Physician with expertise in obesity and diabetes university administrator. Born London, UK, on June 23, 1951, he died there of leukaemia July 9, 2021, aged 70 years. Reaching the highest levels academia as a professor at Barts London School Medicine Dentistry, more than fulfilled Peter Kopelman's ambition to become doctor. As his brother Michael Kopelman, Emeritus Professor Neuropsychiatry King...

We consider certain decision problems for the free model of theory Cartesian monoids. introduce a computation based on notion single stack one-way PDA due to Ginsburg, Greibach and Harrison. This allows us solve such as (1) Given finite set B elements an element F, is F product members B? (2) Is submonoid generated by infinite? fragments monoid. These include right invertible so our results app...

In 1963, Graham [1] proved that all integers greater than 77 (but not 77 itself) can be partitioned into distinct positive integers whose reciprocals sum to 1. He further conjectured [2, Section D11] that for any sufficiently large integer, it can be partitioned into squares of distinct positive integers whose reciprocals sum to 1. In this study, we establish the exact bound for existence of su...