We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. also prove same types results in a generalized setting using ring with linear topology.

WDM optical networks represent the direction to the future high capaclty wide-area network applications. By creating the optical paths between several nodes in the core networks, logical topology can be created over the physical topology. The network can dynamically change its logical topology corresponding to the changing traffic conditions. In this paper we consider the method of logical topo...

The apparent advantages of Multilevel Inverter (MLI) topologies in handling medium and high power with less loss switching lower harmonic distortion an output voltage waveform makes it better than the conventional inverter. However, MLI utilize a large number DC supplies semiconductor devices. They also have higher value total standing (TSV). Moreover, capacitor balancing problems, self-voltage...

In this paper a new class of fuzzy sets, namely r-(τi, τj)-θ-generalized fuzzy closed sets is introduced for smooth bitopological spaces. This class falls strictly in between the class of r-(τj, τi)fuzzy θ-closed sets and the class of r-(τi, τj)generalized fuzzy closed sets. Furthermore, by using the class of r-(τi, τj)-θgeneralized fuzzy closed sets we establish a new fuzzy closure operator wh...

Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we study the relationships between mset relations and mset topology. Moreover, this paper concerns generalized mset approximation spaces via topological methods ...

We discuss the generalized Plateau problem in the 3+1 dimensional Schwarzschild background. This represents the physical situation, which could for instance have appeared in the early universe, where a cosmic membrane (thin domain wall) is located near a black hole. Considering stationary axially symmetric membranes, three different membrane-topologies are possible depending on the boundary con...

In this paper, we will analyze the behavior of the Neighbor Joining algorithm on five taxa and we will show that the partition of the sample (data) space for estimation of a tree topology with five taxa into subspaces, within each of which the Neighbor Joining algorithm returns the same tree topology. A key of our method to partition the sample space is the action of the symmetric group S5 on t...