In this paper, we firstly establish a useful ODE relationship between R1(c) and V1(c) on the steady Ricci soliton. Based on this, we obtain a necessary and sufficient condition for some complete noncompact steady gradient Ricci solitons to have positive asymptotic volume ratio.
A material is spherically uniform when its generalized Hooke´s law at each material point referred to a spherical coordinate system is the same everywhere. We study a sphere of spherically uniform linear anisotropic one-dimensional quasicrystalline material subjected to radial phonon and phason strains on its surface. For a certain range of material parameters the phonon as well as the phason stress diverges at the center. The applied phason strain does not affect the phonon field but the phason field is disturbed by the phonon strain. “White hole” at the center may occur when the sphere is subjected to uniform tension while uniform pressure may cause a “black hole”. This behavior depends only on a dimensionless material parameter and the kind of applied strain but not on its magnitude.
The genetic diversity and population structure of Chrysichthys nigrodigitatus were evaluated using a 443 base pair fragment of the mitochondrial control region. Among the eight populations collected comprising 129 individuals, a total of 89 polymorphic sites defined 57 distinct haplotypes. The mean haplotype diversity and nucleotide diversity of the eight populations were 0.966±0.006 and 0.0359±0.004, respectively. Analysis of molecular variance showed significant genetic differentiation among the eight populations (FST =0.34; P < 0.01). The present results revealed that C. nigrodigitatus populations had a high level of genetic diversity and distinct population structures. We report the existence of two monophyletic matrilineal lineages with mean genetic distance of 10.5% between them. Non-significant negative Tajima’s D and Fu’s Fs for more than half the populations suggests that the wild populations of C. nigrodigitatus underwent a recent population expansion, although a weak one since the late Pleistocene.
In this paper, we deal with the complete non-compact expanding gradient Ricci soliton (Mn,g) with positive Ricci curvature. On the condition that the Ricci curvature is positive and the scalar curvature approaches 0 towards infinity, we derive a useful estimate on the growth of potential functions. Based on this and under the same assumptions, we prove that ∫t0 Rc (γ'(s) , γ' (s))ds and ∫t0 Rc (γ' (,s). v)ds at least have linear growth, where 7(5) is a minimal normal geodesic emanating from the point where R obtains its maximum. Furthermore, some other results on the Ricci curvature are also obtained.
The micellar catalytic field was proposed in surfactant medium by investigating the complexation between p-nitro-o-carboxylbenzeneazo-8-aminoquinoline (NCBAAQ) and Co(II) at pH 8.8. The cationic surfactant, cetyl trimethylammonium bromide (CTAB) was added and the aggregation of NCBAAQ on CTAB obeys the Langmuir isothermal adsorption. The enrichment of NCBAAQ on CTAB micelle resulted in a sensitive and rapid complexation of NCBAAQ with Co(II). The ternary complexation was characterized by the microsurface adsorption – spectral correction (MSASC) technique. Results showed that the complex Co3NCBAAQ12CTAB78 is formed.