Related papers: Extremal Polarization Configurations for Integrabl…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
We establish the existence of solutions to a weakly-coupled competitive system of polyharmonic equations in R^N which are invariant under a group of conformal diffeomorphisms, and study the behavior of least energy solutions as the coupling…
For a symmetric kernel $k:X\times X \to \mathbb{R}\cup\{+\infty\}$ on a locally compact Hausdorff space $X$, we investigate the asymptotic behavior of greedy $k$-energy points $\{a_{i}\}_{1}^{\infty}$ for a compact subset $A\subset X$ that…
The conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a ``reference'' subharmonic operator bounded from below by the dissipative part of the infinitesimal generator. We discuss applications of this…
We give sufficient conditions for a nonlocal perturbation of an integral kernel to be locally in time comparable with the kernel.
The characterization of quantum polarization of light requires knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix. We look into the cumulative distribution…
In this work, we extend the quantum optimal control theory of molecules subject to ultrashort laser pulses to the case of solvated systems, explicitly including the solvent dielectric properties in the system Hamiltonian. A reliable…
We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined…
A new model of physically realizable electromagnetic source is proposed. The source is partially coherent and non-uniformly totally polarized. The coherence and polarization characteristics of this new source are analyzed. The spatial…
Herein, we focus on explicit constructions of $\ell\times\ell$ binary kernels with small scaling exponent for $\ell \le 64$. In particular, we exhibit a sequence of binary linear codes that approaches capacity on the BEC with quasi-linear…
We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…
We consider extensions of differential fields of mappings and obtain a lower energy bound for quasiconformal extension fields in terms of the topological degree. We also consider the related minimization problem for the $q$-harmonic energy,…
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel…
The amount of correlation attainable between the components of a quantum system is constrained if the system is closed. We provide some examples, largely from the field of quantum thermodynamics, where knowing the maximal possible variation…
(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support…
Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization…
We give conditions for the existence of regular optimal partitions, with an arbitrary number $\ell\geq 2$ of components, for the Yamabe equation on a closed Riemannian manifold $(M,g)$. To this aim, we study a weakly coupled competitive…
We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained…
We consider aggregation-diffusion equations with merely bounded nonlocal interaction potential $K$. We are interested in establishing their well-posedness theory when the nonlocal interaction potential $K$ is neither differentiable nor…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…