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A Finite Element Method for Random Differential Equations with Random Coefficients
SIAM Journal on Numerical Analysis, 1979A finite element method is derived for solving equations of the following type \[ - (p(x)u'(x,\omega ))' + (q(x) + r(x)\lambda (\omega ))^2 u(x,\omega ) = f(x,\omega ),\quad 0 \leqq x \leqq l,\] with boundary conditions $u(0,\omega ) \equiv u(l,\omega ) \equiv 0$ where (i) $0 < p \in C^1 [0,l]$; (ii) $q,r \in C[0,l]$; (iii) $f(x,\omega ) = B'(x ...
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Quantum Random Active Element Machine
2013In [4], a computational procedure (Procedure 2) - combining quantum randomness and the active element machine (AEM) [5] - executes a universal Turing machine with Turing incomputable firing patterns. The procedure emulates any digital computer program so its computational steps are incomprehensible to an external observer.
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Probability measures and random elements
2000One of the central topics in our book can be characterized as follows: we discuss appropriate analogues of the Anderson inequality (see Section 2) and demonstrate applications of these analogues in probability theory, mathematical statistics and infinite-dimensional analysis.
V. V. Buldygin, A. B. Kharazishvili
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On convergence for series of random elements
Nonlinear Analysis: Theory, Methods & Applications, 2001Hu, Tien-Chung, Wang, Chunnan
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Random Assembly of Logical Elements
1962Since the notion of random and randomness repeatedly arises in the field we are discussing, I thought that maybe it would be of some interest to build examples of what may happen in certain circumstances when one is using random operations.
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