Related papers: Construction of 2nd stage shape invariant potentia…
In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…
Infinite time Turing machines are extended in several ways to allow for iterated oracle calls. The expressive power of these machines is discussed and in some cases determined.
We show that, for any given dimension $d\geq 2$, the range of distinct possible designs for periodic frameworks with auxetic capabilities is infinite. We rely on a purely geometric approach to auxetic trajectories developed within our…
We introduce the notion of iterated group extensions, which, roughly speaking, is what one obtains by forming a group extension of a group extension. We interpret iterated extensions in terms of group cohomology, in the same way as…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
The group $G_2$ of invertible affine transformations of $\mathbb{R}^2$ has, up to equivalence, one square--integrable representation. Two new realizations of this representation are presented and novel continuous wavelet transforms, acting…
In this article we study convex non-autonomous variational problems with differential forms and corresponding function spaces. We introduce a general framework for constructing counterexamples to the Lavrentiev gap, which we apply to…
An overview of the recent developments in plurifine potential theory.
A Born--Infeld theory describing a $D2$--brane coupled to a 3--form RR potential is reconsidered and a new type of static solution is obtained which is even stable.
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
This paper continues the development of the theory of finite localities that was begun in "Finite Localities I". The emphasis in this Part 2.
We continue the study of random continued fraction expansions, generated by random application of the Gauss and the R\'enyi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous…
This paper is the sequel of the paper "Continuity of volumes on arithmetic varieties", in which we established the arithmetic volume function of smooth hermitian Q-invertible sheaves and proved its continuity. The continuity of the volume…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
In this paper we investigate complex dynamics in infinite dimensions.
In this paper we study a quintessence scalar field in a potential exponentially decreasing with e-folding number, and show that the universe is currently undergoing an accelerated expansion and could probably remain accelerating…
We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the…
We show that hereditarily indecomposable spaces can be characterized by a special instance of the Intermediate Value Theorem in their rings of continuous functions.
We explain the exact meaning of a statement we made in a previous paper on invariants, namely that a complex-valued function of the data of the functional equation of an $L$-function is an invariant if and only if it is stable under the…
An infinite family of nonschurian separable association schemes is constructed.