Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.     

The renaissance of palladium(II)-catalyzed oxidation chemistry

Palladium(II)-catalyzed oxidations constitute a paramount reaction class but have remained immature over the past few decades. Recently, this field has reappeared at the forefront of organometallic catalysis. This emerging area article outlines recent developments in palladium(II)-catalyzed oxidation chemistry with discussion of potential future growth.     

Molecular structure of 4,4′-sulfandiyl-bis-thiophenol from electron diffraction

The molecular structure of 4,4′-sulfanidyl-bis-thiophenol (C₁₂H₁₀S₃) has been determined by gas electron diffraction. Assuming identical geometry and D_2h local symmetry for ---SC₆H₄S--- moieties, the following bond lengths (r_g) and bond angles were obtained: C---H = 1.101 ± 0.005, S---H = 1.388 ± 0.019, (C---C)_mean = 1.400 ± 0.003, (S---C)_mean = 1.778 ± 0.004 Å, C_ar---S---C_ar = 103.5 ± 1.3, C---C(S)---C = 120.4 ± 0.3, C(H)---C(H)---H = 119.1 ± 0.9 and C---S---H = 94.6 ± 3.1°. Two ratational forms were found to reproduce the experimental data, characterized by dihedral angles of the benzene rings with respect to the C_arSC_ar plane; ₁ = 67.8 ± 2.0°, ₂ = 4.5 ± 7.2°, and ₁ = 69.4 ± 2.0δ, ₂ = −26.6 ± 7.1°. Identical signs of ₁ and ₂ indicate that the two benzene rings are rotated in the same direction about the respective S_central---C axes.     

REDUCED PHOTOINACTIVATION OF 10-DODECYL ACRIDINE ORANGE-SENSITIZED YEAST CELLS AT HIGH FLUENCE RATES MEASUREMENTS AND COMPUTER SIMULATIONS

Abstract-During the development of a photodamage cell sorter several photosensitizers were tested for their ability to photoinactivate more than 90% of the sensitized cells after a brief irradiation with a fluence of 10 kJ/m². In pilot experiments, yeast cells sensitized with 10-dodecyl acridine orange (DAO) were effectively photoinactivated after receiving a fluence of 10 kJ/m² delivered in 8 s. However, when the same fluence was delivered in 3 μ s during passage through a focused laser beam in the cell sorter, all cells survived.
Computer simulations of the relevant photophysical and chemical reactions inside the irradiated cell were used to investigate the cause of this phenomenon. The results indicated that the absence of photoinactivation by DAO, after flash irradiations, was caused by the combined effects of (1) limited oxygen diffusion into the cell and (2) a reduced number of collisions between photosensitizer triplet and oxygen molecules during the irradiation due to saturation of the intracellular photosensitizer triplet concentration. The contributions of triplet-triplet annihilation and triplet quenching by ground state photosensitizer molecules were found to be minimal and not significant. These findings indicate that Type II photosensitizers are incapable of rapid selective photoinactivation in cell sorters.     

Rearrangements of 3-heterobicyclo[3.2.0]hept-6-enes

Studies directed at a synthesis of dihydrothiepin 1b have resulted in the elucidation of several factors which effect cyclobutene ring opening in the 3-heterobicyclo[3.2.0]hept-6-ene ring system. We report the unexpected rearrangement of 4a, 4b, 13b and 13c to the synthetically useful a-vinyl-2,5-dihydrothiophenes 7a, 7b, 15a and 15b, respectively. Conversion of 4a to 6 is suggested to occur by a 1,3-rearrangement of 4a to isomeric 3-thiabicyclo[3.2.0]hept-6-ene 19 followed by cyclobutene ring opening in 19.     

Molecular Structure of 1,3,5-Tris (Trimethylstannyl) Benzene: An Electron Diffraction Study

The molecular structure of 1,3,5-tris (trimethylstannyl) benzene has been determined by gas-phase electron diffraction. The C — C bond length is in good agreement with that in benzene. In agreement with the somewhat electron-releasing character of the substituents, the endocyclic bond angles at the substituents are somewhat smaller than 120°. The mean value of Sn — C bond lengths is greater than that in tetraphenyltin and tetramethyltin. The SnMe₃ groups appear freely rotating around the C_aryl — Sn bonds. The following bond lengths (r _g) and bond angles were determined: (Sn — C)_mean 2.150 ± 0.007 Å, C — C 1.399 ± 0.005 Å, (C — H)_mean 1.105 ± 0.006 Å, < C — C(Sn) — C 117.7 ± 1.7º, < C_aryl — Sn — C_methyl 106.7 ± 0.7º < Sn — C — H 111.5 ± 0.9º.