Results 21 to 30 of about 1,340 (266)
Functional Dependence and Analytic Functions [PDF]
Canadian Mathematical Bulletin, 1979 AbstractWithout appealing to the Cauchy theorem or its corollaries, it is proved that the real and imaginary parts of a non-constant complex-valued analytic function of several complex variables are functionally independent. This unifies and generalizes some results sporadically treated in standard treatises on function theory.
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Dispersion relations and exact bounds on CFT correlators
Journal of High Energy Physics, 2021 We derive new crossing-symmetric dispersion formulae for CFT correlators restricted to the line. The formulae are equivalent to the sum rules implied by what we call master functionals, which are analytic extremal functionals which act on the crossing ...
Miguel F. Paulos
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Comptes Rendus. Mathématique, 2021 In this paper we consider two functionals of the Fekete–Szegö type: $\Phi _f(\mu ) = a_2 a_4-\mu a_3{}^2$ and $\Theta _f(\mu ) = a_4-\mu a_2a_3$ for analytic functions $f(z) = z+a_2z^2+a_3z^3+\ldots $, $z\in \Delta $, ($\Delta = \lbrace z\in \mathbb{C ...
Zaprawa, Paweł
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Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints [PDF]
Quantum, 2022 According to the entropy accumulation theorem, proving the unconditional security of a device-independent quantum key distribution protocol reduces to deriving tradeoff functions, i.e., bounds on the single-round von Neumann entropy of the raw key as a ...
Michele Masini +2 more
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Quantum Optimal Control via Semi-Automatic Differentiation [PDF]
Quantum, 2022 We develop a framework of "semi-automatic differentiation" that combines existing gradient-based methods of quantum optimal control with automatic differentiation.
Michael H. Goerz +2 more
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A Modified Analytic Function Space Feynman Integral and Its Applications
Journal of Function Spaces, 2014 We analyze the generalized analytic function space Feynman integral and then defined a modified generalized analytic function space Feynman integral to explain the physical circumstances.
Seung Jun Chang +2 more
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Banach spaces of functions analytic in a polydisc
International Journal of Mathematics and Mathematical Sciences, 1986 This paper is concerned with functions of several complex variables analytic in the unit polydisc. Certain Banach spaces to which these functions might belong are defined and some relationships between them are developed.
Leon M. Hall
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Feynman formulae for solutions of Schrodinger-type equations with fourth-power polinomial potentials [PDF]
Компьютерные исследования и моделирование, 2012 The conditions for the existence of Feynman integrals in a sense of analytic continuation of the exponential functionals with a fourth-power polynomial in the index are studied, their presentations by Gaussian integrals are constructed in the paper.
Anna Konstantinovna Kravtseva
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The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices
Journal of High Energy Physics, 2019 We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in two regimes ...
Dalimil Mazáč, Miguel F. Paulos
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Clustering by analytic functions
Information Sciences, 2012 Data clustering is a combinatorial optimization problem. This article shows that clustering is also an optimization problem for an analytic function. The mean squared error, or in this case, the squared error can expressed as an analytic function. With an analytic function we benefit from the existence of standard optimization methods: the gradient of ...
Malinen Mikko, Fränti Pasi
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