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...

In this paper, we treat 4-dimensional Einstein-Gauss-Bonnet gravity as general relativity with an effective stress-energy tensor. We will study the modified Oppenheimer-Snyder-Datt model of gravitational collapse a star in black hole. The inside geometry is described by spatially flat Friedmann-Robertson-Walker metric and matter distributed uniformly without any pre-assumption about its equatio...