In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames  are given.  A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is ...

In this paper, we use soft linear operators to introduce the notion of discrete frames on Hilbert spaces, which extends classical spaces context algebraic structures sets. Among other results, show that frame operator associated a is bounded, self-adjoint, invertible and with bounded inverse. Furthermore, prove every element in space satisfies decomposition theorem. This theoretical framework p...

The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan’s method of moving frames. The conjecture of Tremblay and Winternitz [J.Phys. A: Math. Gen., 2001, V.34, 9085] on the number and form of elements in the bases i...

In this paper we present a complete quantifier-free axiomatization of several logics on region-based theory of space based on contact relation and connectedness predicates. We prove completeness theorems for the logics in question with respect to three different semantics: algebraic – with respect to several important classes of contact algebras, topological – based on the contact algebras over...

Framings provide a way to construct Quillen functors from simplicial sets to any given model category. A more structured setup studies stable frames giving Quillen functors from spectra to stable model categories. We will investigate how this is compatible with Bousfield localisation to gain insight into the deeper structure of the stable homotopy category. We further show how these techniques ...

This paper proposes an algebra T (T,≻) which can be used to express kinematic transformations in chains of frames that move in threedimensional space. The algebraic structure of T will be discussed end the most relevant properties will be presented. This algebra can be translated into a set of algorithms that fit well into a compact formalism, by exploiting the operator-overloading feature of m...

A new method is presented for solving equivalence problems for the extended jet of nite order of the scale space corresponding to a 2-dimensional input image and the groups of spatially homogeneous aane and orthogonal transformations of local cartesian coordinate frames. By means of this method complete and irreducible sets of algebraic invariants are found that may describe any local and (or) ...

Dual quaternion algebra and its application to robotics have attracted considerable interest in the last two decades. quaternions great geometric appeal easily capture physical phenomena inside an algebraic framework, which is useful for both robot modeling control. Mathematical objects, such as points, lines, planes, infinite cylinders, spheres, coordinate systems, twists, wrenches, are all we...

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.