We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be >/=1. The GM increases with the number of patches (because the sampling error is reduced) and decreases ...

Low seismic velocity regions in the mantle and crust are commonly attributed to the presence of silicate melts. Determining melt volume and geometric distribution is fundamental to understanding planetary dynamics. We present a new model for seismic velocity reductions that accounts for the anomalous compressibility of silicate melt, rendering compressional wave velocities more sensitive to mel...

We present a geometric approach for calculating integrals over irregular domains described by a level-set function. This procedure can be used to evaluate integrals over a lower dimensional interface and may be used to evaluate the contribution of singular source terms. This approach produces results that are second-order accurate and robust to the perturbation of the interface location on the ...

Introduction:  Image  distortion  is  one  of  the  major  problems  of  magnetic  resonance  imaging  (MRI) for use in 3DMRI, velocity MRI, FMRI and radiotherapy treatment planning (RTTP). It is  widely known that the most obvious effect of the inhomogenity of the magnetic fields and the  nonlinearity  of  the  gradient  is  the  Geometric  Distortion  of  MR  tomograms.  In  this  study,  the...

Many situations in real world cannot be described by a single variable. Simul taneous occurrence of multiple events warrants multivariate distributions. For instance, univariate geometric distribution can represent occurrence of failure of one component of a system. However, to study systems with several com ponents that may have different types of failures, such as twin engines of an airplane ...

The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools for teaching mathematical concepts of mentioned areas, and distance education technologies would be indispensable for consolidation of successfully passed t...

We study the cover time of random geometric graphs. Let I(d) = [0, 1] denote the unit torus in d dimensions. Let D(x, r) denote the ball (disc) of radius r. Let Υd be the volume of the unit ball D(0, 1) in d dimensions. A random geometric graph G = G(d, r, n) in d dimensions is defined as follows: Sample n points V independently and uniformly at random from I(d). For each point x draw a ball D(...