The theory of apolarity was first developed by Clebsch, Lasker, Richw x mond, Sylvester, and Wakeford 10, 17, 20 . They were first interested in studying homogeneous polynomials of degree p and in q variables, and in expressing them as sums of pth powers of linear terms. The problem is to minimize the number of pth powers which are required in such a sum. For instance, a result due to Sylvester...

Acknowledgments This study was undertaken at the chemotherapy unit at Guy's and St Thomas' NHS Foundation Trust. The research was made possible through a grant from Dimbleby Cancer Care and the generosity of carers who participated in the study in various ways through sharing their stories, and through both developing and testing the intervention. Without their support this research would not h...

I dedicate this thesis to my wife, Ginny, whose infinite patience, constant encouragement , and sincere understanding have made this work possible. ii ACKNOWLEDGEMENTS The author wishes to thank Dr. Patrick D. Toto for his guidance and constant advice in preparing this thesis. The author further wishes to express his g.ratitude to Dr. Anthony Gargiulo for his continuing interest in this work an...

We reconsider the quasi exactly solvable matrix models constructed recently by R. Zhdanov. The 2×2 matrix operators representing the algebra sl(2) are generalized to matrices of arbitrary dimension and a similar construction is achieved for the algebra sl(n). ∗† Work supported by grant no KBN 2P03B07610 1. Recently Zhdanov [1],[2] considered the realizations of the sl(2) algebra in terms of fir...