Blended implicit methods for solving ODE and DAE problems,and their extension for second-order problems

The use of implicit numerical methods is mandatory when solving general stiff ODE/DAE problems. Their use, in turn, requires the solution of a corresponding discrete problem, which is one of the main concerns in the actual implementation of the methods. In this respect, blended implicit methods provide a general framework for the efficient solution of the discrete problems generated by block implicit methods. In this paper, we review the main facts concerning blended implicit methods for the numerical solution of ODE and DAE problems.     

A non-stationary problem coupling PDEs and ODEs modelizing an automotive catalytic converter

In this article we prove the existence and uniqueness of the solution of a non-stationary problem that modelizes the behavior of the concentrations and the temperature of gases going through a cylindrical passage of an automotive catalytic converter. This problem couples parabolic partial differential equations (PDEs) in a domain with one parabolic partial differential equation and some ordinary differential equations (ODEs) on a part of its boundary.     

First and second moments for self‐similar couplings and Wasserstein distances

We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of couplings, which are measures on the product space with the original measures as prescribed marginals. We focus our attention on self‐similar measures associated to equicontractive iterated function systems consisting of two maps on the unit interval and satisfying the open set condition. We are particularly interested in understanding the restricted family of self‐similar couplings and our main achievement is the explicit computation of the 1st and 2nd moment integrals for such couplings. We show that this family is enough to yield an explicit formula for the 1st Wasserstein distance and provide non‐trivial upper and lower bounds for the 2nd Wasserstein distance for these self‐similar measures.     

Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets

We study Minkowski contents and fractal curvatures of arbitrary self-similar tilings (constructed on a feasible open set of an IFS) and the general relations to the corresponding functionals for self-similar sets. In particular, we characterize the situation, when these functionals coincide. In this case, the Minkowski content and the fractal curvatures of a self-similar set can be expressed completely in terms of the volume function or curvature data, respectively, of the generator of the tiling. In special cases such formulas have been obtained recently using tube formulas and complex dimensions or as a corollary to results on self-conformal sets. Our approach based on the classical Renewal Theorem is simpler and works for a much larger class of self-similar sets and tilings. In fact, generator type formulas are obtained for essentially all self-similar sets, when suitable volume functions (and curvature functions, respectively) related to the generator are used. We also strengthen known results on the Minkowski measurability of self-similar sets, in particular on the question of non-measurability in the lattice case.     

On the complexity of some subgraph problems

We study the complexity of the problem of deciding the existence of a spanning subgraph of a given graph, and of that of finding a maximum (weight) such subgraph. We establish some general relations between these problems, and we use these relations to obtain new NP-completeness results for maximum (weight) spanning subgraph problems from analogous results for existence problems and from results in extremal graph theory. On the positive side, we provide a decomposition method for the maximum (weight) spanning chordal subgraph problem that can be used, e.g., to obtain a linear (or O(nlogn)) time algorithm for such problems in graphs with vertex degree bounded by 3.     

New large deviation results for some super-Brownian processes

We give large deviation results for the super-Brownian excursion conditioned to have unit mass or unit extinction time and for super-Brownian motion with constant non-positive drift. We use a representation of these processes by a path-valued process, the so-called Brownian snake for which we state large deviation principles.     

钙伯三醇的关键中间体——麦角甾烷-5，7（E），10（19）-三烯-6（S）-二氧化硫的合成

麦角甾烷-5,7(E),10(19),22(E)-四烯-6(S)-二氧化硫(1)经臭氧化反应合成了钙伯三醇(MC903)的重要中间体--麦角甾烷-5,7(E),10(19)-三烯-6(S)-二氧化硫(2),其结构经1H NMR和13C NMR表征.较佳的臭氧化反应条件为:1 1.0 mmol,溶剂为V(二氯甲烷):V(甲醇)=4:1,于-65℃～-78℃反应12 min.在此条件下,2中醛基α-位的差相异构化降至最低程度,产率90%.对差相异构化的机理进行了讨论.     

Theoretical study of endohedral metallofullerenes: Sc3−nLanN@C80 (n=0–3)

To provide theoretical insight into the structures and properties of Sc₃N@C₈₀, which has been isolated in high yield and purity as a new stable endohedral metallofullerene, density functional calculations are carried out for the Sc_3?nLa_nN@C₈₀ (n=0–3) series. Because of electron transfer from Sc₃N to C₈₀, the electronic structure of Sc₃N@C₈₀ is formally described as (Sc₃N)⁶⁺C$_{80}^{6-}$. The encapsulated Sc₃N cluster takes a planar structure with long Sc–Sc distances and is highly stabilized inside the I_h cage of C₈₀, which rotates rapidly. As the number of La atoms increases, the Sc_3?nLa_nN cluster is forced to maintain a pyramidal structure in Sc_3?nLa_nN@C₈₀. In addition, the C₈₀ cage takes an open‐shell electronic structure due to an increase in the number of electrons transferring from Sc_3?nLa_nN. These make the endohedral structure less stable and more reactive. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1353–1358, 2001     

胶束液相色谱法测定制剂和尿样中布洛芬

采用胶束液相色谱法分离和测定制剂和尿样中布洛芬,考察了表面活性剂的种类及浓度、柱温、流动相pH值,流速对布洛芬色谱保留行为的影响,探讨并提出了布洛芬在吐温-80为非离子表面活性剂的胶束液相色谱中的色谱保留模型。以ZORBAXExtend-C18色谱柱(4.6mm×250mm,5μm),20mmol.L-1吐温-80和25mmol.L-1磷酸氢二钾(pH7.8)混合溶液为流动相,在263nm处进行测定,布洛芬的保留时间为5.8min。布洛芬的质量浓度在0.2～1.0g.L-1范围内呈线性关系,检出限(3S/N)为1.1ng,平均回收率达98.3%～102.1%。     

2种癸二酸咪唑啉季铵盐的合成及缓蚀性能评价

合成了2种癸二酸咪唑啉季铵盐癸二酸-水杨酸咪唑啉季铵盐(SSAI)和癸二酸咪唑啉季铵盐(SAI),并采用失重法和电化学方法研究了这2种咪唑啉季铵盐对N80钢在1 mol/L HCl溶液中的缓蚀性能和吸附行为。 结果表明,在1 mol/L HCl溶液中这2种化合物对N80钢均有较好的缓蚀作用,缓蚀效率大小顺序为SSAI＞SAI。 SSAI和SAI均为混合偏阳极型缓蚀剂。 2种化合物在N80钢表面的吸附服从Langmuir吸附等温式,属于化学吸附。