Introduction
The Divine Promise to the human species at the time of its exit from the heavens – Q.02:38- 39 – was held through ages of human history. It started with Adam, continued through Enoch, Noah, Abraham, Isaac, Moses, Jesus and culminated with Muhammad. May Allah’s peace and blessings be upon them.
The foundations of Faith are, prima facie, based on the Absolute Supremacy of One Divine Being. The teachings of all Scriptures came from the same Divine Source with the purpose of providing guidance for a life of righteousness within societies along a Straight and Optimal Path
– Qur’an 06:126, 07:16; and The Torah/Proverbs 4:23-27.
The Qur’an is the grand finale of all Divine Revelations and the Ultimate Truth. Allah, The Exalted and The Almighty, guaranteed to preserve its Sacred Arabic Text in its entirety and original form safe from any satanic change – Q.15:09.
Enriched with themes, history, law, images, symbols, language, recitation and a unique literary style – it is a master piece of a revelation that has been bestowed on humanity as a matchless text signifying the very name it carries – Al Kitab – The Book.
As The Qur’an was being revealed on to the last of the Prophets - Prophet Muhammad, in the Arabic language, he would dictate it to his appointed companions to serve as scribes over the 23- year period of its phased-revelation.
The Qur’an contains the narratives of past nations and the events of future generations to facilitate comprehension of the meaning and value of the Qur’anic Message. It also sets out examples and analogies for people so that they may reflect and take heed - Q.39:27. Its message transcends...
Muhammad’s (SAW life is fully reserved and recorded in history. It has been established beyond a shadow of doubt that not only the major and significant events of his life but even the minutest details of his life are also painstakingly preserved by the Muslims. In spite of the availability of abundant authentic documents concerning Muhammad’s (SAW) life, sayings and deeds, some critics of Islam stubbornly refuse to believe in his historicity. Robert Spencer is one such critic who maintains that Muhammad’s (SAW) value is nothing more than a fictional or mythological figure. This article is an attempt to prove the existence of Muhammad (SAW) in contemporary non-Muslims sources. The article is divided into three major parts: the first part of the paper throws light on how much emphasis Muslims lay on historical authenticity of Muhammad (SAW), in the second part of the paper views and doubts of prominent like orientalists Spencer concerning Muhammad’s (SAW) historical authenticity have been summarized, whereas the third part presents Robert Spencer’s views in the same connection and endeavors to refute his views and approach drawing on contemporary non-Muslim Sources.
Multiple hypothesis testing is an important topic in statistics. Therefore, the problem addressed in this thesis is an important one. It is also a topic in which it is difficult to make a significant improvement, for various reasons. One reason is that often different users may have different objectives and with multiple hypotheses there is no unique objective function. In the thesis is recognized this fact and as the objective functions, estimated the quality of made decisions, are used minimization of the probabilities of the errors of one kind at restrictions of the probabilities of the errors of second kind. Such approach is a new one which causes the uniqueness of the regions of acceptance of hypotheses and, consequently, improves the quality of hypothesis testing. Thus conditional Bayesian tasks of testing many hypotheses are stated and solved. The concept of conditionality is used for designation of the fact that the Bayesian tasks are stated as conditional optimization problems where the probabilities of one- type errors are restricted and, under such conditions, the probabilities of second-type errors are minimized. The properties of obtained decision rules are investigated, and, on their basis, it is shown that the classical Bayesian problem of hypotheses testing is a special case of the considered. The calculation results of concrete examples have shown that the qualities of offered conditional tasks surpass the quality of the classical Bayesian task. They completely confirm the results of theoretical investigations. The convenience, simplicity and naturalness of introduction of similar gradation Kiefer, viiviii (1977) by the level of certainty of hypotheses testing on the basis of concrete obser- vation result are shown in offered conditional tasks. Quasi-optimal procedures of many hypotheses testing are offered. They signif- icantly simplify Bayesian algorithms of hypotheses testing and computation of the risk function. The obtained general solutions are reduced to concrete formulae for multivariate normal distribution of probabilities. The methods of approximate com- putation of the risk functions in Bayesian tasks of testing many hypotheses are of- fered. The properties and interrelations of the developed methods and algorithms are investigated. On the basis of simulation, the validity of the obtained results and conclusions made is shown. The results of sensitivity analysis of the conditional Bayesian problems are given and their advantages and drawbacks are considered.