Comparison of Two Reformulation-Linearization Technique Based Linear Programming Relaxations for Polynomial Programming Problems

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.     

An improved linearization strategy for zero-one quadratic programming problems

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.     

XRF estimation of Cd,Hf, Hg,and Gd in uranium solution

A new curriculum in radiochemistry for undergraduate chemistry is described.     

Uptake of thorium ions from aqueous solutions by a molecular sieve (13X type) powder

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 fromK _D 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.     

Dynamics of kink-soliton solutions of the $$(2+1)$$ -dimensional sine-Gordon equation

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...     

The use of microemulsions in flow injection analysis: Spectrofluorimetric determination of primary amines

The use of microemulsion in flow-injection systems is considered, with particular reference to the determination of C₆C₁₀ 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.     

Microcalorimetry, energetics and binding studies of DNA-dimethyltin dichloride complexes

The interaction of dimethyltin dichloride (Me₂SnCl₂) with calf thymus DNA was studied at 27 °C, pH 7.6 using various techniques including isothermal titration calorimetry (ITC) and UV-Vis, fluorescence and IR spectrophotometries. The binding isotherm and enthalpy curve for Me₂SnCl₂-DNA interaction was a biphasic transition process. This was determined by the analysis of the binding data with the Hill equation. The first phase of the enthalpy curve (exothermic process) was consistent with the first set of binding site, the second phase (endothermic process, less exothermicity) was consistent with second set of binding site from the cited interactions. Our results showed that the first set of binding sites is occupied by one mole of ligand bound per near 1 base pair of DNA. The DNA-ethidium bromide (EB) complex, in the presence of Me₂SnCl₂, caused the quenching of the fluorescence emission. The Scatchard plots illustrated a non-intercalating manner for such quenching. The DNA-EB complex results indicated that the binding of Me₂SnCl₂ is with the phosphate groups of DNA at low ligand concentrations (<9 mM). This was confirmed with the IR spectrophotometric spectra. However, the binding at higher ligand concentrations (>9 mM) was with the base groups of DNA. Therefore, these results suggest that the Me₂SnCl₂ binding to DNA at low concentrations occurs through an outside interaction by an exothermic process. However, the partial unfolding of the DNA caused at higher concentrations of Me₂SnCl₂ is through an endothermic process involving interactions with the base groups.     

Study on the formation of the ketonic defects in the thermal degradation of ladder-type poly(p-phenylenes) by vibrational spectroscopy

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.     

Selective adsorption of thorium on activated charcoal from electrolytic aqueous solution

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 K_D 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.     

Adsorption of gadolinium on activated charcoal from electrolytic aqueous solution

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. H^o and S^o were calculated from the slope and intercept of the In K_D 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.