Duality, triality and complementary extremum principles in non-convex parametric variational problems with applications

This paper presents a reasonably complete duality theory anda nonlinear dual transformation method for solving the fullynonlinear, non-convex parametric variational problem inf{W(u- µ) - F(u)}, and associated nonlinear boundary valueproblems, where is a nonlinear operator, W is either convexor concave functional of p = u, and µ is a given parameter.Detailed mathematical proofs are provided for the complementaryextremum principles proposed recently in finite deformationtheory. A method for obtaining truly dual variational principles(without a dual gap and involving the dual variable p* of uonly) in n-dimensional problems is proposed. It is proved thatfor convex W(p), the critical point of the associated LagrangianL_µ(u, p*) is a saddle point if and only if the so-calledcomplementary gap function is positive. In this case, the systemhas only one dual problem. However, if this gap function isnegative, the critical point of the Lagrangian is a so-calledsuper-critical point, which is equivalent to the Auchmuty'sanomalous critical point in geometrically linear systems. Wediscover that, in this case, the system may have more than oneprimal-dual set of problems. The critical point of the Lagrangianeither minimizes or maximizes both primal and dual problems.An interesting triality theorem in non-convex systems is proved,which contains a minimax complementary principle and a pairof minimum and maximum complementary principles. Applicationsin finite deformation theory are illustrated. An open problemleft by Hellinger and Reissner is solved completely and a purecomplementary energy principle is constructed. It is provedthat the dual Euler-Lagrange equation is an algebraic equation,and hence, a general analytic solution for non-convex variational-boundaryvalue problems is obtained. The connection between nonlineardifferential equations and algebraic geometry is revealed.     

On-line speciation and determination of Cr(III) and Cr(VI) in drinking and waste water samples by reversed-phase high performance liquid chromatography coupled with atomic absorption spectrometry

A simple, rapid, and selective on-line method for the speciation and determination of Cr(III) and Cr(VI) in aqueous solutions by ion-pairing HPLC coupled with flame atomic absorption spectrometry (FAAS) is described. The composition of the mobile phase has been optimized for better separation. The effects of column temperature, volume of injection loop, fuel flow rate of FAAS, and nebulizer suction rate of FAAS have also been investigated. Separation is accomplished in almost 2.5 min on a 25 cm length C18 column at 40 degrees C. The selectivity of the method has been established by investigating the effect of interfering elements on chromium determination. The detection limit (3sigma) achieved by the method was calculated as 3.7 ng/mL for Cr(III) and 2.0 ng/mL for Cr(VI). The proposed method has been validated by analyzing certified reference material (BCR 544) and successfully applied to the analysis of drinking water and wastewater samples with a relative error below 6%.     

Comment on “Correlation of entrainment for annular flow in horizontal pipes”, by Pan,L., Hanratty,T.J., Int. J. Multiphase flow, 28(3), (2002), pp. 385–408

The above referenced paper, published in International Journal of Multiphase Flow (Pan and Hanratty, 2002), proposed an entrainment fraction correlation for annular flow in horizontal pipes. The entrainment fraction in annular flow is defined as the ratio of the mass flow rate of the liquid droplets in the gas to the total mass flow of liquid, F_E = W_LE/W_L. The proposed correlation was verified with experimental data for liquids with viscosities close to that of water. The proposed entrainment fraction correlation includes another correlation for the critical film flow rate, W_F,cr to estimate a maximum entrainment fraction F_E,max. It is shown that the critical film flow rate correlation can result in negative maximum entrainment fraction values, for low liquid flow rates.     

Method validation for the determination of lead in raw cow's milk by electrothermal atomic absorption spectrometry

In this study, lead in raw cow's milk has been determined by validated electrothermal atomic absorption spectrometry (ETAAS) with Zeeman-effect background correction. Maximum pyrolysis and optimum atomization temperatures of lead were determined in the presence of modifiers. Pd + Mg(NO3)2 has been found a powerful modifier mixture for the determination of lead. The analytical parameters of the method such as limit of detection, limit of quantification and the effect of interfering ions have been investigated. The detection limit (3sigma) achieved by the method was calculated to be 0.62 ng/mL for Pb. Repeatability of the method evaluated as the relative standard deviation of 16-17 replicates using 5 ng/mL, under optimum experimental conditions were about 1.5% for synthetic sample solution and about 3% for real sample (N = 5). The described method has been validated by analyzing certified reference material (BCR-CRM 150) and by comparing the results with those obtained by inductively coupled plasma mass spectrometry (ICP-MS). The validated method was applied to raw cow's milk samples produced in 7 different regions of Turkey in 2003-2004. Raw cow's milk contained a mean (range) of 31.4 (2.5 - 313) microg kg(-1) lead with a relative error below 2%.     

Benchmark calculations of some molecular properties of O2, CN and other selected small radicals using the ROHF-CCSD(T) method

The capability of the ROHF-CCSD(T) method in obtaining accurate molecular properties in a defined and controlled way is analysed. Electron affinity, polarizability, and hyperpolarizability of the oxygen molecule in its ground state, electron affinity, electric dipole moment of the CN radical, and some other molecules serve as model cases for obtaining the ‘right result for the right reason’. Most calculated CCSD(T) data were extrapolated to the complete basis set (CBS) limit in order to minimize the basis set dependence of results. Some problems, specific to open shell systems include effects due to the spin adaptation, and details in the selection of the reference orbitals and related selection of denominators in non-iterative triples and other subtleties, which can affect the accuracy of the final ROHF-CCSD(T) results, are investigated.     

Modeling of oil–water flow using energy minimization concept

A new model is developed to predict flow behaviors including flow pattern, pressure gradient and holdup for oil–water flow in horizontal and slightly inclined pipes. The model is based on the universal principle that a system stabilizes to its minimum total energy. The structural configurations observed in two-phase flow systems can be interpreted in terms of total energy minimization. Performance of the developed model is tested against several experimental data, and comparisons with existing models are presented. It is evident from the results and comparisons that the model estimates the pressure gradient and flow pattern very well. The model provides extensive information about oil–water flow characteristics.     

Methods to determine neutrino flux at low energies

We present a set of recommendations for the presentation of LHC results on searches for new physics, which are aimed at providing a more efficient flow of scientific information between the experimental collaborations and the rest of the high energy physics community, and at facilitating the interpretation of the results in a wide class of models. Implementing these recommendations would aid the full exploitation of the physics potential of the LHC.