For any weightable quasi-metric space (X, d) having a maximum with respect to the associated order ≤d, the notion of the quasi-metric of complexity convergence on the the function space (equivalently, the space of sequences) X, is introduced and studied.We observe that its induced quasi-uniformity is finer than the quasi-uniformity of pointwise convergence and weaker than the quasi-uniformity o...

We construct a quasi-Banach space which cannot be given an equivalent plurisubharmonic quasi-norm, but such that it has a quotient by a onedimensional space which is a Banach space. We then use this example to construct a compact convex set in a quasi-Banach space which cannot be atfinely embedded into the space L0 of all measurable functions.

A realization of a graph G is pair (G,p) where p maps the vertices into Euclidean space Rd. The injective if and quasi-injective for each edge G, endpoints to different points in space. globally rigid any (G,q) Rd with same lengths congruent (G,p). In this paper we characterize graphs that have an (quasi-injective, respectively) non-globally R1, show problem recognizing these NP-complete both c...

Let a be a positive real number, a < 1/2. A standard construction of a self-similar Cantor set in the plane starts with the unit square [0, 1]× [0, 1], replaces it with the four corner squares with sidelength a, then replaces each of those squares with their four corner squares of sidelength a, and so on. At the nth stage one has 4 squares with sidelength a, and the resulting Cantor set has Hau...

We show that the Hamiltonian dynamics of the self-interacting, abelian p-form theory in D = 2p+ 2 dimensional space-time gives rise to the quasi-local structure. Roughly speaking, it means that the field energy is localized but on closed 2p-dimensional surfaces (quasi-localised). From the mathematical point of view this approach is implied by the boundary value problem for the corresponding fie...

Many parallels have been drawn between the geometric properties of the Teichmüller space of a Riemann surface, and those of complete, negatively curved spaces (see for example [B, K2, W]). This paper investigates one such parallel – the contracting properties of certain projections to geodesics. We will use the Teichmüller metric throughout the paper (the other famous metric on Teichmüller spac...

A novel nonlinear scale space framework is proposed for the purpose of multi-scale image representation. The scale space decomposition problem is formulated as a general Bayesian least-squares estimation problem. A quasi-random density estimation approach is introduced for estimating the posterior distribution between consecutive scale space realizations. In addition, the application of the pro...

We show how to construct stable quasi-interpolation schemes in the bivariate spline spaces S r d (4) with d 3r+2 which achieve optimal approximation order. In addition to treating the usual max norm, we also give results in the L p norms, and show that the methods also approximate derivatives to optimal order. We pay special attention to the approximation constants, and show that they depend on...

We consider several distances between two sets of points, which are modifications of the Hausdorff metric, and apply them to describe some fractals such as δ-quasi-self-similar sets, and some other geometric notions in Euclidean space, such as tilings with quasi-prototiles and patterns with quasi-motifs. For the δ-quasi-self-similar sets satisfying the open set condition we obtain the same resu...