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pro vyhledávání: '"Burris, Stanley"'
Autor:
Burris, Stanley
In Boole's famous 1854 book {\em The Laws of Thought\/} the mathematical analysis of Aristotelian logic was relegated to Chapter XV, the last chapter before his treatment of probability theory. This chapter is Boole's tour de force to show that he ha
Externí odkaz:
http://arxiv.org/abs/2305.14199
Autor:
Burris, Stanley
An examination of George Boole's mysterious use of the Algebra of Numbers to create an Algebra of Logic, and subsequent research connected to this.
Comment: 8 pages, no figures
Comment: 8 pages, no figures
Externí odkaz:
http://arxiv.org/abs/2304.11878
Autor:
Burris, Stanley, Sankappanavar, H. P.
In modern algebra it is well-known that one cannot, in general, apply ordinary equational reasoning when dealing with partial algebras. However Boole did not know this, and he took the opposite to be a fundamental truth, which he called the Principle
Externí odkaz:
http://arxiv.org/abs/1412.2953
Autor:
Burris, Stanley, Sankappanavar, H. P.
A rigorous, modern version of Boole's algebra of logic is presented, based partly on the 1890s treatment of Ernst Schroder.
Externí odkaz:
http://arxiv.org/abs/1404.0784
Let $K$ be a field of characteristic zero and suppose that $f:\mathbb{N}\to K$ satisfies a recurrence of the form $$f(n)\ =\ \sum_{i=1}^d P_i(n) f(n-i),$$ for $n$ sufficiently large, where $P_1(z),...,P_d(z)$ are polynomials in $K[z]$. Given that $P_
Externí odkaz:
http://arxiv.org/abs/1105.6078
Let $\cT$ be a monadic-second order class of finite trees, and let $\bT(x)$ be its (ordinary) generating function, with radius of convergence $\rho$. If $\rho \ge 1$ then $\cT$ has an explicit specification (without using recursion) in terms of the o
Externí odkaz:
http://arxiv.org/abs/1004.1128
In a previous work we introduced an elementary method to analyze the periodicity of a generating function defined by a single equation y=G(x,y). This was based on deriving a single set-equation Y = Gammma(Y) defining the spectrum of the generating fu
Externí odkaz:
http://arxiv.org/abs/0911.2494
Publikováno v:
Elec. J. Combin. 17 (2010), #R121
Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems.
Comment: 28 pages.
Comment: 28 pages.
Externí odkaz:
http://arxiv.org/abs/0905.2585
Autor:
Burris, Stanley, Yeats, Karen
If F(x) = e^G(x), where F(x) = \sum f(n)x^n and $G(x) = \sum g(n)x^n, with 0 \le g(n) = O(n^{theta n}/n!),theta in (0,1), and gcd(n : g(n) > 0)=1, then f(n) = o(f(n-1)). This gives an answer to Compton's request in Question 8.3 for an ``easily verifi
Externí odkaz:
http://arxiv.org/abs/math/0608735