Geometric methods proposed by Stallings [17] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [1, 6, 10, 11, 15, 16, 20]. In the present paper we employ the generalized Stallings’ folding method developed in [12] to introduce a procedure, which given a subgroup H of a free product ...

Let M be the moduli space of generalized parabolic bundles (GPBs) of rank r and degree d on a smooth curve X . Let ML̄ be the closure of its subset consisting of GPBs with fixed determinant L̄. We define a moduli functor for which ML̄ is the coarse moduli scheme. Using the correspondence between GPBs on X and torsion-free sheaves on a nodal curve Y of which X is a desingularization, we show that M...

In this paper, Generalized Aggregated Uncertainty measure 2 (GAU2), as a newuncertainty measure, is considered to evaluate uncertainty in a localization problem in which cameras’images are used. The theory that is applied to a hierarchical structure for a decision making to combinecameras’ images is Dezert-Smarandache theory. To evaluate decisions, an analysis of uncertainty isexecuted at every...

If P is a p-group for some prime p we shall write M (P ) to denote the set of all maximal subgroups of P and Md(P ) = {P1, ..., Pd} to denote any set of maximal subgroups of P such that ∩d i=1 Pi = Φ(P ) and d is as small as possible. In this paper, the structure of a finite group G under some assumptions on the c-normal or s-quasinormally embedded subgroups in Md(P ), for each prime p, and Syl...

The generalized Mordell-Lang conjecture (GML) is the statement that the irreducible components of the Zariski closure of a subset of a group of finite rank inside a semi-abelian variety are translates of closed algebraic subgroups. In [6], M. McQuillan gave a proof of this statement. We revisit his proof, indicating some simplifications. This text contains a complete elementary proof of the fac...

Vagueness is a common human knowledge and linguistic phenomenon, typically manifested by predicates that lack clear applicability conditions and boundaries such as High, Expert or Bad. In the context of ontologies and semantic data, the usage of such predicates within ontology element definitions (classes, relations etc.) can hamper the latter’s quality, primarily in terms of shareability and m...

We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a pushout involving a generalized triangle group. Using the theory of generalized triangle groups, we extend the range of conditions under which a number of results for one-relator products of groups, such as the...

Soft set theory, proposed by Molodtsov has been regarded as an effective mathematical tool to deal with uncertainties. Vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of [0, 1]. Such a set is characterized by a truth-membership function and a falsemembership function. Thus, a vague set is actually a form of fuzzy set, albeit a more ...