1. Induction proofs, type I: Sum/product formulas: The most common, and the easiest, application of induction is to prove formulas for sums or products of n terms. All of these proofs follow the same pattern. (a) ∑n i=1 i(i+ 1) = n(n+1)(n+2) 3 (b) ∑n i=0 2 i = 2n+1 − 1 (sum of powers of 2) (c) ∑n i=0 r i = 1−r n+1 1−r (r 6= 1) (sum of finite geometric series) (d) ∑n i=0 i!i = (n+ 1)!− 1. Soluti...

17 Helicobacter pylori VacA is a secreted pore-forming toxin that is comprised of two 18 domains, designated p33 and p55. The p55 domain has an important role in binding of VacA to 19 the cell surface. About 111 residues at the amino-terminus of p55 (residues 312-422) are 20 essential for the intracellular activity of VacA, which suggests that this region may constitute a 21 subdomain with an a...

The role of Pasteuria penetrans in suppressing numbers of root-knot nematodes was investigated in a 7-year monocuhure of tobacco in a field naturally infested with a mixed population of Meloidogyne incognita race 1 and M. javanica. The suppressiveness of the soil was tested using four treatments: autoclaving (AC), microwaving (MW), air drying (DR), and untreated. The treated soil bioassays cons...

Helicobacter pylori VacA is a secreted pore-forming toxin that is comprised of two domains, designated p33 and p55. The p55 domain has an important role in the binding of VacA to eukaryotic cell surfaces. A total of 111 residues at the amino terminus of p55 (residues 312 to 422) are essential for the intracellular activity of VacA, which suggests that this region may constitute a subdomain with...

The plant Gossypium Hirsutum genotypes were grown in Qwshtapa district, Grdmala village, which is 30 kilometres from the centre of Erbil, Iraq. cotton there included Coker 310, Lachata (Iraqi genotypes), Cafko, Dunn 1047, Montana, Stone Ville (USA Bakhtegon, Khdorda, and Vanamin (Iranian genotypes). anatomical investigation demonstrates distinct petioles, midribs, laminas, margin outline shapes...

CAL: HIGH POROSITY ≠ HIGH PERMEABILITY P. A. Bland, M. D. Jackson, R. F. Coker, B. A. Cohen, G. K. Benedix. Impacts & Astromaterials Research Centre (IARC), Dept. Earth Sci. & Eng., Imperial College London, SW7 2AZ, UK. E-mail: [email protected]. IARC, Dept. Mineralogy, Natural History Museum, London SW7 5BD, UK. Los Alamos National Lab., Los Alamos, NM 87545, USA. Inst. Meteoritics, Universit...