Alkylation of cyclododecanone with α,ω-dibromoalkanes under conditions of phase-transfer catalysis

Alkylation of cyclododecanone with ,-dibromoalkanes Br(CH) _n Br (n=3, 4, 5) under conditions of phase-transfer catalysis in the presence of KOH results in the formation of either bicyclic ketones forn=3 and 5 or a mixture of bicyclic and spirocyclic ketones forn=4.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1436–1438, August, 1994.     

Relationship between tetrahedron shape measures

Tetrahedron shape measures are used for evaluating the quality of tetrahedra in finite element meshes. Three shape measures, theminimum solid angle _min theradius ratio , and themean ratio , are discussed in this paper. A new formula for the computation of a solid angle of tetrahedron is derived. For different shape measures andv (with values 1), we establish a relationship between andv of the form wherec ₀,c ₁,e ₀, ande ₁ are positive constants. This means that if one measure approaches zero for a poorly-shaped tetrahedron, so does the other. Combined with the property that each measure attains a maximum value only for the regular tetrahedron, this means that the shape measures are equivalent.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

On stable geometries

Within the concept of projective lattice geometry we are considering the class of stable geometries which have also been introduced in [14]. The investigation of their basic properties will result in fundamental structure theorems which especially give a lattice-geometric characterization of free left modules of rank 6 over proper right Bezout rings of stable rank 2. This yields a proper generalization of previous results of ours.     

Production of helium fragments in197Au-emulsion collisions at 10.6 A GeV

We present a systematic analysis on the helium projectile fragments produced from 10.6 A GeV¹⁹⁷Auemulsion interactions in an experiment conducted at the Brookhaven AGS. Total charge changing and partial production cross-sections are measured experimentally on the basis of helium multiplicity. The multiplicity distribution of helium fragments which are produced collectively obey a KNO scaling. The transverse momentum distribution of these particles indicates that they are produced from two different independent sources.We are thankful to the BNL technical staff and specially to Dr. D. Beavis for his help in the exposure of emulsion stacks. Thanks are due to Profs. Y. Takahashi and G. Romano for their help in the preparation and development of the emulsion stacks. We appreciate the discussions with Prof. H. Stocker and J. Aichelin. This work was supported by D.O.E. under Grant No. DE-FGO2-90ER 40566.     

Inclusion-exclusion: Exact and approximate

It is often required to find the probability of the union of givenn eventsA ₁ ,...,A _n . The answer is provided, of course, by the inclusion-exclusion formula: Pr(A _i )= _i – _i<j Pr(A _i A _j )±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A _i ), from the above data with an additive error of exp . In the present article we develop an expression that can be computed in polynomial time, that, given the sums _|S|=j Pr( _iS A _i ) forj=1,...k, approximates Pr(A _i ) with an additive error of exp . This error is optimal, up to the logarithmic factor implicit in the notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v _l ^m C _i is an instance of the general problem that had been extensively studied [7]. HereA _i is the set of assignments that satisfyC _i , and Pr( _iS A _i )=a _S /2ⁿ where _iS C _i is satisfied bya _S assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa _S for, say, all cardinalities . Quite surprisingly, already the numbersa _S over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation.     

Free differential algebras: Their use in field theory and dual formulation

The gauging of free differential algebras (FDA's) produces gauge field theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer equations of ordinary Lie algebras by incorporating p-form potentials (p>1). We study here the algebra of FDA transformations. To every p-form in the FDA, we associate an extended Lie derivative l generating a corresponding gauge transformation. The field theory based on the FDA is invariant under these new transformations. This gives geometrical meaning to the antisymmetric tensors. The algebra of Lie derivatives is shown to close and provides the dual formulation of FDA's.     

K 16Mn连铸坯热装炉轧制对轧材组织性能影舷

采用高温固溶加热法,在φ300轧机上模拟现场连铸坯热装炉轧制工艺,分别考察了K16Mn钢不同热装温度和开轧温度对轧材组织性能的影响.结果表明,热装轧制和常规冷装轧制屈服、抗拉强度相当,热装轧制成品塑性、韧性均较好.热装轧制工艺对K16Mn钢组织的影响,随着热装温度的提高,轧前奥氏体晶粒变得粗大,并且轧后组织混晶程度提高.这可通过提高开轧温度,首道次采用大压下量促使铸坯发生完全再结晶来消除.从而细化晶粒.改善成品组织性能.     

新型钢管砼框架节点试验研究及其应用

给出了钢管混凝土框架节点的试验结果,并采用有限元法对新型节点模式进行了应力场分析。介绍了该新型节点的设计方案及在实际工程中的应用。     

LF-CD-CC过程中钢液温度控制模型

在分析ＬＦ－ＶＤ－ＣＣ过程各阶段热平衡状况的基础上,开发了ＬＦ－ＶＤ－ＣＣ过程中钢液温度控制模型。用该模型模拟计算了ＬＦ－ＶＤ－ＣＣ过程的温度变化。结果表明,该模型对预报过程钢水温度,计算的命中率较高,可用于工业生产．     

火力发电厂汽机房屋盖结构选型分析

本文对汽机房屋盖结构的两种受力体系进行了技术经济比较,阐述了空间网架在我国的应用情况,介绍了平板型网架应用在火力发电厂汽机房屋盖中的可行性及经济性。根据工业厂房建筑中的传力路线,分析了用于汽机房屋盖结构的平板型网架考虑吊车水平刹车力作用时的内力分布特点及其应用,提出了汽机房屋盖结构使用平板型网架的观点