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1997
Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order,εdependent parabolic partial differential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the...

1997
Kouritzin, Michael, Dawson, Donald
A general Hilbertspacebased stochastic averaging theory is brought forth herein for arbitraryorder parabolic equations with (possibly long range dependent) random coefficients. We use regularity conditions onView the MathML sourcewhich are slightly stronger than those required to prove...

2004
This article presents notes that Russell made while reading the works of Gottlob Frege in 1902. These works include Frege’s books as well as the packet of offprints Frege sent at Russell’s request in June of that year. Russell relied on these notes while composing “Appendix A: The Logical and...

1994
Heunis, A. J., Kouritzin, Michael
In this note we consider the almost sure convergence (as ϵ→0) of solution Xϵ(·), defined over the interval 0 ≤ τ ≤ 1, of the random ordinary differential equation View the MathML source Here {F(x, t, ω), t ≥ 0} is a strong mixing process for each x and (x, t) → F(x, t, ω) is subject to regularity...

2006
Zalta, Edward N. , Linsky, Bernard
Logicism is a thesis about the foundations of mathematics, roughly, that mathematics is derivable from logic alone. It is now widely accepted that the thesis is false and that the logicist program of the early 20th century was unsuccessful. Frege's [1893/1903] system was inconsistent and the...