C1-continuous time integration based on cubic Hermite interpolation

We discuss a C¹-continuous time integration method based on piecewise cubic Hermite approximation. This method, denoted as p2-scheme, belongs to a class of one-step integration methods derived recently [1]. It exhibits a convergence rate of order four and shows properties similar to variational integrators, such as an excellent long-term energy preservation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Higher order variational integrators in optimal control theory

Higher order variational integrators are analyzed and applied to optimal control problems posed with mechanical systems. First, we derive two different kinds of high order variational integrators based on different dimensions of the underlying approximation space. While the first well-known integrator is equivalent to a symplectic partitioned Runge-Kutta method, the second integrator, denoted as symplectic Galerkin integrator, yields a method which in general, cannot be written as a standard symplectic Runge-Kutta scheme [1]. Furthermore, we use these integrators for the discretization of optimal control problems. By analyzing the adjoint systems of the optimal control problem and its discretized counterpart, we prove that for these particular integrators optimization and discretization commute [2]. This property guarantees that the accuracy is preserved for the adjoint system which is also referred to as the Covector Mapping Principle. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Melamine-(H_2SO_4)_3 and PVP-(H_2SO_4)_n as solid acids:Synthesis and application in the first mono-and di-nitration of bisphenol A and other phenols

Melamine and poly vinylpyrrolidone（PVP） reacted with neat sulfuric acid readily to form two new organic solid acids namely melamine-（H₂SO₄）₃ and PVP-（H₂SO₄）_n.These solid acids were used for the first nitration of bisphenol A as well as other phenols in the presence of NH₄NO₃.Mono- and di-nitro bisphenol A have been characterized with IR and ¹H NMR techniques.     

Homogeneous and inhomogeneous manifolds

All metaLindelöf, and most countably paracompact, homogeneous manifolds are Hausdorff. Metacompact manifolds are never rigid. Every countable group can be realized as the group of autohomeomorphisms of a Lindelöf manifold. There is a rigid foliation of the plane.

     

Computation of derivatives for structure preserving optimal control using automatic differentiation

In this work we combine a recently developed method, Discrete Mechanics and Optimal Control (DMOC), with the well established Automatic Differentiation package ADOL-C. DMOC is based on the discretization of the variational structure of the mechanical system which leads to structure (symplectic-momentum) preserving time-stepping equations. The discretized equations provide equality constraints for the resulting finite dimensional nonlinear optimization problem. For the solution of this problem standard nonlinear optimization techniques like sequential quadratic programming (SQP) are used. To ensure robustness of these techniques the computation of derivatives of the objective function and the constraints is of great importance. The concept of Automatic Differentiation (AD) is used to improve the performance of the SQP method. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization for discretized switched systems

Switching time optimization is a crucial topic in the optimal control of hybrid systems. Since it is rare that such problems can be solved analytically, the use of numerical discretization schemes for the integration of state and adjoint systems is indispensable. Thus, in this contribution, the switching time optimization problem is studied in a discretized formulation directly from the beginning. An analysis of the discretized problem reveals that smoothness of the original (continuous time) problem is lost, i.e. the problem will in general become nondifferentiable in discrete time. This has to be taken into account when deriving an adjoint-based formula for the optimization of the discretized problem. A hybrid double pendulum example is used for illustration of the results. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A variational approach to define robustness for parametric multiobjective optimization problems

In contrast to classical optimization problems, in multiobjective optimization several objective functions are considered at the same time. For these problems, the solution is not a single optimum but a set of optimal compromises, the so-called Pareto set. In this work, we consider multiobjective optimization problems that additionally depend on an external parameter ${\lambda \in \mathbb{R}}$ , so-called parametric multiobjective optimization problems. The solution of such a problem is given by the λ-dependent Pareto set. In this work we give a new definition that allows to characterize λ-robust Pareto points, meaning points which hardly vary under the variation of the parameter λ. To describe this task mathematically, we make use of the classical calculus of variations. A system of differential algebraic equations will turn out to describe λ-robust solutions. For the numerical solution of these equations concepts of the discrete calculus of variations are used. The new robustness concept is illustrated by numerical examples.     

Evaluating and selecting the supplier in detergent production industry using hierarchical fuzzy TOPSIS

Supply chain management has increasingly attracted attention as a systematic approach to integrate the supply chain in order to planning and controlling the materials and information from suppliers to customers. One of the most important issues in supply chain management is selection of the appropriate supplier which has significant effect on purchasing cost decrease and increase in the organization’s competition ability. Selection of the best supplier is naturally complex with no definite structure, and dependent on the type of suppliers’ activity. In the process of decision making about suppliers and many qualitative and quantitative performance indicators such as quality, price, flexibility, and due date should be considered. Then, the supplier selection problem is a multi-criteria decision making problem where numerous methods have been proposed to solve this problem so far. In the current paper, four suppliers of imported raw material “Tripolyphosphate (TPP)” (primary material to produce the detergent powder with a case study in Iran) are evaluated based on 25 effective criteria using the hierarchical fuzzy TOPSIS (HFTOPSIS) approach.     

Should retail stores also RFID-tag ‘cheap’ items?

Despite their implementations in a wide variety of applications, there are very few instances where every item sold at a retail store is RFID-tagged. While the business case for expensive items to be RFID tagged may be somewhat clear, we claim that even ‘cheap’ items (i.e., those that cost less than an RFID tag) should be RFID tagged for retailers to benefit from efficiencies associated with item-level visibility. We study the relative price premiums a retailer with RFID tagged items can command as well as the retailer’s profit to illustrate the significance of item-level RFID-tagging both cheap and expensive items at a retail store. Our results indicate that, under certain conditions, item-level RFID tagging of items that cost less than an RFID tag has the potential to generate significant benefits to the retailer. The retailer is also better off tagging all items regardless of their relative price with respect to that of an RFID tag compared to the case where only the expensive item is RFID-tagged.     

Graphene oxide‐induced polymerization and crystallization to produce highly conductive polyaniline/graphene oxide composite

Graphene oxide (GO)–polyaniline (PANI) composite is synthesized by in situ polymerization of aniline in the presence of GO as oxidant, resulting in highly crystalline and conductive composite. Fourier transform infrared spectrum confirms aniline polymerization in the presence of GO without using conventional oxidants. Scanning electron microscopic images show the formation of PANI nanofibers attached to GO sheets. X‐ray diffraction (XRD) patterns indicate the presence of highly crystalline PANI. The sharp peaks in XRD pattern suggest GO sheets not only play an important role in the polymerization of aniline but also in inducing highly crystalline phase of PANI in the final composite. Electrical conductivity of doped GO–PANI composite is 582.73 S m^?1, compared with 20.3 S m^?1 for GO–PANI obtained by ammonium persulfate assisted polymerization. The higher conductivity appears to be the result of higher crystallinity and/or chemical grafting of PANI to GO, which creates common conjugated paths between GO and PANI. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1545–1554