title: The gcd-sum function

authors: Broughan, Kevin A.

subjects: mathematics

abstract: The gcd-sum is an arithmetic function defined as the sum of the gcd's of the first n integers with n: g(n) = sumi=1..n (i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of partial sums of the Dirichlet series at real values are derived, including estimates for error terms.

text: The gcd-sum function The gcd-sum is an arithmetic function defined as the sum of the gcd's of the first n integers with n: g(n) = sumi=1..n (i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of partial sums of the Dirichlet series at real values are derived, including estimates for error terms.

year: 2001

title: An extremely thermostable extracellular proteinase from a strain of the archaebacterium Desulfurococcus growing at 88 degrees C.

authors: Cowan, Don A.

subjects: biology

abstract: An organism growing at 88 degrees C that closely resembles Desulfurococcus mucosus produced a single extracellular proteinase. We have purified this enzyme and carried out a preliminary characterization. The proteinase, which is a serine-type enzyme, had a molecular mass of 52,000 Da by SDS/polyacrylamide-gel electrophoresis, but only 10,000-13,000 Da by gel-permeation chromatography. Molecular mass values from sucrose-gradient centrifugation were of the same order as those from SDS/polyacrylamide-gel electrophoresis. It had an isoelectric point of 8.7, and was inhibited by di-isopropyl phosphorofluoridate, phenylmethanesulphonyl fluoride and chymostatin. Substrate-specificity studies suggested a possible preference for hydrophobic residues on the C-terminal side of the splitting point. The thermostability of this enzyme is probably greater than any other reported proteinase (t1/2 at 95 degrees C, 70-90 min; t1/2 at 105 degrees C, 8-9 min). Ca2+ chelation does not appear to be implicated in stabilization of the protein structure. The stability of the Desulfurococcus proteinase was not greatly affected by the presence of reducing reagents (e.g. dithiothreitol), some chaotropic agents (e.g. NaSCN) and some detergents, but activity was lost rapidly at 95 degrees C in the presence of the oxidizing agent NaBO3. Proteolytic activity was readily detected at temperatures up to and including 125 degrees C, although denaturation was very rapid above 115 degrees C. A number of Figures supporting some of the findings reported in this paper have been deposited in supplement SUP 50137 (14 pages) at the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies may be obtained on the terms indicated in Biochem. J. (1987) 241, 5.

text: An extremely thermostable extracellular proteinase from a strain of the archaebacterium Desulfurococcus growing at 88 degrees C. An organism growing at 88 degrees C that closely resembles Desulfurococcus mucosus produced a single extracellular proteinase. We have purified this enzyme and carried out a preliminary characterization. The proteinase, which is a serine-type enzyme, had a molecular mass of 52,000 Da by SDS/polyacrylamide-gel electrophoresis, but only 10,000-13,000 Da by gel-permeation chromatography. Molecular mass values from sucrose-gradient centrifugation were of the same order as those from SDS/polyacrylamide-gel electrophoresis. It had an isoelectric point of 8.7, and was inhibited by di-isopropyl phosphorofluoridate, phenylmethanesulphonyl fluoride and chymostatin. Substrate-specificity studies suggested a possible preference for hydrophobic residues on the C-terminal side of the splitting point. The thermostability of this enzyme is probably greater than any other reported proteinase (t1/2 at 95 degrees C, 70-90 min; t1/2 at 105 degrees C, 8-9 min). Ca2+ chelation does not appear to be implicated in stabilization of the protein structure. The stability of the Desulfurococcus proteinase was not greatly affected by the presence of reducing reagents (e.g. dithiothreitol), some chaotropic agents (e.g. NaSCN) and some detergents, but activity was lost rapidly at 95 degrees C in the presence of the oxidizing agent NaBO3. Proteolytic activity was readily detected at temperatures up to and including 125 degrees C, although denaturation was very rapid above 115 degrees C. A number of Figures supporting some of the findings reported in this paper have been deposited in supplement SUP 50137 (14 pages) at the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies may be obtained on the terms indicated in Biochem. J. (1987) 241, 5.

year: 1987

title: Te Awa Tupua (Whanganui river claims settlement) Bill – the endless quest for justice

authors: Te Aho, Linda

abstract: Linda Te Aho continues her review of the new legal framework for Te Awa Tupua (the Whanganui River system) as part of the settlement of historical claims by Whanganui iwi about the Whanganui River.

text: Te Awa Tupua (Whanganui river claims settlement) Bill – the endless quest for justice Linda Te Aho continues her review of the new legal framework for Te Awa Tupua (the Whanganui River system) as part of the settlement of historical claims by Whanganui iwi about the Whanganui River.

year: 2016-08