This paper presents an effective quasi one-dimensional (1-D) computational simulation methodology and some important results for steady annular/stratified (or film wise) internal condensing flows of pure vapor. Though the approach is strictly valid for smooth, laminar vapor/laminar condensate flows, it is also approximately valid for laminar condensate and turbulent vapor which are laminar in t...

Thermal desalination plants consume large quantifies of heat energy for seawater evaporation. In condensing water vapor procured in evaporators and cooling distillate, a major part of heat energy is lost in the environment. Heat energy in processes of condensation and evaporation in desalination of seawater is quantitatively equal but these processes take place under different temperatures. Dif...

Evolution of Network Structure with a Fixed Number of Edges and Nodes Carissa Flocken June 2012 Abstract We consider a model that incorporates local rewiring of nodes and edges. We use a high-degree expansion in order to describe the first model that we believe would produce a power law with an exponential cuts off at the tail. However, we find that non-trivial correlations exist between degree...

Let K and T be convex open bounded bodies in R . We will discuss in this note C1-diffeomorphic bijections8:K → T with constant determinant of the Jacobian. So, if volK = vol T our maps are measure preserving. There are several such distinguished maps. For example, a Knothe map ([K]) 8:K → T has a triangular Jacobian with a positive diagonal and may be naturally associated with any fixed orthogo...

This paper defines and establishes properties of a class of normalized radial visualizations (NRVs) that includes the RadViz mapping onto the two-dimensional unit disk. A NRV normalizes data to map highdimensional records into lower dimensional space, where records’ images are convex combinations of points called dimensional anchors. NRVs are radial visualizations because dimensional anchors ar...

Given an initial point, x0, sets Si for i = 1, . . . , r and their corresponding nearest point projections PSi , the method of alternating projections (MAP) attempts to finds a point in ∩i=1Si by cyclically projecting onto the sets. The original alternating projection result was due to von Neumann (1933) who was able to prove that if the sets are subspaces MAP converges in norm to P∩i=1Si . Usi...

Introduction. Kakutani's fixed point theorem [3]1 states that in Euclidean «-space a closed point to (nonvoid) convex set map of a convex compact set into itself has a fixed point. Kakutani showed that this implied the minimax theorem for finite games. The object of this note is to point out that Kakutani's theorem may be extended to convex linear topological spaces, and implies the minimax the...