JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association.Many statistical models, and in particular autoregressive-moving average time series models, can be regarded as means of transforming the data to white noise, that is, to an uncorrelated sequence of errors. If the parameters are known exactly, this random sequence can be computed directly from the observations; when this calculation is made with estimates substituted for the true parameter values, the resulting sequence is referred to as the "residuals," which can be regarded as estimates of the errors. If the appropriate model has been chosen, there will be zero autocorrelation in the errors. In checking adequacy of fit it is therefore logical to study the sample autocorrelation function of the residuals. For large samples the residuals from a correctly fitted model resemble very closely the true errors of the process; however, care is needed in interpreting the serial correlations of the residuals. It is shown here that the residual autocorrelations are to a close approximation representable as a singular linear transformation of the autocorrelations of the errors so that they possess a singular normal distribution. Failing to allow for this results in a tendency to overlook evidence of lack of fit. Tests of fit and diagnostic checks are devised which take these facts into account.1509

Many statistical models, and in particular autoregressive-moviiifi average time series models, can be regarded as means of transforniing the data t o n-hite noise, that is, to an uncorrelated sequence of errors. If the parameters are known exactly, this random sequence can be comput.ctl dircct,ly from the nlmrvations; when this calculation is mnde with estimates substituted for the true parameter values, the resulttirig sequence is referred to as the "residuals," which can be regarded as estimates of the errors.If t,he appropriate model has been chosen, there will he zern autocorrelation in t,he errors. I n checking adcquncy of fit it is thercfore logical to study the sample autocorrelation function of t8he residuals. For large samples the residuals from a correctly fittcd model resemble very clo~cly the true errors of the process; however, care is needed in interpreting the serial correlations of the residuals. It is shown here that the residual nutocorrelations are to a close approximation representable as a singular linear transformation of the autocorrelations of the crrors so that they posvess a singular normal distribution. Failing t o allow for this results in a tendency to overlook evidence of lack of fit.. Tests of fit and diagnostic checlcs are devised which take these facts into account.

Iodine ( 129 I and 131 I) is one of the radionuclides released in nuclear fuel reprocessing and poses a risk to public safety due to its involvement in human metabolic processes. In order to prevent the release of hazardous radioactive iodine into the environment, its effective capture and sequestration is pivotal. In the context of finding a suitable matrix for capturing radioactive iodine, several sulfidic chalcogels were explored as iodine sorbents including NiMoS 4 , CoMoS 4 , Sb 4 Sn 3 S 12 , Zn 2 Sn 2 S 6 , and K 0.16 CoS x (x = 4−5). All of the chalcogels showed high uptake, reaching up to 225 mass % (2.25 g/g) of the final mass owing to strong chemical and physical iodine−sulfide interactions. Analysis of the iodine-loaded specimens revealed that the iodine chemically reacted with Sb 4 Sn 3 S 12 , Zn 2 Sn 2 S 6 , and K 0.16 CoS x to form the metal complexes SbI 3 , SnI 4 , and, KI, respectively. The NiMoS 4 and CoMoS 4 chalcogels did not appear to undergo a chemical reaction with iodine since iodide complexes were not observed with these samples. Once heated, the iodine-loaded chalcogels released iodine in the temperature range of 75 to 220 °C, depending on the nature of iodine speciation. In the case of Sb 4 Sn 3 S 12 and Zn 2 Sn 2 S 6 , iodine release was observed around 150 °C mainly in the form of SnI 4 and SbI 3 , respectively. The NiMoS 4 , CoMoS 4 , and K 0.16 CoS x released elemental iodine at ∼75 °C, which is consistent with physisorption. Preliminary investigations on consolidation of iodine-loaded Zn 2 Sn 2 S 6 chalcogel with Sb 2 S 3 as a glass forming additive produced glassy material whose iodine content was around 25 mass %.

Powders of a Sn2S3 chalcogen-based aerogel (chalcogel) were combined with powdered polyacrylonitrile (PAN) in different mass ratios (SnS33, SnS50, and SnS70; # = mass% of chalcogel), dissolved in dimethyl sulfoxide, and added dropwise to deionized water to form pellets of a porous PAN-chalcogel hybrid material. These pellets, along with pure powdered (SnSp) and granular (SnSg) forms of the chalcogel, were then used to capture iodine gas under both dynamic (dilute) and static (concentrated) conditions. Both SnSp and SnSg chalcogels showed very high iodine loadings at 67.2 and 68.3 mass%, respectively. The SnS50 hybrid sorbent demonstrated a high, although slightly reduced, maximum iodine loading (53.5 mass%) with greatly improved mechanical rigidity. In all cases, X-ray diffraction results showed the formation of crystalline SnI4 and SnI4(S8)2, revealing that the iodine binding in these materials is mainly due to a chemisorption process, although a small amount of physisorption was observed.

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We rework the foundations of the theory of differentially closed fields of characteristic zero in a geometric setting. The ''new'' axioms will say that if V is an irreducible variety and W is an irreducible subvariety of the appropriate torsor Ž . V projecting generically onto V, then W has a generic point of the form Ž Ž .. a,D a . ᮊ