Inferring consensus weights from pairwise comparison matrices without suitable properties

Pairwise comparison is a popular method for establishing the relative importance of n objects. Its main purpose is to get a set of weights (priority vector) associated with the objects. When the information gathered from the decision maker does not verify some rational properties, it is not easy to search the priority vector. Goal programming is a flexible tool for addressing this type of problem. In this paper, we focus on a group decision-making scenario. Thus, we analyze different methodologies for getting a collective priority vector. The first method is to aggregate general pairwise comparison matrices (i.e., matrices without suitable properties) and then get the priority vector from the consensus matrix. The second method proposes to get the collective priority vector by formulating an optimization problem without determining the consensus pairwise comparison matrix beforehand.     

Results of the first electrostatic proficiency testing program IEC 60079-0 versus IEC 60079-32-2 and necessary consequences

Laboratories in the field of explosion protection (Ex-testing laboratories) are required to participate in proficiency testing programs in order to fulfill the requirement of performing interlaboratory comparisons. This paper introduces the electrostatic proficiency testing program titled "Electrostatic Charge – Test Round 2015″ as part of the “PTB Ex Proficiency Testing Scheme”, which represents the first comprehensive proficiency testing scheme in explosion protection. More than 50 laboratories all over the world performed surface resistance measurements and transferred charge tests in accordance with IEC 60079-0 (2011) and IEC 60079-32-2 (2015) on various types of test samples.Although both standards use what is essentially the same test setup, there exist several differences between the test procedures, which may lead to different results. The analysis of the participants' results shows that factors such as the type of electrodes, the level of the measuring voltage, the precleaning procedure, the relative humidity and the definition of the threshold limits can have an influence on the outcome of the tests. In this work, the differences between both standards – IEC 60079-0 (2011) and IEC 60079-32-2 (2015) – and the issues associated with using two different procedures to reach the same goal are discussed and illustrated.     

Development and validation of stability indicating RP-HPLC and HPTLC for determination of Niclosamide in bulk and in synthetic mixture

Two simple, specific, sensitive, accurate and precise stability indicating methods were described for quantitative determination of the anthelmintics drug Niclosamide. The first method was high performance liquid chromatographic with the use of a reversed phase hibar^R C-18 column (250 mm × 4.66 mm, 5 μm) and mobile phase of methanol: 1 mM ammonium phosphate buffer (85:15 v/v) at a flow rate of 1.2 mL/min. The retention time of drug was found to be 6.45 ± 0.02 min. Quantification of drug was achieved with diode array detection (DAD) at 332 nm. Linear calibration curve was obtained in concentration range 0.01–100 μg/mL with r² value of 0.999. The limit of detection and limit of quantification were found to be 0.048 μg/mL and 0.01 μg/ml respectively. The second method involved a high performance thin layer liquid chromatographic. Chromatographic separation was carried out with precoated silica gel G60 F254 aluminum sheets using toluene:ethyl acetate (7:3% v/v) as a mobile phase. Linearity of proposed method was found to be 200–700 ng/band at 332 nm with retention factor of 0.59 and r² value of 0.998. The limit of detection and limit of quantification were found to be 36.21 ng/band and 109.7 ng/band respectively. Both the developed methods were successfully validated as per International Conference on Harmonization guideline (ICH). Niclosamide was subjected to different stress conditions. The degraded product peaks were well resolved from the pure drug peak with significant difference in their retention time. Stress samples were successfully assayed by developed high performance liquid chromatographic and high performance thin layer liquid chromatographic method. Statistically analysis proves that there were no statistical significant differences between two developed methods.     

Stability and persistence of two-dimensional patterns

The canonical equations for evolution of the amplitude order parameters order parameters describing the nonlinear development and persistence of two-dimensional three-mode spatial patterns generated by Turing instability in dissipative systems are considered. The stability conditions for persistent hexagonal patterns are generalized, and the conditions under which patterns are either disrupted, exhibit bounded quasiperiodic or chaotic behavior, or decay under nonlinear evolution are derived. These conditions are applied to the specific three-mode amplitude evolution equations derived for the Schnakenberg model and a delay predator system in Chapter 3. Numerical results are presented for the persistence, disruption and decay of patterns in these systems, including fairly detailed comparisons with simulations results for the Snackenberg model.     

Orthogonally invariant estimation of the skew-symmetric normal mean matrix

The unbiased estimator of risk of the orthogonally invariant estimator of the skew-symmetric normal mean matrix is obtained, and a class of minimax estimators and their order-preserving modification are proposed. The estimators have applications in paired comparisons model. A Monte Carlo study to compare the risks of the estimators is given.     

Experiments with successive quadratic programming algorithms

There are many variants of successive quadratic programming (SQP) algorithms. Important issues include: the choice of either line search or trust region strategies; the QP formulation to be used; and how the QP is to be solved. Here, we consider the QP's proposed by Fletcher and Powell and discuss a specialized reduced-gradient procedure for solving them. A computer implementation is described, and the various options are compared on some well-known test problems. Factors influencing robustness and speed are identified.     

Effects of gender and ethnicity on fourth graders’ knowledge states in mathematics

This study sheds light on the achievement gap between two culturally diverse populations in Israel by employing a diagnostic model for analysing responses of a representative sample of Jewish and Arab fourth graders on a national mathematics test. The results indicated large significant differences, in favour of the Jewish group, on most attributes underlying the test, and relatively small significant gender effects only in the Jewish group, where boys outscored girls on higher-order thinking attributes. These results were discussed in light of cultural differences between the two populations, educational resources, and prevalent instruction–learning–assessment cultures in their respective schools.     

Numerical Computation of Multivariate Normal and Multivariate-t Probabilities over Convex Regions

Abstract

A methodology has been developed and Fortran 90 programs have been written to evaluate multivariate normal and multivariate-t integrals over convex regions. The Cholesky transformation is used to transform the integrand into a product of standard normal or spherically symmetric t variables. For any random direction from the origin, an unbiased estimate of the value of the integral is Pr[X ² ≥ r²] (multivariate normal) or Pr[F ≥ r²/k] (multivariate-t), where r is the distance from the origin to the boundary in a randomly chosen direction, and k is the dimension of the integral. Two Fortran 90 programs have been written. MVI uses the average of many estimates. MVIB uses a binning procedure to obtain an empirical distribution of the distance from the origin to the boundary. Gauss-Legendre quadrature is then used to estimate the value of the integral. The running time for MVIB is modestly smaller than that for MVI. However, in solving certain integral equations (e.g., using an iterative procedure to find the percentage point of a statistic), using MVIB usually requires no Monte Carlo sampling after the first iteration, and is considerably more efficient. MVIB and MVI are highly efficient for the evaluation of integrals whose value is large. “Naive” Monte Carlo (MC) may be competitive with MVI or MVIB only if the value of the probability integral is small or the shape of the region is “extreme.”     

The optimal control of just-in-time-based production and distribution systems and performance comparisons with optimized pull systems

In just-in-time (JIT) production systems, there is both input stock in the form of parts and output stock in the form of product at each stage. These activities are controlled by production-ordering and withdrawal kanbans. This paper discusses a discrete-time optimal control problem in a multistage JIT-based production and distribution system with stochastic demand and capacity, developed to minimize the expected total cost per unit of time. The problem can be formulated as an undiscounted Markov decision process (UMDP); however, the curse of dimensionality makes it very difficult to find an exact solution. The author proposes a new neuro-dynamic programming (NDP) algorithm, the simulation-based modified policy iteration method (SBMPIM), to solve the optimal control problem. The existing NDP algorithms and SBMPIM are numerically compared with a traditional UMDP algorithm for a single-stage JIT production system. It is shown that all NDP algorithms except the SBMPIM fail to converge to an optimal control.Additionally, a new algorithm for finding the optimal parameters of pull systems is proposed. Numerical comparisons between near-optimal controls computed using the SBMPIM and optimized pull systems are conducted for three-stage JIT-based production and distribution systems. UMDPs with 42 million states are solved using the SBMPIM. The pull systems discussed are the kanban, base stock, CONWIP, hybrid and extended kanban.     

Determination of Nicarbazin in Animal Feed by High-Performance Liquid Chromatography with Interlaboratory Evaluation

A liquid chromatographic method was developed for the determination of nicarbazin in feed. The samples were extracted with 90 percent acetonitrile, purified on alumina, and analyzed by high-performance liquid chromatography. The developed method was validated in-house and further verified by interlaboratory studies. The limits of detection and quantification of the method were 0.05 and 0.10 milligram per kilogram, respectively. The recoveries of nicarbazin in feed ranged between 98.3 and 111 percent, with acceptable intralaboratory reproducibility. In the interlaboratory comparison, one contaminated and three uncontaminated poultry feed samples were analyzed by thirteen laboratories using the method developed in this study. Statistical analysis confirmed the accuracy and precision of the method with verification in the interlaboratory comparison.