A word is called unbordered, if it has no proper prefix which is also a suffix of that word. Let μ(w) denote the length of the longest unbordered factor of a word w. Let a word where the longest unbordered prefix is equal to μ(w) be called Duval extension. A Duval extension is called trivial, if its longest unbordered factor is of the length of the period of that Duval extension. In 1982 it was...

M. Beaumont, M. G. DuVal, W. A. Farhat, G. K. Sàndor, and H-L. M. Cheng Research Institute & Diagnostic Imaging, The Hospital for Sick Children, Toronto, Ontario, Canada, Oral and Maxillofacial Surgery, University of Toronto, Toronto, Ontario, Canada, Research Institute & Urology, The Hospital for Sick Children, Toronto, Ontario, Canada, Regea Institute for Regenerative Medicine, University of ...

M. Beaumont, M. G. DuVal, Y. Loai, W. A. Farhat, G. K. Sándor, and H-L. M. Cheng The Research Institute and Diagnostic Imaging, The Hospital for Sick Children, Toronto, Ontario, Canada, Department of Oral and Maxillofacial Surgery, University of Toronto, Toronto, Ontario, Canada, Division of Urology, The Hospital for Sick Children, Toronto, Ontario, Canada, Department of Medical Biophysics, Uni...

We compute the C∗-equivariant quantum cohomology ring of Y , the minimal resolution of the DuVal singularity C/G where G is a finite subgroup of SU(2). The quantum product is expressed in terms of an ADE root system canonically associated to G. We generalize the resulting Frobenius manifold to non-simply laced root systems to obtain an n parameter family of algebra structures on the affine root...

Fault diagnosis of power transformers have always drawn the attention among the users, without removing the transformers from the service. Thus it is necessary to detect the incipient fault of a power transformer at an early stage and diagnose properly on optimum way. Dissolved gas analyses (DGA) is widely used to detect incipient faults in oil filled power transformers. Throughout the world, d...

A word v = wu is a (nontrivial) Duval extension of the unbordered word w, if (u is not a prefix of v and) w is an unbordered factor of v of maximum length. After a short survey of the research topic related to Duval extensions, we show that, if wu is a minimal Duval extension, then u is a factor of w. We also show that finite, unbordered factors of Sturmian words are Lyndon words.

9. Huot C, De Serres G, Duval B, MarandaAubut R, Ouakki M, Skowronski DM. The cost of preventing rabies at any cost: post-exposure prophylaxis for occult bat contact. Vaccine. 2008;26:4446–50. doi:10.1016/j.vaccine.2008.06.076 10. Frantz SC, Laniewicz BR. Comprehensive management of commensal bats. In: Brittingham MC, Kays J, McPeake R, editors. The ninth wildlife damage management conference p...