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Closed-form expression

Related publications (169)

A new set of analytical formulae for the computation of the bootstrap current and the neoclassical conductivity in tokamaks

A new set of analytical formulae for calculating the bootstrap current and the neoclassical conductivity in tokamak experiments is presented. Previous works comparing the widely used Sauter model with results of recently developed numerical neoclassical so ...

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This paper presents a review of lightning M-component models. M-component models are classified into two main categories: (i) the guided-wave M-component model and its extensions and (ii) nonlinear M-component models. Other models and assumptions, in which ...

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Support and approximation properties of Hermite splines

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Shayan Aziznejad

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

2020

Pulay forces in density-functional theory with extended Hubbard functionals: From nonorthogonalized to orthogonalized manifolds

Nicola Marzari, Iurii Timrov, Matteo Cococcioni, Francesco Aquilante, Luca Binci

We present a derivation of the exact expression for Pulay forces in density-functional theory calculations augmented with extended Hubbard functionals and arising from the use of orthogonalized atomic orbitals as projectors for the Hubbard manifold. The de ...

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This paper examines the binning of two types of parts with random characteristics, so that a componentwise monotonic evaluation criterion exhibits a minimum deviation to a given target value over all possible realizations. The optimal matching classes are ...

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Full field dependence of primary aberrations in perturbed double-plane symmetric systems with a circular pupil

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This paper deals with the theory of primary aberrations for perturbed double-plane symmetric optical systems consisting of a combination of tilted and decentered surfaces and a circular pupil. First, the analytical expressions describing the full field beh ...

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Linear Stochastic Dividend Model

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The macroscopic dynamics of large populations of neurons can be mathematically analyzed using low-dimensional firing-rate or neural-mass models. However, these models fail to capture spike synchronization effects and nonstationary responses of the populati ...

AMER PHYSICAL SOC2020

Stochastic Learning Under Random Reshuffling With Constant Step-Sizes

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In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works have pursued ju ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

On the Exact Gevrey Order of Formal Puiseux Series Solutions to the Third Painleve Equation

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In this paper, we study the third Painleve equation with parameters gamma = 0, alpha delta not equal 0. The Puiseux series formally satisfying this equation (after a certain change of variables) asymptotically approximate of Gevrey order one solutions to t ...

2019

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