties theory. In this paper, we mainly terms be ℓ-connected, ℓ-deficient, ℓ-Hamiltonian ℓ−-independent, respectively. cannot dropped.