Related papers: Exotic Differential Structures in Dimension 2

Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional…

Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…

In this present paper, we study geometric structures of rank two prolongations of implicit second-order partial differential equations (PDEs) for two independent and one dependent variables and characterize the type of these PDEs by the…

We construct a continuously differentiable curve in the plane that can be covered by a collection of lines such that every line intersects the curve at a single point and the union of the lines has Hausdorff dimension 1. We show that for…

We investigate the uniqueness of so-called exotic structures on certain exact symplectic manifolds by looking at how their symplectic properties change under small nonexact deformations of the symplectic form. This allows us to distinguish…

In this paper, we consider a nonlinear Fuchsian type partial differential equation of the second order in the complex domain. Under a very weak assumption, we show the uniqueness of the solution. The result is applied to the problem of…

The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index class…

Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of the former. Basically, this is a feature of three-dimensional bodies. At variance,…

For a second-order elliptic equation of nondivergence form in the plane, we investigate conditions on the coefficients which imply that all strong solutions have first-order derivatives that are Lipschitz continuous or differentiable at a…

Unconventional fermions in the immensely studied topological semimetals are the source for rich exotic topological properties. Here, using symmetry analysis and first-principles calculations, we propose the coexistence of multiple…

We study tangent spaces in the setting of diffeological spaces. Several distinct tangent functors have been introduced, each of which extends the classical tangent functor from smooth manifolds. In this paper, we construct infinitely many…

We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions…

In this paper we study the existence of solutions to an isotropic differential inclusion.

We provide an approach to study exotic phenomena in relatively small 4-manifolds that captures many different exotic behaviors under one umbrella. These phenomena include exotic smooth structures on 4-manifolds with $b_2=1$, examples of…

We construct an algebra of dimension $2^{\aleph_0}$ consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain…

Geometrical properties of holonomic and non holonomic varieties defined by the Pfaff equations connected with a first order systems of differential equations are studied. The Riemann extensions of affine connected spaces for investigation…

The projection of a two dimensional planar system on the higher Landau levels of an external magnetic field is formulated in the language of the non commutative plane and leads to a new class of star products.

We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories ${\mathcal D}_{2n}$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element…

In this note we prove that every non characteristically filiform Lie algebra is endowed with an affine structure.

Some aspects of the "exotic" particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized…