We use phase space methods to investigate closed, flat, and open FriedmannRobertson-Walker cosmologies with a scalar potential given by the sum of two exponential terms. The form of the potential is motivated by the dimensional reduction of M-theory with non-trivial four-form flux on a maximally symmetric internal space. To describe the asymptotic features of run-away solutions we introduce the...

We show that the satisfiability problem for CTL, the branching time logic that allows boolean combinations of path formulas inside a path quantifier but no nesting of them, is 2-EXPTIME-hard. The construction is inspired by Vardi and Stockmeyer’s 2-EXPTIME-hardness proof of CTL∗’s satisfiability problem. As a consequence, there is no subexponential reduction from CTL to CTL which preserves sati...

We provide a rather general asymptotic scheme for combinatorial parameters that asymptotically follow a discrete double-exponential distribution. It is based on analysing generating functions Gh(z) whose dominant singularities converge to a certain value at an exponential rate. This behaviour is typically found by means of a bootstrapping approach. Our scheme is illustrated by a number of class...

This paper reviews two simple numerical algorithms particularly useful in Computational ElectroMagnetics (CEM): the Weighted Averages (WA) algorithm and the Double Exponential (DE) quadrature. After a short historical introduction and an elementary description of the mathematical procedures underlying both techniques, they are applied to the evaluation of Sommerfeld integrals, where WA and DE c...

soil water retention curve is one of the crucial input parameters in any modeling study on water flow and solute transport in soils. direct measurement of soil water retention curve is time-consuming and costly. alternatively, pedotransfer functions (ptfs) may be used to indirectly estimate the soil water retention curve from easily measured soil properties. many equations for the soil water re...

A weak-shock solution is obtained for the nonlinear propagation of a waveform that initially has the form of an asymmetric double exponential. Such a wave shocks at its peak, so that shock growth and wave-amplitude attenuation occur simultaneously. Simple formulas for wave amplitude, shock amplitude, and arrival time are given as is an expression for the waveform. We also present a general tech...

Dictyostelium discoideum has been used as a genetically tractable model organism to study many biological phenomena. High-efficiency transformation is a prerequisite for successful genetic screens such as mutant complementation, identification of suppressor genes, or insertional mutagenesis. Although exponential decay electroporation is the standard transformation technique for D. discoideum, i...