非线性边界条件下二阶奇异差分方程的正解

本文我们考虑如下二阶奇异差分边值问题\begin{equation*}\begin{cases}-\Delta^{2} u(t-1)=\lambda g(t)f(u) ,\ t\in [1,T]_\mathbb{Z},\\u(0)=0,\\ \Delta u(T)+c(u(T+1))u(T+1)=0,\end{cases}\end{equation*}正解的存在性. 其中, $\lambda>0$, $f:(0,\infty)\rightarrow \mathbb{R}$ 是连续的,且允许在~$0$ 处奇异.通过引入一个新的全连续算子, 我们建立正解的存在性.     

Physico-chemical properties of Tecoma stans Linn. seed oil: a new crop for vegetable oil

Tecoma stans Linn. is known to have various medicinal and therapeutic properties. However, to our knowledge, no information is available regarding their seed oils. In this study, the fatty acid (FA) compositions, physico-chemical properties and antioxidant capacities of T. stans seed oils (TSOs) were investigated. The oil content of the seeds was 15%. The FAs of the TSOs were analysed by GC–MS. α-Linolenic (45.47%), oleic (23.56%), linoleic (11.48%), palmitic (6.09%) and stearic (4.12%) acids were the major detected FAs. γ-Linolenic acid and stearidonic acid, unusually FAs, were also present (1.04% and 6.65%, respectively). The total tocol content in the TSOs was found to be 266.06 mg/100 g. The main component was γ-tocopherol (78.93%). The total phenolic content (168.69 mg GAE/100 g oil) and total flavonoid content (5.54 mg CE/g oil) were also determined in the TSOs.     

Reversible addition-fragmentation chain transfer polymerization of N-isopropylacrylamide: a comparison between a conventional and a fast initiator

The reversible addition-fragmentation chain transfer (RAFT) polymerization of N-isopropylacrylamide (NIPAM) was studied to determine the reasons for deviation of experimental molecular weights to lower molecular weight at high monomer conversion when S-1-dodecyl-S-(alpha,alpha'-dimethyl-alpha' '-acetic acid)trithiocarbonate (CTAm) and S,S-bis(alpha,alpha'-dimethyl-alpha' '-acetic acid)trithiocarbonate (CTAd) were used as RAFT agents at 65 degrees C. For this purpose, experiments were performed in N,N'-dimethylformamide (DMF) at the NIPAM/CTA ratio of 200 with initiators capable of yielding fast and slow initiation, respectively by photochemical and thermal process, either at ambient temperature or at 65 degrees C. When the polymerization of NIPAM was conducted under these conditions with Irgacure-2959 (IRGC) as photoinitiator, a continuing supply of primary radicals by incremental initiator addition was required to achieve reasonably high conversion. This effect was also apparent by the loss of linearity of the first-order kinetic plot with a conventional initiator (4,4-azobis(4-cyanovaleric acid) (ACVA) as azo-initiator, 10h (t1/2) decomposition at 65 degrees C) indicating that steady-state concentration of the macroradical decreases significantly with the initiator consumption. Nevertheless, polymers with predictable number-average molecular weight Mn (i.e., based on [monomer]/([CTA] + [initiator]) ratio) and narrow polydispersities were obtained (PDIs < 1.2) with CTAm indicating that the process of chain growth was controlled. When CTAd was used, instead of CTAm, the polymers obtained were characterized by a larger polydispersity (1.2 < PDIs < 1.3). The so-called "living steady-state concentration" in chain equilibration together with the linear dependence of Mn vs conversion was observed only when the 200/1 NIPAM/CTA mixture in DMF was subjected to a permanent photoirradiation at 65 degrees C. With ACVA, the deviation of the experimentally measured molecular weights at high conversion was accounted for by the simultaneous self-initiated polymerization of NIPAM with the controlled process in the presence of CTA at 65 degrees C. Similar drift from the linear dependence Mn vs conversion was also observed at 65 degrees C when a significant number of low molecular weight polymer chains were generated intentionally by photodecomposition of IRGC.     

Crystal structure of monomethylammonium monochlorodibromomercurate(II)

The crystal structure of monomethylammonium monochlorodibromomercurate (II) was refined from single crystal X-ray data including the fractional contribution of centrosymmetric domains. The refinement converged toR=0.05 in space groupC2. The fraction of structure and its inverse were detected in the refinement. The structure is one-dimensional consisting of distorted tetrahedra (HgCl₂Br₂) connected together by chlorine atoms, The CH₃NH ₃ ⁺ groups are connected to the chains by hydrogen bonds to the halogen atoms contributing to the cohesion of the crystal.     

Crystal structure of monomethylammonium monochlorodibromomercurate(II)

The crystal structure of monomethylammonium monochlorodibromomercurate (II) was refined from single crystal X-ray data including the fractional contribution of centrosymmetric domains. The refinement converged toR=0.05 in space groupC2. The fraction of structure and its inverse were detected in the refinement. The structure is one-dimensional consisting of distorted tetrahedra (HgCl₂Br₂) connected together by chlorine atoms, The CH₃NH ₃ ⁺ groups are connected to the chains by hydrogen bonds to the halogen atoms contributing to the cohesion of the crystal.     

New Sobolev-Weinstein Spaces and Applications

In this paper, we consider the generalized Weinstein operator $\Delta_{W}^{d,\alpha,n}$, we introduce new Sobolev-Weinstein spaces denoted $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1}),$ $s\in\mathbb{R},$ associated with the generalized Weinstein operator and we investigate their properties. Next, as application, we study the extremal functions on the spaces $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1})$ using the theory of reproducing kernels.     

可交联聚醚醚酮酮交替共聚物的合成与热交联研究

聚芳醚酮类特种工程塑料以其优异的机械性能、热稳定性、耐溶剂、耐辐照等特性在运输、航空航天、军事、电子、信息、核能等领域得到了广泛应用_{[1].聚醚醚酮的玻璃化转变温度(Tg)和熔点(Tm)分别为416和607 K,其长期使用温度为513 K,而其热分解温度在800 K以上,是热稳定性较好的聚合物之一.为了满足一些特殊需求,人们通过在聚芳醚酮的主链中引入刚性结构链,提高其主链的刚性程度,从而提高其T g和Tm,进而提高其使用温度[2～4].文献[5]报道的新型聚芳醚酮的T g和T m最高可达482和742 K,采用常规方法进行加工难度较大.为了在不提高加工温度的前提下提高聚芳醚酮类材料的使用温度,我们已成功地在聚醚醚酮的主链中引入可交联的硫醚结构,得到使用温度更高的可控交联聚醚醚酮材料,其可利用热塑性材料的加工方法进行加工,加工温度与聚醚醚酮相同,交联后的材料具有热固性材料的使用特性[6,7].为了拓宽可交联聚芳醚酮材料的种类,本文合成了一种类新型的可交联型聚醚醚酮酮材料,并对其热交联性能进行了研究.}     

刚性环状低聚物的二维有序单分子膜结构

近十年来 ,为了解决耐高温高分子材料加工温度高、熔体粘度大等问题 ,材料学家们研制和开发了一系列刚性环状齐聚物 ,如环状聚芳醚酮[1] 、环状聚芳醚砜[2 ] 和环状聚苯硫醚[3] 等 .但早期人们主要把含有刚性链段的环状齐聚物 (RCO)作为结构材料研究 .1 993年 ,Miyashita[4 ] 等发现 ,含有近似刚性的酰胺键的手性环状二苯胺低聚物具有与经典 LB分子相似的双亲性 ,可以获得手性 LB膜 .近来我们合成了一系列直径可控、含有不同活性功能基团的 RCO.RCO是一类潜力巨大的有机纳米功能材料 ,其具有以下性质 :(1 )纳米空穴直径稳定且可控 ;(2…