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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
Malinowska, Agnieszka B., Torres, Delfim
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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
Malinowska, Agnieszka B., Torres, Delfim
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Quantum Probability Calculus as Fuzzy-Kolmogorovian Probability Calculus
AIP Conference Proceedings, 2009Representation of quantum logics by families of fuzzy sets allows to build fuzzy set‐theoretic models of quantum probability spaces in a way fully analogous to the Kolmogorov construction of a classical probability space. Therefore, quantum probability calculus on the one hand may be seen as a special kind of fuzzy probability calculi, and on the other
Jarosław Pykacz +7 more
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1986
The basic integrator processes of quantum stochastic calculus, namely, creation, conservation, and annihilation, are introduced in the Hilbert space of square integrable Brownian functionals. Stochastic integrals with respect to these processes and a quantum Ito’s formula are described.
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The basic integrator processes of quantum stochastic calculus, namely, creation, conservation, and annihilation, are introduced in the Hilbert space of square integrable Brownian functionals. Stochastic integrals with respect to these processes and a quantum Ito’s formula are described.
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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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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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1996
We saw in Chapter 10 that the quantum correspondent to first-order set algebra and first-order class algebra is a Grassmann double algebra of antisymmetric tensors. (More accurately: is the ray structure of a Grassmann algebra; this is to be understood throughout.) We now work out a quantum correspondent to the classical set calculus, the higher-order ...
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We saw in Chapter 10 that the quantum correspondent to first-order set algebra and first-order class algebra is a Grassmann double algebra of antisymmetric tensors. (More accurately: is the ray structure of a Grassmann algebra; this is to be understood throughout.) We now work out a quantum correspondent to the classical set calculus, the higher-order ...
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Itô’s Lemma with Quantum Calculus (q-Calculus): Some Implications
Foundations of Physics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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