In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

In this paper, the error distribution function is estimated for the single index model by the empirical distribution function and the kernel distribution function. Refined minimum average variance estimation (RMAVE) method is used for estimating single index model. We use simulation experiments to compare the two estimation methods for error distribution function with different sample sizes, the results show that the kernel distribution function is better than the empirical distribution function.

Skull image separation is one of the initial procedures used to detect brain abnormalities. In an MRI image of the brain, this process involves distinguishing the tissue that makes up the brain from the tissue that does not make up the brain. Even for experienced radiologists, separating the brain from the skull is a difficult task, and the accuracy of the results can vary quite a little from one individual to the next. Therefore, skull stripping in brain magnetic resonance volume has become increasingly popular due to the requirement for a dependable, accurate, and thorough method for processing brain datasets. Furthermore, skull stripping must be performed accurately for neuroimaging diagnostic systems since neither non-brain tissues nor

      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

The research talks about the interest and its impact on polygamy as a legitimate social psychological issue, where she talked about the concept of polygamy, and evidence of the legitimacy of polygamy, and clarify the conditions, and then touched on the great interests for which the law allowed polygamy, and mentioned some practical models in polygamy, including What is in the interest of men in pluralism, including in the interest of women in pluralism, including in the interests of both sexes in pluralism . 

Secure information transmission over the internet is becoming an important requirement in data communication. These days, authenticity, secrecy, and confidentiality are the most important concerns in securing data communication. For that reason, information hiding methods are used, such as Cryptography, Steganography and Watermarking methods, to secure data transmission, where cryptography method is used to encrypt the information in an unreadable form. At the same time, steganography covers the information within images, audio or video. Finally, watermarking is used to protect information from intruders. This paper proposed a new cryptography method by using thre

In this paper we show that if ? Xi is monotonically T2-space then each Xi is monotonically T2-space, too. Moreover, we show that if ? Xi is monotonically normal space then each Xi is monotonically normal space, too. Among these results we give a new proof to show that the monotonically T2-space property and monotonically normal space property are hereditary property and topologically property and give an example of T2-space but not monotonically T2-space.

Skull image separation is one of the initial procedures used to detect brain abnormalities. In an MRI image of the brain, this process involves distinguishing the tissue that makes up the brain from the tissue that does not make up the brain. Even for experienced radiologists, separating the brain from the skull is a difficult task, and the accuracy of the results can vary quite a little from one individual to the next. Therefore, skull stripping in brain magnetic resonance volume has become increasingly popular due to the requirement for a dependable, accurate, and thorough method for processing brain datasets. Furthermore, skull stripping must be performed accurately for neuroimaging diagnostic systems since neither no