Abstract:
Several hundred million tons of ion-adsorption rare earth tailings exist in Ganzhou, Southern China,
which is a severe environmental hazard. To reduce and reutilize the tailing, kaolinite has been
separated from the tailings by mechanical separation in laboratory scale and pilot scale. The results
show that the tailing is mainly composed of fine kaolinite and coarse quart. Quartz and kaolinite
can be separated by sieves, shaker, spiral chute or hydrocyclone, which has the similar results
in laboratory scale and pilot scale. 30.2% of the tailings can be re-sourced and applied in ceramic
industries. 41.7% of kaolinite can be obtained after sorting and iron removal by magnetic separator
in pilot scale, which can be applied in ceramic industries according to the Chinese national
standard (TC-3). The results give a progressive solution to re-source the tailings economically.

Abstract:
The ion-adsorption rare earth tailings have become a serious environmental pollution in Southern
China, yet the potential of their economical value has not been fully exploited. In this work, the
chemical and mineral compositions of the ion-adsorption rare earth tailings were characterized
by Mineral Liberation Analyze (MLA) and XRF. The results show that 91.98 wt% of the tailings are
composed of kaolinite and quartz, latter of which was removed by the sieving method. The other
minor minerals contain feldspar, biotite, muscovite, titanomagnetite and limonite. Amongst these,
the iron-bearing minerals are mostly found in the titanomagnetite and limonite which can be
mostly removed by using a periodic high-gradient magnetic separator with a magnetic induction
of 0.6 Tesla. The Fe_{2}O_{3} content of the tailings changed from 2.11 wt% to 1.06 wt% after the sorting
process, which met the Chinese national standard of TC-3 grade raw materials for ceramic industry
applications. The Fe_{2}O_{3} content in kaolinite was further decreased after Na_{2}S_{2}O_{4} treatment.

Abstract:
In this paper, we develop a diamond graph theory and apply the theory to the (co)homology of the Lie algebra generated by positive systems of the classical semi-simple Lie algebras over the field of complex numbers. As an application, we give the weight decomposition of the diamond Lie algebra with Dynkin graph $A_{n+1}$ and compute the rank of every weight subgraph of it.

Abstract:
In this paper, we find weight decomposition and rank of a weight in the integral (co)homology of the positive system of a semi-simple Lie algebra over $\Bbb C$ and prove that the (co)homology of the weight subcomplex over a field of characteristic p is 0 if the rank of the weight is not divisible by p. This generalizes Kostant theorem to the integral cohomology of the positive system.

Abstract:
In this paper, we compute the cohomology ring of all homology split polyhedral product spaces and the cohomology algebra over a field of all polyhedral product spaces. As an application, we give two polyhedral product spaces such that all the cohomology homomorphisms induced by inclusion map are the same, but the cohomology ring of the two polyhedral product spaces are not isomorphic.

Abstract:
In this paper, we define a new bigraded L-homology on finite simplicial complexes and prove that L-homology is a homeomorphism invariant of polyhedra.

Abstract:
In this paper, we compute the homology coalgebra and cohomology algebra over a field of all generalized moment-angle complexes and give a duality theorem on complementary moment-angle complexes.

Abstract:
YSZ--Al$_{2}$O$_{3}$ composite membranes with different composition were introduced to reduce the stress occurred during heat treatment, which could make the membrane have defects and microcracks. The degree of components and the thickness of the composite membrane were considered simultaneously. The data showed that linear expansion coefficient and sintered shrinkage increased with the increase of YSZ content. The sintered shrinkage was an important factor to choose the composition. Two composite membranes with 20\% (volume fraction) and 80\% of YSZ content were prepared. And the pore sizes of two composite membranes are 0.72 $\mu$m and 0.36 $\mu$m, respectively. The composite membrane is an excellent microfiltration membrane and a support for the preparation of YSZ ultrafiltration membrane and nanofiltration membrane.

Abstract:
A simplicial complement P is a sequence of subsets of [m] and the simplicial complement P corresponds to a unique simplicial complex K with vertices in [m]. In this paper, we defined the homology of a simplicial complement $H_{i,\sigma}(\Lambda^{*,*}[P], d)$ over a principle ideal domain k and proved that $H_{*,*}(\Lambda[P], d)$ is isomorphic to the Tor of the corresponding face ring k(K) by the Taylor resolutions. As applications, we give methods to compute the ring structure of Tor_{*,*}^{k[x]}(k(K), k)$, $link_{K}\sigma$, $star_{K}\sigma$ and the cohomology of the generalized moment-angle complexes.

Abstract:
In this paper, we define homeology group, reduced homeology group, cohomeology group and reduced cohomeology group on finite simpicial complexes and prove that these groups are homeomorphism invariants of polyhedra. We also define homeotopy type of polyhedra which is finer than homotopy type but coarser than homeomorphism class.