In this paper we introduce a new notion of generalized metric, called i-metric. This generalization is made by changing the valuation space of the distance function. The result is an interesting distance function for the set of fuzzy numbers of Interval Type with non negative fuzzy numbers as values. This example of i-metric generates a topology in a very natural way, based on open balls. We pr...

We survey the generalized Baues problem of Billera and Sturmfels. The problem is one of discrete geometry and topology, and asks about the topology of the set of subdivisions of a certain kind of a convex polytope. Along with a discussion of most of the known results, we survey the motivation for the problem and its relation to triangulations, zonotopal tilings, monotone paths in linear program...

It is known that a generalized open Jackson queueing network after appropriate scaling (in both time and space) converges almost surely to a uid network under the uniform topology. Under the same topology, we show that the distance between the scaled queue length process of the queueing network and the uid level process of the corresponding uid network converges to zero in probability at an exp...

We show that a Dedekind-finite, semi-π-regular ring with a “nice” topology is an א0-exchange ring, and the same holds true for a strongly clean ring with a “nice” topology. We generalize the argument to show that a Dedekind-finite, semi-regular ring with a “nice” topology is a full exchange ring. Putting these results in the language of modules, we show that a cohopfian module with finite excha...

In this paper, the consensus problem of noise perturbed multi-agents following leader with stochastic switching topology is investigated. The stochastic switching topology is dependent on a continuous time Markovian process. Based on Lyapunov stability theory and generalized Itô formula, the sufficient condition is given to guarantee the mean square consensus of all the agents following the vir...

In this paper we propose new three-input XOR and three-input XNOR gate based on generalized threshold gate (GTG) topology. The GTG topology is main part is monostable-bistable logic element (MOBILE). The proposed gates use fewer elements count in comparison with other implementations which utilize MOBILE as a main structure. By exploiting the new three-input XOR gate and a carry generator, we p...

In generalized tree alignment problem, we are given a set S of k biologically related sequences and we are interested in a minimum cost evolutionary tree for S. In many instances of this problem partial topology of the phylogenetic tree for S is known. In such instances, we would like to make use of this knowledge to restrict the tree topologies that we consider and construct a biologically rel...

in this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎we study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎

In this paper, the consensus problem of descriptor multi-agent systems is considered. Each agent’s dynamics is given in general form of continuous-time linear descriptor system, and the communication topology among the agents is assumed to be directed under fixed topology case and balanced under switching topology case. To solve the multi-agent consensus problem, three kinds of distributed obse...

In this paper we establish a direct connection between stable approximate unitary equivalence for ∗-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity assumptions. To this purpose we show that a topology on the Kasparov groups can be defined in terms of approximate unitary equivalence for Cuntz pairs and that this to...