scholarly journals Structural theorems for symbolic summation

2009 ◽  
Vol 21 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Carsten Schneider
Keyword(s):  
Symbolic Summation ◽  
Structural Theorems

Structural theorems for multiplicative systems of functions

1985 ◽  
Vol 46 (1-2) ◽  
pp. 111-127
Author(s):  
J. Jakubowski
Keyword(s):  
Multiplicative Systems ◽  
Structural Theorems

scholarly journals Intelligence via ultrafilters: structural properties of some intelligence comparators of deterministic Legg-Hutter agents

2019 ◽  
Vol 10 (1) ◽  
pp. 24-45
Author(s):  
Samuel Allen Alexander
Keyword(s):  
Structural Properties ◽  
Intelligent Agents ◽  
Intelligent Agent ◽  
Related Question ◽  
Practical Intelligence ◽  
Guiding Principle ◽  
Intelligence Measures ◽  
Open Question ◽  
Structural Theorems

Abstract Legg and Hutter, as well as subsequent authors, considered intelligent agents through the lens of interaction with reward-giving environments, attempting to assign numeric intelligence measures to such agents, with the guiding principle that a more intelligent agent should gain higher rewards from environments in some aggregate sense. In this paper, we consider a related question: rather than measure numeric intelligence of one Legg-Hutter agent, how can we compare the relative intelligence of two Legg-Hutter agents? We propose an elegant answer based on the following insight: we can view Legg-Hutter agents as candidates in an election, whose voters are environments, letting each environment vote (via its rewards) which agent (if either) is more intelligent. This leads to an abstract family of comparators simple enough that we can prove some structural theorems about them. It is an open question whether these structural theorems apply to more practical intelligence measures.

scholarly journals Structural theorems for quasiasymptotics of ultradistributions

2019 ◽  
Vol 114 (1-2) ◽  
pp. 1-18 ◽  
Author(s):  
Lenny Neyt ◽  
Jasson Vindas
Keyword(s):  
Structural Theorems

scholarly journals -Analogues of Symbolic Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Michael J. Dancs ◽  
Tian-Xiao He
Keyword(s):  
Linear Operators ◽  
Derivative Operator ◽  
Symbolic Summation ◽  
Series Transformation ◽  
Transformation Formulas ◽  
Symbolic Substitution

Here presented are -extensions of several linear operators including a novel -analogue of the derivative operator . Some -analogues of the symbolic substitution rules given by He et al., 2007, are obtained. As sample applications, we show how these -substitution rules may be used to construct symbolic summation and series transformation formulas, including -analogues of the classical Euler transformations for accelerating the convergence of alternating series.

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