Lagrangian actions for elliptical solutions of 2-body and 3-body problems with fixed energies

Based on the works of Gordon (1977) and Zhang and Zhou (2001) on the variational minimizing properties for Keplerian orbits and Lagrangian solutions of Newtonian 2-body and 3-body problems, we use the constrained variational principle of Ambrosetti and Coti Zelati (1990) to compute the Lagrangian actions on Keplerian and Lagrangian elliptical solutions with fixed energies. We also find an interesting relation between the period and the energy for Lagrangian elliptical solutions with Newtonian potentials.     

A Mixed Mann Iteration Process for Fixed Points of Mixed Increasing Operators in Ordered Banach Spaces

In this paper, we develop a new mixed Mann iteration process to approximate the fixed points of mixed increasing operators in ordered Banach spaces and discuss the convergence analysis of the iterative sequences generated by the iteration process. As an application, we develop a new iterative method for solving a class of nonlinear integral equations.     

Enhanced process development using automated continuous reactors by self-optimisation algorithms and statistical empirical modelling

Reaction optimisation and understanding is fundamental for process development and is achieved using a variety of techniques. This paper explores the use of self-optimisation and experimental design as a tandem approach to reaction optimisation. A Claisen-Schmidt condensation was optimised using a branch and fit minimising algorithm, with the resulting data being used to fit a response surface model. The model was then applied to find new responses for different metrics, highlighting the most important for process development purposes.     

Characterization of surfactant complex mixtures using Raman spectroscopy and signal extraction methods: Application to laundry detergent deformulation

This paper presents the analysis of surfactants in complex mixtures using Raman spectroscopy combined with signal extraction (SE) methods. Surfactants are the most important component in laundry detergents. Both their identification and quantification are required for quality control and regulation purposes. Several synthetic mixtures of four surfactants contained in an Ecolabel laundry detergent were prepared and analyzed by Raman spectroscopy. SE methods, Independent Component Analysis and Multivariate Curve Resolution, were then applied to spectral data for surfactant identification and quantification. The influence of several pre-processing treatments (normalization, baseline correction, scatter correction and smoothing) on SE performances were evaluated by experimental design. By using optimal pre-processing strategy, SE methods allowed satisfactorily both identifying and quantifying the four surfactants. When applied to the pre-processed Raman spectrum of the Ecolabel laundry detergent sample, SE models remained robust enough to predict the surfactant concentrations with sufficient precision for deformulation purpose. Comparatively, a supervised modeling technique (PLS regression) was very efficient to quantify the four surfactants in synthetic mixtures but appeared less effective than SE methods when applied to the Raman spectrum of the detergent sample. PLS seemed too sensitive to the other components contained in the laundry detergent while SE methods were more robust. The results obtained demonstrated the interest of SE methods in the context of deformulation.     

An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces

ABSTRACT

In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces. Inspired by the projection and contraction method and the hybrid descent approximation method, a new and efficient iterative method for solving the problem is introduced. Strong convergence theorem of the proposed method is established under standard and mild conditions. Our scheme generalizes and extends some of the existing results in the literature, and moreover, its computational effort is less per each iteration compared with related works.     

Synthesis and application of molecularly imprinted nanoparticles combined ultrasonic assisted for highly selective solid phase extraction trace amount of celecoxib from human plasma samples using design expert (DXB) software

In this work molecular imprinted nanoparticles (MINPs) was synthesized and applied for ultrasonic assisted solid phase extraction of celecoxib (CEL) from human plasma sample following its combination by HPLC–UV. The MINPs were prepared in a non-covalent approach using methacrylic acid as monomer, CEL as template, ethylene glycol dimethacrylate as cross-linker, and 2,2-azobisisobutyronitrile (AIBN) as the initiator of polymerization. pH, volume of rinsing and eluent solvent and amount of sorbent influence on response were investigated using factorial experimental design, while optimum point was achieved and set as 250 mg sorbent, pH 7.0, 1.5 mL washing solvent and 2 mL eluent by analysis of results according to design expert (DX) software. At above specified conditions, CEL in human plasma with complicated matrices with acceptable high recoveries (96%) and RSD% lower than 10% was quantified and estimated.The proposed MISPE-HPLC–UV method has linear responses among peak area and concentrations of CEL in the range of 0.2–2000 μg L⁻¹, with regression coefficient of 0.98. The limit of detection (LOD) and quantification (LOQ) based on three and ten times of the noise of HPLC peaks correspond to blank solution were 0.08 and 0.18 μg L⁻¹, respectively.     

The cut condition for robust network design

We consider the Robust Network Design problem, i.e. the problem of dimensioning the capacities on the edges of a graph to serve point-to-point traffic demands subject to uncertainty. The scope of the paper is to investigate when the cut condition is sufficient to guarantee the feasibility for such problem.     

Local-in-time adjoint-based method for design optimization of unsteady flows

We present a new local-in-time discrete adjoint-based methodology for solving design optimization problems arising in unsteady aerodynamic applications. The new methodology circumvents storage requirements associated with the straightforward implementation of a global adjoint-based optimization method that stores the entire flow solution history for all time levels. This storage cost may quickly become prohibitive for large-scale applications. The key idea of the local-in-time method is to divide the entire time interval into several subintervals and to approximate the solution of the unsteady adjoint equations and the sensitivity derivative as a combination of the corresponding local quantities computed on each time subinterval. Since each subinterval contains relatively few time levels, the storage cost of the local-in-time method is much lower than that of the global methods, thus making the time-dependent adjoint optimization feasible for practical applications. Another attractive feature of the new technique is that the converged solution obtained with the local-in-time method is a local extremum of the original optimization problem. The new method carries no computational overhead as compared with the global implementation of adjoint-based methods. The paper presents a detailed comparison of the global- and local-in-time adjoint-based methods for design optimization problems governed by the unsteady compressible 2-D Euler equations.     

MICROEMULSION SYSTEMS WITH A NONIONIC COSURFACTANT

The conditions to obtain W/0 microemulsions using ionic surfactants and a nonionic cosurfactant, a polyoxyethylene alkyl ether, were investigated. The length of the polyoxyethylene chain was critical to obtain the typical water solubilization maximum

The variation of the W/0 microemulsion region with hydrocarbon content was different from that of the usual type of microemulsions having a medium chain length alcohol as cosurfactant. In the present systems the W/0 microemulsion region was not a direct continuation of the inverse micellar area at zero content of hydrocarbon. Addition of hydrocarbon was necessary for the formation of inverse micelles

The microemulsion regions were sensitive to the kind of hydrocarbon used; a sign of the importance of the nonionic surfactant for the stability of this kind of microemulsions.