Ni‐Catalyzed [4+3+2] Cycloaddition of Ethyl Cyclopropylideneacetate and Dienynes: Scope and Mechanistic Insights

A detailed study of the Ni‐catalyzed [4+3+2] cycloaddition reaction between ethyl cyclopropylideneacetate and dienynes has been conducted, resulting in the development of a new method for the synthesis of compounds containing nine‐membered rings. We studied the reactivity of various dienynes, together with their substituent and conformational effects. The mechanism of the reaction was probed by examining the stoichiometric reactions of the Ni complexes and dienynes.     

多级离心泵内叶轮出口压力脉动研究

为研究瞬态工况下离心泵叶轮出口处的压力脉动情况,为离心泵泄漏流道流动提供边界条件,建立了包含叶轮和导叶流道的离心泵模型,基于CFD方法计算得到了其在不同工况下的性能参数,利用测试数据对结果进行了验证。分析了瞬态工况下叶轮出口处压力的变化趋势,比较了不同工况对叶轮出口压力脉动的影响,发现叶轮出口压力随叶轮旋转呈周期性变化,压力脉动频率与转速及叶轮数量有关;偏工况时叶轮出口压力脉动趋势与额定工况基本一致,但脉动频率及脉动幅值有较大区别;随离心泵转速增加,叶轮出口处压力脉动的最大值和最小值均呈减小趋势,但幅值随转速增加而增加,且增幅明显。     

Invariants of matrix pairs over discrete valuation rings and Littlewood-Richardson fillings

Let M and N be two r×r matrices of full rank over a discrete valuation ring R with residue field of characteristic zero. Let P,Q and T be invertible r×r matrices over R. It is shown that the orbit of the pair (M,N) under the action (M,N)?(PMQ^-1,QNT^-1) possesses a discrete invariant in the form of Littlewood-Richardson fillings of the skew shape λ/μ with content ν, where μ is the partition of orders of invariant factors of M, ν is the partition associated to N, and λ the partition of the product MN. That is, we may interpret Littlewood-Richardson fillings as a natural invariant of matrix pairs. This result generalizes invariant factors of a single matrix under equivalence, and is a converse of the construction in Appleby (1999) [1], where Littlewood-Richardson fillings were used to construct matrices with prescribed invariants. We also construct an example, however, of two matrix pairs that are not equivalent but still have the same Littlewood-Richardson filling. The filling associated to an orbit is determined by special quotients of determinants of a matrix in the orbit of the pair.     

Gorenstein flatness and injectivity over Gorenstein rings

Let R be a Gorenstein ring.We prove that if I is an ideal of R such that R/I is a semi-simple ring,then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical.In addition,we prove that if R→S is a homomorphism of rings and SE is an injective cogenerator for the category of left S-modules,then the Gorenstein flat dimension of S as a right R-module and the Gorenstein injective dimension of E as a left R-module are identical.We also give some applications of these results.     

On the shepherding of Uranian epsilon ring

To explain the long-term existence of Uranian narrow rings, we study the dynamical evolution of Uranian epsilon ring under the influence of its two shepherding satellites: Cordelia and Ophelia. The model of planar-elliptic restricted three-body problem is employed, in which the three bodies are Uranus, a satellite and a test particle. Dissipations due to interparticle collisions are also taken into consideration. A mapping system has been obtained based on the differential equation system. Numerical results show that only those particles originally lying in the libration region of the resonance can be shepherded. The size of the libration region depends mainly on the orbital eccentricity and mass of the shepherd satellite. For the outer shepherd Ophelia with larger orbital eccentricity, if its mass is a third of the nominal mass 2.5 × 10¹⁹ g, most of the orbits are regular and the outer edge of the ring can be shepherded, but more fuzzy than the inner edge. Thus we infer that Ophelia has a smaller mass.     

Thermal behavior of aromatic polyamic acids and polyimides containing oxadiazole rings

Two aromatic polyimides and the corresponding poly(amic acid)s, with oxadiazole and para/meta phenoxyphenylene rings in the backbone, were synthesized and the structure — thermal properties correlation was followed by dynamic mechanical analysis. Concerning the poly(amic acid)s, the glass transition domain was emphasized only for the compound with meta-oriented rings because the process of imidization takes place with increasing temperature. A multiplex experiment was performed to calculate the activation energy of the transition localized under 200°C. Consecutive heating-cooling-heating cycles were accomplished. All phenomena are discussed by cross-examination of the storage modulus (E′), loss modulus (E″) and loss factor tanδ variation with temperature.     

亚直不可约环成为全矩阵环的条件

给出了亚直不可约环是除环上的全矩阵环的一个新的条件。     

Molecular complexity from aromatics: synthesis of highly functionalized spiro δ-lactones

A novel, general, and efficient method has been developed for the synthesis of highly functionalized spiro δ-lactones from aromatic precursors. Our methodology involves a tandem oxidative dearomatization-rearrangement of tertiary furyl carbinols and ring-closing metathesis as key features. This method allows an access to the spirolactones attached to carbocycles of various sizes.