Nonnegative Radix Representations for the Orthant

Let be a nonnegative real matrix which is expanding, i.e. with all eigenvalues , and suppose that is an integer. Let consist of exactly nonnegative vectors in . We classify all pairs such that every in the orthant has at least one radix expansion in base using digits in . The matrix must be a diagonal matrix times a permutation matrix. In addition must be similar to an integer matrix, but need not be an integer matrix. In all cases the digit set can be diagonally scaled to lie in . The proofs generalize a method of Odlyzko, previously used to classify the one--dimensional case.

     

Orthogonal array design (OAD) for the optimization of mercury extraction from soils by dilute acid with microwave heating

The use of dilute acid for mercury extraction from geological samples with microwave assisted heating was investigated. An orthogonal array design OA(16)(4(1)x2(12)) was applied to select the optimum conditions. The effects of the concentration of HNO(3), the additions of HCl and H(2)S0(4), the extraction time and their interactions were evaluated by the mixed-level orthogonal array design (OAD). The results indicated that the addition of small amount of HCl would improve significantly the extraction of mercury from soil matrices. From the study, it is seen that the mercury in the soil matrices could be extracted completely by 14% (v/v) HNO(3) with small quantity of HCl. The effects of the pressure within the digestion vessel and the sample mass were studied under the optimum conditions derived from the OAD. The extraction methods with optimum conditions were evaluated by determining mercury in NIST SRM 1645 River Sediment, NIES CRM No. 2 Pond Sediment and NRCC BCSS-1 Marine Sediment. Recoveries of 78-109% were achieved. Good mean recoveries of 95-98% were also obtained from real soil samples spiked with different species of mercury.