Related papers: Constrained energy problems with external fields
In this paper we consider the setting of a locally compact, non-complete metric measure space $(Z,d,\nu)$ equipped with a doubling measure $\nu$, under the condition that the boundary $\partial Z:=\overline{Z}\setminus Z$ (obtained by…
Bessiere et al. (AAAI'08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixed-parameter…
This paper presents a new general formulation of the Radon-Nikodym theorem in the setting of abstract measure theory. We introduce the notion of weak localizability for a measure and show that this property is both necessary and sufficient…
In this note we study a minimization problem for a vector of measures subject to a prescribed interaction matrix in the presence of external potentials. The conductors are allowed to have zero distance from each other but the external…
Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…
The main observation of this paper is that some sequential weak compactness arguments in Hilbert space theory can be replaced by Heine/Borel compactness arguments (for the strong topology). Even though the latter form of compactness fails…
We study the boundary value problem with Radon measures for nonnegative solutions of $L_Vu:=-\Delta u+Vu=0$ in a bounded smooth domain $\Gw$, when $V$ is a locally bounded nonnegative function. Introducing some specific capacity, we give…
The electromagnetic properties of neutrinos have attracted considerable attention from researchers for many decades (see [1] for a review). However, until recently, there was no indication in favour of nonzero electromagnetic properties of…
We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained…
We propose a new formalism to analyse the extremum structure of scale-invariant effective potentials. The problem is stated in a compact matrix form, used to derive general expressions for the stationary point equation and the mass matrix…
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to…
We perform a detailed study of a simple mathematical model addressing the problem of optimally regulating a process subject to periodic external forcing, which is interesting both in view of its direct applications and as a prototype for…
In this paper, we investigate discrete logarithmic energy problems in the unit circle. We study the equilibrium configuration of $n$ electrons and $n-1$ pairs of external protons of charge $+1/2$. It is shown that all the critical points of…
Gravitational positivity bounds provide consistency conditions for effective field theories with gravity. They turn out to be phenomenologically useful by providing lower bounds in parameters of new physics beyond the Standard Models (BSM).…
Starting from a subinvariant positive definite kernel under a branching pullback, we attach to the resulting kernel tower a canonical electrical network on the word tree whose edge weights are the diagonal increments. This converts diagonal…
This paper extends the characterization of compactness established in \cite{cao2024} to bilinear singular integral operators with mild kernel regularity. The exponent we obtain coincides with the best known sufficient condition for the…
We consider the Klein-Gordon equation in FRW-like spacetimes, with compact space sections (not necessarily isotropic neither homogeneous). The bi-scalar kernel allowing to select the positive-frequency part of any solution is developed on…
Our main result shows that if a lower-semicontinuous kernel K satisfies some mild additional hypotheses, then asympotitically polarization optimal configurations are precisely those that are asymptotically distributed according to the…
Under the condition of small external forces, we obtain existence of a weak solution of the steady Hall-MHD system with H\"{o}lder continuous magnetic field. We also established regularity of weak solutions provided that magnetic fields are…
In this brief review, we examine the theoretical consistency and viability of phantom dark energy. Almost all data sets from cosmological probes are compatible with dark energy of the phantom variety (i.e., equation-of-state parameter…