Stability in the presence of degeneracy and error estimation

Received February 10, 1997 / Revised version received June 6, 1998 Published online October 9, 1998     

Non-Glycosidic Azides of D-Altro- and D-Gulopyranose

ABSTRACT

Starting with methyl 2-O-cyclohexylcarbamoyl-3,4-O-(2,2,2-trichloroethylidene)-α-D-altropyranoside (1), methyl 4-O-cyclohexylcarbamoyl-2,3-O-(2,2,2-trichloroethylidene)-β-D-gulopyranoside (12), and methyl 6-O-cyclohexylcarbamoyl-2,3-O-(2,2,2-trichloroethylidene)-β-D-gulopyranoside (21), the 6-azido-6-deoxyaltroses 4, 6, 11, the 6-azido-6-deoxy-D-gulose 14, the 4-azido-4,6-dideoxy-D-gulose 20, and the 4-azido-4-deoxy-D-gulose 26 were synthesised via iodinated or tosylated precursors. Additionally, two gluco-configured azides, the 3-azido-3,6-dideoxy-D-glucose (19) and the 3-azido-3-deoxy-D-glucose (25), were obtained besides the desired 4-azido-4-deoxy-D-gulosides 20 and 26, when methyl 6-deoxy-4-O-tosyl-β-D-gulopyranoside (18) and methyl 6-O-cyclohexylcarbamoyl-4-O-tosyl-β-D-gulopyranoside, respectively, were reacted with sodium azide. An X-ray analysis is presented for methyl 2,4-di-O-acetyl-3-azido-3,6-dideoxy-zl-D-glucose (19).     

Active constraints,indefinite quadratic test problems,and complexity

The observation that at leasts constraints are active when the Hessian of the Lagrangian hass negative eigenvalues at a local minimizer is used to obtain two results: (i) a class of nearly concave quadratic minimization problem can be solved in polynomial time; (ii) a class of indefinite quadratic test problems can be constructed with a specified number of positive and negative eigenvalues and with a known global minimizer.The authors thank the reviewers for their constructive comments. The first author was supported by the National Science Foundation Grant DMS-85-20926 and by the Air Force Office of Scientific Research Grant AFOSR-ISSA-86-0091.     

Mass measurements of neutron-deficient nuclides close to A = 80 with a Penning trap

The masses of ^{80, 81, 82, 83}Y, ^{83, 84, 85, 86, 88}Zr and ^{85, 86, 87, 88}Nb have been measured with a typical precision of 7keV by using the Penning trap setup at IGISOL. The mass of ⁸⁴Zr has been measured for the first time. These precise mass measurements have improved S_p and Q_EC values for astrophysically important nuclides.     

Aetherische Oele

Ohne Zusammenfassung     

Reply to the Comment by S. J. Kowalski,TIPM 40, 113, 2000

Transport in Porous Media -     

Supercritical flow in manholes with a bend extension

 Bend manholes of sewers with 45° deflection angles are considered. Previous results are reconsidered by introducing the so-called bend extension. It is demonstrated that the discharge capacity of the 45°- and the 90°-bend manholes is identical if the bend extension, a U-shaped straight downstream portion, is added to the 45° manhole. In addition, the effect of the bend cover is analyzed as a general means to suppress shock waves. Both bend extensions and bend covers may be added to existing structures that convey discharge close to or over the design discharge. The hydraulics of bend manholes are analyzed in detail, including the wave profiles along the inner and the outer bend walls, the complete free surface, the recirculation zone, the pressure distributions on the walls and flow in the downstream sewer. Received: 12 March 2001 / Accepted: 10 August 2001