The swift evolution of biofeedback control has opened up new voyages in the field of biomedical engineering and provides powerful perspective to researchers for viewing many real problems such as tumor, surgeries of sensitive parts of body, control of glucose level of a patient, heart diseases and brain disorders associated with humans. Consequently, mysterious and intricate biological phenomena can now be studied and investigated by utilizing the knowledge of control and nonlinear dynamics of physical systems. The emerging theory of biofeedback control can be more fruitful for understanding the brain functioning in order to cope with various neural disorders. Neuron, being an innate sophisticated structural entity of nervous system, plays an imperative role owing to its chief biophysical features and key mechanism of operations, for effective transmission of neuronal signals to the brain and the muscles. The probe of neuron doctrine gives an insight into understanding of brain information processing and information transmittance among neurons which may further ii corroborate a close relevance between the synchronization of neural systems and the information of cerebral process. Thus, neuronal synchronization under deep brain stimulation has become a potential application in the study of clinical treatment mechanisms for neurodegenerative disorders. Moreover, the famous FitzHugh-Nagumo (FHN) model under external electrical stimulation (EES; e.g. deep brain stimulation), is extensively used as synchronization study tool for its utility in symbolizing the dynamical behavior of neurons. The embryonic impact of biofeedback control in improving external therapies for patients suffering cognitive disorders such as Parkinson’s disease, epilepsy and dystonia is the main motivation to this research work. “This thesis presents an efficient novel mechanism for synchronization of two different, chaotic and distant coupled neurons with unknown parameters subjected to external electrical stimulation and disturbances” This research investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons iii of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme to cope with infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via simulation results. Keywords: Chaos synchronization; FitzHugh-Nagumo model; External electrical stimulation; Robust adaptive control; Lyapunov function.
Former Egyptian Muḥaddithīn of the each centuries have played a well-regarded, venerated and esteemed role in services of Ḥadīth and its sciences. Their outstanding contribution in this regard has been appreciated in each century of Islamic history. Those Muḥaddithīn have left valuable work on Ḥadīth and its sciences in their popular and basic sources of Ḥadīth for coming generations. Muḥaddithīn of 20th century were not less than the former in their involvement in the field of Hadith. Their dynamic and marvelous efforts are needed to be unveiled for scholars and students of Ḥadīth. Al-shaykh Abdur Raḥmān al Banna Al sāʻātī is known as one of the prominent Egyptian Muḥaddithīn in 20th century. He made extraordinary efforts in the field of Ḥadīth and its sciences through compiling and writing various remarkable books in this regard. His marvelous work in Alfatḥ Al-Rabbānī li Tartīb Musnad Al-Imām Aḥmad bin Hanbal Al-Shaybānī on Musnad Imām Aḥmad bin Hanbal in its rearranging, categorizing and organizing its Ḥadīth is deserved to be cherished and focused on due to its significance and importance in the field of Ḥadīth. He is the first Muḥaddith who presented the Aḥādīth of Musnad in seven outstanding chapters to facilitate the researchers in their accessing to the main theme of the Musnad. In this paper the life sketch of Al-Shayk Abdur Raḥmān, his scholarly contribution in the field of Ḥadīth and his methodology in his renowned book alfatḥ al-Rabbānī has been discussed and highlighted its valuable aspects.
A Researched and Implemented Analysis of the Meaning of Command (AMR) and Forbiddance (NAHI) (According to
the opinions of ulame e usool)
The thesis is in the field of Islamic law and within Islamic law it is specialized in the field of Usool e Fiqh. The detailed
study is based on the concept of Amr and Nahi and their meaning and application under the rulings of Usool e Fiqh.
Mostly Ahkam of Shariah in Islam hava been given in the form of those things which are under the category of
commands (Amr) and forbiddance (Nahi). That is why it is necessary to research that which is a command and
forbiddance. In this thesis firstly, the literal meanings of commands and forbiddance has been researched. Through this
research it has been proved that the literal meaning of commands (Amr) are related to "Nisbat e Irsalya or Ba'asiya
which has means the nature of the relationship between commander and commanded is to act in one direction. It has
also been proved that forbiddance (Nahi) is related to "Nisbat e Zajariya or Imsakya" which means the nature of the
relationship between the forbidder and the forbade is to refrain from acting in one direction. Also certain phrases have
been used to describe the meaning of command (Amr) and forbiddance (Nahi) which have also been researched and
explained as to their relationship to providing the meaning of Amr and Nahi.
After establishing the connection of Amr and Nisbat e Irsalya, the concept has been further researched on how to prove
the meaning of Amr for Wujoob, Istihbab, and Ibaha which are also part of Ahkam e Shariah. Similarly for Nahi it has
also been researched how to prove its meaning for Hurmat and Karaha which are also part of ahkam e shariah.
We have also discussed in the final chapter some of the different but still logical meanings of and applications of Amr
and Nahi in different circumstances which are different to the literal meaning and the rules of interpretation as given
above but still within the meaning of Ahkam e Shariah.