Characterizing geometric designs, II

We provide a characterization of the classical point-line designs PG₁(n,q), where n?3, among all non-symmetric 2-(v,k,1)-designs as those with the maximal number of hyperplanes. As an application of this result, we characterize the classical quasi-symmetric designs PGn−2(n,q), where n?4, among all (not necessarily quasi-symmetric) designs with the same parameters as those having line size q+1 and all intersection numbers at least qn−4+?+q+1. Finally, we also give an explicit lower bound for the number of non-isomorphic designs having the same parameters as PG₁(n,q); in particular, we obtain a new proof for the known fact that this number grows exponentially for any fixed value of q.     

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.     

Hybrid Monte Carlo on Hilbert spaces

The Hybrid Monte Carlo (HMC) algorithm provides a framework for sampling from complex, high-dimensional target distributions. In contrast with standard Markov chain Monte Carlo (MCMC) algorithms, it generates nonlocal, nonsymmetric moves in the state space, alleviating random walk type behaviour for the simulated trajectories. However, similarly to algorithms based on random walk or Langevin proposals, the number of steps required to explore the target distribution typically grows with the dimension of the state space. We define a generalized HMC algorithm which overcomes this problem for target measures arising as finite-dimensional approximations of measures π which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert space. The key idea is to construct an MCMC method which is well defined on the Hilbert space itself.We successively address the following issues in the infinite-dimensional setting of a Hilbert space: (i) construction of a probability measure Π in an enlarged phase space having the target π as a marginal, together with a Hamiltonian flow that preserves Π; (ii) development of a suitable geometric numerical integrator for the Hamiltonian flow; and (iii) derivation of an accept/reject rule to ensure preservation of Π when using the above numerical integrator instead of the actual Hamiltonian flow. Experiments are reported that compare the new algorithm with standard HMC and with a version of the Langevin MCMC method defined on a Hilbert space.     

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.     

Separation and determination of arsenic species in water by selective exchange and hybrid resins

A simple and efficient method for separation and determination of inorganic arsenic (iAs) and organic arsenic (oAs) in drinking, natural and wastewater was developed. If arsenic is present in water prevailing forms are inorganic acids of As(III) and As(V). oAs can be found in traces as monomethylarsenic acid, MMA(V), and dimethylarsenic acid, DMAs(V). Three types of resins: a strong base anion exchange (SBAE) and two hybrid (HY) resins: HY-Fe and HY-AgCl, based on the activity of hydrated iron oxides and a silver chloride were investigated. It was found that the sorption processes (ion exchange, adsorption and chemisorptions) of arsenic species on SBAE (ion exchange) and HY resins depend on pH values of water. The quantitative separation of molecular and ionic forms of iAs and oAs was achieved by SBAE and pH adjustment, the molecular form of As(III) that exists in the water at pH <8.0 was not bonded with SBAE, which was convenient for direct determination of As(III) concentration in the effluent. HY-Fe resin retained all arsenic species except DMAs(V), which makes possible direct measurements of this specie in the effluent. HY-AgCl resin retained all iAs which was convenient for direct determination of oAs species concentration in the effluent. The selective bonding of arsenic species on three types of resins makes possible the development of the procedure for measuring and calculation of all arsenic species in water. In order to determine capacity of resins the preliminary investigations were performed in batch system and fixed bed flow system. Resin capacities were calculated according to breakthrough points in a fixed bed flow system which is the first step in designing of solid phase extraction (SPE) module for arsenic speciation separation and determination. Arsenic adsorption behavior in the presence of impurities showed tolerance with the respect to potential interference of anionic compounds commonly found in natural water. Proposed method was established performing standard procedures: with external standard, certified reference material and standard addition method. Two analytical techniques: the inductively coupled plasma mass spectrometry (ICP-MS) and atomic absorption spectroscopy-hydride generation (AAS-GH) were comparatively applied for the determination of arsenic in all arsenic species in water. ICP-MS detection limit was 0.2 μg L⁻¹ and relative standard deviation (RSD) of all arsenic species investigated was between 3.5 and 5.1%.     

Highly selective in situ metal ion determination by hybrid electrochemical "adsorption-desorption" and colorimetric methods

A novel and facile hybrid analytical method coupling electrochemical “adsorption–desorption” and colorimetric analyses was developed to detect heavy metal ions in turbid water samples. The target metal ions were deposited onto an electrode inserted into the original sample, which was referred to as the “adsorption” process. After changing the medium, the concentrated target metal ions were dissolved in a new, clean buffer (blank buffer), which was referred to as the “desorption” process. The concentrations of the target metal ions were measured by colorimetric analyses after the addition of specific indicator amounts. We demonstrated the applicability of this method by detecting Cd²⁺, Pb²⁺ and Cu²⁺ with co-depositing Bi³⁺ on portable screen-printed electrodes (SPEs). A good correlation (correlation coefficient of R = 0.997) was observed between concentrations ranging from 1 to 200 μM and absorbance values. After the multiple “desorption” process, the even better detection limits as low as 10, 10 and 100 nM were achieved for Cd²⁺, Pb²⁺ and Cu²⁺, respectively. The practicality of this hybrid method was confirmed by the detection of Cd²⁺, Pb²⁺ and Cu²⁺ in wastewater samples, and these results were in agreement with inductively coupled plasma atomic emission spectroscopy (ICP-AES). Overall, this hybrid method provides a simple, selective and effective technique for environmental pollutant analyses.