Results 291 to 300 of about 81,951 (325)

On Ostrowski inequality for quantum calculus

Applied Mathematics and Computation, 2021
We disprove a version of Ostrowski inequality for quantum calculus appearing in the literature. We derive a correct statement and prove that our new inequality is sharp. We also derive a midpoint inequality.
Ana Žgaljić Keko   +3 more
openaire   +1 more source

The Quantum Probability Calculus

Synthese, 1974
Quantum mechanics has opened a vast sector of physics to probability calculus. In fact most of the physical interpretation of the formalism of quantum mechanics is expressed in terms of probability statements ...
openaire   +2 more sources

Symmetric Quantum Calculus [PDF]

open access: possible, 2002
The q- and h-differentials may be “symmetrized“ in the following way, $$ \tilde d_q f(x) = f(qx) - f(q^{ - 1} x), $$ (26.1) $$ \tilde d_h g(x) = g(x + h) - g(x - h), $$ (26.2) where as usual, q ≠ 1 and h ≠ 0. The definitions of the corresponding derivatives follow obviously: $$ \tilde D_q f(x) = \frac{{\tilde d_q f(x)}} {{\tilde
Pokman Cheung, Victor G. Kac
openaire   +1 more source

Quantum Variational Calculus

2014
International ...
Malinowska, Agnieszka B., Torres, Delfim
openaire   +2 more sources

On the quantum differential calculus and the quantum holomorphicity

Journal of Mathematical Physics, 1992
Under some natural assumptions [less restrictive than in the paper by Wess and Zumino (preprint CERN-TH-5697/90, LAPP-TH-284/90)] differential calculi on the quantum plane are found and investigated. Complex structure, complex derivatives, and holomorphic functions on the quantum plane are defined.
Tomasz Brzeziński   +2 more
openaire   +2 more sources

The Power Quantum Calculus

2013
In this chapter we introduce the power difference calculus based on the operator \(D_{n,q} [f](t) = \frac{f(qt^n)-f(t)}{qt^n -t}\), where \(n\) is an odd positive integer and ...
Delfim F. M. Torres   +1 more
openaire   +2 more sources

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