This paper proposes a holistic lexicon-reduction method for ancient and modern handwritten Arabic documents. The word shape is represented by the weighted topological signature vector (W-TSV), which encodes graph data into a low-dimensional vector space. Three directed acyclic graph (DAG) representations are proposed for Arabic word shapes, based on topological and geometrical features. Lexicon...

Let A be a partial *-algebra endowed with a topology that makes it into a locally convex topological vector space AA]. Then A is called a topological partial *-algebra if it satisses a number of conditions, which all amount to require that the topology ts with the multiplier structure of A. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of...

There is a fundamental asymmetry between algebras and their dual objects, coalgebras, namely that the dual of a coalgebra is an algebra, but the converse is only true in finite dimensions. We prove that there exists a differential graded coalgebra whose continuous dual is the differential graded algebra of differential forms. This coalgebra will be constructed as an explicit subspace of de Rham...

In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.

We denote the class of analytic functions in the unit disk D = {z ∈ C : |z| < 1} by H(D), and we think of H(D) as a topological vector space endowed with the topology of uniform convergence over compact subsets of D. Denote by S∗ the subclass of functions φ ∈ H(D) with φ(0) = 0 such that φ maps D univalently onto a domain Ω = φ(D) that is starlike with respect to the origin. That is, tφ(z) ∈ φ(...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...

Perturbing usual type B topological matter with vector (0, 1)-forms we find a topological theory which contains explicitly Kodaira-Spencer deformation theory. It is shown that, in genus zero, three-point correlation functions give the Yukawa couplings for a generic point in the moduli space of complex structures. This generalization of type B topological matter seems to be the correct framework...

Huang and Zhang 1 generalized the notion of metric space by replacing the set of real numbers by ordered Banach space, deffined a cone metric space, and established some fixed point theorems for contractive type mappings in a normal cone metric space. Subsequently, several other authors 2–5 studied the existence of common fixed point of mappings satisfying a contractive type condition in normal...