2nd Annual CIBPA Awards for Excellence, 2002

A certificate award from the Canadian Italian Business and Professional Association of Niagara. Mr. Ziraldo is presented with the Business Excellence award on October 26, 2002. The certificate is signed by Walt Lastewka, M.P. Caucus Advocate for SME's.

Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.

Plan of levels of marsh land on the line of the proposed ditch from Lyons Creek Culvert on the Welland Canal to lot no. 32 in the 2nd concession of Wainfleet

Plan of levels of marsh land on the line of the proposed ditch from Lyons Creek Culvert on the Welland Canal to lot no. 32 in the 2nd concession of Wainfleet (1 page, hand drawn), n.d.

Certificate that Joseph Kingsmill, sheriff, has sold 7 acres in Lot no. 24 in the 2nd Concession of Caistor to W. H. Dickson

Certificate that Joseph Kingsmill, sheriff, has sold 7 acres in Lot no. 24 in the 2nd Concession of Caistor to W. H. Dickson, May 23, 1857.