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Home > Impact of Fta on Total Trade and Trade Balance of Member Countries A Case Study of Afta, Nafta, and Safta

Impact of Fta on Total Trade and Trade Balance of Member Countries A Case Study of Afta, Nafta, and Safta

Thesis Info

Author

Muhammad Rizwan Manzoor

Supervisor

Muhammad Mazhar Iqbal

Department

Department of Economics, QAU

Program

Mphil

Institute

Quaid-i-Azam University

Institute Type

Public

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2014

Thesis Completion Status

Completed

Page

59

Subject

Economics

Language

English

Other

Call No: DISS/M. Phil/ Eco / 719

Added

2021-02-17 19:49:13

Modified

2023-02-19 12:33:56

ARI ID

1676717362205

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86. Al-Tariq/The Star of Brilliant Brightness

86. Al-Tariq/The Star of Brilliant Brightness

I/We begin by the Blessed Name of Allah

The Immensely Merciful to all, The Infinitely Compassionate to everyone.

86:01
a. By the celestial realm and the Tariq.

86:02
a. And what may enable you to comprehend the Tariq?

86:03
a. Tariq is the star of brilliant brightness before dawn.

86:04
a. There is a guardian angel set up over every human being.

86:05
a. So let every human being reflect of what insignificant substance he is created -

86:06
a. - he is created out of a mingling of seminal and ovarian spurting fluid,

86:07
a. emerging from between the male’s hip and the female’s pelvis.

86:08
a. Surely, HE is Able to bring him back to life-

86:09
a. - at the Time when all secrets of his deeds, dealings and speech will be exposed and judged,

86:10
a. then he will have no power to hide them, and
b. no supporter to help him avoid the consequences.

86:11
a. By the sky clouds giving rain, time and again,

86:12
a. and the land/earth too splitting time and again -
b. for gushing of springs and growth of vegetation.
c. and human beings during the Time of Resurrection.

728 Surah 86 * Al-Tariq

86:13
a. Indeed, this - Qur’an - is the Decisive Word!

86:14
a. And it is not for amusement.

86:15
a. Indeed, they are devising a plot/false arguments against The Prophet,

86:16

Components of Valid Interrogation Techniques under Islamic Law

Valid interrogation of the accused is an art or skill in today’s modern world. The law and techniques of interrogation varies in the developed and developing world. Similarly, the Islamic law is not silent about the techniques of valid interrogation. There are specific rules and procedures for the interrogation of an accused either a criminal, an enemy, a spy or a war prisoner. This paper gives a detailed analysis about the principles and procedures of a valid interrogation process in Islam and its computability with the International Human Rights standards of interrogations. The paper argue that understanding the psychic-analytical niceties of interrogation helps an investigator to reach the truth. The paper finds that Islamic law gives full protection and safeguard to the rights of persons under custody and restrict the authorities to follow free and fair interrogation for ensuring justice. In this regard Islam presents a balanced view of the rights of the persons under custody and the executives exercise of legitimate force for interrogation. Islam strongly forbids torture and other inhuman ways of interrogation.

Homomorphic Images of Generalized Triangle Subgroups of Psl 2, Z

The modular group generated by two linear fractional transformations, u : z 7! 1 z and v : z 7! z1 z , satisfying the relations u2 = v3 = 1 [46]. The linear transformation t : z 7! 1 z inverts u and v, i,e, t2 = (vt)2 = (ut)2 = 1 and extends PSL(2; Z) to PGL(2;Z). In [72] a condition for the existence of t is explained. G. Higman introduced coset diagrams for.PSL(2; Z) and PGL(2;Z): Since then, these have been used in several ways, particularly for nding the subgroups which arise as homomorphic images or quotients of PGL(2;Z). The coset diagrams of the action of PSL(2;Z) represent permutation representations of homomorphic images. In these coset diagrams the three cycles of the homomorphic image of v, say v, are represented by small triangles whose vertices are permuted counter-clockwise, any two vertices which are interchanged by homomorphic image of u, say u, are joined by an edge, and t is denoted by symmetry along the vertical line. The xed points of u and v, if they exist are denoted by heavy dots. The xed points of t lies on the vertical line of symmetry. A real quadratic irrational eld is denoted by Qpd, where d is a square free positive integer. If =a1 + b1pdc1 is an element of Qpd, where a1;b1;c1;d; are integers, then has a unique representation such that a1;a2 1 dc1 and c1 are relatively prime. It is possible that ; and and its algebraic conjugate = a1 pdc1 have opposite signs. In this case is called an ambiguous number by Q. Mushtaq in [69]. The coset diagrams of the action of PSL(2;Z) on Qpddepict interesting results. It is shown in [69] that for a xed value of d, there is only one circuit in the coset diagram of the orbit, corresponding to each .Any homomorphism 1 : PGL(2;Z) ! PGL(2;q) give rise to an action on PL(Fq): We denote the generators ()1; ()1 and (t)1 by ; and t: If neither of the generators , and t lies in the kernel of 1; so that , and t are of order 2, 3 and 2 respectively, then 1 is said to be a non-degenerate homomorphism: In addition to these relations, if another relation ( )k = 1 is satised by it, then it has been proved in [74] that the conjugacy classes of non-degenerate homomorphisms of PGL(2;Z) into PGL(2;q) correspond into one to one way with the conjugacy classes of 1 and an element of Fq: That is, the actions of PGL(2;Z) on PL(Fq) are parametrized by the elements of Fq: This further means that there is a unique coset diagram, for each conjugacy class corresponding to 2 Fq. Finally, by assigning a parameter 2 Fq to the conjugacy class of 1, there exists a polynomial f() such that for each root i of this polynomial, a triplet ; ; t 2 PGL(2;q) satises the relations of the triangle group (2;3;k) =D ; ; t : 2 = 3 = ( t)2 = ( )k = ( t)2 = ( t)2 = 1E: Hence, we can obtain the triangle groups (2;3;k) through the process of parametrization. Thegeneralizedtrianglegrouphasthepresentationu;v : ur;vs;Wk;where r; s; k are integers greater than 1, and W = u1v1:::ukvk, where k > 1;0 < i < r and 0 < i < s for all i. These groups are obtained by natural generalization of (r;s;k) dened by the presentationsDu;v : ur = vs = (uv)k = 1E, where r;s and k are integers greater than one. It was shown in [37] that G is innite if 1 r + 1 s + 1 k 1 provided r 3 or k 3 and s 6, or (r; s;k) = (4;5;2): This was generalized in [4], where it was shown that G is innite whenever 1 r + 1 s + 1 k 1 . A proof of this last fact can be seen in [101].A generalized triangle group may be innite when 1 r + 1 s + 1 k > 1. The complete classication of nite generalized triangle groups is given in 1995 by J. Howie in [39] and later by L. Levai, G. Rosenberger, and B. Souvignier in [57] which are fourteen in number. As there are fourteen, generalized triangle groups classied as nite [39], our area of interest is the set of groups which are homomorphic images or quotients of PSL(2;Z). Out of these fourteen only eight groups are quotients of the modular group. In this study, we have extended parametrization of the action of PSL(2;Z) on PL(Fp), where p is a prime number, to obtain the nite generalized triangle groupsD 2 = 3 = 23 = 1E by this parametrization. By parametrization of action of PGL(2;Z) on PL(Fp) we have obtained the coset diagrams of D 2 = 3 = 23 = 1E for all 2 Fp. This thesis is comprised of six chapters. The rst chapter consists of some basic denitions and concepts along with examples. We have given brief introduction of linear groups, the modular and the extended modular group, real quadratic irrational elds, nite elds, coset diagrams, triangle groups, and generalized triangle groups. In the second chapter, we show that entries of a matrix representing the element g =(v)m1v2m2l where l 1 of PSL(2;Z) =;v : 2 = v3 = 1are denominators of the convergents of the continued fractions related to the circuits of type (m1;m2); for all m1;m2 2N: We also investigate xed points of a particular class of circuits of type (m1;m2) and identify location of the Pisot numbers in a circuit of a coset diagram of the action of PSL(2;Z) on Qpd[f1g, where d is a non-square positive integer.In the third chapter we attempt to classify all those subgroups of the homomor phic image of PSL(2;Z) which are depicted by coset diagrams containing circuits of the type (m1; m2). In the fourth chapter we devise a special parametrization of the action of modular group PSL(2;Z) on PL(Fp), where p is prime, to obtain the generalized triangle groups D 2 = 3 = 2k = 1E and by parametrization we obtain the coset diagrams of D 2 = 3 = 2k = 1E for all 2 Fp. In the fth chapter we investigate the action of PSL(2;Z) on PL(F7n) for di⁄erent values of n, where n 2 N, which yields PSL(2;7). The coset diagrams for this action are obtained, by which the transitivity of the action is inspected in detail by nding all the orbits of the action. The orbits of the coset diagrams and the structure of prototypical D168 Schwarzite [48], are closely related to each other. So, we investigate in detail the relation of these coset diagram with the carbon allotrope structures with negative curvature D168 Schwarzite. Their relation reveals that the diagrammatic structure of these orbits is similar to the structure of hypothetical carbon allotrope D56 Protoschwarzite which has a C56 unit cell. In the last chapter, we investigate the actions of the modular group PSL(2;Z) on PL(F11m) for di⁄erent values of m; where m 2 N and draw coset diagrams for various orbits and prove some interesting results regarding the number of orbits that occur.