Three-dimensional blow-up solutions of the Navier-Stokes equations

In this paper we extend the plane blow-up results of Grundy& McLaughlin (1997) to the three-dimensional Navier-Stokes equations.Using a solution structure originally due to Lin we first providenumerical evidence for the existence of blow-up solutions on- < x, z < , 0 y 1 with boundary conditions on y = 0and y = 1 involving derivatives of the velocity components.The formulation enables us to consider plane and radial flowas special cases. Various features of the computations are isolatedand are used to construct a formal asymptotic solution closeto blow-up. We show that the numerical and asymptotic analysesprovide a mutually consistent global picture which supportsthe conclusion that, for the family of problems we considerhere, blow-up in fact can take place in three dimensions butat an inverse linear rate rather than the faster inverse squareof the plane case.     

A homologous series of regioselectively tetradeprotonated group 8 metallocenes: new inverse crown ring compounds synthesized via a mixed sodium-magnesium tris(diisopropylamide) synergic base

Subjecting ferrocene, ruthenocene, or osmocene to the synergic amide base sodium-magnesium tris(diisopropylamido) affords a unique homologous series of metallocene derivatives of general formula [(M(C(5)H(3))(2))Na(4)Mg(4)(i-Pr(2)N)(8)] (where M = Fe (1), Ru (2), or Os (3)). X-ray crystallographic studies of 1-3 reveal a common molecular "inverse crown" structure comprising a 16-membered [(NaNMgN)(4)](4+) "host" ring and a metallocenetetraide [M(C(5)H(3))(2)](4-) "guest" core, the cleaved protons of which are lost selectively from the 1, 1', 3, and 3'-positions. Variable-temperature NMR spectroscopic studies indicate that 1, 2, and 3 each exist as two distinct interconverting conformers in arene solution, the rates of exchange of which have been calculated using coalescence and EXSY NMR measurements.     

Isolation and characterisation of the mixed-metal alkyl amide [(TMEDA)Na(mu-Bu)(mu-TMP)Mg(TMP)], an unexpected chelate-trapped intermediate in the formation of inverse crowns

Only two-fold amination occurs when 3 molar equivalents of TMPH are offered to a 1:1 BuNa-Bu2Mg mixture; adding TMEDA gives the mixed alkyl amide [(TMEDA)Na(mu-Bu)(mu-TMP)Mg(TMP)], which itself affords the phenyl-bridged analogue when reacted with benzene.     

Long-term retention of ice-nucleating active Pseudomonas fluorescens by overwintering colorado potato beetles

Ice nucleating-active Pseudomonas fluorescens F264C was fed to Colorado potato beetles to determine bacterial retentioin in the beetle gut and its effect on the cold hardiness of this insect pest. The bacrterium was present in beetles recovered after overwintering in the field, seven months after their exposure to P. fluorescens. Retention was evident not only in the detection of the P. fluorescens ice nucleating gene, inaW, in bacterial cultures from beetle guts but also in the elevated supercooling points of some treated beetles.     

Phosphoryl chloride induced ring contraction of 1,4-benzodiazepinones to chloromethylquinazolines

A ring contraction of 1,4-benzodiazepin-2-one to 2-chloromethylquinazoline in phosphoryl chloride is described. The intermediacy of an aziridinoquinazoline is proposed.     

Introduction to financial optimization: Mathematical Programming Special Issue

Optimization models are effective for solving significant problems in finance, including long-term financial planning and other portfolio problems. Prominent examples include: asset-liability management for pension plans and insurance companies, integrated risk management for intermediaries, and long-term planning for individuals. Several applications will be briefly mentioned. Three distinct approaches are available for solving multi-stage financial optimization models: 1) dynamic stochastic control, 2) stochastic programming, and 3) optimizing a stochastic simulation model. We briefly review the pros and cons of these approaches, discuss further applications of financial optimization, and conclude with topics for future research. Published online December 15, 2000     

Relaxation techniques for strictly convex network problems

Gauss—Seidel type relaxation techniques are applied in the context of strictly convex pure networks with separable cost functions. The algorithm is an extension of the Bertsekas—Tseng approach for solving the linear network problem and its dual as a pair of monotropic programming problems. The method is extended to cover the class of generalized network problems. Alternative internal tactics for the dual problem are examined. Computational experiments — aimed at the improved efficiency of the algorithm — are presented.This research was supported in part by National Science Foundation Grant No. DCR-8401098-A01.