in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

the applicability of hollow fiber-based liquid phase microextraction (hf-lpme) was evaluated for the extraction and preconcentration of loratadine prior to determination by hplc. in order to obtain high extraction recovery, the parameters affecting the hf-lpme including type of organic phase, ph of the source and receiving phases, stirring rate, extraction time and salt addition were studied an...

We first demonstrate a simple "one-pot" method to synthesis uniform Fe3O4 hollow microspheres in the presence of PEG in ethylene glycol by using urea to control their morphologies. The interior cavity of the hollow spheres can be tunable by reaction time. The Lamer model was used to explain the formation of magnetite hollow spherical structures based on the experimental observations. The obtain...

Novel nanosized lead tungstate (PbWO4) hollow spindles were successfully synthesized, for the first time, via a Pluronic P123- (EO20PO70EO20-) assisted sonochemical process. The triblock copolymer acted as a structure-directing agent and played a key role in the formation of the hollow spindles. An in situ micelle templating mechanism has been proposed for the possible formation mechanism of th...

One hundred fifty to 300-nm-sized monodisperse iron oxide (Fe3O4) hollow microspheres were synthesized by the one-pot hydrothermal method. The morphology and crystal structure of the as-prepared hollow microspheres was characterized by scanning electron microscopy, X-ray diffraction, transmission electron microscopy, and high-resolution transmission electron microscopy, while the magnetic prope...

Gold octahedra with hollow features have been synthesized in high yield via the controlled overgrowth of preformed concave cube seeds. This Ag(+)-assisted, seed-mediated synthesis allows for the average edge length of the octahedra and the size of the hollow features to be independently controlled. We propose that a high concentration of Ag(+) stabilizes the {111} facets of the octahedra throug...

Background and purpose - A tapered, polished and collarless stem is normally equipped with a hollow centralizer to prevent the stem from becoming end-bearing in the cement as the stem subsides. In a randomized clinical trial, we evaluated such a stem (MS-30), which was initially introduced with a solid centralizer but was later recommended to be fitted with a hollow centralizer. We hypothesized...

MoS₂/RGO composite hollow microspheres were hydrothermally synthesized by using SiO₂/GO microspheres as a template, which were obtained via the sonication-assisted interfacial self-assembly of tiny GO sheets on positively charged SiO₂ microspheres. The structure, morphology, phase, and chemical composition of MoS₂/RGO hollow microspheres were systematically investigated by a series of technique...