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A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a…
In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…
Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates.…
The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions…
A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann-Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian…
We introduce a novel framework for the analysis of linear wave equations on nonstationary asymptotically flat spacetimes, under the assumptions of mode stability and absence of zero energy resonances for a stationary model operator. Our…
We choose a complete set of square integrable functions as basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent wave operator is tridiagonal and…
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…
We describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be…
Collective variable-based enhanced sampling methods are routinely used on systems with metastable states, where high free energy barriers impede proper sampling of the free energy landscapes when using conventional molecular dynamics…
In this paper, we study the spectrality and frame-spectrality of exponential systems of the type $E(\Lambda,\varphi) = \{e^{2\pi i \lambda\cdot\varphi(x)}: \lambda\in\Lambda\}$ where the phase function $\varphi$ is a Borel measurable which…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
An implementation of the generalized time-dependent generator coordinated method (TD-GCM) is developed, that can be applied to the dynamics of small- and large-amplitude collective motion of atomic nuclei. Both the generator states and…
The objective of this paper is to apply the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs versus ordinary operational matrices (OOMs). Up to now, a few studies…
The exact factorization (EF) approach to coupled electron-ion dynamics recasts the time-dependent molecular Schr\"odinger equation as two coupled equations, one for the nuclear wavefunction and one for the conditional electronic…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
The Ultra Weak Variational Formulation (UWVF) is a special Trefftz discontinuous Galerkin method, here applied to the time-harmonic Maxwell's equations. The method uses superpositions of plane waves to represent solutions element-wise on a…
The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partial noncentering can be used to accelerate…