The one-dimensional cutting stock problem with usable leftover – A heuristic approach

In this work we consider a one-dimensional cutting stock problem in which the non-used material in the cutting patterns may be used in the future, if large enough. This feature introduces difficulties in comparing solutions of the cutting problem, for example, up to what extent a minimum leftover solution is the most interesting one when the leftover may be used. Some desirable characteristics of good solutions are defined and classical heuristic methods are modified, so that cutting patterns with undesirable leftover (not large enough to be used, nor too small to be acceptable waste) are redesigned. The performance of the modified heuristics is observed by solving instances from the literature, practical instances and randomly generated instances.     

On stochastic spatial patterns and neuronal polarity

To investigate the statistical behavior in the sizes of finite clusters for percolation, cluster size distribution n _s (p) for site and bond percolations at different lattices and dimensions was simulated using a modified algorithm. An equation to approximate the finite cluster size distribution n _s (p) was obtained and expressed as: log?(n _s (p)) = as ? b log?s + c. Based on the analysis of simulation data, we found that the equation is valid for p from 0 to 1 on site and for the bond percolation of two-dimensional (2D) and three-dimensional (3D) lattices. Furthermore, the relationship between the coefficients of the equation and the occupied ratio p was studied using the finite-size scaling method. When \(x = D(p - p_c )L^{y_t }\) , p < p _c , and D was a nonuniversal metric factor. a was found to be related only to p, and the a-x curves of different lattices were nearly overlapped; b was related to the dimensions and p, and the scaled data of the b of all lattices with the same dimension tended to fall on the same curves. Unlike a and b, c apparently had a quadratic relation with x in 2D lattices and linear relation with x in 3D lattices. The results of this paper could significantly reduce the amount of tasks required to obtain numerical data of on the cluster size distribution for p from 0 to p _c .     

Graphene functionalisation with a conjugated poly(fluorene) by click coupling: striking electronic properties in solution

Graphene flakes covalently modified with a conjugated polymer, poly[(9,9-dihexylfluorene)-co-alt-(9,9-bis-(6-azidohexyl)fluorene)] (PFA), were efficiently synthesised by a Cu-catalysed Huisgen 1,3-dipolar cycloaddition between alkyne-modified graphene and an azide-functionalised polymer. Two approaches for the modification of graphene with alkyne groups were investigated (coupling with a diazonium salt generated in situ or an amidation reaction) and the optimum conditions determined. The success of the click-coupling approach was confirmed by FTIR, (1)H?NMR, Raman, and X-ray photoelectron spectroscopy (XPS). The absorption and emission spectra of the click product show a strong solvent dependency.     

Efficient and suitable preparation of N-sulfonyl-1,2,3,4-tetrahydroisoquinolines and ring analogues using recyclable H6P2W18O62·24H2O/SiO2 catalyst

Silica gel-supported H₆P₂W₁₈O₆₂·24H₂O is an efficient and recyclable catalyst for the synthesis of biologically important molecules. Several substituted N-sulfonyl-1,2,3,4-tetrahydroisoquinolines and ring analogues can be prepared in very good yields and purity by direct reaction of N-aralkylsulfonamides and sym-trioxane by a Pictet-Spengler reaction in the presence of a catalytic amount of silica gel-supported H₆P₂W₁₈O₆₂·24H₂O. Reactions were performed in a low volume of toluene, at 70 °C and for a short time, typically 15 to 30 min. The title heterocyclic compounds were prepared in very good yields (60%–95%) using the described procedure results in a clean and useful alternative, which has the advantages of a greener methodology with operative simplicity, use of a reusable and non-corrosive solid catalyst, soft reaction conditions, low reaction times, and good yields.     

Synthesis of 3-alkyl-5-hydroxycyclohex-2-enones via aldolic addition/sulfinate elimination tandem reactions

The first synthesis of 3-alkyl-5-hydroxycyclohex-2-enones is reported. An intramolecular cyclization by means of an aldolic addition/sulfinate elimination tandem reactions, performed under mild basic conditions was the key step.     

Comparative study of 2‐amino and 3‐aminobenzoic acid copolymerization with aniline synthesis and copolymer properties

Polyanilines soluble in an aqueous basic medium were synthesised by copolymerization of aniline (ANI) with both 2 and 3‐aminobenzoic acids (ABA). Different composition copolymers were prepared by varying the ANI/ABA feed ratio. Poly(aniline‐co‐2‐aminobenzoic acid) (PANI2ABA) and poly(aniline‐co‐3‐aminobenzoic acid) (PANI3ABA) displayed differences in their properties, such as specific charge and fluorescence behavior because the reactivity of 2‐aminobenzoic (2ABA) and 3‐aminobenzoic (3ABA) acids are very different. The new materials were characterized by X‐ray photoelectron, Fourier transform infrared, and Raman spectroscopies. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5587–5599, 2004     

Membrane triangles with corner drilling freedoms—I. The EFF element

This paper is the first of a three-part series that studies the formulation of 3-node, 9-dof membrane elements with normal-to-element-plane rotations (the so-called drilling freedoms) within the context of parametrized variational principles. These principles supply a unified basis for several advanced element-construction techniques; in particular: the free formulation (FF), the extended free formulation (EFF) and the assumed natural deviatoric strain (ANDES) formulation. In Part I we construct an element of this type using the EFF. This derivation illustrates the basic steps in the application of that formulation to the construction of high-performance, rank-sufficient, nonconforming elements with corner rotations. The element is initially given the twelve degress of freedom of the linear strain triangle (LST), which allows the displacement expansion to be a complete quadratic in each component. The expansion basis contains the six linear basic functions and six energy-orthogonal quadratic higher-order functions. Three degrees of freedom, defined as the midpoint deviations from linearity along the triangle-median directions, are eliminated by kinematic constraints. The remaining hierarchical midpoint freedoms are transformed to corner rotations. The performance of the resulting element is evaluated in Part III.     

Investigation of 3D Contour Map and Intermolecular Interaction of Dopamine with β-Cyclodextrin and 2-Hydroxypropyl-β-cyclodextrin

The interactions of the neurotransmitter dopamine (DA) with β-cyclodextrin and 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) was characterized using UV–visible, 2D fluorescence, 3D fluorescence, FT–IR, PXRD and SEM techniques. PM3, PM7 and DFT methods were used to optimize the structures of the inclusion complexes in the gas phase. The absorbance and fluorescence intensities of DA increased in the presence of CDs in aqueous solution. The binding energy, HOMO–LUMO energy gap and Mulliken atomic charges were computed for the inclusion complexes. NBO analysis revealed a greater number of intermolecular hydrogen bonds in DA:HP-β-CD. Experimental and theoretical results suggested that the DA molecule is deeply embedded in the cavities of both CDs.