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Background risk and quantum calculus
Risk and Decision Analysis, 2013Infinitesimal calculus is heavily used in decision making analysis. This paper demonstrates that the application of quantum calculus in analysing preferences choice directly introduces background risk and its effects on risk-aversion, subjective probabilities and moment preferences.
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Tutorial: Graphical Calculus for Quantum Circuits
2013We explain the graphical zx-calculus for reasoning about qubits without any reference to the underlying categorical semantics, and illustrate its use on quantum circuits.
Coecke, Bob, Duncan, Ross
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2014
Introduces readers to the treatment of the calculus of variations with q-differences and Hahn difference operators Provides the reader with the first extended treatment of quantum variational calculus Shows how the techniques described can be applied to economic models as well as other mathematical systems This Brief puts together two subjects, quantum
Agnieszka B. Malinowska +1 more
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Introduces readers to the treatment of the calculus of variations with q-differences and Hahn difference operators Provides the reader with the first extended treatment of quantum variational calculus Shows how the techniques described can be applied to economic models as well as other mathematical systems This Brief puts together two subjects, quantum
Agnieszka B. Malinowska +1 more
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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 ...
Agnieszka B. Malinowska +1 more
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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 ...
Agnieszka B. Malinowska +1 more
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Journal of Soviet Mathematics, 1991
The main aim of this paper is to introduce the reader into the quantum stochastic calculus in the symmetric Fock space from the stochastic processes point of view. The author discusses the quantum Itô formula, applications to probabilistic representations of solutions of differential equations, and applications to extensions of dynamical semigroups ...
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The main aim of this paper is to introduce the reader into the quantum stochastic calculus in the symmetric Fock space from the stochastic processes point of view. The author discusses the quantum Itô formula, applications to probabilistic representations of solutions of differential equations, and applications to extensions of dynamical semigroups ...
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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: $$ \tilde D_q f(x) = \frac{{\tilde d_q f(x)}} {{\tilde
Victor Kac, Pokman Cheung
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The q- and h-differentials may be “symmetrized“ in the following way, $$ \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
Victor Kac, Pokman Cheung
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Image Denoising Based on Quantum Calculus of Local Fractional Entropy
Symmetry, 2023Rabha W Ibrahim, Ibrahim Rabha W
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Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus
Open Mathematics, 2021Muhammad Aamir Ali +2 more
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Equivalence Checking of Quantum Circuits With the ZX-Calculus
IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2022Tom Peham +2 more
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A Comprehensive Review of the Hermite–Hadamard Inequality Pertaining to Quantum Calculus
Foundations, 2023Muhammad Tariq +2 more
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