Convergence in law of random sums with non-random centering

We extend results obtained in Kruglov,⁽⁷⁾ and Finkelstein and Tucker⁽³⁾ to obtain necessary and sufficient conditions for convergence in law of random sums of non-identically distributed independent random variables under non-random centering. Thei.i.d. case is also considered for random variables attracted to a stable law. Necessary and sufficient conditions for convergence in law of these random variables under non-random centering, and in some cases, under non-random norming, are also obtained. The distribution functions for the limit laws are determined as well, generalizing results of Robbins.⁽¹⁰⁾ Supported in part by The State University of New York and United States Information Agency Grant No. IA AEMP69193692.     

The discovery of hidden arsenic species in coastal waters

The analysis of ultraviolet (UV)-irradiated and untreated seawater samples has shown that the dissolved arsenic content of marine waters cannot be completely determined by hydride generation–atomic absorption spectrophotometry without sample pretreatment. Irradiation of water samples obtained during a survey of arsenic species in coastal waters during the summer of 1988 gave large increases in the measured speciation. Average increases in the measured speciation. Average increases in total arsenic, monomethylarsenic and dimethylarsenic were 0.29 μg As dm^?3 (25%), 0.03 μg As dm^?3 (47%) and 0.12 μg As dm^?3 (79%), respectively. Overall, an average 25% increase in the concentration of dissolved arsenic was observed following irradiation. This additional arsenic may be derived from compounds related to algal arsenosugars or to their breakdown products. These do not readily yield volatile hydrides when treated with borohydride and are not therefore detected by the normal hydride generation technique. This has important repercussions as for many years this procedure, and other analytical procedures which are equally unlikely to respond to such compounds, have been accepted as giving a true representation of the dissolved arsenic speciation in estuarine and coastal waters. A gross underestimate may therefore have been made of biological involvement in arsenic cycling in the aquatic environment.     

An optimization function and its application to the multidimensional thin-layer chromatography of protein amino acids

The multicomponent mobile-phase systems in thin-layer chromatography (TLC) can be optimized by using an overall figure of merit for the separation. To simulate the normally subjective appraisals of resolution in TLC, the figure of merit (FOM) is based on an equation which defines the extent of separation of pairs of spots. Contributions to the FOM range from zero at complete overlap to a maximum value with complete resolution. A small degree of spot overlap causes only a limited decrease in the FOM but the decrease is rapid with deteriorating resolution. The approach is shown to be effective in simplex optimization of the separation of 17 amino acids by two-dimensional TLC on cellulose plates with two 4-component solvent systems, one basic and one acidic. The problem was considered as two distinct one-dimensional separations. The acidic mobile phase was optimized first. The eight spots left unseparated were completely resolved by the basic phase. Optimum mobile-phase compositions were: 12.0/6.0/1.52/2.48 (by volume) t-butanol/ammonia (25%)/methyl ethyl ketone/water for the first elution and 10.29/6.82/5.06/ 3.65 n-butanol/acetone/acetic acid/water for the second elution.     

Phonon lifetimes in fused quartz at low temperatures

Thermal Brillouin scattering from fused quartz has been observed with high resolution at low temperatures. At 2.4 K the longitudinal phonons of ν = 33 GHz are very well-defined excitations, with a lifetime of (2.0±.2)×10^-7 sec. This value is in substantial disagrement with those reported by Pelous and Vacher¹.     

Studies in sulphur heterocyles. 2—The 13C NMR spectra of thienocoumarins

¹³C NMR spectra of 3- substituted thieno[2,3-h][1]benzopyran-2-ones and 8-substituted thieno[3,2-f]-[1]benzopyran-7-ones are reported and the substituent dependence of certain ¹³C chemical shifts is noted.     

The effect of water on the secondary dielectric relaxations in nylon 66

Dielectric data were taken on nylon 66 at several moisture levels at frequencies from 10 to 10⁵ Hz and temperatures from ?70°C to room temperature. Moisture increases the frequency and the peak height for the β relaxation and reduces its activation energy. The peak height of the γ relaxation is reduced by moisture and shifts to slightly higher frequencies with little change in activation energy. The β relaxation follows the pattern of Jonscher and Ngai for a cooperative many-body process. The γ relaxation is slightly broader than a Debye relaxation and approaches that model quite closely as the temperature is increased. The high-frequency end of the β relaxation overlaps the γ relaxation.