Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one-loop helicity amplitudes of all 2 → 3 parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all 2 → 4 parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.     

Click chemistry in materials synthesis. III. Metal‐adhesive polymers from Cu(I)‐catalyzed azide–alkyne cycloaddition

1,2,3‐Triazole‐based polymers generated from the Cu(I)‐catalyzed cycloaddition between multivalent azides and acetylenes are effective adhesive materials for metal surfaces. The adhesive capacities of candidate mixtures of azide and alkyne components were measured by a modified peel test, using a customized adhesive tester. A particularly effective tetravalent alkyne and trivalent azide combination was identified, giving exceptional strength that matches or exceeds the best commercial formulations. The addition of Cu catalyst was found to be important for the synthesis of stronger adhesive polymers when cured at room temperature. Heating also accelerated curing rates, but the maximum adhesive strengths achieved at both room temperature and high temperature were the same, suggesting that crosslinking reaches the same advanced point in all cases. Polytriazoles also form adhesives to aluminum, but copper is bound more effectively, presumably because active Cu(I) ions may be leached from the surface to promote crosslinking and adhesion. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5182–5189, 2007     

Cyclobut-2-enones from Alkynes via Dichlorocyclobut-2-enones

The [2 + 2]-cycloaddition of dichloroketene (prepared in situ from CCl₃COCl and Zn(Cu)) with three alkynes 1a–c to form 2,3-dimethyl-( 2a ), 2,3-diethyl-( 2b ) and 3-butyl-4,4-dichlorocyclobut-2-enone ( 2c ) proceeds rapidly in the absence of POCl₃. The primary products 2a–c rearrange in situ to the 2,4-dichlorocyclobut-2-enones 3a–c under the influence of ZnCL₂ produced during the reaction. ZnCl₂ converts both 2a and 3a into a 4:6 equilibrium mixture of the two; this isomerization does not occur with LiCl. The Cl-atoms of both 2a , b and 3a , b and of 2c may reductively be removed with Zn(Cu) in AcOH/pyridine to afford the alkylcyclobutenones 4a-c . Without pyridine, this reduction gives ca. 1:1 mixtures of the double-bond isomers 4 and 5 in low yields. The cyclobutenones 2c and 4c may be deuterated by CD₃COOD in the presence of pyridine. D -Atom is introduced into 2c at C(4) and at C(γ), and into 4c at C(2) and C(4). A mechanism for this deuteration is considered, which does not involve a cyclobutadienolate 7 , but rather a cyclobutenolate of type 8 . The reductions of 2 and 3 to 4 might also pass through the same type of intermediate 8 .     

Rydberg-London potential for diatomic molecules and unbonded atom pairs

We propose and test a pair potential that is accurate at all relevant distances and simple enough for use in large-scale computer simulations. A combination of the Rydberg potential from spectroscopy and the London inverse-sixth-power energy, the proposed form fits spectroscopically determined potentials better than the Morse, Varnshi, and Hulburt-Hirschfelder potentials and much better than the Lennard-Jones and harmonic potentials. At long distances, it goes smoothly to the London force appropriate for gases and preserves van der Waals's "continuity of the gas and liquid states," which is routinely violated by coefficients assigned to the Lennard-Jones 6-12 form.     

Polar Substituent Effects in the Solvolysis of Primary and Tertiary Alkyl Halides. Polar Effect IX

When the Hammett-Taft equation log (k/k_o)=ρ^q · σ is applied to the solvolysis of the 3-substituted propyl bromides 6a-6i in ethanol/water 4:1 (v/v) log k correlates linearly with σ except in cases where R exerts an anchimeric effect. The reaction constant ρ^q for 6 is ? 0.12 and is typical for a nucleophilic solvent-assisted k_s process at a primary C-atom. The tertiary halides 1 and 3 , however, which react with little or no nucleophilic solvent assistance, i.e. by k_c processes, lead to larger ρ^q values of ?0.71 and ?1.14, respectively. The reaction constant p^q is therefore a sensitive gauge for charge development in the transition state for solvolysis of saturated compounds.     

Einsatz der echten Integration in der Atomabsorptions-Spektroskopie

An improvement of the signal-to-noise ratio in atomic absorption spectroscopy may be obtained by each of the following three methods of signal averaging:

increase of the time constant

digital signal averaging

true integration of the signal

The most adequate of these methods appears to be true integration. Two examples are presented to demonstrate the improved signal-to-noise ratio due to the application of this method:

trace analysis of mercury in water by means of flameless AAS. The detection limit appears to be 0.2 ng which corresponds to a concentration of 2 · 10^?13 g/ml.

trace analysis of copper in human urine by means of flame AAS: 1,3 · 10^?8 g/ml copper could be detected without any solvent extraction process.

     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

Relation between structure and enthalpy for stacking interactions of aromatic molecules

An approximately linear correlation has been found between the enthalpy of complexation and the area of overlap of the chromophores using published structural and thermodynamical data on the self- and hetero-association of aromatic molecules measured under similar solution conditions. This finding is consistent with the assumption that short-range van-der-Waals forces dominate over other contributions to the enthalpy of stacking of aromatic molecules. It provides a ‘model-independent’ approach for a priori estimation of the enthalpy of aromatic–aromatic stacking interactions from knowledge of the structural properties or vice versa.