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.     

Wavelength-scanning Talbot effect and its application for arbitrary three-dimensional step-height measurement

We demonstrate the phenomenon of Talbot self-image plane shift by tuning the wavelength of the broadband light source. A superluminescent diode (SLD) is used as a broad-band light source and an acousto-optic tunable filter (AOTF) as wavelength-scanning device. A periodic grating is illuminated by the wavelength tuned light of SLD using AOTF and Talbot self-image plane is shifted continuously in the longitudinal direction without mechanically moving the grating. The wavelength-scanning Talbot effect is then implemented for the measurement of arbitrary step-height of discontinuous objects with extended range. The main advantages of the proposed system are non-mechanical scanning, high stability because of it’s common-path geometry and compactness. Since the measurement of the phase is not required the system is free from phase ambiguity problem and therefore, the range of measurement is large as compare to interferometric techniques.     

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.     

Photochemical and thermal transformations of azomethine imines

The thermal and photochemical fragmentations of a few bisazoalkenes have been investigated. 2-Phenyl-4,5-disubstituted-1, 2,3-triazoles were obtained both in the thermolysis and photolysis of 1, 2-bisphenylazo-(4, 4′-dichloro) stilbene, 1, 2-bisphenylazo(4, 4′-dimethoxy)stilbene, 1, 2-bisphenylazocyclohexene and o-(phenylazo) phenyldiazocyanide. Both 2, 3-bisphenylazo-2-butene and 1, 2-bisphenylazoethylene failed to undergo either photolysis or thermolysis in the expected manner. However, 2, 3-bisphenylazo-2-butene underwent an acid-catalysed valence isomerisation to anhydro 1-phenylimino-2-phenyl-4, 5-dimethyl-1, 2, 3-trizolium hydroxide, which on photolysis gave 2-phenyl-4, 5-dimethyl-1, 2, 3-triazole. The same iminotriazolium intermediate gave a cycloadduct, 2, 6-diphenyl-3, 3a-dimethyl-4, 5-dicarbomethoxypyrazolino [2.3.c][1.2.3] triazole, on treatment with dimethyl acetylenedicarboxylate, whereas treatment with carbon disulphide gave 2-phenyl-4, 5-dimethyl-1, 2, 3-triazole. Both photolysis and thermolysis of C-biphenylene-N^α(4-chlorophenyl)-N^β-cyanoazomethine imine gave 9-fluorenone-N- (4-chlorophenyl) anil. Photolysis of 1, 2-bisphenylazoacenaphthylene in methanol gave acenaphthenequinone monophenylhydrazone.     

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.