Spherical coordinate representations of solvent composition for liquid chromatography method development using experimental design

One of the major techniques used for the method development of ternary and quaternary high performance liquid chromatography (HPLC) systems has been to use mixture designs, often referred to as "Glajch's Triangle". This technique does not allow for the systematic and simultaneous optimization of other factors such as gradient time, pH and temperature that affect the quality of separations. An alternative approach is to use experimental designs. The condition, however, that the composition of all components of the mobile phase must total 100% presents a problem when trying to mathematically represent ranges of each mobile phase constituent of a ternary or quaternary system. A method is described here, based on spherical coordinate representations, that adheres to the constraints of the mobile phase composition and allows experimental designs, such as central composite and factorial designs, to be applied to the simultaneous optimization of the mobile phase composition. Other factors, in particular temperature and gradient time, can then be included in the design. As a result of applying these designs to the HPLC separation of phenols and corticosteroids, it was found necessary to include three-way interactions between experimental factors in the model. The significance of these interactions shows that they need to be considered in HPLC method development.     

Hydride generation atomic fluorescence spectrometric determination of As, Bi, Sb, Se(IV) and Te(IV) in aqua regia extracts from atmospheric particulate matter using multivariate optimization

A highly sensitive and simple method, based on hydride generation and atomic fluorescence detection, has been developed for the determination of As, Bi, Sb, Se(IV) and Te(IV) in aqua regia extracts from atmospheric particulate matter samples. Atmospheric particulates matter was collected on glass fiber filters using a medium volume sampler (PM1 particulate matter). Two-level factorial designs have been used to optimise the hydride generation atomic fluorescence spectrometry (HG-AFS) procedure. The effects of several parameters affecting the hydride generation efficiency (hydrochloric acid, sodium tetrahydroborate and potassium iodide concentrations and flow rates) have been evaluated using a Plackett-Burman experimental design. In addition, parameters affecting the hydride measurement (delay, analysis and memory times) have been also investigated. The significant parameters obtained (sodium tetrahydroborate concentration, sodium tetrahydroborate flow rate and analysis time for As; hydrochloric acid concentration and sodium tetrahydroborate flow rate for Se(IV); and sodium tetrahydroborate concentration and sodium tetrahydroborate flow rate for Te(IV)) have been optimized by using 2ⁿ + star central composite design. Hydrochloric acid concentration and sodium tetrahydroborate flow rate were the significant parameters obtained for Sb and Bi determination, respectively. Using a univariate approach these parameters were optimized. The accuracy of methods have been verified by using several certified reference materials: SRM 1648 (urban particulate matter) and SRM 1649a (urban dust). Detection limits in the range of 6 × 10⁻³ to 0.2 ng m⁻³ have been achieved. The developed methods were applied to several atmospheric particulate matter samples corresponding to A Coruña city (NW Spain).     

Optimization of a nitrogen analyser based on the Dumas method

The objectives of this work was to obtain a total nitrogen concentration in milk with the Dumas method for industrial and research applications. This method was faster than the Kjheldal method (5 min against 2 h or 3 h) but less precise. A three factor experimental design was performed to optimize the instrument, a FP-2000 supplied by LECO. The first interpretation of the experimental design was disappointing and no conclusion could be done. It was not a failure of experimental design but a lack of thinking on the physical and chemical aspect of the problem. Selection and construction of composite responses based on chemical and physical consideration were the keys to optimize the Dumas method. This method is now as precise as the Kjheldal method, but considerably faster.     

Investigation of the limitations of saturated fractional factorial experimental designs,with confounding effects for an HPLC ruggedness test

Summary Recently much attention has been directed to the validation of analytical methods. The level of validation will depend on the method application. If a method is developed for general use, for instance by different analysts, instruments or laboratories, then the effect of these changes need evaluation. This is normally referred to as ruggedness testing, where the limitations of the method to changes in the specified conditions are examined.This paper examines the use of Plackett-Burman fractional factorial experiment designs for ruggedness testing in high performance liquid chromatography (HPLC). The ability of these designs to identify confounding effects is applied to the stability indicating analysis of Salbutamol and its major degradation product, AH4045. The results show that confounding effects, proving extremely pertinent to HPLC, can be identified.The assay proved rugged to most tested changes although not to the use of column packing material from different manufacturers.     

Locally s-distance transitive graphs and pairwise transitive designs

The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper shows that the study of locally s-distance transitive graphs with a star quotient is equivalent to the study of a particular family of designs with strong symmetry properties that we call nicely affine and pairwise transitive. We show that a group acting regularly on the points of such a design must be abelian and give general construction for this case.     

Gray codes extending quadratic matchings

Is it true that every matching in the n-dimensional hypercube can be extended to a Gray code? More than two decades have passed since Ruskey and Savage asked this question and the problem still remains open. A solution is known only in some special cases, including perfect matchings or matchings of linear size. This article shows that the answer to the Ruskey–Savage problem is affirmative for every matching of size at most . The proof is based on an inductive construction that extends balanced matchings in the completion of the hypercube by edges of into a Hamilton cycle of . On the other hand, we show that for every there is a balanced matching in of size that cannot be extended in this way.     

The maximum number of columns in supersaturated designs with

Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle .     

On the threshold problem for Latin boxes

Let m ≤ n ≤ k. An m × n × k 0‐1 array is a Latin box if it contains exactly m n ones, and has at most one 1 in each line. As a special case, Latin boxes in which m = n = k are equivalent to Latin squares. Let be the distribution on m × n × k 0‐1 arrays where each entry is 1 with probability p, independently of the other entries. The threshold question for Latin squares asks when contains a Latin square with high probability. More generally, when does support a Latin box with high probability? Let ε > 0. We give an asymptotically tight answer to this question in the special cases where n = k and , and where n = m and . In both cases, the threshold probability is . This implies threshold results for Latin rectangles and proper edge‐colorings of K_n,n.     

一类正交空间填充设计的构造

空间填充设计在计算机试验中应用十分广泛,当拟合回归模型时,正交的空间填充设计保证了因子效应估计的独立性.基于广义正交设计,文章给出了构造二阶正交拉丁超立方体设计和列正交设计的方法,新构造的设计不仅满足任意两列之间相互正交,还能保证每一列与任一列元素平方组成的列以及任两列元素相乘组成的列都正交.当某些正交的空间填充设计不存在时,具有较小相关系数的近似正交设计可作为替代设计使用.设计构造的灵活性为计算机试验在实践中的广泛应用提供了必要的支持.