相关论文: Rhythmos, Diathige, Trope

We consider Hamiltonian diffeomorphisms of the Euclidean space, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have…

Differential calculus on metric spaces is contained in the algebraic study of normed groupoids with $\delta$-structures. Algebraic study of normed groups endowed with dilatation structures is contained in the differential calculus on metric…

We give a survey of Darboux type theorems in multisymplectic geometry. These theorems establish when a closed differential form of a certain type admits a constant-coefficient expression in some local coordinate system. Beyond the classical…

The groundstate configuration and the eigenmodes of two parallel two-dimensional classical atoms are obtained as function of the inter-atomic distance (d). The classical particles are confined by identical harmonic wells and repel each…

The analogy of the nonlinear dislocation theory in crystals and the electromagnetism theory is studied. The nature of some quantities is discussed.

Since black holes lack a straightforward notion of geometrical volume due to their event horizon structure and coordinate dependence, various approaches have been proposed to introduce a meaningful geometric and thermodynamic volume. In…

Let P be an object such as tiling, Delone set and weighted Dirac comb. There corresponds a dynamical system to P, called the corresponding dynamical system. Such dynamical systems are geometric analogues of symbolic dynamics. It is…

Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the…

We study geometric inequalities for the circumradius and diameter with respect to general gauges, partly also involving the inradius and the Minkowski asymmetry. There are a number of options for defining the diameter of a convex body that…

Amorphous solids are mechanically rigid while possessing a disordered structure similar to that of dense liquids. Recent research indicates that dynamical heterogeneity, spatio-temporal fluctuations in local dynamical behavior, might help…

Deforming the algebraic structure of geometric algebra on the phase space with a Moyal product leads naturally to supersymmetric quantum mechanics in the star product formalism.

Finite size effects in the multicriticity point and boundaries between phases are calculated. There are anomalous large finite size effects on the boundary of ferromagnetic phase with paramagnetic or spin-glass. Multicriticity point is not…

We survey mathematical properties of quasicrystals, first from the point of view of harmonic analysis, then from the point of view of morphic and automatic sequences. Nous proposons un tour d'horizon de propri\'et\'es math\'ematiques des…

New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…

Nonmagnetic and spherically symmetric dielectric material media are investigated in their generality as analogue models, in the domains of geometrical optics, for a few relevant static and spherically symmetric solutions of gravitation,…

Differences between measured nuclear masses and those calculated using the Finite Range Droplet Model are analyzed. It is shown that they have a well defined, clearly correlated oscillatory component as a function of the proton and neutron…

Quasifuchsian hyperbolic manifolds, or more generally convex co-compact hyperbolic manifolds, have infinite volume, but they have a well-defined ``renormalized'' volume. We outline some relations between this renormalized volume and the…

A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional property that the set of all its simplices…

This preprint deals with the symmetry of parametrized families of systems and the changes therein as the parameter changes. There are (at least ?) two kinds of symmetry: generic and specific which behave in almost totally opposite ways as…

The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…