Bioassay-guided isolation of antioxidants from Astragalus altaicus by combination of chromatographic techniques

An efficient method for bioassay-guided preparative isolation of antioxidants from the n-butanol extract of Astragalus altaicus Bunge was ingeniously developed by combination of silica gel column chromatography and high-speed counter-current chromatography. Under the bioassay-guidance of antioxidant activities, the antioxidants were gradually separated from the crude sample of Astragalus altaicus Bunge by silica gel column chromatography and high-speed counter-current chromatography. Silica gel column chromatography separation was performed with chloroform, chloroform-methanol (100:1~5:1, v/v) and chloroform-methanol-water (5:1:0.1~2:1:0.1, v/v/v). High-speed counter-current chromatography separation was performed with a two-phase solvent system composed of ethyl acetate-n-butanol-water (2:1:6, v/v/v), which was successfully selected by thin layer chromatography analysis, at a flow rate of 1.5 mL/min. As a result, isorhamnetin-3-gentiobioside (20.8 mg), rutin (82.0 mg), and narcissin (12.8 mg) were obtained for the first time from 200 mg of the crude sample, ABS-5 of Astragalus altaicus Bunge. The purities were all at over 95% by high-performance liquid chromatography analysis, and their structures were unambiguously identified by mass spectroscopy, (1) H, and (13) C nuclear magnetic resonance spectroscopy. Antioxidant activities of the three compounds were also assayed by in vitro ABTS [2,2'-azino-bis-(3-ethylbenzothiazoline-6-sulphonic acid) diamonium salt] radical cation scavenging activity. Among them, rutin possessed the highest antioxidant capacity with SC(50) value of 22.15 μg/mL.     

西兰花中13种有机含磷农药在不同色谱柱上的色谱保留行为

应用Agilent GC 6890气相色谱仪(附FPD检测器)对13种残留于西兰花中的有机含磷农药(OPP′s)在4种不同极性的毛细管色谱柱(即DB-1、DB-5、DB-1701及DB-35MS)上的保留行为作了研究。结果表明:采用由DB-5及DB-1701串联组成的色谱柱单元,西兰花中13种残留OPP′s可达到有效分离和测定。     

Mixed-integer programming models for nesting problems

Several industrial problems involve placing objects into a container without overlap, with the goal of minimizing a certain objective function. These problems arise in many industrial fields such as apparel manufacturing, sheet metal layout, shoe manufacturing, VLSI layout, furniture layout, etc., and are known by a variety of names: layout, packing, nesting, loading, placement, marker making, etc. When the 2-dimensional objects to be packed are non-rectangular the problem is known as the nesting problem. The nesting problem is strongly NP-hard. Furthermore, the geometrical aspects of this problem make it really hard to solve in practice. In this paper we describe a Mixed-Integer Programming (MIP) model for the nesting problem based on an earlier proposal of Daniels, Li and Milenkovic, and analyze it computationally. We also introduce a new MIP model for a subproblem arising in the construction of nesting solutions, called the multiple containment problem, and show its potentials in finding improved solutions.     

The plane‐width of graphs

Map the vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least unit distance apart. The plane‐width of a graph is the minimum diameter of the image of its vertex set over all such mappings. We establish a relation between the plane‐width of a graph and its chromatic number. We also connect it to other well‐known areas, including the circular chromatic number and the problem of packing unit discs in the plane. © 2011 Wiley Periodicals, Inc. J Graph Theory 68: 229‐245, 2011     

Scheduling inspired models for two-dimensional packing problems

We propose two exact algorithms for two-dimensional orthogonal packing problems whose main components are simple mixed-integer linear programming models. Based on the different forms of time representation in scheduling formulations, we extend the concept of multiple time grids into a second dimension and propose a hybrid discrete/continuous-space formulation. By relying on events to continuously locate the rectangles along the strip height, we aim to reduce the size of the resulting mathematical problem when compared to a pure discrete-space model, with hopes of achieving a better computational performance. Through the solution of a set of 29 test instances from the literature, we show that this was mostly accomplished, primarily because the associated search strategy can quickly find good feasible solutions prior to the optimum, which may be very important in real industrial environments. We also provide a comprehensive comparison to seven other conceptually different approaches that have solved the same strip packing problems.     

Performance of short-chain alcohols versus acetonitrile in the surfactant-mediated reversed-phase liquid chromatographic separation of β-blockers

Organic solvents are traditionally added to micellar mobile phases to achieve adequate retention times and peak profiles, in a chromatographic mode which has been called micellar liquid chromatography (MLC). The organic solvent content is limited to preserve the formation of micelles. However, at increasing organic solvent contents, the transition to a situation where micelles do not exist is gradual. Also, there is no reason to neglect the potentiality of mobile phases containing only surfactant monomers instead of micelles (high submicellar chromatography, HSC). This is demonstrated here for the analysis of β-blockers. The performance of four organic solvents (methanol, ethanol, 1-propanol, and acetonitrile) was compared in mobile phases containing the anionic surfactant sodium dodecyl sulphate in the MLC and HSC modes. The association of the organic solvent molecules with micelles gives rise to a significant loss in the elution strength of the organic solvent; whereas upon disruption of micelles, it tends to that observed in the hydro-organic mode. The elution behaviour of the β-blockers was modelled to predict the retention times. This allowed the detailed exploration of the selectivity and resolution of the chromatographic systems in relatively wide ranges of concentration of surfactant and organic solvent. The best performance in terms of resolution and analysis time was achieved using HSC with acetonitrile, being able to base-line resolve a mixture of eight β-blockers. Ethanol also provided a good separation performance, significantly improved with respect to methanol and 1-propanol. In contrast, the hydro-organic mode using acetonitrile or any of the short-chain alcohols could not succeed with the separation of the β-blockers, owing to the poorer selectivity and wider peaks.     

An agent-based approach to the two-dimensional guillotine bin packing problem

The two-dimensional guillotine bin packing problem consists of packing, without overlap, small rectangular items into the smallest number of large rectangular bins where items are obtained via guillotine cuts. This problem is solved using a new guillotine bottom left (GBL) constructive heuristic and its agent-based (A–B) implementation. GBL, which is sequential, successively packs items into a bin and creates a new bin every time it can no longer fit any unpacked item into the current one. A–B, which is pseudo-parallel, uses the simplest system of artificial life. This system consists of active agents dynamically interacting in real time to jointly fill the bins while each agent is driven by its own parameters, decision process, and fitness assessment. A–B is particularly fast and yields near-optimal solutions. Its modularity makes it easily adaptable to knapsack related problems.     

Heuristic approaches to large-scale periodic packing of irregular shapes on a rectangular sheet

The nesting problem is a two-dimensional cutting and packing problem where the small pieces to cut have irregular shapes. A particular case of the nesting problem occurs when congruent copies of one single shape have to fill, as much as possible, a limited sheet. Traditional approaches to the nesting problem have difficulty to tackle with high number of pieces to place. Additionally, if the orientation of the given shape is not a constraint, the general nesting approaches are not particularly successful. This problem arises in practice in several industrial contexts such as footwear, metalware and furniture. A possible approach is the periodic placement of the shapes, in a lattice way. In this paper, we propose three heuristic approaches to solve this particular case of nesting problems. Experimental results are compared with published results in literature and additional results obtained from new instances are also provided.     

Non-linear anonymous pricing combinatorial auctions

In combinatorial auctions the pricing problem is of main concern since it is the means by which the auctioneer signals the result of the auction to the participants. In order for the auction to be regarded as fair among the various participants the price signals should be such that a participant that has won a subset of items knows why his bid was a winning bid and that agents that have not acquired any item easily can detect why they lost. The problem in the combinatorial auction setting is that the winner determination problem is a hard integer programming problem and hence a linear pricing scheme supporting the optimal allocation might not exist.     

Exact algorithms for the two-dimensional strip packing problem with and without rotations

We propose exact algorithms for the two-dimensional strip packing problem (2SP) with and without 90° rotations. We first focus on the perfect packing problem (PP), which is a special case of 2SP, wherein all given rectangles are required to be packed without wasted space, and design branch-and-bound algorithms introducing several branching rules and bounding operations. A combination of these rules yields an algorithm that is especially efficient for feasible instances of PP. We then propose several methods of applying the PP algorithms to 2SP. Our algorithms succeed in efficiently solving benchmark instances of PP with up to 500 rectangles and those of 2SP with up to 200 rectangles. They are often faster than existing exact algorithms specially tailored for problems without rotations.