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About 10,000 papers for “Elementary function”

An elementary belief function logic

Didier Dubois, Lluı́s Godo, Henri Prade · Journal of Applied Non-Classical Logics · 2023

Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and plausibility functions as well as between upper and lower probabilities extend the duality between possibility and necessity modalities to the graded environment. It has been shown that the all-or-nothing version of possibility theory can be exactly captured by a minimal epistemic logic (MEL) that uses a very small fragment of the KD modal logic, without resorting to relational semantics. Independently, a belief function logic has been obtained by extending the modal logic S5 to probabilistic graded modalities using Łukasiewicz logic, albeit using relational semantics. This paper shows that a simpler belief function logic can be devised by adding Łukasiewicz logic on top of MEL. It allows for a more natural semantics in terms of Shafer basic probability assignments.

Cited by 2Open access

Implementing an elementary function library

Peter Thompson · ACM SIGNUM Newsletter · 1987

This paper describes the author's experience of implementing a comprehensive library of elementary functions in the INMOS proprietry language occam, to support scientific and engineering applications of transputers.

Cited by 0

Elementary Remarks on Mobius ’ Function

Michel Balazard A · 2011

To the memory of A.A. Karatsuba, on the occasion of his 75th anniversary Abstract—Starting from identities obtained by Möbius inversion, we prove some inequalities involving the ordinary and logarithmic summatory functions of the Möbius function. DOI: 10.1134/S008154381201004X 1.

Cited by 0

Efficient elementary function generation with multipliers

H.M. Ahmed · 2003

Virtually all numerical techniques for elementary function generation share the common property of avoiding multiplication by iteratively performing shift operations. However, with the advent of VLSI, multiplier economics are considerably less formidable than before. The author proposes combining multipliers with these multiplication-free algorithms to construct fast methods of elementary function generation. He demonstrates the idea by combining multipliers with the CORDIC algorithm to achieve fast vector rotation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cited by 30

AN ELEMENTARY INEQUALITY FOR PSI FUNCTION

Yu‐Ming Chu, Xiaoming Zhang, Xiaomin Tang · 2013

For x&amp;gt; 0, let Γ(x) be the Euler’s gamma function, and be the psi function. In this paper, we prove that (b−L(a,b))Ψ(b)+(L(a,b)−a)Ψ(a)&amp;gt; (b−a)Ψ ( √ ab) for b&amp;gt; a ≥ 2, where L(a, b) = b−a log b−log a. 1.

Cited by 7

Elementary constraints on autocorrelation function scalings

Jorge Kurchan · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2002

Elementary algebraic constraints on the form of an autocorrelation function C(t(w)+tau,t(w)) rule out some two-time scalings found in the literature as possible long-time asymptotic forms. The same argument leads to the realization that two usual definitions of many-time scale relaxation for aging systems are not equivalent.

Cited by 15Open access

Elementary constraints on autocorrelation function scalings

Kurchan, Jorge · arXiv (Cornell University) · 2001

Elementary algebraic constraints on the form of an autocorrelation function C(tw+t,tw)= rule out some two-time scalings found in the literature as possible long-time asymptotic forms. The same argument leads to the realization that two usual definitions of {\em many-time scale} relaxation for aging systems are not equivalent.

Cited by 0Open access

Numerical Algorithms On Non-Elementary Function

Gejia Zhang · 2021 International Conference on Internet, Education and Information Technology (IEIT) · 2021

This paper discusses how numerical algorithms can be used to approximate a function using algebraic polynomials. With the two elementary methods, we try to estimate the given function as accuracy as possible. One of the methods is a very elegant numerical technique that has been widely used in applied mathematics such as numerical integration, etc. The other method is quite popular in statistical sciences and optimization. They both give some insights in approximating a function to algebraic polynomials without using too many advanced and complicated theories.

Cited by 0

An elementary formulation of Riemann’s Zeta function

Poli, R, Langdon, WB · UCL Discovery (University College London) · 2005

We rewrite Riemann’s Zeta function as a sum over the primes. Each term of the sum is a product that depends only on the summation index (a prime) and the primes following it.

Cited by 0