Total Synthesis of (+)‐β‐Himachalene

An enantioselective synthesis of (+)‐β‐himachalene ( 2 ) was accomplished starting from (1S,2R)‐1,2‐epoxy‐p‐menth‐8‐ene ( 3 ) in 15 or 16 steps with an overall yield of ca. 6% (Schemes 3, 5, and 6). Key transformations include an Ireland–Claisen rearrangement, a Corey oxidative cyclization, and a ring expansion.     

Formation of spiro ketolactones versus alkoxy radical fragmentation-promoted three-atom ring enlarged lactones from cyclic ketones

A dual pathway from readily available 2-allyl-2-carboethoxycycloalkanones 1 provides a new facile stereoselective synthesis either of functionalized spiro ketolactones 4 or of ring enlarged lactones 7 in one-step. Thus, iodination of 5-8-membered 2-allyl-2-carboethoxycycloalkanones 1a-d led, in excellent yields, to spiro ketolactones 4a-d, respectively, as single stereoisomers. On the other hand, iodination of 1a-d under alkoxy radical fragmentation conditions via incipient hemiketals produced the 8-, 9-, 10-, or 11-membered, three-atom ring enlarged, poly-functionalized lactones 7a-c as two stereoisomers and 8 as a single isomer.     

Titanium(IV) chloride-mediated intramolecular ring enlargement of methylenecyclopropanes with propargylic esters: a concise synthesis of bicyclo[4.2.0]oct-5-ene derivatives

Titanium(IV) chloride-mediated intramolecular ring enlargement of methylenecyclopropanes with propargylic esters has been described in this context, affording the corresponding chlorinated bicyclo[4.2.0]oct-5-ene derivatives in moderate to good yields under mild conditions. The E- and Z-methylenecyclopropanes could all be converted to the corresponding bicyclo[4.2.0]oct-5-enes with moderate to high diastereoselectivities.     

大分子引发－转移－终止剂

大分子引发－转移－终止剂杨文君，李俊柏，沈家骢（青岛化工学院橡塑工程研究所，青岛，２６６０４２）（吉林大学化学系，长春，１３００２３）关键词聚苯乙烯，聚丙烯酰胺，嵌段共聚，扩链反应，引发－转移－终止剂含有二乙基二硫代氨基甲酸基的有机硫化物或大分子，在...     

Nonstandard perturbation approximation and travelling wave solutions of nonlinear reaction diffusion equations

This paper deals with the construction of a nonstandard numerical method to compute the travelling wave solutions of nonlinear reaction diffusion equations at high wave speeds. Related general properties are studied using the perturbation approximation. At high wave speed the perturbation parameter approaches to zero and the problem exhibits a multiscale character. That is, there are thin layers where the solution varies rapidly, while away from these layers the solution behaves regularly and varies slowly. Most of the conventional methods fail to capture this layer behavior. Thus, the quest for some new numerical techniques that may handle the travelling wave solutions at high wave speeds earns relevance. In this paper, one such parameter robust nonstandard numerical scheme is constructed, in the sense that its numerical solution converges in the maximum norm to the exact solution uniformly well for all finite wave speeds. To overcome the difficulty due to the nonlinearity, the problem is linearized using the quasilinearization process followed by nonstandard finite difference discretization. An extensive amount of analysis is carried out which uses a suitable decomposition of the error into smooth and singular component and a comparison principle combined with appropriate barrier functions. The error estimates are obtained, which ensures uniform convergence of the method. A set of numerical experiment is carried out in support of the predicted theory that validates computationally the theoretical results. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

气体钻水平井井径扩大环空流动特征的数值模拟

由于气体钻水平井中岩屑受力状态与直井有很大不同,特另0是遇到井径扩大,更是携岩的关键点。因此,在分析了气体钻水平并岩屑运移特点以及建立环空连续性方程和动能方程的基础上,以实际并为例考虑了不同井径扩大率,数值模拟了其扩径段气固两相的流动状态,包括气固速度、岩屑浓度、压力分布等。研究结果表明：气体在经历扩径段时环空压力有个降落又回升的过程,随着井眼扩径系数的增大,压力下降又回升,所经历的长度会逐渐增长;扩径系数大于一定值时,扩径变径处存在一定区域的零流动区;扩径系数越大,低速区和回流区就越大越长,扩径下部区域越容易堆积岩屑,填充井眼。     

On the theory of grossone

A trivial formalization is given for the informal reasonings of a series of papers by Ya. D. Sergeyev on a positional numeral system with an infinitely large base, grossone; the system which is groundlessly opposed by its originator to the classical nonstandard analysis.     

Ring Enlargement of Alkaloids

Previouspublications'fromourlaboratoryhadreportedtheringenlargementreactionofquatemaryarnrnoniumsaltSofN-methyl-tetTahydroisoquinolinefollowedbyreductivedecyanationwiththenetresuItoftheinserti0nofanextraCH2group,assh0wninSckemeI.ThemethodologyfailedwithsomenatUrallyoccurringalkaloidssuchascephalotaxineandatropine'.Onereasonisthatsomeofthequaternaryammoniumsaltsaredifficulttoprepare,theotheroneisthatsome0fthequaternaryafnmoniumsaItsunderwentHofinarineliminationorSofnmeletrearrangement'.But…     

Application of a Mickens finite‐difference scheme to the cylindrical Bratu‐Gelfand problem

The boundary value problem Δu + λe^u = 0 where u = 0 on the boundary is often referred to as “the Bratu problem.” The Bratu problem with cylindrical radial operators, also known as the cylindrical Bratu‐Gelfand problem, is considered here. It is a nonlinear eigenvalue problem with two known bifurcated solutions for λ < λ_c, no solutions for λ > λ_c and a unique solution when λ = λ_c. Numerical solutions to the Bratu‐Gelfand problem at the critical value of λ_c = 2 are computed using nonstandard finite‐difference schemes known as Mickens finite differences. Comparison of numerical results obtained by solving the Bratu‐Gelfand problem using a Mickens discretization with results obtained using standard finite differences for λ < 2 are given, which illustrate the superiority of the nonstandard scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 327–337, 2004