Approximate minimum-cost multicommodity flows in\tilde O(ɛ −2 KNM) timetime

We show that an ε-approximate solution of the cost-constrainedK-commodity flow problem on anN-nodeM-arc network,G can be computed by sequentially solving O(K(? ^?2+logGK) logGM log (G? ^?1 GK)) single-commodity minimum-cost flow problems on the same network. In particular, an approximate minimum-cost multicommodity flow can be computed in $\tilde O$ (G? ^?2 GKNM) running time, where the notation Õ(·) means “up to logarithmic factors”. This result improves the time bound mentioned by Grigoriadis and Khachiyan [4] by a factor ofM/N and that developed more recently by Karger and Plotkin [8] by a factor of? ^?1. We also provide a simple $\tilde O$ (NM)-time algorithm for single-commodity budget-constrained minimum-cost flows which is $\tilde O$ (? ^?3) times faster than the algorithm developed in the latter paper.     

The effects of temperature and pressure on the lifetime of benzophenone emission

The variation in the lifetime of flash-excited gaseous benzophenone with pressure and temperature indicates that (1) self-quenching is a relatively inefficient process for the long-lived emission, k_sq = 9 × 10⁵ M^?1 s^?1 (estimated from solution data) at 25°C and 1.2 × 10⁷ M^?1 s^?1 at 170°C and (2) the lifetime decreases with increasing temperature as a result of photochemical and photophysical decay pathways which have significant activation energies. The importance of diffusion to the walls on lifetime measurements is discussed.     

Synthesis, structure, theoretical studies, and Ligand exchange reactions of monomeric, T-shaped arylpalladium(II) halide complexes with an additional, weak agostic interaction

A series of monomeric arylpalladium(II) complexes LPd(Ph)X (L = 1-AdPtBu2, PtBu3, or Ph5FcPtBu2 (Q-phos); X = Br, I, OTf) containing a single phosphine ligand have been prepared. Oxidative addition of aryl bromide or aryl iodide to bis-ligated palladium(0) complexes of bulky, trialkylphosphines or to Pd(dba)2 (dba = dibenzylidene acetone) in the presence of 1 equiv of phosphine produced the corresponding arylpalladium(II) complexes in good yields. In contrast, oxidative addition of phenyl chloride to the bis-ligated palladium(0) complexes did not produce arylpalladium(II) complexes. The oxidative addition of phenyl triflate to PdL2 (L = 1-AdPtBu2, PtBu3, or Q-phos) also did not form arylpalladium(II) complexes. The reaction of silver triflate with (1-AdPtBu2)Pd(Ph)Br furnished the corresponding arylpalladium(II) triflate in good yield. The oxidative addition of phenyl bromide and iodide to Pd(Q-phos)2 was faster than oxidative addition to Pd(1-AdPtBu2)2 or Pd(PtBu3)2. Several of the arylpalladium complexes were characterized by X-ray diffraction. All of the arylpalladium(II) complexes are T-shaped monomers. The phenyl ligand, which has the largest trans influence, is located trans to the open coordination site. The complexes appear to be stabilized by a weak agostic interaction of the metal with a ligand C-H bond positioned at the fourth-coordination site of the palladium center. The strength of the Pd.H bond, as assessed by tools of density functional theory, depended upon the donating properties of the ancillary ligands on palladium.     

Selective mixed coupling of carboxylic acids (II). — photolysis of unsymmetrical diacylperoxides with alkenyl-, halo-, keto-, carboxyl-groups and a chiral α-carbon. Comparison with the mixed kolbe electrolysis

Alkenoyl and functionalized alkanoyl dodecanoyl peroxides are prepared in 70 to 97 % yield and photolyzed at ?78° C. Thereby 4- to 10-alkenoyl and 4-alkanoyl peroxides afford good yields (56 – 68 %) of unsymmetrical coupling products. Similarly α- to σ-haloalkanoyl, cholanoyl or 3- and 4-carboxyalkanoyl peroxides can be coupled (40 – 70 %). The α-chiral diacyl peroxide ls undergoes the photochemical coupling reaction with 80 % retention of its configuration. The photolysis of diacyl peroxides at ?78° C proves to be a favorable supplement of the Kolbe-electrolysis in cases, where the electrolysis fails or produces low yields.     

7-Deazaadenosine: Oligoribonucleotide building block synthesis and autocatalytic hydrolysis of base-modified hammerhead ribozymes

A 7-deazaadenosine ( = tubercidin; c⁷A; 1 ) building block for solid-phase oligoribonucleotide synthesis was prepared. The amino group of 1 was protected with the (dimethylamino)methylidene residue (→ 3 ), and the monomethoxytrityl group was introduced at OH? C(5′) (→ 4 ). Protection of OH? C(2′) was carried out by silylation, showing that use of the (i-Pr)₃Si group resulted in high 2′-O-selectivity (→ 5b , 80%). Reaction of 5b with PCl₃ afforded the phosphonate 7 which was used in solid-phase oligoribonucleotide synthesis. The autocatalytic hydrolysis of hammerhead ribozymes using pG-G-G-A-G-U-C-A-G-U-C-C-C-U-U-C-G-G-G-G-A-C-U-C-U-G-A-A-G-A-G-G-C-G-C as substrate strand (S) and modified G-C-G-C-C-G-A-A-A-C-U-C-C-C as enzyme strand (E) was studied. When c⁷A replaced A¹³ or A¹⁴, a small decrease of catalytic activity was observed, while modification in position A¹⁵ enhanced the autocatalytic hydrolysis. The results demonstrate, that the atom N(7) of adenosine in any of these positions is not crucial for ribozyme action.     

Synthesis and structural characterization of novel bridged platinum(II) biscarbene complexes

Novel bridged platinum(II) biscarbene complexes are reported: 1,1′-dimethyl-3,3′-methylene-4-diimidazolin-2,2′-diylidene platinum(II) (3) and 1,1′-dimethyl-3,3′-ethylene-4-diimidazolin-2,2′-diylidene platinum(II) complexes 4 are directly accessible in high yields starting from platinum halides. The one-pot synthesis obviates the need for multi-step reactions via metal precursors or free carbenes. An X-ray crystal structure of 1,1′-dimethyl-3,3′-methylene-4-diimidazolin-2,2′-diylidene platinum(II) dibromide (3b) confirmed the structural similarity to the known corresponding palladium complexes. Since free 1,1′-di-R-3,3′-methylene-4-diimidazolin-2,2′-diylidenes are only available in low yields this synthetic route provides an easy access to the corresponding carbene complexes.     

Ground states of molecules. 64.MNDO Calculations for compounds containing bromine

MNDO has been parametrized for bromine. Since d atomic orbitals (AOS) are not included, the calculations are restricted to Br^I. Heats of formation, molecular geometries, ionization energies, and dioole moments are reproduced with useful accuracy.     

Enantioselective total synthesis of (+)-gigantecin: exploiting the asymmetric glycolate aldol reaction

The enantioselective synthesis of the potent, selective, cytotoxic, annonaceous acetogenin, (+)-gigantecin, has been completed. An asymmetric glycolate aldol serves to establish the stereocenters at C13,14 and at C21,22. A Carreira asymmetric acetylide addition is used to establish the C17 stereocenter.     

Synthesis of tetrazolopiperazine building blocks by a novel multi-component reaction

A novel Ugi-five-centre-four-component reaction (U-5C-4CR) of aldehydes, primary amines, trimethylsilylazide and 2-isocyanoethyltosylate yielding tetrazolopiperazine building blocks is described.