We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise al...

This paper deals with the worst case setting for approximating multivariate tensor product linear operators defined over Hilbert spaces. Approximations are obtained by using a number of linear functionals from a given class of information. We consider the three classes of information: the class of all linear functionals, the Fourier class of inner products with respect to given orthonormal elem...

We report the results of a benchmarking study on hybrid, hybrid-meta, long-range-corrected, meta-generalized gradient approximation (meta-GGA), and GGA density functional theory (DFT) methods for aluminum (Al) clusters. A range of DFT functionals, such as B3LYP, B1B95, PBE0, mPW1PW91, M06, M06-2X, ωB97X, ωB97XD, TPSSh, BLYP, PBE, mPWPW91, M06-L, and TPSS, have been used to optimize the molecula...

A set of density functionals coming from different rungs on Jacob's ladder is employed to evaluate the electronic excited states of three Ru(II) complexes. While most studies on the performance of density functionals compare the vertical excitation energies, in this work we focus on the energy gaps between the electronic excited states, of the same and different multiplicity. Excited state ener...

The exchange-correlation functionals of the generalized gradient approximation GGA are still the most used for the calculations of the geometry and electronic structure of solids. The PBE functional J. P. Perdew et al., Phys. Rev. Lett. 77, 3865 1996 , the most common of them, provides excellent results in many cases. However, very recently other GGA functionals have been proposed and compete i...

Abstract: We investigate four diatomic molecules containing transition metals using two variants of hybrid functionals. We compare global hybrid functionals that only partially counteract self-interaction to local hybrid functionals that are designed to be formally free from one-electron self-interaction. As d-orbitals are prone to be particularly strongly influenced by self-interaction errors,...

This paper is concerned with energy-based image segmentation problems. We introduce a general class of regional functionals defined as an arbitrary non-linear combination of regional unary terms. Such (high-order) functionals are very useful in vision and medical applications and some special cases appear in prior art. For example, our general class of functionals includes but is not restricted...

We prove that every irreducible, admissible representation π of GSp(4, F ), where F is a non-archimedean local field of characteristic zero, admits a Bessel functional, provided π is not onedimensional. If π is not supercuspidal, we explicitly determine the set of all Bessel functionals admitted by π, and prove that Bessel functionals of a fixed type are unique. If π is supercuspidal, we do the...