70. Al-M’arij/The Ascensions
I/We begin by the Blessed Name of Allah
The Immensely Merciful to all, The Infinitely Compassionate to everyone.
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a. A disbelieving questioner mockingly asked The Prophet about the punishment in the realm of the Hereafter which is bound to befall -
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a. – the disbelievers.
b. And no one can prevent the coming of it -
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a. as it is coming from Allah.
b. And, Allah is Rabb - The Lord - The Lord of the Ascensions.
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a. Ascensions to where the angels and the spirit take a day to ascend,
b. where duration of a day would be equivalent to fifty thousand years of your count.
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a. So O The Prophet!
b. Be patient with a gracious patience.
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a. They perceive this punishment to be far away,
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a. while WE see it as quite near at hand as an inevitable reality -
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a. it will befall at the Time when the celestial realm will be like molten copper,
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a. and the mountains will be floating about in the air like flakes of wool/yarn,
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a. and no close friend will ask any other close friend about his fate,
b. for everyone will be preoccupied with his own predicament -
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a. even though they could see one another.
b. The criminal would wish to ransom himself from the inevitable punishment of that Time by
offering his own children,
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a. and even his spouse and his brother/siblings,
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a. and his relatives...
The article titled: the rights of foetus in Islamic law, aims at explaining the rights of foetus without discussing different theories of the scholars in this regards. It also defines the foetus and gives literal and technical meanings besides different stages of foetus mentioned in the Holy Quran and the Hadith. The article explains the rights granted to foetus in the lights of serah before birth and these rights are a binding on the concerned people and violation of foetus’ s rights is prohibited and it is a cognizable offence. The article also discusses the attitude of west regarding foetus rights as the western society is totally ignorant about the rights of foetus and their legislation in this regard is contrary and several western laws are causing the violation of foetus’s rights. Thus, the champions of human’s rights are blind to the rights of foetus which is foundation and beginning of human life and first step for the human race. It is that has given these rights to mankind for the first time and informed human being about their rights through the first human’s rights charter given at the time of the Noble Prophet {blessing of Allah and peace be upon him}. This charter is known as the charter of Madina between the Muslims and the Jews. The article concludes: mankind cannot be protected unless the sperm of man is protected and foetus is protected in the womb of the mother from abortion because these are the future of humanity.
Let J G denote the binomial edge ideal of a connected undirected graph G on n vertices. This is the ideal generated by the binomials x i y j −x j y i , 1 ≤ i < j ≤ n, in the polynomial ring S = K[x 1 , . . . , x n , y 1 , . . . , y n ] where {i, j} is an edge of G. Our aim in this thesis is to compute certain algebraic invariants like dimension, depth, system of parameters, regular sequence, Hilbert series and multiplicity of J G of some particular classes of binomial edge ideals of graphs. A large amount of information of an ideal is carried by its minimal free resolution. So we give information on the minimal free resolution on certain binomial edge ideals. We also give a complete description of the structure of the modules of deficiencies of binomial edge ideals of some classes of graphs. A generalization of the concept of a Cohen-Macaulay ring was introduced by S. Goto [7] under the name approximately Cohen-Macaulay. In this thesis we collect a few graphs G such that the associated ring S/J G is approximately Cohen-Macaulay. We also characterize all the trees that are approximately Cohen-Macaulay. As more generalized notion than approximately Cohen-Macaulay we also study se- quentially Cohen-Macaulay property for binomial edge ideals. We give a nice con- struction principle in this topic. ̃ on n vertices has the property that S/J̃ is a Cohen-Macaulay The complete graph G G domain with a 1-linear resolution. As one of the main results we clarify the structure of S/J K m,n , where K m,n denotes the complete bipartite graph.