X̄ chart with variable sample size and sampling intervals

Recent theoretical studies have shown that the X̄ chart with variable sampling intervals (VSI) and the X̄ chart with variable sample size (VSS) are quicker than the traditional X̄ chart in detecting shifts in the process. This article considers the X̄ chart with variable sample size and sampling intervals (VSSI). It is assumed that the amount of time the process remains in control has exponential distribution. The properties of the VSSI X̄ chart are obtained using Markov chains. The VSSI X̄ chart is even quicker than the VSI or VSS X̄ charts in detecting moderate shifts in the process.

A refinement of the gauss-lucas theorem

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society.

VSSI X̄ charts with sampling at fixed times

A standard X̄ chart for controlling the process mean takes samples of size n0 at specified, equally-spaced, fixed-time points. This article proposes a modification of the standard X chart that allows one to take additional samples, bigger than n0, between these fixed times. The additional samples are taken from the process when there is evidence that the process mean moved from target. Following the notation proposed by Reynolds (1996a) and Costa (1997) we shortly call the proposed X chart as VSSIFT X chart where VSSIFT means variable sample size and sampling intervals with fixed times. The X chart with the VSSIFT feature is easier to be administered than a standard VSSI X chart that is not constrained to sample at the specified fixed times. The performances of the charts in detecting process mean shifts are comparable. Copyright © 1998 by Marcel Dekker, Inc.

Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals

Recent studies have shown that the X̄ chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both the X̄ and R charts. A Markov chain model is used to determine the properties of the joint X and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint X̄ and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.

Invex nonsmooth alternative theorem and applications

An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion's approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

Use of the internal standardization for difficult sampling by graphite furnace atomic absorption spectrometry

This work shows the potentiality of As as internal standard to compensate errors from sampling of sparkling drinking water samples in the determination of selenium by graphite furnace atomic absorption spectrometry. The mixture Pd(NO 3) 2/Mg(NO 3) 2 was used as chemical modifier. All samples and reference solutions were automatically spiked with 500 μg l -1 As and 0.2% (v/v) HNO 3 by the autosampler, eliminating the need for manual dilutions. For 10 μl dispensed sample into the graphite tube, a good correlation (r=0.9996) was obtained between the ratio of analyte absorbance by the internal standard absorbance and the analyte concentrations. The relative standard deviations (R.S.D.) of measurements varied from 0.05 to 2% and from 1.9 to 5% (n=12) with and without internal standardization, respectively. The limit of detection (LD) based on integrated absorbance was 3.0 μg l -1 Se. Recoveries in the 94-109% range for Se spiked samples were obtained. Internal standardization (IS) improved the repeatability of measurements and increased the lifetime of the graphite tube in ca. 15%. © 2004 Elsevier B.V. All rights reserved.

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.

Investigation into the impact of embedded generators on distribution system performance using theorem of superposition

Since the 1980s, huge efforts have been made to utilise renewable energy sources to generate electric power. One of the interesting issues about embedded generators is the question of optimal placement and sizing of the embedded generators. This paper reports an investigation of impact of the integration of embedded generators on the overall performances of the distribution networks in the steady state, using theorem of superposition. Set of distribution system indices is proposed to observe performances of the distribution networks with embedded generators. Results obtained from the case study using IEEE test network are presented and discussed.

Synthetic control charts with two-stage sampling for monitoring bivariate processes

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control bivariate processes. During the first stage, one item of the sample is inspected and two correlated quality characteristics (x;y) are measured. If the Hotelling statistic T1 2 for these individual observations of (x;y) is lower than a specified value UCL 1 the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the Hotelling statistic T2 2 for the sample means of (x;y) is computed. When the statistic T2 2 is larger than a specified value UCL2, the sample is classified as nonconforming. According to the synthetic control chart procedure, the signal is based on the number of conforming samples between two neighbor nonconforming samples. The proposed chart detects process disturbances faster than the bivariate charts with variable sample size and it is from the practical viewpoint more convenient to administer.

Double sampling X̄ control chart for a first order autoregressive process

In this paper we propose the Double Sampling X̄ control chart for monitoring processes in which the observations follow a first order autoregressive model. We consider sampling intervals that are sufficiently long to meet the rational subgroup concept. The Double Sampling X̄ chart is substantially more efficient than the Shewhart chart and the Variable Sample Size chart. To study the properties of these charts we derived closed-form expressions for the average run length (ARL) taking into account the within-subgroup correlation. Numerical results show that this correlation has a significant impact on the chart properties.

Determination of copper in fish feed by graphite furnace atomic absorption spectrometry using slurry sampling

The present work develops and optimizes a method to determine copper in samples of feces and fish feed by graphite furnace atomic absorption spectrometry (GFAAS) through the direct introduction of slurries of the samples into the spectrometer's graphite tube coated internally with metallic rhodium and tungsten carbide that acts as chemical modifiers. The limits of detection (LOD) and quantification (LOQ) calculated for 20 readings of the blank of the standard slurries (0.50% m/v of feces or feed devoid of copper) were 0.24 and 0.79 μg L -1 for the standard feces slurries and 0.26 and 0.87 μg L -1 for the standard feed slurries. The proposed method was applied in studies of absorption of copper in different fish feeds and their results proved compatible with that obtained from samples mineralized by acid digestion using microwave oven. © Springer Science+Business Media, LLC 2008.

A Bayesian approach to estimate the accuracy of in-house ELISA assay to measure rabies antibodies from compulsory vaccinated dogs and cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Regeneração natural de espécies da Mata Atlǎntica em sub-bosque de Eucalyptus saligna Smith. em uma antiga unidade de produção forestal no Parque das Neblinas, Bertioga, SP

This study aimed at characterizing the potential for natural regeneration of native vegetation in the under-story of an earlier Eucalyptus saligna Smith production stand. The study was carried out at the Parque das Neblinas, Bertioga municipality, SP, in a 45 ha third rotation stand; which had been abandoned 15 years ago for natural regeneration to occur. The sampling was done in 24 plots of 20 × 40 m. The sampled area was of 19,200 m2, with inventory made of 100% of the eucalyptus trees. All regeneration trees with a height ≥ 1.30 m and DBH ≥ 5.0 cm were measured, as well as adult individuals with DBH ≥ 5.0 cm; surveyed in two size classes. 1,417 individuals of E. saligna were measured, with a density of 738,02 individuals/ha and a basal area of 22.69 m2/ha. Among 2,763 natural regeneration individuals, 111 species belonged to 66 genera and 34 botanical families. The species represented 43.7% of the tree richness of neighboring native forest fragments. The total estimated density and the basal area were respectively 1,052.6 individuals/ha and 6.4 m2/ha of autochthonous trees with DBH ≥ 5.0 cm (Class 1); while for regeneration there were 3,864.58 individuals/ha, and 2.76 m2/ha of individuals with a height ≥ 1.30 m and DBH < 5.0 cm (Class 2). Shannon diversity (H') was 2.83 and 3.68, respectively, for Classes 1 and 2, and the corrected species richness for a 1000-individual sample (R1000) were 75.6 and 87.29 (Fisher's a index) for the same classes. The majority of the species (34.84%) was typical from the understory of wet tropical forest and had zoochoric fruit dispersal (67.57%). The results indicate that, under these conditions, a eucalyptus forest is able to provide adequate regeneration niches for native vegetation, and may represent a sink habitat for local populations.

Liouville's theorem and power series for quaternionic functions

In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [1]-[6]. Some of these results are similar to well known cases in one complex variable, op. cit. [5], [6]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version. © 2011 Academic Publications, Ltd.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.