Divisible designs and semi-regular relative difference sets from additive Hadamard cocycles

Additive Hadamard cocycles are a natural generalization of presemifields. In this paper, we study divisible designs and semi-regular relative difference sets obtained from additive Hadamard cocycles. We show that the designs obtained from additive Hadamard cocycles are flag transitive. We introduce a new product construction of Hadamard cocycles. We also study additive Hadamard cocycles whose divisible designs admit a polarity in which all points are absolute. Our main results include generalizations of a theorem of Albert and a theorem of Hiramine from presemifields to additive Hadamard cocycles. At the end, we generalize Maiorana-McFarland?s construction of bent functions to additive Hadamard cocycles.     

A-optimal designs for an additive cubic model

Chan et al. (1998a) obtained A-optimal designs for an additive quadratic mixture model for q≥3 mixture components. In this paper, we obtain the A-optimal designs for an additive cubic model for q≥3 mixture components using the class of symmetric weighted centroid designs based on barycentres of various depths. We observe that barycentres of depths 0 and 2 are possible support points for an A-optimal design. We have also given the optimal weights of A-optimal designs for 3≤q≤17.     

Small Box-Behnken design

Box-Behnken design has been popularly used for the second-order response surface model. It is formed by combining two-level factorial designs with incomplete block designs in a special manner—the treatments in each block are replaced by an identical design. In this paper, we construct small Box-Behnken design. These designs can fit the second-order response surface model with reasonably high efficiencies but with only a much smaller run size. The newly constructed designs make use of balanced incomplete block design (BIBD) or partial BIBD, and replace treatments partly by 2_III³⁻¹ designs and partly by full factorial designs. It is shown that the orthogonality properties in the original Box and Behnken designs will be kept in the new designs. Furthermore, we classify the parameters into groups and introduce Group Moment Matrix (GMM) to estimate all the parameters in each group. This allows us to significantly reduce the amount of computational costs in the construction of the designs.     

Product design and selection using fuzzy QFD and fuzzy MCDM approaches

Quality function deployment (QFD) is a useful analyzing tool in product design and development. To solve the uncertainty or imprecision in QFD, numerous researchers have applied the fuzzy set theory to QFD and developed various fuzzy QFD models. Three issues are investigated by examining their models. First, the extant studies focused on identifying important engineering characteristics and seldom explored the subsequent prototype product selection issue. Secondly, the previous studies usually use fuzzy number algebraic operations to calculate the fuzzy sets in QFD. This approach may cause a great deviation in the result from the correct value. Thirdly, few studies have paid attention to the competitive analysis in QFD. However, it can provide product developers with a large amount of valuable information. Aimed at these three issues, this study integrates fuzzy QFD and the prototype product selection model to develop a product design and selection (PDS) approach. In fuzzy QFD, the α-cut operation is adopted to calculate the fuzzy set of each component. Competitive analysis and the correlations among engineering characteristics are also considered. In prototype product selection, engineering characteristics and the factors involved in product development are considered. A fuzzy multi-criteria decision making (MCDM) approach is proposed to select the best prototype product. A case study is given to illustrate the research steps for the proposed PDS method. The proposed method provides product developers with more useful information and precise analysis results. Thus, the PDS method can serve as a helpful decision-aid tool in product design.     

Mathematical models and solution algorithms for computational design of RC piles under structural effects

The paper presents mathematical models and solution algorithms for RC pile design, through scanning soil stratums from top to downwards with an interactive scanner band. The equilibrium of transferred loads from the superstructure, friction forces and tip bearing forces are considered for the design, which leads to optimum pile length. The most important contribution of this research for designers is supplying an efficient tool to obtain optimum pile length and reinforced concrete design of pile foundation systems. A program package has been developed in MATLAB depending on the proposed algorithm. Soil behaviors depending on external effects, active and passive zone distributions are considered. All possible effects in all freedom degrees are taken into account in design process. Stress and strain distributions due to axial loads, bending moments, shear forces and torsional moments may be monitored. The optimum pile length, cross section dimension and reinforcement details may be found by using developed algorithm.     

Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling

Simulated computer experiments have become a viable cost-effective alternative for controlled real-life experiments. However, the simulation of complex systems with multiple input and output parameters can be a very time-consuming process. Many of these high-fidelity simulators need minutes, hours or even days to perform one simulation. The goal of global surrogate modeling is to create an approximation model that mimics the original simulator, based on a limited number of expensive simulations, but can be evaluated much faster. The set of simulations performed to create this model is called the experimental design. Traditionally, one-shot designs such as the Latin hypercube and factorial design are used, and all simulations are performed before the first model is built. In order to reduce the number of simulations needed to achieve the desired accuracy, sequential design methods can be employed. These methods generate the samples for the experimental design one by one, without knowing the total number of samples in advance. In this paper, the authors perform an extensive study of new and state-of-the-art space-filling sequential design methods. It is shown that the new sequential methods proposed in this paper produce results comparable to the best one-shot experimental designs available right now.     

Determination of per- and polyfluorinated substances in airborne particulate matter by microwave-assisted extraction and liquid chromatography-tandem mass spectrometry

A sensitive and confirmatory analytical method has been developed for the determination of 12 ionic per- and polyfluorinated alkyl substances (PFAS) in fine airborne particulate matter (PM2.5) at trace levels. The proposed method includes extraction of PM2.5-bound PFAS by microwave-assisted extraction (MAE) followed by centrifugation and injection into the liquid chromatograph coupled to a triple quadrupole tandem mass spectrometry system (LC-MS/MS). The main parameters affecting the performance of MAE were optimised using statistical design of experiments (DoE). Recoveries ranged from 83 to 120% and the method quantification limit (MQL) was 1.4 pg m(-3), when air volumes of 720 m(3) were sampled. This method was successfully applied to 41 samples collected from five stations of the monitoring network of the Valencian Regional Government (Spain) during April-July 2010. Eight out of 12 PFCs investigated were quantified in at least one sample (PFBA, PFPeA, PFHxS, 6:2 FTS, PFOA, PFNA, PFOS and PFDA). The measured concentrations ranged from 1.4 to 34.3 pg m(-3).     

Modelling oligomer formation in chromatographic separations

Oligomer forms of proteins are formed by self and cross association or complex formation with ligands. Modelling studies using an ion-exchange adsorbent have demonstrated that the formation of an oligomer form of a target protein can improve a chromatographic separation because the oligomer form displaces the impurities. The results of the investigation show that the process is very robust, that the purity, the yield, and the productivity increase with increasing load and increasing salt concentration in the eluant. An impurity level less than 1 ppm is easy to achieve having a yield of 98%. A universal model for the adsorption equilibria of mono and oligomer forms of proteins on ion-exchange, hydrophobic, and bimodal adsorbents has been developed.     

A new C2-symmetric azolium compound for Cu-catalyzed asymmetric conjugate addition of R2Zn to cyclic enone

A new chiral N-heterocyclic carbene (NHC) ligand was designed. Thus, an efficient synthetic route to C₂-symmetric bis(hydroxyamide)-functionalized benzimidazolium salts from chiral β-amino alcohols was developed. The combination of Cu(OTf)₂ and the chiral azolium compound efficiently promoted the conjugate addition reaction of cyclic enone with dialkylzinc to give the corresponding adduct in good yield. Among a series of chiral NHC proligands, the functionalized benzimidazolium chloride possessing a tert-butyl group as a stereodirecting group was found to be the best choice of ligand. Under optimized reaction conditions, an excellent enantioselectivity (96% ee) was realized by allowing 2-cyclohepten-1-one to react with Bu₂Zn at room temperature.