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.

     

A sensitive solid-phase fluoroimmunoassay for detection of opiates in urine

An automated flow fluorometer designed for kinetic binding analysis was adapted to develop a solid-phase competitive fluoroimmunoassay for urinalysis of opiates. The solid phase consisted of polymer beads coated with commercial monoclonal antibodies (MAbs) raised against morphine. Fluorescein-conjugated morphine (FL-MOR) was used as the fluorescein-labeled hapten. The dissociation equilibrium constant (K _D ) for the binding of FL-MOR to the anti-MOR MAb was 0.23 nM. The binding of FL-MOR to the anti-MOR MAb reached steady state within minutes and was displaced effectively by morphine and other opiates. Morphine-3-glucuronide (M3G), the major urinary metabolite of heroin and morphine, competed effectively with FL-MOR in a concentration-dependent manner for binding to the antimorphine MAb and was therefore used to construct the calibration curve. The sensitivity of the assay was 0.2 ng/mL for M3G. The assay was effective at concentrations of M3G from 0.2 to 50 ng/mL, with an IC₅₀ of 2 ng/mL. Other opiates and heroin metabolites that showed >50% crossreactivity when present at 1 μg/mL included codeine, morphine-6-glucuronide, and oxycodone. Methadone showed very low crossreactivity (<5%), which is a benefit for testing in patients being treated for opiate addictions. The high sensitivity of the assay and the relatively high cutoff value for positive opiate tests allows very small sample volumes (e.g., in saliva or sweat) to be analyzed. A double-blind comparison using 205 clinical urine samples showed good agreement between this single-step competitive assay and a commercially performed enzyme multiplied immunoassay technique for the detection of opiates and benzoylecgonine (a metabolite of cocaine).     

Topochemical models for anti-HIV activity of 1-alkoxy-5-alkyl-6-(arylthio)uracils

Relationship between topochemical indices and anti-HIV-1 (HTLV-III) inhibitory activity of 1-alkoxy-5-alkyl-6-(arylthio)uracils has been studied. Superadjacency, an adjacency-cum-distance-based, topochemical index and Wiener’s, a distance-based, topochemical index were calculated for a set of 36 1-alkoxy-5-alkyl-6-(arylthio)uracils. Resulting data were analyzed and suitable models were developed after identification of the active ranges. Subsequently, a biological activity was assigned to each of the compounds using these models and compared with the reported anti-HIV-1 activity. High accuracy of prediction was observed using these models. Statistical analysis revealed significance of the proposed models as well as a lack of correlation between the topochemical indices employed for the chosen data set.     

Structure-activity study of antiepilepticN-aryl-isoxazolecarboxamides/N-isoxazolylbenzamide analogs using Wiener's topological index

The relationship between Wiener's topological index and the antiepileptic activity of a series ofN-aryl-isoxazole carboxamides/N-isoxazolylbenzamide analogs has been investigated. Values of Wiener's topological index for 69 compounds constituting the training set were computed and an active range was identified. Each analog was subsequently assigned an activity which was then compared with the reported antiepileptic activity against the maximal electroshock seizure (MES) test. Due to significant correlation between antiepileptic activity and Wiener's topological index, it was possible to predict antiepileptic activity with an accuracy of 91 % in the active range.     

Asymptotic expansions of the distributions of some test statistics

Summary A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as the Wald and Rao statistics under both the null and alternative hypotheses are obtained. The powers of these statistics are compared and its is shown that for special structures of parameters some statistics have same power in the sence of order . The results obtained are applied for testing the hypothesis about the covariance matrix of the multivariate normal distribution and it is shown that none of the tests based on the above statistics is uniformly superior. Research supported by the National Science Foundation Grant MCS 830149.     

Pressure dependence of the compressibility of alkali halides

The parameterC ₁=[(1/K _T )/P] _T , which describes the pressure variation of the compressibility, has been examined correlating the thermodynamical and interatomic potential approaches employing fewer approximations than has been usual heretofore. General expressions have been derived forC ₁ by including the thermal correction terms, which have generally been ignored in previous studies concerning thermal properties of ionic crystals. The parameterC ₁ has also been related to the Grüneisen parameter, , using a relation given earlier. The applicability of the derived equations is investigated and discussed for alkali halides employing few realistic potential forms. A good general accord is found with the available experimental data, which exhibits an essential improvement over other theoretical determinations.