In this paper we study the congruences of *-regular semigroups, involution semigroups in which every element is p-related
to a projection (an idempotent fixed by the involution). The class of *-regular semigroups was introduced by Drazin in 1979,
as the involutorial counterpart of regular semigroups. In the standard approach to *-regular semigroup congruences, one ,starts
with idempotents, i.e. with traces and kernels in the underlying regular semigroup, builds congruences of that semigroup,
and filters those congruences which preserve the involution. Our approach, however, is more evenhanded with respect to the
fundamental operations of *-regular semigroups. We show that idempotents can be replaced by projections when one passes from
regular to *-regular semigroup congruences. Following the trace-kernel balanced view of Pastijn and Petrich, we prove that
an appropriate equivalence on the set of projections (the *-trace) and the set of all elements equivalent to projections (the
*-kernel) fully suffice to reconstruct an (involution-preserving) congruence of a *-regular semigroup. Also, we obtain some
conclusions about the lattice of congruences of a *-regular semigroup.
Authors:Zhongyu Wu, K. Inn, Zhichao Lin, and C. McMahon
One of the most critical elements of a performance evaluation (PE) program for radioactivity measurements is the traceability of the PE materials to the national standards. The requirements and criteria for the production of traceable environmental and radiobioassay PE materials have been defined by ANSI N42.22 and ANSI N13.30 standards. It is important to note that use of traceable source materials does not necessarily ensure the traceability of subsequently derived PE materials unless verification measurements exist in conjunction with the preparation processes. This paper describes the protocol currently used by NIST for the preparation and verification of air filter, acidified water, spiked soil, synthetic urine, and synthetic fecal PE materials for low-level radioactivity measurements. The process involves gravimetric dilutions and mixing of primary radionuclide NIST Standard Reference Materials (SRMs), addition of the derived master solution to sample matrices, and subsequent verification measurements. Several gamma-emitters were used to trace the gravimetric dilutions and spike addition through an unbroken chain of gamma comparison measurements. The massic activities of alpha- and beta-emitters in the diluted solutions and PE samples were also measured by radiochemical methods and compared with their gravimetric values. A correlation analysis demonstrated that the gamma emitters quantitatively followed 90Sr, 238U, 238Pu, and 241Am throughout the dilution and spiking and can be used as effective process monitors. The statistical results from t-tests, box plots, and normal probability tests suggested that traceability of radionuclides in the PE materials to their primary standards can be verified to within 1%, with an overall precision better than 2% (1s).
Authors:D. Baimonda, G. Bernasconi, N. Haselberger, A. Markowicz, and V. Valkovic
X-ray fluorescence has been applied as an analytical technique for the trace element characterization of Mongolian coals. Coal, samples from five regions of Mongolia are found to contain variable amounts of many trace elements. Various approaches to quantitative XRF analysis including a simple quantitative method, an emission-transmission method and a full fundamental parameter method are compared.
A method is proposed by which the significance of the differences between trace element concentrations of sample and control
can be estimated without detailed knowledge of the distribution in the total population. Both sample and control are cut in
half and the trace element concentrations of all four pieces are determined. The concentration values of the two halves of
each sample are compared with each other and so are the concentration values of the two samples. This cross-comparison is
essentially the application of Student's t-test to the smallest possible number of data. The calculation is reduced to a simple
formula, and tables of confidence limits are not needed. The implications of lack of general background knowledge are discussed.
Since it cannot always be known whether a certain trace element follows a normal or log-normal distribution pattern, or whether
simultaneously determined concentrations of several trace elements are correlated with each other, the most cautious estimate
of the significance is recommended.
The ultimate purpose of all studies on environmental contamination is to protect human life; as a consequence the knowledge
of the trace element pathways from environment to man is of paramount importance because it allows the assessment of a clear
relationship between any environmental contamination and its effects on man. To this extent two different kinds of environmental
studies will be described in this paper: (a) Studies of the geographic variations on the whole national territory of the natural
levels of trace elements in water, food and some human tissues. (b) Studies of selected areas where a critical population
group is exposed to abnormal levels of some trace elements. The main trace elements considered are: Co, Cr, Cs, Fe, Hg, Ni,
Rb, Sb, Sc, Se and Zn; all the measurements were performed by means of non-destructive neutron activation analysis.
Ferrites have been used to separate a wide range of substances such as dissolved metal species, particulate matter, and organic and biological materials; they have been used almost exclusively for metal waste treatment applications. However, ferrites can be used to remove and concentrate selected trace metals in a wide variety of feed solutions requiring analysis. A brief overview of ferrite properties and recent applications for trace metal recovery and concentration will be presented.