Sum of ratios problem occurs frequently in various areas of engineering practice and management
science, but most solution methods for this kind of problem are often designed for determining local solutions . In this paper, we develop a reduced space branch and bound algorithm for globally solving sum of convex-concave ratios problem. By introducing some auxiliary variables, the initial problem is converted into an equivalent problem where the objective function is linear. Then the convex relaxation problem of the equivalent problem is established by relaxing auxiliary variables only in the outcome space. By integrating some acceleration and reduction techniques into branch and bound scheme, the presented global optimization algorithm is developed for solving these kind of problems. Convergence and optimality of the algorithm are presented and numerical examples taken from some recent literature and MINLPLib are carried out to validate the performance of the proposed algorithm.
In this paper, we propose a formula to describe the relationship between the Miller indices h, k and the row-row distance for the monoclinic system, which effectively overcomes the difficulty in indexing defective selected-area electron diffraction (SAED) patterns and Fourier transform of high-resolution transmission electron microscopy (HRTEM) images. Such defective SAED patterns are often found in clay minerals and other beam-sensitive materials. The spot-to-spot indexing is therefore transformed into the row-to-row measurement and calculation. This significantly improves the indexing for electron diffraction patterns. According to this formula proposed here, it is only necessary to measure the distance between rows [00L] and [HKL] and then the h and k and hence the l can be evaluated. This not only indexes the reflections, but also helps to judge the incident electron beam direction. The reliability and practicality of this row-indexing method were verified by both a simulated SAED pattern of chlorite and HRTEM experiments of illite and palygorskite. Formulae of row-indexing for the orthorhombic, rhombohedral, tetragonal, hexagonal and cubic systems are also presented.
Two new interesting entangled structures, namely, [Ni1.5(L)(bpy)2(H2O)3]n·3nH2O (I) and [Cd3(L)2(bbi)2]n · nH2O (II) (where H3L is 4-(4-carboxyphenoxy)-phthalic acid, bpy is 4,4´- bipyridine, and bbi is 1,1´-(1,4-butanediyl)bis(imidazole)) have been synthesized and characterized by elemental analysis (EA), infrared spectra (IR), X-ray powder diffraction (XRPD), solid fluorescence and thermogravimetric analysis (TGA). Single-crystal X-ray diffraction analysis revealed that complex I possesses a 3D self-penetrating framework constructed from ladder-like and fishbone-like subunits. Complex II shows a 3D framework of two-fold interpenetration assembled from trinuclear Cd(II) clusters bridged by bbi and L3− ligands.
Al-Li alloy 2198 exhibits good combination of toughness and strength but its application is strongly limited by the poor weldability due to the formation of porosities during fusion-welding. This is the first study proposing and verifying a new approach to produce defect-free laser welds of poorly fusion-weldable Al-Li alloy 2198 with applied external pressure, i.e., feasibility of laser pressure welding to Al-Li alloy 2198 was examined. The microstructures associated with tensile shear behavior of laser pressure welded Al-Li alloy 2198 obtained at various welding parameters were analyzed. The results showed that formation of the welding defect in the weld could be successfully suppressed by applying laser pressure welding, even without shielding gas. Three microstructural zones, including the chill zone, the columnar zone and the equiaxed zone were observed in the fusion zone. Size of fusion zone and area fraction of porosities generally increased with increasing roller pressure and welding heat-input, and they dominantly affected the tensile shear behavior, including the peak load and the failure mode, of the weld.
Ascaridia galli (Schrank, 1788) is a common parasite of various galliform birds worldwide. Although A. galli has been extensively studied by many author, knowledge of the morphology of this species in detail is still insufficient. In the present paper, the detailed morphology of A. galli was further studied using light and scanning electron microscopy, based on specimens collected from the endangered green peafowl Pavo muticus Linnaeus (Galliformes: Phasianidae) in China. The results revealed some erroneous and previously unreported morphological features, including the lips lacking real denticles, the lateral alae beginning at some distance posterior to the base of the ventrolateral lips and the caudal papillae with 4 different morphotypes. The present morphological and morphometric data complement previous descriptions and enable us to recognize this species more precisely.