In this paper, we compare two strategies for constructing linear programmingrelaxations for polynomial programming problems using aReformulation-Linearization Technique (RLT). RLT involves an automaticreformulation of the problem via the addition of certain nonlinear impliedconstraints that are generated by using the products of the simple boundingrestrictions (among other products), and a subsequent linearization based onvariable redefinitions. We prove that applying RLT directly to the originalpolynomial program produces a bound that dominates in the sense of being atleast as tight as the value obtained when RLT is applied to the jointcollection of all equivalent quadratic problems that could be constructed byrecursively defining additional variables as suggested by Shor. 相似文献
We present a new linearized model for the zero-one quadratic programming problem, whose size is linear in terms of the number of variables in the original nonlinear problem. Our derivation yields three alternative reformulations, each varying in model size and tightness. We show that our models are at least as tight as the one recently proposed in [7], and examine the theoretical relationship of our models to a standard linearization of the zero-one quadratic programming problem. Finally, we demonstrate the efficacy of solving each of these models on a set of randomly generated test instances. 相似文献
The adsorption of thorium(IV) ions on molecular sieve (13X type) powder from aqueous solutions has been studied as a function of shaking time pH, thorium ion concentration and temperature. The conditions of maximum adsorption of thorium ions obeys Langmuir and D-R isotherms over the entire concentration range studied. Thermodynamic quantities such as H, G and S have been calculated fromKD values determined at various temperatures. The results show endothermic heat of adsorption, but negative free energy value indicates that the process of thorium adsorption on molecular sieve powder is favored at high temperature. The influence of various cations and anions on thorium(IV) ion adsorption was examined. A wavelength dispersive X-ray fluorescence spectrometer was used for measuring the thorium ion concentration in solutions. 相似文献
Theoretical and Mathematical Physics - We study the dynamics of explicit solutions of the $$(2+1)$$ -dimensional (2D) sine-Gordon equation. The Darboux transformation is applied to the associated... 相似文献
The use of microemulsion in flow-injection systems is considered, with particular reference to the determination of C6C10 primary amines by derivatization with o-phthal-aldehyde and 2-mercaptoethanol. Microemulsions provide an ideal interface for reactions between a water-soluble reagent and a non-aqueous sample. The effect of reaction conditions (R value, droplet concentration, pH and flow rate) on the fluorescence signal is discussed and calibration data for three primary alkylamines are given. 相似文献
We have investigated the thermal degradation in air by Fourier transform infrared spectroscopy of a ladder-type copolymer containing fluorene units in the backbone (Me-LPF), to reveal the formation of the ketonic defects. As thermal treatment of Me-LPF film at 200 degrees C in air proceeds, a new group of complex absorption bands due to degradation products arises in the range between 1800 and 1600 cm(-1). The observed overlapping bands were separated and assigned by utilizing the second-derivative IR spectral analysis, which can narrow the peak width to one-third of the originals and thereby eases the analysis. The degraded products were assigned as fluorenone (1718 cm(-1)) and benzophenone (Ar-(C=O)-Ar) (1665 cm(-1)), formed by the oxidation of the backbone, and acylphenone (Ar-(C=O)-R) (1685 cm(-1)) from the side chain. The fluorenone was found to be the major component among the degraded products in the main chain, and the time and temperature dependence indicated that the oxidation is a kind of autocatalytic radical-chain process. The oxidation can reach a very high degree (approximately 30% for 6 h oxidation at 240 degrees C estimated by absorption of the alkyl). Our results suggest the possibility of the oxidation of the 9-bialkylfluorene sites. We propose that the degradation of the alkyl in the side chain can help the radicals to propagate in the chain reaction. 相似文献
The adsorption of thorium on activated charcoal has been studied as a function of shaking time, amount of adsorbent, pH, concentration of adsorbate and temperature. Adsorption of thorium obeys the Langmuir isotherm. H0 and S0 were calculated from the slope and intercept of ln KD vs. 1/T plots. The influence of different anions and cations on thorium adsorption has been examined. The adsorption of other metal ions on activated charcoal has been studied under specified conditions to check its selectivity. Consequently, thorium was removed from Cs, Co, Ba, Cr, Sr, Cd, Cu, Mn and Zn. More than 98% adsorbed thorium on activated charcoal can be recovered with 55 ml 3M HNO3 solution. Wavelength dispersive X-rays fluorescence spectrometer was used for measuring thorium concentration. 相似文献
Adsoprtion of gadolinium on activated charcoal has been studied as a function of shaking time, pH, concentration of adsorbate and temperature. Gadolinium adsorption obeys the Langmuir isotherm. Ho and So were calculated from the slope and intercept of the In KD 1/T plot. The influence of different cations and anions on gadolinium adsorption has been examined. The adsorption of other metal ions on activated charcoal has been studied under optimum conditions to check the selectivity of gadolinium adsorption. Consequently, gadolinium was removed from Ni, V, Zn, Cu, Rb, Sr and Mn. More than 97% of the adsorbed gadolinium on activated charcoal can be recovered with 35 ml of 3M HNO3 solution. Wavelength dispersive X-ray fluorescence spectrometer was used for measuring gadolinium concentration. 相似文献
In this study, the Co-based catalyst was prepared by cobalt immobilization on the surface of functionalized silica-coated magnetic NPs (Fe3O4@SiO2-CT-Co) as a magnetically core–shell nanocatalyst and characterized by FT-IR, TGA, XRD, VSM, SEM, TEM, EDX, EDX mapping, and ICP techniques and appraised in the Suzuki–Miyaura cross-coupling reaction under mild reaction conditions. The results displayed the superparamagnetic behavior of the Fe3O4 NPs core encapsulated by SiO2 shell, and the size of the particles was estimated about 30 nm. Compared with the previously reported catalysts, the engineered Fe3O4@SiO2-CT-Co catalyst provided perfect catalytic performance for the Suzuki–Miyaura cross-coupling reaction in water as a green solvent and it was much cheaper in the comparison with the traditional Pd-based catalysts. Importantly, the durability of magnetic nanocatalyst was studied and observed that it is stable under the reaction conditions and could be easily reused for at least six successive cycles without any significant decrease in its catalytic activity.