reference evapotranspiration is an important parameter in irrigation systems' design that is evaluated through either direct (lysimeter) or calculated method (empirical equations). when there is a lack of lysimeters' data, penman monteith fao method could be employed as a standard method for evaluating the other empirical methods' results. in this research, 13 year evaporation pa...

I have long enjoyed teaching, and have had a wide variety of teaching jobs over the past dozen years. I’ve worked in many different capacities at summer math programs for nine summers, I taught a sophomore tutorial at Harvard, I’ve given over 30 seminar talks at Berkeley, and I taught four sections of Calculus at U.C. Berkeley. Beyond a general interest in teaching, I have strong particular int...

We introduce the notion of a half-ribbon Hopf algebra, which is a Hopf algebra H along with a distinguished element t ∈ H such that (H, R,C) is a ribbon Hopf algebra, where R = (t ⊗ t)∆(t) and C = t. The element t is closely related to the topological ‘half-twist’, which twists a ribbon by 180 degrees. We construct a functor from a topological category of ribbons with half-twists to the categor...

Subfactors of the hyperfinite II1 factor of index less than or equal to 4 were classified in the late 80s and early 90s through work of Jones, Ocneanu, Popa, and many others. There is an ADE classification, and all of the examples are closely related to quantum or classical SU(2). When the index is larger than 4, there is one family of A∞ subfactors related to quantum SU(2) which are difficult ...