Factoriality for the reductive Zassenhaus variety and quantum enveloping algebra

Let U(g)$U(\mathfrak{g})$ be the enveloping algebra of a finite dimensional reductive Lie algebra g$\mathfrak{g}$ over an algebraically closed field of prime characteristic. Let _U?,P(s:)$U_{?,P}(\mathfrak{s}:)$ be the simply connected quantum enveloping algebra at the root of unity ?  , of a complex semi-simple finite dimensional Lie algebra s:$\mathfrak{s}:$. We show, by similar proofs, that the centers of both are factorial. While the first result was established by R. Tange [32] (by different methods), the second one confirms a conjecture in [4]. We also provide a general criterion for the factoriality of the centers of enveloping algebras in prime characteristic.     

Graded regulation technology for enhanced oil recovery and water shutoff in pore-cavity-fracture carbonate reservoirs

Although a single type of chemical agent (eg, gels, microspheres, surfactants, etc.) has achieved some effects in enhanced oil recovery of carbonate reservoirs, for pore-cavity-fracture carbonate reservoirs, the use of a single type of chemical agent does not perform well. The main objective of this study is to study the effect of different types of chemical agents in enhanced oil recovery of complex carbonate reservoirs. In order to determine the screening principle of chemical agents, the types of water channeling in the North Troyes reservoir were analyzed. For complex fractures, step by step plugging, multi-agent and multi-slug comprehensive intervention is carried out to ensure the plugging of high-permeability channels and inhibit the seepage of large channels. It can plug channeling fracture channel, adjust secondary dominant channel and reduce matrix flow resistance, so as to expand macroscopic swept volume and improve microscopic water flooding efficiency. The results show that it is difficult to comprehensively control water channeling in pore-cave-fracture carbonate reservoir, and the reservoir heterogeneity in the test area can be improved by mixing different types of control and flooding agents and carrying out deep profile control. The plugging rate of gel is 97.18 %, and the oil–water selection ratio is 0.45 in fractured core; the expansion rate of nano - microspheres is more than 3 times; the wetting modifier can improve the imbibition oil displacement efficiency by 14.76%, and the test result shown that nano - microspheres and wetting modifier have good synergistic oil displacement effect. The field application result shown that daily oil production of oil well in the test area increased by 5.0 m³/d and the daily water rate decreased by 19.0% compared with that before the control flooding. The findings of this study can help for better understanding of enhanced oil recovery in pore-cave-fracture carbonate reservoir.     

Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras

Using deformation theory, Braverman and Joseph constructed certain primitive ideals in the enveloping algebras of the simple Lie algebras. Except in the case sl(2,C)$\mathfrak{s}\mathfrak{l}(2,\mathbb{C})$, there is a special value of the deformation parameter giving an ideal of infinite codimension. For the classical Lie algebras, the uniqueness of the special value is equivalent to the existence of tensors with very particular properties. The existence of these tensors was concluded abstractly by Braverman and Joseph but here we present explicit formulae. This allows a rather direct computation of the special value of the deformation parameter.     

溶胶-凝胶法制备Pb(Zr1?xTix)O3复合梯度薄摸以及介电与热释电特性

"在Pt/Ti/SiO2/Si基片上用溶胶-凝胶法生长制备了PZT(Pb(Zr1-xTix)O3)复合梯度铁电薄膜． 薄膜最终结构由6层组成,"向上"梯度薄膜在Pt底电极上的第一层从PbZrO3开始,顶层是PZT(50/50),即第一层是PbZrO3,第二层PZT90/10 (10%Ti),第三层是PZT80/20,第四层PZT70/30,第五层PZT60/40,第六层PZT50/50．每一层与此相反的是"向下"梯度PZT薄膜．用X射线衍射、俄歇电子能谱和阻抗分析来研究梯度薄膜的结构与介电特性．600     

Electrical and optical properties of Si-doped indium tin oxides as transparent electrode and anti-reflection coating for solar cells

We have studied the electrical and optical properties of Si-doped indium tin oxides (ITSOs) as transparent electrodes and anti-reflection coatings for Si-based solar cells. The ITSO thin films were obtained by co-sputtering of ITO and SiO₂ targets under target power control. The resistivity of the ITSO thin films deposited at 0.625 in terms of power ratio (ITO/SiO₂) were 391 Ωcm. In this condition, the ITSO thin films showed very high resistivity compared to sputted pure ITO thin films (1.08 × 10⁻³ Ωcm). However, refractive index of ITSO thin films deposited at the same condition at 500 nm is somewhat lowered to 1.97 compared to ITO thin films (2.06). The fabricated graded refractive index AR coatings using ITO, ITSO, and SiO₂ thin films kept over 80% of transmittance regardless of their thickness varing from 97 nm to 1196 nm because of their low extinction coefficient. As the AR coating with graded refractive indices using ITO, ITSO, and SiO₂ layers was applied to general silicon-based solar cell, the current level increased nearly twice more than that of bare silicon solar cell without AR coating.     

Modules of the Intermediate Series over Not-finitely Graded Lie Algebras W(Γ)

Let W(Γ)be a class of not-finitely graded Lie algebras related to gener-alized Virasoro algebras with basis{Lα,i,C | α ∈ Γ,i ∈ Z+},which satisfies relations[Lα,i,Lβ,j]=(β-α)Lα+β,i+j+(j-i)Lα+β,i+j+1+δα+β,0δi+j,0α3-α/12C and[C,Lα,i]=0.In this paper,W(Γ)-modules of the intermediate series satisfying some conditions are con-structed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra.     

Quantizer–dequantizer operators as a tool for formulating the quantization procedure

We consider the quantization procedure and investigate the application of the quantizer–dequantizer method and star-product technique to construct associative products and the associative algebras formed by the quantizer–dequantizer operators and their symbols. The corresponding Lie algebras are also constructed. We study the case where the quantizer–dequantizer operators form a self-dual system and show that the structure constants of the Lie algebras satisfy some identity, in addition to the Jacobi identity. Using tomographic quantizer–dequantizer operators and their symbols, we construct the continuous associative algebra and the corresponding Lie algebra.