Related papers: High-order Uncertain Differential Equation and Its…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying…
Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are constructed, which are extended to nonconforming finite…
We consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust $H_\infty$ estimation for…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
Modern applications of atomic physics, including the determination of frequency standards, and the analysis of astrophysical spectra, require prediction of atomic properties with exquisite accuracy. For complex atomic systems,…
In this paper, using the similarity method, we construct particular solutions with singularities for degenerate high-order equations. The considered equations have singularities of the first and second kind. Particular solutions are…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis…
Despite recent advances and focus on rigorous uncertainty quantification for microscopic models of quantum many-body systems, the uncertainty on the dynamics of those systems has been under-explored. To address this, we have used…
A system of U(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz. The highest weight property of the solutions is proved and some examples of solutions are calculated explicitly. (Part II of…
There have been great efforts on the development of higher-order numerical schemes for compressible Euler equations. The traditional tests mostly targeting on the strong shock interactions alone may not be adequate to test the performance…
The status of RHIC theory and phenomenology is reviewed with an emphasis on the indications for the creation of a new deconfined state of matter. The critical role of high energy nuclear physics in the development of theoretical tools that…
The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with $A\le 4$. In particular, by applying the Rayleigh-Ritz or Kohn variational principle, both…
The equation of state of neutron-star cores can be constrained by requiring a consistent connection to the perturbative Quantum Chromodynamics (QCD) calculations at high densities. The constraining power of the QCD input depends on…
The concentration of radiation-induced point defects in general materials under irradiation is commonly described by the point defect kinetics equations based on rate theory. However, the parametric uncertainty in describing the rate…
The generation of high harmonics in laser-irradiated light homonuclear diatomics (H2+, N2 and O2) compared to that in atomic counterparts (of nearly identical binding energy) is studied within the velocity gauge version of conventional…
Calculations truncated at a fixed order in perturbation theory are accompanied by an associated theoretical uncertainty, which encodes the missing higher orders (MHOU). This is typically estimated by a scale variation procedure, which has…
A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.