For any graph X with the adjacency matrix A, the transition matrix of the continuous-time quantum walk at time t is given by the matrix-valued function H X (t) = e itA . We say that there is perfect state transfer in X from the vertex u to the vertex v at time τ if |H X (τ ) u,v | = 1. It is an important problem to determine whether perfect state transfers can happen on a given family of graphs. In this paper we characterize all the graphs in the Johnson scheme which have this property. Indeed, we show that the Kneser graph K(2k, k) is the only class in the scheme which admits perfect state transfers. We also show that, under some conditions, some of the unions of the graphs in the Johnson scheme admit perfect state transfer.

The study entitled " Implementation Of The Islamic Law Transformation’s Rule (Taghayyur Ahkām) During Covid-19 Pandemic In The Perspective Of Majelis Tarjih Muhammadiyah In Indonesia" aims to uncover and analyze one of the methods and rules of law-making (istinbāth ahkām) carried out by the Muhammadiyah fatwa institution, the Majelis Tarjih dan Tajdid, or known as "Manhaj Tarjih Muhammadiyah." One of the many methods used by Majelis Tarjih in issuing legal decisions and fatwas is the Rules of Islamic Law Transformation (taghayyur ahkām). The research also attempts to contextualize the rules of Islamic law transformation with the decisions or guidelines for the implementation of worship (Ibadah) that have been issued by the Muhammadiyah Central Leadership through the Majelis Tarjih, especially during the current Covid-19 pandemic. The results of this study are beneficial both practically and theoretically. The practical benefit of this research is that it may provide guidelines for the implementation of worship during the Covid-19 pandemic based on argumentative arguments and the principles and objectives of Islamic law, one of which is guarding religion (Hifz ad-Dīn) and guarding human lives (Hifz an-Nafs). Meanwhile, the theoretical benefits from this research are to expand the knowledge and discourse of Islamic scholarship, especially in the field of Islamic law. Thus, Islam can manifest in the midst of mankind to provide real solutions to existing problems. This research uses qualitative research focusing on library research with descriptive analysis. Consequently, the researchers applied the Ijtihād of Majelis Tarjih’s Method known as "Manhaj Tarjih Muhammadiyah" written by Syamsul Anwar as well as based on the results of the Tarjih National Assembly (Munas) XXX in Makassar in 2018, also the decision of the Muhammadiyah Central Leadership No. 02/EDR/1.0/E/2020 regarding Guidelines for Worship in Covid-19 Emergency conditions and several other Tarjih fatwas related to guidelines for carrying out worship during the Covid-19 pandemic as primary data. In addition, the secondary data are from various sources, such as  fiqh books, ushul fiqh, and maqaṣid as-syarī'ah. Besides, the study uses a content analysis approach to bring up the messages objectively and systematically.

 يتحرّى هذا المقال القضايا الأخلاقيّة القانونيّة إزاء إنهاء الحمل بسبب الثلاسيميّة مع التركيز على ما قد تفضّل به مقاصد الشريعة تكاملا مع النظام الأخلاقيّ. كانت الدراسة من الأهمّيةّ بمكان؛ لأنها تتصدّى لبعض القضايا المعاصرة التي يهتمّ بها العلماء المتخصّصون في المجال الطبّيّ والشريعة الإسلاميّة. والرجاء أنّها ستكون عونا مفيدا للعلماء المسلمين في المهنة الطبّيّة كاشفة كلّ شبهات قد تعترضهم خلال القيام بواجباتهم وتقديم خدماتهم المدنيّة في المجتمع. وعلى وجه التحديد، يعنى هذا البحث أساسا بتسليط الضوء على مفهوم الثلاسيميّة وإخلالها بالصّحّة خاصّة منذ المرحلة الجنينيّة، مبيّنا أنسب الحلّ لإنهاء الحمل جراء التشخيص الذي ينعقد قبل الولادة، ومجموعة من القضايا الأخلاقيّة القانونيّة تتعلّق بإنهاء الحمل بسبب الثلاسيميّة، ثمّ إبراز أهمّيّة مقاصد الشريعة بالنسبة للرعاية الصّحّيّة في هذه الأزمنة الأخيرة. الكلمات المفتاحية: التوجيهات، الأخلاقية، الثلاسيميّة، مقاصد الشريعة، إنهاء الحمل

This article aims to study the financial intermediation in Islamic banks, in term of the degree of extent and achievement according to Islamic rules and Maqasid of Shariah. The objectives of this study has been done theoretically and practically through the study of some applications on the light of Maqasid. This study shows that the financial intermediation achieving the Magasid of Shariah without contradiction if it is applied correctly. Practically, this study was applied on the Kuwait Finance House Malaysia. Results show that Islamic intermediation implementing the Maqasid of Shariah in some aspects, however the study also highlights that the practice of some types of fictitious contracts like Tawaruq, Mudarabah with Tawaruq, lease and sublease, seem to contradict the Islamic rules of the Shariah and its Maqasid. This study recommends the avoidance of fictitious contracts, and to replace them with direct investment according to the comprehensive Islamic banking model of the Islamic banking system.

It has been asked in [3] whether there are trees other than P 2 and P 3 which can admit perfect state transfers. In this note we show that the answer is negative.