Environment perception is a crucial ability for robot’s interaction into an environment. One of the first steps in this direction is the combined problem of simultaneous localization and mapping (SLAM). A new method, called G-SLAM, is proposed, where the map is considered as a set of scattered points in the continuous space followed by a probability that states the existence of an obstacle in t...

In this paper, we give some mapping theorems on g-metrizable spaces in terms of some sequence-covering mappings, σ-mappings and π-mappings.

The continuous cohomology of Lie algebras of C-vector fields has proven to be a subject of great geometrical interest: One of its most famous applications is the construction of the Virasoro algebra as the universal central extension of the Lie algebra of vector fields on the circle. So there is the natural problem of calculating the continuous cohomology of the Lie algebra of holomorphic vecto...

Frame theory has a great revolution for recent years. This been extended from Hilbert spaces to C ∗ -modules. In this paper, we define and study the new concept of controlled continuous id="M6"> - id="M7"> K id="M8"> g -frames id="M9"> -modules establish some prope...

It is shown that a barycentrically soft compactum is necessarily an absolute retract of weight ≤ ω1. Since softness of a map is the mapping version of the property of a space to be an absolute retract, the above mentioned result can be considered as mapping version of the Ditor–Haydon Theorem stating that if P (X) is an absolute retract then the compactum X is of weight ≤ ω1 [2]. All spaces con...

Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping, consider the induced multiplication operator Mπ : F → F given by Mπ(f)(x) := π(x)f(x), f ∈ G, x ∈ coz(F). In this paper we give necessary a...

Consider the Zakharov-Shabat (or Dirac) operator Tzs on L 2(R) L2(R) with real periodic vector potential q = (q1; q2) 2 H = L 2(T) L2(T). The spectrum of Tzs is absolutely continuous and consists of intervals separated by gaps (z n ; z + n ); n 2 Z. >From the Dirichlet eigenvalues mn; n 2 Z of the Zakharov-Shabat equation with Dirichlet boundary conditions at 0; 1, the center of the gap and the...

The present paper aims to study $c$-$g$-woven for Hilbert $C^ {*} $-module spaces, first, we give some definitions and fundamental properties which will be useful introduce the notion. And also of his are given. Finally, discuss perturbation $c$-$g$-woven.

Objectives: The goal of this paper is to introduce the ideas Contra soft generalized** (briefly g**). Continuous functions and almost g**) – in topological spaces. Additionally, we discussed some its characteristics. Methods: To obtain definition contra g**- continuous functions, used previously introduced definition(1) (i.e. inverse image every closed set FQ g**-closed FP). Also, regular open ...