Weak convergence of the U-statistic and weak invariance of the one-sample rank order statistic for Markov processes and ARMA models

Harel and Puri (1989, J. Multivariate Anal. 29) studied the asymptotic behavior of the U-statistic and the one-sample rank order statistic for nonstationary absolutely regular processes. In this note, we present some applications of these results for Markov processes as well as ARMA processes.     

Central limit theorem for Banach space valued fuzzy random variables

In this paper we prove a central limit theorem for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.

     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

Two methods for semi-automated quantification of changes in ventricular volume and their use in schizophrenia

Two semi-automated methods for quantification of ventricular volume change from baseline and follow-up magnetic resonance imaging scans have been developed. Technique 1 employs direct segmentation of the ventricles from both the scans using thresholding and contour extraction. Technique 2 operates on difference images produced by voxel based intensity subtraction of the baseline from the registered follow-up images. Here, all voxels with intensities above a noise threshold and in a restricted area are monitored to compute volumetric changes. In phantom measurements the first technique was accurate to 0.0046%, the second to 0.167% of the phantom volume. Results from normal volunteers was that the average ventricular volume changed by 1.52% and 1.54% for images acquired within 9 months using techniques 1 and 2, respectively. With schizophrenic patients mean change of 10.78% and 9.43% were found employing the first and second procedures, respectively. All measurements agreed with a radiologist’s visual grading of the changes. Robust, objective, fast, easy-to-use, and fairly accurate procedures have been developed and validated to quantify volumetric changes.     

Differential pulse polarographic determination of trace amounts of vanadium and molybdenum in various standard alloys and environmental samples after preconcentration of their morpholine-4-carbodithioates on microcrystalline naphthalene or morpholine-4-dithiocarbamate cetyltrimethyl-ammonium bromide-naphthalene adsorbent

A highly selective, sensitive, and fairly rapid and economical differential pulse polarographic (DPP) method has been reported for the determination of trace amounts of vanadium and molybdenum in standard alloys and various environmental samples. The morpholine-4-carbodithioates of these metals were retained (>99% recovery) quantitatively on microcrystalline naphthalene in the pH range 4.5-6.9 for vanadium and 1.5-4.5 for molybdenum. These metals were determined by DPP after desorption with 10 ml of 1 M HCl. Vanadium and molybdenum may also be preconcentrated by passing their aqueous solutions under similar conditions on morpholine-4-dithiocarbamate CTMAB-naphthalene adsorbent packed in a column at a flow rate of 1-5 ml min(-1) and determined similarly. The detection limits are 0.20 ppm for vanadium and 0.04 ppm for molybdenum at minimum instrumental settings (signal to noise ratio=2). The linearity is maintained in the following concentration ranges, vanadium 0.50-10.0 and molybdenum 0.10-9.0 ppm, with a correlation factor of 0.9996 (confidence interval of 95%, slopes 0.0196 and 0.01497 muA mug(-1), intercepts 3.65x10(-3) and -1.92x10(-3) respectively) and relative standard deviation of 1.1% in the microcrystalline method, while in the column method, the linearity is maintained in the concentration ranges, 0.50-6.5 for vanadium and 0.10-5.5 ppm for molybdenum with correlation factor of 0.9994 (with confidence interval of 95%, slopes 0.0194, 0.015 muA mug(-1), intercepts 3.60x10(-3) and -1.90x10(-3) respectively) and relative standard deviation of 1.4%. Various parameters such as the effect of pH, reagent, naphthalene and CTMAB concentrations, volume of aqueous phase and interference of a large number of metal ions on the estimation of vanadium and molybdenum have been studied in detail to optimize the conditions for their voltammetric determination at trace level in various standard alloys and environmental samples.     

A Polarographic Study of ϵ-Caprolactam Complexes of Uranium and Tellurium

The polarographic behaviour of uranium and tellurium has been studied in the presence of increasing concentration of complex forming agent viz. ?-caprolactam at pH 4.4 for U(VI) and at pH 10.0 for Te(IV) at μ=0.1 M KNO₃. In both cases the waves have been found to be diffusion controlled and irreversible. The values of kinetic parameters (σπ_a and K°_f,h) have been calculated as a function of the ligand concentration. Method is suitable for the quantitative determination of these metals individually and simultaneously with the effect of diverse ions.     

Column preconcentration of trace manganese with the ion pair of 2-nitroso-1-naphthol-4-sulfonic acid tetradecyldimethylbenzyl-ammonium chloride supported on naphthalene and determination by derivative spectrophotometry

A column preconcentration method has been developed for the determination of trace amounts of manganese by preconcentration on 2-nitroso-1-naphthol-4-sulfonic acid (nitroso-S)-tetradecyldimethylbenzylammonium (TDBA) naphthalene as an adsorbent using a simple funnel tipped glass tube. Manganese reacts with nitroso-S to form a water soluble brown colored chelate anion. The chelate anion forms a water insoluble Mn-Nitroso-S-TDBA ion pair on naphthalene packed in a column in the pH range 9.6-10.5 at a flow rate of 1-2 ml/min. The solid mass consisting of manganese complex and naphthalene is dissolved in 5 ml of dimethylformamide (DMF) and the metal determined by second derivative spectrophotometry. The calibration curve is linear in the concentration range 0.25-35.0 micrograms of Mn in 5 ml of the final DMF solution. Eight replicate determinations of 25 micrograms of standard manganese solution give a mean peak height of 4.0 with a correlation coefficient of 0.9995 and relative standard deviation of +/- 1.1%. The sensitivity was calculated to be 0.502(d2 A/d lambda 2)/microgram ml-1 from the slope of the calibration curve. The detection limit was 0.020 microgram ml-1 for manganese at the minimum instrumental settings (signal to noise ratio = 2). Various parameters effecting the method such as the effect of pH, volume of aqueous phase and interference of a number of metal ions on the determination of manganese have been evaluated to optimize the conditions for its determination in standard alloys and biological samples.     

Ammonium tetraphenylborate-naphthalene adsorbent for the preconcentration and trace determination of iron in alloys and biological samples using 2-(5-bromo-2-pyridylazo)-5-diethylaminophenol by third derivative spectrophotometry

A solid ion-pair material produced from ammonium tetraphenylborate on naphthalene (ATPB-naphthalene) provides a simple, rapid, economical and selective technique for preconcentrating iron from approximately 500 ml of aqueous solution of standard alloys and biological samples. Iron reacts with 2-(5-bromo-2-pryidlazo)-5-diethylaminophenol (5-Br-PADAP) to form a water-soluble cationic complex. When the aqueous solution of this cationic species in the pH range 3.2-8.5 is passed over the adsorbent ATPB-naphthalene at a flow rate of 1 ml min(-1), it is quantitatively retained on naphthalene as an uncharged ion-associated complex. The solid mass from the column was dissolved out with 5 ml of dimethylformamide (DMF) and iron is determined by third derivative spectrophotometry by measuring the signal d(3)A/ dlambda(3) between lambda(2)(773 nm) and lambda(3)(737 nm). The calibration curve is linear over the concentration range 0.10-25.0 mug of iron in 5 ml of DMF solution. Eight replicate determinations of 5 mug of iron gave a mean intensity (peak-to-peak signal between lambda(2) and lambda(3)) of 1.534 with a relative standard deviation of 0.90%. The sensitivity of the method is 0.307 (d(3)A/dnm(3) )/mug found from the slope of the calibration curve. The interference of a large number of anions and cations has been studied and the optimized conditions developed were utilized for the trace determination of iron in various standard alloys and biological samples.     

Simultaneous determination of lead and cadmium in various environmental and biological samples by differential pulse polarography after adsorption of their morpholine-4-carbodithioates onto microcrystalline naphthalene or morpholine-4-dithiocarbamate-CTMAB-naphthalene adsorbent

A highly selective, sensitive and rapid differential pulse polarographic method (DPP) has been developed for the simultaneous estimation of trace amounts of lead and cadmium in standard alloys, biological and environmental samples. The morpholine-4-carbodithioates of the samples were absorbed on microcrystalline naphthalene in the pH range of 5-10 for lead and 3.4-11 for cadmium. The metal complexes were desorbed with 10 ml of 1M HCl and determined simultaneously with a differential pulse polarograph. These metals can alternatively be quantitatively adsorbed on morpholine-4-dithiocarbamate-cetyltrimethylammonium bromide-naphthalene adsorbent packed in a column and determined similarly. The detection limits are 0.14 ppm for Pb and 0.014 ppm for Cd at minimum instrumental settings (signal-to-noise ratio = 2). The linearity is maintained in the concentration ranges of Pb, 0.7-15 ppm and Cd, 0.07-10 ppm with a correlation factor of 0.9997 and relative standard deviations of 0.95 and 0.81%, respectively. Various parameters such as the effect of pH, volume of aqueous phase, and interference of a number of metal ions on the estimation of lead and cadmium have been studied in detail to optimize the conditions for their simultaneous estimation in various biological and environmental samples.