Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Optimization of a method for determination of phenolic acids in exotic fruits by capillary electrophoresis

In this work, the separation of nine phenolic acids (benzoic, caffeic, chlorogenic, p-coumaric, ferulic, gallic, protocatechuic, syringic, and vanillic acid) was approached by a 32 factorial design in electrolytes consisting of sodium tetraborate buffer(STB) in the concentration range of 10-50 mmol L(-1) and methanol in the volume percentage of 5-20%. Derringer`s desirability functions combined globally were tested as response functions. An optimal electrolyte composed by 50 mmol L(-1) tetraborate buffer at pH 9.2, and 7.5% (v/v) methanol allowed baseline resolution of all phenolic acids under investigation in less than 15 min. In order to promote sample clean up, to preconcentrate the phenolic fraction and to release esterified phenolic acids from the fruit matrix, elaborate liquid-liquid extraction procedures followed by alkaline hydrolysis were performed. The proposed methodology was fully validated (linearity from 10.0 to 100 mu g mL(-1), R(2) > 0.999: LOD and LOQ from 1.32 to 3.80 mu g mL(-1) and from 4.01 to 11.5 mu g mL(-1), respectively; intra-day precision better than 2.8% CV for migration time and 5.4% CV for peak area; inter-day precision better than 4.8% CV for migration time and 4.8-11% CV for peak area: recoveries from 81% to 115%) and applied successfully to the evaluation of phenolic contents of abiu-roxo (Chrysophyllum caimito), wild mulberry growing in Brazil (Morus nigra L.) and tree tomato (Cyphomandra betacea). Values in the range of 1.50-47.3 mu g g(-1) were found, with smaller amounts occurring as free phenolic acids. (C) 2009 Elsevier B.V. All rights reserved.

Multivariant optimization, validation, and application of capillary electrophoresis for simultaneous determination of polyphenols and phenolic acids in Brazilian wines

A method for the simultaneous determination of the stilbene resveratrol, four phenolic acids (syringic, coumaric, caffeic, and gallic acids), and five flavonoids (catechin, rutin, kaempferol, myricetin, and quercetin) in wine by CE was developed and validated. The CE electrolyte composition and instrumental conditions were optimized using 2(7-3) factorial design and response surface analysis, showing sodium tetraborate, MeOH, and their interaction as the most influential variables. The optimal electrophoretic conditions, minimizing the chromatographic resolution statistic values, consisted of 17 mmol/L sodium tetraborate with 20% methanol as electrolyte, constant voltage of 25 kV, hydrodynamic injection at 50 mbar for 3 s, and temperature of 25 degrees C. The R(2) values for linearity varied from 0.994 to 0.999; LOD and LOQ were 0.1 to 0.3 mg/L and 0.4 to 0.8 mg/L, respectively. The RSDs for migration time and peak area obtained from ten consecutive injections were less than 2% and recoveries varied from 97 to 102%. The method was applied to 23 samples of inexpensive Brazilian wines, showing wide compositional variation.

Detection of Paraquat in Oral Fluid, Plasma, and Urine by Capillary Electrophoresis for Diagnosis of Acute Poisoning

FAPESP

Determination of sorbate and benzoate in beverage samples by capillary electrophoresis - Optimization of the method with inspection of ionic mobilities

The aim of this study was to develop a fast capillary electrophoresis method for the determination of benzoate and sorbate ions in commercial beverages. In the method development the pH and constituents of the background electrolyte were selected using the effective mobility versus pH curves. As the high resolution obtained experimentally for sorbate and benzoate in the studies presented in the literature is not in agreement with that expected from the ionic mobility values published, a procedure to determine these values was carried out. The salicylate ion was used as the internal standard. The background electrolyte was composed of 25 mmol L(-1) tris(hydroxymethyl)aminomethane and 12.5 mmol L(-1) 2-hydroxyisobutyric acid, atpH 8.1.Separation was conducted in a fused-silica capillary(32 cm total length and 8.5 cm effective length, 50 mu m I.D.), with short-end injection configuration and direct UV detection at 200 nm for benzoate and salicylate and 254 nm for sorbate ions. The run time was only 28 s. A few figures of merit of the proposed method include: good linearity (R(2) > 0.999), limit of detection of 0.9 and 0.3 mg L(-1) for benzoate and sorbate, respectively, inter-day precision better than 2.7% (n =9) and recovery in the range 97.9-105%. Beverage samples were prepared by simple dilution with deionized water (1:11, v/v). Concentrations in the range of 197-401 mg L(-1) for benzoate and 28-144 mg L(-1) for sorbate were found in soft drinks and tea. (c) 2008 Elsevier B.V. All rights reserved.

Determination of ciclopirox olamine in pharmaceutical products by capillary electrophoresis with capacitively coupled contactless conductivity detection

This paper describes the determination of ciclopirox olamine in pharmaceutical formulations using capillary electrophoresis with capacitively coupled contactless conductivity detection. In an alkaline medium, ciclopirox olamine is converted into an anionic species and its detection is possible in capillary electrophoresis with capacitively coupled contactless conductivity detection without an electroosmotic flow modifier, because it is a low-mobility species. A linear working range from 2.64 to 264 mu g/mL in sodium hydroxide electrolyte as well as low detection limit (0.39 mu g/mL) and a good repeatability (RSD = 3.4% for 264 mu g/mL ciclopirox solution (n = 10)) were achieved. It was also possible to determine olamine in its cationic form when acetic acid was used as the electrolyte solution. The results obtained include a linear range from 26.4 to 184.8 mu g/mL and a detection limit of 2.6 mu g/mL olamine. The proposed methods were applied to the analysis of commercial pharmaceutical products and the results were compared with the values indicated by the manufacturer as well as those obtained using a titrimetric method recommended by American Pharmacopoeia.

Development of a fast capillary electrophoresis method to determine inorganic cations in biodiesel samples

The aim of this study was to develop a fast capillary electrophoresis method for the determination of inorganic cations (Na(+), K(+), Ca(2+), Mg(2+)) in biodiesel samples, using barium (Ba(2+)) as the internal standard. The running electrolyte was optimized through effective mobility curves in order to select the co-ion and Peakmaster software was used to determine electromigration dispersion and buffer capacity. The optimum background electrolyte was composed of 10 mmol L(-1) imidazole and 40 mmol L(-1) of acetic acid. Separation was conducted in a fused-silica capillary (32 cm total length and 23.5 cm effective length, 50 mu m I.D.), with indirect UV detection at 214 nm. The migration time was only 36 s. In order to obtain the optimized conditions for extraction, a fractional factorial experimental design was used. The variables investigated were biodiesel mass, pH, extractant volume, agitation and sonication time. The optimum conditions were: biodiesel mass of 200 mg, extractant volume of 200 mu L. and agitation of 20 min. The method is characterized by good linearity in the concentration range of 0.5-20 mg kg(-1) (r > 0.999), limit of detection was equal to 0.3 mg kg(-1), inter-day precision was equal to 1.88% and recovery in the range of 88.0-120%. The developed method was successfully applied to the determination of cations in biodiesel samples. (c) 2010 Elsevier B.V. All rights reserved.

Development of a fast capillary electrophoresis method for the determination of propranolol-Total analysis time reduction strategies

The aim of this study was to develop a fast capillary electrophoresis method for the determination of propranolol in pharmaceutical preparations. In the method development the pH and constituents of the background electrolyte were selected using the effective mobility versus pH curves. Benzylamine was used as the internal standard. The background electrolyte was composed of 60 mmol L(-1) tris(hydroxymethyl)aminomethane and 30 mmol L(-1) 2-hydroxyisobutyric acid,at pH 8.1. Separation was conducted in a fused-silica capillary (32 cm total length and 8.5 cm effective length, 50 mu m I.D.) with a short-end injection configuration and direct UV detection at 214 nm. The run time was only 14 s. Three different strategies were studied in order to develop a fast CE method with low total analysis time for propranolol analysis: low flush time (Lflush) 35 runs/h, without flush (Wflush) 52 runs/h, and Invert (switched polarity) 45 runs/h. Since the three strategies developed are statistically equivalent, Mush was selected due to the higher analytical frequency in comparison with the other methods. A few figures of merit of the proposed method include: good linearity (R(2) > 0.9999); limit of detection of 0.5 mg L(-1): inter-day precision better than 1.03% (n = 9) and recovery in the range of 95.1-104.5%. (C) 2009 Elsevier B.V. All rights reserved.

Rapid method for the determination. of organic acids in wine by capillary electrophoresis with indirect UV detection

A capillary electrophoresis method for organic acids in wine was developed and validated. The optimal electrolyte consisted of 10 mmol/L 3,5-dinitrobenzoic acid (DNB) at pH 3.6 containing 0.2 mmol/L cetyltrimethylammonium bromide as flow reverser. DNB was chosen because it has an effective mobility similar to the organic acids under investigation, good buffering capacity at pH 3.6, and good chromophoric characteristics for indirect UV-absorbance detection at 254 nm. Sample preparation involved dilution and filtration. The method showed good performance characteristics: Linearity at 6 to 285 mg/L (r > 0.99); detection and quantification limits of 0.64 to 1.55 and 2.12 to 5.15 mg/L, respectively; separation time of less than 5.5 min. Coefficients of variation for ten injections were less than 5% and recoveries varied from 95% to 102%. Application to 23 samples of Brazilian wine confirmed good repeatability and demonstrated wide variation in the organic acid concentrations. (C) 2008 Elsevier Ltd. All rights reserved.

Determination of amino acids by capillary electrophoresis-electrospray ionization-mass spectrometry: An evaluation of different protein hydrolysis procedures

In this work, a CE equipment, online hyphenated to an IT MS analyzer by a linear sheath liquid interface promoting ESI, was used to develop a method for quantitative determination of amino acids. Under appropriate conditions (BGE composition, 0.8% HCOOH, 20% CH(3)OH; sheath liquid composition, 0.8% HCOOH, 60% methanol; V(ESI), +4.50 W), analytical curves of all amino acids from 3 to 80 mg/L were recorded presenting acceptable linearity (r > 0.99). LODs in the range of 16-172 mu mol/L were obtained. BSA, a model protein, was submitted to different hydrolysis procedures (classical acid and basic, and catalyzed by the H(+) form of a cation exchanger resin) and its amino acid profiles determined. In general, the resin-mediated hydrolysis yields were overall similar or better than those obtained by classical acid or basic hydrolysis. The resulting experimental-to-theoretical BSA concentration ratios served as correction factors for the quantitation of amino acids in Brazil nut resin generated hydrolysates.

Determination of polyamines in organic extracts from roots of Canavalia ensiformis by capillary electrophoresis

A rapid, selective and specific capillary zone electrophoresis method to determine polyamines in organic extracts from roots of Canavalia ensiformis (Jack Beans) was developed using ultra violet (UV) detection. Canavalia ensiformis is relatively free from diseases and it is used as reference in allelopathy studies. Polyamines are widely distributed in plant and it could be involved in plant pathogen interactions. Optimal separation was achieved using 15 mmol.L-1formic acid (pH 3.0) + 4 mmol.L-1 imidazole as a background electrolyte. It was possible to identify and quantify the polyamines on herbal samples in the presence of other phytochemical substances and analyze them quickly (up to 6 min). The applicability of this method was evaluated in crude organic extracts from roots of Canavalia ensiformis.

Fast separation of selective serotonin reuptake inhibitors antidepressants in plasma sample by nonaqueous capillary electrophoresis

A simple, fast, and sensitive liquid-liquid extraction method followed by nonaqueous capillary electrophoresis (LLE/NACE) was developed and validated for Simultaneous determination of four antidepressants (fluoxetine, sertraline, citalopram and paroxetine) in human plasma. Several experimental separation conditions using aqueous and nonaqueous media separation were tested by varying the electrolyte pH value (for aqueous medium) and the ionic strength concentration considering the similar mobility of the compounds. High-resolution separation was achieved with a mixture of 1.25 mol L(-1) of phosphoric acid in acetonitrile. The quantification limits of the LLE/CE method varied between 15 and 30 ng mL(-1), with a relative standard deviation (RSD) lower than 10.3%. The method was successfully applied in therapeutic drug monitoring and should be employed in the evaluation of plasma levels in urgent toxicological analysis. (C) 2009 Elsevier B.V. All rights reserved.

Analytical Assessment of a Home Made Capillary Electrophoresis Equipment with Linear Charge Coupled Device for Visible Light Absorption Detection in the Determination of Food Dyes

The performance of modular home made capillary electrophoresis equipment with spectrophotometric detection, at a visible region by means of a miniaturized linear charge coupled device, was evaluated for the determination of four food dyes. This system presents a simple but efficient home made cell detection scheme. A computer program that converts the spectral data after each run into the electropherograms was developed to evaluate the analytical parameters. The dyes selected for analytical evaluation of the system were Brilliant Blue FCF, Fast Green FCF, Sunset Yellow FCF, and Amaranth. Separation was carried out in a 29cm length and 75 mu m I.D fused silica capillary, using 10mmolL-1 borate buffer at pH 9, with separation voltage of 7.5kV. The detection limits for the dyes were between 0.3 and 1.5mgL-1 and the method presented adequate linearity over the ranges studied, with correlation coefficients greater than 0.99. The method was applied for determination and quantification of these dyes in fruit juices and candies.