Publications related to Analytic function

On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, an ...

MDPI2024

Functional-Basis Analysis of Non-Stationary Signals in Modern Power Grids: Theory and Implementation in Embedded Systems

Alexandra Cameron Karpilow

Situational awareness strategies are essential for the reliable and secure operation of the electric power grid which represents critical infrastructure in modern society. With the rise of converter-interfaced renewable generation and the consequent shift ...

EPFL2024

Stability: a search for structure

Wouter Jongeneel

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

EPFL2024

On the Use of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytical Functions for the Calculation of Infinite Sums and the Analysis of Zeroes of Analytical Functions

Serguei Sekatski

Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calcul ...

MDPI2023

The Källén-Lehmann representation in de Sitter spacetime

Kamran Salehi Vaziri, Manuel Loparco, João Miguel Augusto Penedones Fernandes

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Kallen-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we ...

Springer Nature2023

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Nicolas Henri Bernard Flammarion

We consider the problem of sampling from a density of the form p(x) ? exp(-f (x) - g(x)), where f : Rd-+ R is a smooth function and g : R-d-+ R is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Hastings framework. Under ...

Microtome Publishing2022

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

An analytical inverse analysis to determine equi-biaxial tensile properties of strain-hardening UHPFRC from ringon-ring test (vol 53, 123, 2020)

Eugen Brühwiler, Emmanuel Denarié, Xiujiang Shen, Wanghu Peng

The article "An analytical inverse analysis to determine equi-biaxial tensile properties of strain-hardening UHPFRC from ringon-ring test", written by Xiujiang Shen, Eugen Bruhwiler, Emmanuel Denarie and Wanghu Peng was originally published electronically ...

SPRINGER2021

Coarse graining and large-N behavior of the d-dimensional N-clock model

Matthias Ruf, Matthias Benjamin Ruf

We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...

2021

Functional Tucker Approximation Using Chebyshev Interpolation

Daniel Kressner, Christoph Max Strössner

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function approximations tha ...

SIAM PUBLICATIONS2021

A Continuized View on Nesterov Acceleration

Nicolas Henri Bernard Flammarion, Raphaël Jean Berthier

We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...

2021

On the asymptotic behavior of the solutions to parabolic variational inequalities

Maria Colombo

We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...

2020

Thermal CFTs in momentum space

Andrea Manenti

We study some aspects of conformal field theories at finite temperature in momentum space. We provide a formula for the Fourier transform of a thermal conformal block and study its analytic properties. In particular we show that the Fourier transform vanis ...

Springer Nature2020

Loops in AdS: from the spectral representation to position space

Din Carmi

We compute a family of scalar loop diagrams in AdS. We use the spectral representation to derive various bulk vertex/propagator identities, and these identities enable to reduce certain loop bubble diagrams to lower loop diagrams, and often to tree- level ...

Springer Nature2020

The index of singular zeros of harmonic mappings of anti-analytic degree one

Robert Gerhard Jérôme Luce

We study harmonic mappings of the form , where h is an analytic function. In particular, we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the critical set of f, where the Jacobian of f is non-vanishing, it ...

TAYLOR & FRANCIS LTD2021

Optimal Spline Generators for Derivative Sampling

Michaël Unser, Shayan Aziznejad, Alireza Naderi

The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions ...

IEEE2019

Specification of aspherical surfaces used as refractive elements in micro-optical systems

Toralf Scharf, Wilfried Noell, Jeremy Béguelin

The optical performance of refractive plano-convex microlenses is mainly related to the quality of their (a)spherical surface. An efficient tolerancing of this surface is a key step towards the manufacturing of high quality microlenses. However, we demonst ...

SPIE-INT SOC OPTICAL ENGINEERING2019

Beyond Phasors: Modeling of Power System Signals Using the Hilbert Transform

Mario Paolone, Asja Derviskadic, Guglielmo Frigo

Modern power systems are at risk of largely reducing the inertia of generation assets and prone to experience extreme dynamics. The consequence is that, during electromechanical transients triggered by large contingencies, transmission of electrical power ...

IEEE Institute of Electrical and Electronics Engineers2019

System Architectures for Multiports, Bidirectional and Buffered Charging Units for EV’s

Alfred Rufer

Bidirectional buffered units for Multiports charging of EV’s are presented, allowing to charge with high power even if the line current capability is limited. The systems are also dedicated to operate as reactive power compensators, or to provide grid syst ...

2018

Perivascular macrophages in health and disease

Michele De Palma

Macrophages are a heterogeneous group of cells that are capable of carrying out distinct functions in different tissues, as well as in different locations within a given tissue. Some of these tissue macrophages lie on, or close to, the outer (abluminal) su ...

Nature Publishing Group2018