We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain
than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain
the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q2|≪M2, in addition to the usual condition |q2|≪W2,W being theV+V− invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q2||q′2|W4 ≪ 16M8, in addition to |q2| ≪M2, |q′2| ≪M2 and |q2| ≪W2, |q′2| ≪W2. Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q2| ≪W2 and |q′2| ≪W2.
We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge
theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q2||q′2|W4 ≪ 16M8 is shown to be removed. 相似文献
l-cysteine undergoes facile electron transfer with heteropoly 10-tungstodivanadophosphate,
[ \textPV\textV \textV\textV \textW 1 0 \textO 4 0 ]5 - , \left[ {{\text{PV}}^{\text{V}} {\text{V}}^{\text{V}} {\text{W}}_{ 1 0} {\text{O}}_{ 4 0} } \right]^{5 - } , at ambient temperature in aqueous acid medium. The stoichiometric ratio of [cysteine]/[oxidant] is 2.0. The products of the
reaction are cystine and two electron-reduced heteropoly blue, [PVIVVIVW10O40]7−. The rates of the electron transfer reaction were measured spectrophotometrically in acetate–acetic acid buffers at 25 °C.
The orders of the reaction with respect to both [cysteine] and [oxidant] are unity, and the reaction exhibits simple second-order
kinetics at constant pH. The pH-rate profile indicates the participation of deprotonated cysteine in the reaction. The reaction
proceeds through an outer-sphere mechanism. For the dianion −SCH2CH(NH3+)COO−, the rate constant for the cross electron transfer reaction is 96 M−1s−1 at 25 °C. The self-exchange rate constant for the
- \textSCH2 \textCH( \textNH3 + )\textCOO - \mathord
Among the possible new materials for microelectronics, quinones have a number of significant advantages. Similarly, polymers
with quinone functionality possess biodegradability. Because natural polymers are promising candidates for functional materials
for the future, we have initiated studies on the polymers of natural products. In the present study, a natural quinone (a
plant substance) extracted from Embelier libes distributed in the Kerala state of India was electrochemically polymerized and its properties were investigated. The redox
activity, electrical conductivity, and biodegradability are discussed. 相似文献
Four structures of oxoindolyl α‐hydroxy‐β‐amino acid derivatives, namely, methyl 2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐methoxy‐2‐phenylacetate, C24H28N2O6, (I), methyl 2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐ethoxy‐2‐phenylacetate, C25H30N2O6, (II), methyl 2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐[(4‐methoxybenzyl)oxy]‐2‐phenylacetate, C31H34N2O7, (III), and methyl 2‐[(anthracen‐9‐yl)methoxy]‐2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐phenylacetate, C38H36N2O6, (IV), have been determined. The diastereoselectivity of the chemical reaction involving α‐diazoesters and isatin imines in the presence of benzyl alcohol is confirmed through the relative configuration of the two stereogenic centres. In esters (I) and (III), the amide group adopts an anti conformation, whereas the conformation is syn in esters (II) and (IV). Nevertheless, the amide group forms intramolecular N—H...O hydrogen bonds with the ester and ether O atoms in all four structures. The ether‐linked substituents are in the extended conformation in all four structures. Ester (II) is dominated by intermolecular N—H...O hydrogen‐bond interactions. In contrast, the remaining three structures are sustained by C—H...O hydrogen‐bond interactions. 相似文献
Using in situ electrical conductivity and ex situ X-ray photoelectron spectroscopy (XPS) measurements, we have examined how the hydrogen uptake of single-walled carbon nanotubes (SWNTs) is influenced by the addition of Pt nanoparticles. The conductivity of platinum-sputtered single-walled carbon nanotubes (Pt-SWNTs) during molecular hydrogen exposure decreased more rapidly than that of the corresponding pure SWNTs, which supports a hydrogenation mechanism facilitated by "spillover" of dissociated hydrogen from the Pt nanoparticles. C 1s XPS spectra indicate that the Pt-SWNTs store hydrogen by means of chemisorption, that is, covalent C-H bond formation: molecular hydrogen charging at elevated pressure (8.27 bar) and room temperature yielded Pt-SWNTs with up to 16 ± 1.5 at. % sp(3)-hybridized carbon atoms, which corresponds to a hydrogen-storage capacity of 1.2 wt % (excluding the weight of Pt nanoparticles). Pt-SWNTs prepared by the Langmuir-Blodgett (LB) technique exhibited the highest Pt/SWNT ratio and also the best hydrogen uptake. 相似文献
Single crystals of pure, Ca2+ and Sr2+ doped NH4Sb3F10 are grown by slow evaporation technique. The effect of dopants on the growth and physicochemical properties also have been investigated and reported for the first time. The grown crystals are characterized with the aid of single crystal X-ray diffractometry to confirm the crystal structure. EDAX studies are done to confirm the presence of dopants in the crystal lattice. The vibrational frequencies of various group ligands in the crystals have been derived from the Fourier transform infrared (FT-IR) spectrum. From the optical absorption spectrum the band gap energy was calculated and it was found to be 5.76, 6.29 and 6.35 eV for pure, Ca2+ and Sr2+ doped NH4Sb3F10 crystals respectively. Thermal stability of the sample has been analysed using TG-DTA analysis. The activation energy of pure, Ca2+ and Sr2+ doped NH4Sb3F10 crystals were calculated from the dc conductivity measurements and it is found to be 0.2728, 0.2816 and 0.3622 eV Experimental results shows improved physicochemical properties when the dopant is added to the pure material. 相似文献
A general analysis of the renormalisation corrections to the unification results for the coupling constants of strong and electroweak interactions is attempted. In particular, the effects of introducing an energy scale intermediate between the unification energy and the low-energy regions are studied and found to be important. This analysis is applied to unification schemes of both kinds, namely, unification at superhigh energies, and unification at accessible energies. 相似文献
The statistical model for fission is used to calculate the isotopic distribution of Rb and Cs in the fission of 238U induced by high-energy protons and reactor neutrons. The double-humped behaviour of the isotope yield curve as observed in high-energy proton-induced fission and the experimentally observed hump on the neutron-rich side in neutron-induced fission are semi-quantitatively reproduced. 相似文献
Solving a sparse system of linear equations Ax=b is one of the most fundamental operations inside any circuit simulator. The equations/rows in the matrix A are often rearranged/permuted before factorization and applying direct or iterative methods to obtain the solution. Permuting the rows of the matrix A so that the entries with large absolute values lie on the diagonal has several advantages like better numerical stability for direct methods (e.g., Gaussian elimination) and faster convergence for indirect methods (such as the Jacobi method). Duff (2009) [3] has formulated this as a weighted bipartite matching problem (the MC64 algorithm). In this paper we improve the performance of the MC64 algorithm with a new labeling technique which improves the asymptotic complexity of updating dual variables from O(|V|+|E|) to O(|V|), where |V| is the order of the matrix A and |E| is the number of non-zeros. Experimental results from using the new algorithm, when benchmarked with both industry benchmarks and UFL sparse matrix collection, are very promising. Our algorithm is more than 60 times faster (than Duff’s algorithm) for sparse matrices with at least a million non-zeros. 相似文献