From Wallis to Ramanujan, in companionship with RW Gosper

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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, ...

General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a dist ...

We consider three classes of linear differential equations on distribution functions, with a fractional order alpha is an element of [0; 1]. The integer case alpha = 1 corresponds to the three classical extreme families. In general, we show that there is a ...

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic problems in high gra ...

We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but increasing sets of types. A pathwise approach is then used to sho ...

A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. W ...

Modifier adaptation (MA) is a real-time optimization (RTO) method characterized by its ability to enforce plant optimality upon convergence despite the presence of model uncertainty. The approach is based on correcting the available model using gradient es ...

The identification of reaction kinetics represents the main challenge in building models for reaction systems. The identification task can be performed via either simultaneous model identification (SMI) or incremental model identification (IMI), the latter ...

Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian ...

We propose and analyse a new discontinuous reduced basis element method for the approximation of parametrized elliptic PDEs in partitioned domains. The method is built upon an offline stage (parameter independent) and an online (parameter dependent) one. I ...

Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizers. The existing convergence results assume uniform ...

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...

Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in studying photonic ...

In this paper we consider, from the numerical point of view, a thermoelastic diffusion porous problem. This is written as a coupled system of two hyperbolic equations, for the displacement and porosity fields, and two parabolic equations, for the temperatu ...

Inspired by the BBM formula and by work of G. Leoni and D. Spector, we analyze the asymptotic behavior of two sequences of convex nonlocal functionals (Psi(n)(u)) and (Phi(n)(u)) which converge formally to the BV-norm of u. We show that pointwise convergen ...

From Wallis to Ramanujan, in companionship with RW Gosper

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On the asymptotic behavior of the solutions to parabolic variational inequalities

Convergent momentum-space OPE and bootstrap equations in conformal field theory

Fractional extreme distributions

Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

A pathwise approach to the extinction of branching processes with countably many types

Numerical Homogenization And Model Order Reduction For Multiscale Inverse Problems

Use of Transient Measurements for Static Real-Time Optimization

Global Identification of Kinetic Parameters via the Extent-based Incremental Approach

Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation

A Discontinuous Galerkin Reduced Basis Element Method For Elliptic Problems

Convergence Of Variance-Reduced Learning Under Random Reshuffling

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Efficient Analysis of Confined Guided Modes in Phoxonic Crystal Slabs

Numerical Analysis Of A Thermoelastic Diffusion Problem With Voids

Two subtle convex nonlocal approximations of the BV-norm