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Systems of neutral interacting mesons are investigated, concerning in particular the validity of their description by an effective hamiltonian. First, I study its connection to quantum field theory and show that the spectrum of such systems…

This paper focuses on the stability of self-adjointness of linear relations under perturbations in Hilbert spaces. It is shown that a self-adjoint relation is still self-adjoint under bounded and relatively bounded perturbations. The…

The theoretical basis of the phenomenon of effective and exact dimensional reduction, or holographic correspondence, is investigated in a wide variety of physical systems. We first derive general inequalities linking quantum systems of…

It is known that there is a close analogy between "Euclidean t-designs vs. spherical t-designs" and "Relative t-designs in binary Hamming association schemes vs. combinatorial t-designs". In this paper, we want to prove how much we can…

We establish a sharp criterion for the stability of a class of compactly supported, homogeneous density``minimal compact solitons'' or MCS states, of the time-dependent discrete nonlinear Schr\"odinger equation on a multi-lattice, $\mathbb…

We show that artificial magnetism of periodic dielectric or metal/dielectric structures has limitations and is subject to at least two "uncertainty principles". First, the stronger the magnetic response (the deviation of the effective…

In this note we provide explicit constructions of exact Lagrangian embeddings of tori and Klein bottles inside the symplectisation of an overtwisted contact three-manifold. Note that any closed exact Lagrangian in the symplectisation is…

This paper focuses on the homogenization of high-contrast dielectric elastomer composites, materials that deform in response to electrical stimulation. The considered heterogeneous material consisting of an ambient material with inserted…

Though extensively studied, hardness, defined as the resistance of a material to deformation, still remains a challenging issue for a formal theoretical description due to its inherent mechanical complexity. The widely applied Teter's…

The goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and…

We show that, under certain combinations of the parameters governing the interaction of a harmonically trapped ion with a laser beam, it is possible to find one or more exact eigenstates of the Hamiltonian, with no approximations except the…

We suggest a way to associate to a rational map of the Riemann sphere a three dimensional object called a hyperbolic orbifold 3-lamination. The relation of this object to the map is analogous to the relation of a hyperbolic 3-manifold to a…

An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…

The cohomology ring of the moduli space of stable holomorphic vector bundles of rank n and degree d over a Riemann surface of genus g>1 has a standard set of generators when n and d are coprime. When n=2 the relations between these…

We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…

We theoretically consider specific adhesion of a fluctuating membrane to a hard substrate via the formation of bonds between receptors attached to the substrate and ligands in the membrane. By integrating out the degrees of freedom of the…

We derive the exact longitudinal plasmon dispersion relations, $\omega(k)$ of classical one and two dimensional Wigner crystals at T=0 from the real space equations of motion, of which properly accounts for the full unscreened Coulomb…

In linear elasticity, a fourth order elasticity (stiffness) tensor of 21 independent components completely describes deformation properties of a material. Due to Voigt, this tensor is conventionally represented by a $6\times 6$ symmetric…

A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of homogeneity:…

Two-dimensional (2D) equations describing the nonlinear interaction between upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal nonlinearity in the equations results in the possibility of existence of stable 2D nonlinear…