No abstract

No abstract

Maps between 3-manifolds has been studied by many people long times ago, and become an active subject again after Thurston's revolution on 3-manifold theory. We refer to [BW], [LWZ1] for various results and references on the subject.This paper addresses the following natural question which was raised around 1990, see also Kirby's Problem List,[K, 3.100].Question 1. Let M be a closed orientable 3-manifold. Are there at most finitely many closed, irreducible and orientable 3-manifolds N such that there exists a degree one map f : M → N ?Remarks on the conditions in Question 1. (i) If Poincare Conjecture fails, i.e., there is a homotopy 3-sphere N which is not S 3 , then one can get infinitely many reducible homotopy 3-spheres by doing connected sums on N . Since there always exists degree one map from a 3-manifold M to a homotopy 3-sphere, the condition "irreducible" on the target N is posed to avoid this unclear case.(ii) The condition "closed" is posed on M and N just for simplicity. Indeed we can replace "closed" by "compact", and meanwhile replace "degree one map" by "degree one proper map". A map f :For simplicity, we adapt the following definition from [BW]. Let M and N be two compact orientable 3-manifolds. Say M (1-)dominates N if there is a proper map f : M → N of non-zero degree (degree 1).A closed orientable 3-manifold is called geometric if it admits one of the following geometries: H 3 (hyperbolic),

Abstract. In this paper we study some necessary conditions and sufficient conditions for the nested polygonal solutions of planar 2N-body problems.

Two multisubstituted D-pi-A type pyridinium salts, N-methyl-2,6-di[(E)-p-dimethylaminophenylethenyl]pyridinium iodide (1) and N-methyl-2,4,6-tri[(E)-p-dimethylaminophenylethenyl]pyridinium iodide (2), were synthesized with good yields by a modified method, and the structure of 1 was confirmed by X-ray diffraction. The nonlinear optical absorption (NOA) properties of the two compounds in the solution state were investigated by the Z-scan technique. Compounds 1 and 2 both exhibited very strong saturated absorption at picosecond pulse, and 1 displayed reverse saturated absorption, while 2 revealed saturated absorption properties at the nanosecond pulse. The electron-donating ability, number of side chains, and molecular coplanar characteristics of the compounds have a significant impact on their NOA properties.

No abstract

We address the question that if π1-surjective maps between closed aspherical 3-manifolds have the same rank on π1 they must be of non-zero degree. The positive answer is proved for Seifert manifolds, which is used in constructing the first known example of minimal Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3-manifolds. Many examples are given.

The rhizosphere and the phyllosphere represent two different epiphytic compartments of host plant, which are closely related to plant growth, health, and productivity. However, the understanding of the diversity, composition, and assembly of the bacterial communities in different epiphytic microenvironments of large emerged macrophytes has remained elusive, especially the abundant and rare taxa across rhizosphere and phyllosphere communities. In this study, we collected samples of two different epiphytic compartments (rhizosphere and phyllosphere) of Phragmites australis. Both 16S rRNA gene-based high-throughput sequencing and null-model analysis were employed to determine the difference in the composition and assembly of above-mentioned epiphytic bacterial communities. Our results indicated that bacterial communities of rhizosphere exhibited higher diversity and richness than those of phyllosphere. Deterministic processes dominated the assembly of bacterial community in both compartments, and stochastic processes contributed a certain proportion (30.30%) in the assembly of phyllosphere bacterial community. We also found that rare taxa contributed more significantly to the alpha- and beta-diversity of bacterial community than those of abundant taxa. The obtained data are useful for better understanding the bacterial community of different epiphytic compartments of P. australis.