On-shell methods in perturbative QCD

We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider.     

The first solid enols of anhydrides. Structure, properties, and enol/anhydride equilibria(1)

Reaction of beta-methylglutaconic anhydride with NaOMe followed by reaction with methyl or phenyl chloroformate gave the corresponding O-methoxy (and O-phenoxy) carbonylation derivatives. Reaction of the anhydride with MgCl2/pyridine, followed by methyl chloroformate gave C-methoxycarbonylation at C3 of the anhydride. The product (4) was previously suggested by calculation to be the enol of the anhydride 5 and this is confirmed by X-ray crystallography (bond lengths: C-OH, 1.297 A; C1C2 1.388 A; HO...O=C(OMe) distance 2.479 A) making it the first solid enol of an anhydride. In CDCl3, CD3CN, or C6D6 solution it displays the OH as a broad signal at ca. 15 ppm, suggesting a hydrogen bond with the CO2Me group. NICS calculations indicate that 4 is nonaromatic. With D2O in CDCl3 both the OH and the C5H protons exchange rapidly the H for D. An isomeric anhydride 5a of 5 is formed in equilibrium with 4 in polar solvents. In solution, anhydride(s)/enol equilibria are rapidly established with Kenol of 6.40 (C6D6, 298 K), 0.52 (CD3CN, 298 K), 9.8 (CDCl3, 298 K), 22.8 (CDCl3, 240 K), and decreasing Kenol in CDCl3:CD3CN mixtures with the increase in percent of CD3CN. The percentage of the rearranged anhydride in CDCl3:(CD3)2CO increases with the increased percent of (CD3)2CO. In DMSO-d6 and DMF-d7 the observed species are mainly the conjugated base 4- and 5a. Deuterium effects on the delta(13C) values were determined. An analogous C2-OH enol of anhydride 15 substituted by 3-CO2Me and 4-OCO2Me groups was prepared. Its structure was confirmed by X-ray crystallography (CO bond length 1.298 A, O...O distance 2.513 A); delta(OH) = 12.04-13.22 ppm in CDCl3, THF-d8, and CD3CN, and Kenol = > or = 100, 7.7, and 3.4 respectively. In DMSO-d6 enol 15 ionizes to its conjugate base. Substantial upfield shifts of the apparent delta("OH") proton on diluting the enol solutions are ascribed to the interaction of the H+ formed with the traces of water in the solvent to give H3O+, which gives the alleged "OH proton" signal.     

Dialkoxyphosphinyl-substituted enols of carboxamides

Reactions of isocyanates XNCO (e.g., X = p-An, Ph, i-Pr) with (MeO)2P(=O)CH2CO2R [R = Me, CF3CH2, (CF3)2CH] gave 15 formal "amides" (MeO)2P(=O)CH(CO2R)CONHX (6/7), and with (CF3CH2O)2P(=O)CH2CO2R [R = Me, CF3CH2] they gave eight analogous amide/enols 17/18. X-ray crystallography of two 6/7, R = (CF3)2CH systems revealed Z-enols of amides structures (MeO)2P(=O)C(CO2CH(CF3)2)=C(OH)NHX 7 where the OH is cis and hydrogen bonded to the O=P(OMe)2 group. The solid phosphonates with R = Me, CF3CH2 have the amide 6 structure. The structures in solution were investigated by 1H, 13C, 19F, and 31P NMR spectra. They depend strongly on the substituent R and the solvent and slightly on the N-substituent X. All systems displayed signals for the amide and the E- and Z-isomers. The low-field two delta(OH) and two delta(NH) values served as a probe for the stereochemistry of the enols. The lower field delta(OH) is not always that for the more abundant enol. The % enol, presented as K(enol), was determined by 1H, 19F, and 31P NMR spectra, increases according to the order for R, Me < CF3CH2 < (CF3)2CH, and decreases according to the order of solvents, CCl4 > CDCl3 approximately THF-d8 > CD3CN >DMSO-d6. In DMSO-d6, the product is mostly only the amide, but a few enols with fluorinated ester groups were observed. The Z-isomers are more stable for all the enols 7 with E/Z ratios of 0.31-0.75, 0.15-0.33, and 0.047-0.16 when R = Me, CF3CH2, and (CF3)2CH, respectively, and for compounds 18, R = Me, whereas the E-isomers are more stable than the Z-isomers. Comparison with systems where the O=P(OMe)2 is replaced by a CO2R shows mostly higher K(enol) values for the O=P(OMe)2-substituted systems. A linear correlation exists between delta(OH)[Z-enols] activated by two ester groups and delta(OH)[E-enols] activated by phosphonate and ester groups. Compounds (MeO)2P(=O)CH(CN)CONHX show 相似文献   

The Quintile Share Ratio in location analysis

The inequality measure “Quintile Share Ratio” (QSR or sometimes S80/S20) is the primary income inequality measure in the European Union’s set of indicators on social cohesion. An important reason for its adoption as a leading indicator is its simplicity. The Quintile Share Ratio is “The ratio of total income received by the 20% of the population with the highest income (top quintile) to that received by the 20% of the population with the lowest income (lowest quintile)”. The QSR concept is used in this paper in the context of obnoxious facility location where the inequality is in distances to the obnoxious facility. The single facility location problem minimizing the QSR is investigated. The problem is investigated for continuous uniform demand in an area such as a disk, a rectangle, and a line; when demand is generated at a finite set of demand points; and when the facility can be located anywhere on a network. Optimal solution algorithms are devised for demand originating at a finite set of demand points and at nodes of the network. Computational experiments demonstrate the effectiveness of the algorithms.     

Tailoring the trajectory of cell rolling with cytotactic surfaces

Cell separation technology is a key tool for biological studies and medical diagnostics that relies primarily on chemical labeling to identify particular phenotypes. An emergent method of sorting cells based on differential rolling on chemically patterned substrates holds potential benefits over existing technologies, but the underlying mechanisms being exploited are not well characterized. In order to better understand cell rolling on complex surfaces, a microfluidic device with chemically patterned stripes of the cell adhesion molecule P-selectin was designed. The behavior of HL-60 cells rolling under flow was analyzed using a high-resolution visual tracking system. This behavior was then correlated to a number of established predictive models. The combination of computational modeling and widely available fabrication techniques described herein represents a crucial step toward the successful development of continuous, label-free methods of cell separation based on rolling adhesion.     

Competitive facility location under attrition

Equilibrium problems provide a mathematical framework which includes optimization, variational inequalities, fixed point and saddle point problems, and noncooperative games as particular cases. In this paper sufficient conditions for the existence of solutions of an equilibrium problem are given by weakening the assumption of quasiconvexity of the involved equilibrium bifunction. The existence of solutions is established both in presence of compactness of the feasible set as well with a coercivity assumption. The results are obtained in an infinite dimensional setting, and they are based on the so called finite solvability property which is weaker than the recently introduced finite intersection property and in turn, weaker than most common cyclic and proper quasimonotonicity. Some examples are presented to illustrate the various cases in which other existence results for equilibrium problems do not apply. Finally, applications to the solution of quasiequilibrium problems, quasioptimization problems and generalized quasivariational inequalities are discussed.