Abstract: A topological space is said to be epi -regular if a coarser topology

on exists such that

is

-regular. In this article we introduce and implement this property and give some examples to

show the relationships between epi -regular, epiregular, epinormal, submetrizable semiregular and Almost -

normal (almost -normal)..

Keywords: Epiregular, Epi -regular, Epinormal, Semiregular, Submetrizable, and Almost -normal (almost

-normal).

A novel non-blind audio watermarking algorithm, using chirp z-transform in combination with discrete wavelet transform and singular value decomposition, is presented in this paper. In the proposed method, a watermark audio signal (about 13 seconds in length) is hidden into an original audio signal (about 51 seconds in length) by applying discrete wavelet transform, chirp z-transform, and singular value decomposition. The effectiveness of the proposed algorithm has been tested using signal-to-noise ratio, objective difference grade (ODG), and normalised cross- correlation of watermarked audio signal under various common audio attacks. Experimental results demonstrate that the algorithm has a high capacity (352.8 kbps), without significant perceptual distortion (ODG > -0.29) and provides good robustness against common audio attacks, including: re-sampling, echo addition, MP3 compression, additive white Gaussian noise, re- quantisation, cutting, and low-pass filtering. This algorithm has a high capacity and excellent audio quality compared with other audio watermarking algorithms.

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MANETs is a type of Mobile Ad Hoc Networks and it contains a set of nodes that do not need central management to communicate with each other because each node can act as a sender, receiver and router at the same time. All these nodes can perform self-configuration. The ad hoc stationary or mobile networks face many challenges such as limited bandwidth, congestion and data transfer speed. Therefore, it is extremely important to develop an intelligent routing protocol to encounter these challenges. An evaluation study is also important to perform the backoff contention window effectively in order to know the obstacles and avoid them. This paper concentrates on the performance of backoff contention window using the main routing protocols such as DSR, DSDV and AODV for MANETs networks in crowded areas with random movement. The important parameters which include network throughput …

 Cognitive radio (CR) is a form of wireless communication in which a transceiver can intelligently detect which communication channels are in use. Upon the result of the detection, the system instantly moves into vacant channels while avoiding occupied ones. To improve the capacity of CR systems, the unused sub-channels by primary user (PU) could be aggregated. However, when secondary user (SU) system aggregates more channels, more collisions may occur. This collision occurs due to the PU backto reuse its channels during SU transmission on them. Moreover, there are other reasons for collisions as misdetection which happens when wrongly detected absence of PU may occur as well.

In this paper a Proposed Channel Aggregation Algorithm is introduced in which the CR data rate is maximized by aggregating multiple channels for the SU while satisfying the minimum collision requirements. Moreover, channel capacity is maximized under collision constraints. Matlab simulation is conducted to implement the proposed algorithm and the rustles showed that, very low collision probability was observed as compared to previous work. The capacity of CR was also improved as well.