On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

Simultaneous fitting of exponential decay curves /

Includes bibliographies (p. 23).

Computing a perfect strategy for n x [i.e. superscript] n chess requires time exponential in n /

"UILU-ENG 79 1716."

Radix 16 division, multiplication, logarithmic and exponential algorithms based on continued product representations,

Thesis (M.S.)--University of Illinois at Urbana-Champaign.

An exponential lower bound for a restricted class of monotone formulae for 2-unsatisfiability /

"UILU-ENG 78-1734."

Continued-product algorithms for division, logarithm, exponential and square root in radix ten /

Typescript.

Computing programs for the complex exponential integral /

Photocopy. Arlington, Va. : Armed Services Technical Information Agency, [1970] -- 34 leaves ; 26 x 34 cm.

Inverse table of the exponential integral /

Mode of access: Internet.

An elementary treatise on algebra : to which are added exponential equations and logarithms /

Mode of access: Internet.

Optical precursors and Beer's law violations; non-exponential propagation losses in water

We develop a model for exponential decay of broadband pulses, and examine its implications for experiments on optical precursors. One of the signature features of Brillouin precursors is attenuation with a less rapid decay than that predicted by Beer's Law. Depending on the pulse parameters and the model that is adopted for the dielectric properties of the medium, the limiting z-dependence of the loss has been described as z(-1/2), z(-1/3), exponential, or, in more detailed descriptions, some combination of the above. Experimental results in the search for precursors are examined in light of the different models, and a stringent test for sub-exponential decay is applied to data on propagation of 500 femtosecond pulses through 1-5 meters of water. (C) 2005 Optical Society of America.

A scalarization technique for computing the power and exponential moments of gaussian random matrices

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X=A+BWC for positive integer s and real t, where W is a standard normal random vector and A, B, C are appropriately dimensioned constant matrices. We solve the problems by a matrix product scalarization technique and interpret the solutions in system-theoretic terms. The results of the paper are applicable to Bayesian prediction in multivariate autoregressive time series and mean-reverting diffusion processes.

A worldwide correlation for exponential bed particle size variation in subaerial aqueous flows

The particle size of the bed sediments in or on many natural streams, alluvial fans, laboratory flumes, irrigation canals and mine waste deltas varies exponentially with distance along the stream. A plot of the available worldwide exponential bed particle size diminution coefficient data against stream length is presented which shows that all the data lie within a single narrow band extending over virtually the whole range of stream lengths and bed sediment particle sizes found on Earth. This correlation applies to both natural and artificial flows with both sand and gravel beds, irrespective of either the solids concentration or whether normal or reverse sorting occurs. This strongly suggests that there are common mechanisms underlying the exponential diminution of bed particles in subaerial aqueous flows of all kinds. Thus existing models of sorting and abrasion applicable to some such flows may be applicable to others. A comparison of exponential laboratory abrasion and field diminution coefficients suggests that abrasion is unlikely to be significant in gravel and sand bed streams shorter than about 10 km to 100 km, and about 500 km, respectively. Copyright (C) 1999 John Wiley & Sons, Ltd.