Monin-Obukhov theory predicts the well-known log-linear form of the vertical wind speed profile. Two parameters, namely the aerodynamic surface roughness length and the Monin-Obukhov-length, are needed to predict the vertical wind speed profile from a measurement at one height. Different models to estimate these parameters for conditions important for offshore wind energy utilisation are discus...

Let X be a projective Frobenius split variety over an algebraically closed field with splitting θ : F∗OX → OX . In this paper we give a sharp bound on the number of subvarieties of X compatibly split by θ. In particular, suppose L is a sufficiently ample line bundle on X (for example, if L induces a projectively normal embedding) with n = dimH(X,L ). We show that the number of d-dimensional irr...

A data structure is presented for the Mergeable Dictionary abstract data type, which supports the following operations on a collection of disjoint sets of totally ordered data: PredecessorSearch, Split and Merge. While Predecessor-Search and Split work in the normal way, the novel operation is Merge. While in a typical mergeable dictionary (e.g. 2-4 Trees), the Merge operation can only be perfo...

We consider the model of random trees introduced by Devroye [SIAM J Comput 28, 409– 432, 1998]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion in the nodes of a tree. The total path length (sum of depths of the items) is a natural measure of the efficiency of the algorithm/data structure. Using renewa...

We study the nodal set of Laplace eigenfunctions on flat 2d torus $${\mathbb {T}}^2$$ . prove an asymptotic law for length such eigenfunctions, under some growth assumptions their Fourier coefficients. Moreover, we show that is asymptotically equidistributed The proofs are based Bourgain’s de-randomisation technique and main new ingredient, which might be independent interest, integrability arb...

Dumbbell trees were introduced in [1]. A detailed description of non-binary dumbbell trees appears in Chapter 11 of [3]. These notes show how binary dumbbell trees can be obtained, and how they can be used to construct, in O(n log n) time, a spanner of bounded degree and weight proportional to O(log n) times the weight of a minimum spanning tree. The reader is assumed to be familiar with the sp...