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We investigate the Michel-type accretion onto a static spherically symmetric black hole. Using a Hamiltonian dynamical approach, we show that the standard method employed for tackling the accretion problem has masked some properties of the fluid flow. We determine new analytical solutions that are neither transonic nor supersonic as the fluid approaches the horizon(s); rather, they remain subsonic for all values of the radial coordinate. Moreover, the three velocity vanishes and the pressure diverges on the horizon(s), resulting in a flowout of the fluid under the effect of its own pressure. This is in favor of an earlier prediction that pressure-dominant regions form near the horizon. This result does not depend on the form of the metric and it applies to a neighborhood of any horizon where the time coordinate is timelike. For anti-de Sitter-like f(R) black holes we discuss the stability of the critical flow and determine separatrix heteroclinic orbits. For de Sitter-like f(R) black holes, we construct polytropic cyclic, non-homoclinic, physical flows connecting the two horizons. These flows become non-relativistic for Hamiltonian values higher than the critical value allowing for a good estimate of the proper period of the flow.

In this paper, we study the accretion process for fluids flowing near a black hole in the context of f(T) teleparallel gravity. Specifically, by performing a dynamical analysis by a Hamiltonian system, we are able to find the sonic points. After that, we consider different isothermal test fluids in order to study the accretion process when they are falling onto the black hole. We find that these flows can be classified according to the equation of state and the black hole features. Results are compared in f(T) and f(R) gravity.

Introduction of technology has revolutionised the postgraduate medical education in the twenty-first century. 1 Technology is proving useful in attaining desired professional growth through easy access to learning resources, and effective utilisation of this information for the development of knowledge and skills. 2,3 Electronic databases such as electronic portfolios (e-portfolio) or electronic logbooks, are now rapidly replacing the traditional paper-based logbooks. 4 College of Physicians and Surgeons Pakistan (CPSP) is the prime postgraduate medical institute of Pakistan. Traditionally, CPSP has used paper based logbooks which, although quite useful for training monitoring, had certain limitations. 5,6 To counter these deficiencies, CPSP introduced the electronic version of logbook, the e-logbook, in 2011. 7 The e-logbook of CPSP is in its 9 th year of induction. Earlier studies have shown e-logbook to be a valuable tool for training monitoring. 6,8 The success of an electronic logbook system depends on its ability to focus on students' satisfaction, flexible nature, ease of access to the learning material, costeffectiveness and strengthening of supervisorsupervisee relationship. 9,10 The question is, after nine years of induction, does the e-log system of CPSP fulfill these fundamental requirements? E-log system has undergone various modifications from time to time to make it a more useful tool. The impact of these changes still remains to be ascertained. This study was, therefore, designed with the aim to determine the feedback of supervisors regarding role of e-logbook in monitoring of training, strengthening supervisor-supervisee relationship, and improving

This study empirically estimates farmers' willingness to pay (WTP) for a planned adaptation programme for addressing climate issues in Pakistan's agricultural sectors. The contingent valuation method (CVM) was employed to determine a monetary valuation of farmers' preferences for a planned adaptation programme by ascertaining the value attached to address climatic issues. The survey was conducted by distributing structured questionnaires among Pakistani farmers. The study found that 67 % of respondents were willing to pay for a planned adaptation programme. However, several socioeconomic and motivational factors exert greater influence on their willingness to pay (WTP). This paper specifies the steps needed for all institutional bodies to better address issues in climate change. The outcomes of this paper will support attempts by policy makers to design an efficient adaptation framework for mitigating and adapting to the adverse impacts of climate change.

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Asymptotically safe gravity is one effective approach to quantum gravity. It is important to differentiate the modified gravity inspired by asymptotically safe gravity. In this paper, we examine the matter particles dynamics near the improved version of Schwarzschild black hole. We assume that in the context of asymptotically safe gravity scenario the ambient matter surrounding the black hole is of isothermal in nature and investigate the spherical accretion of matter by deriving solutions at critical points. The analysis for the various values of the state parameter for isothermal test fluids, viz., k = 1, 1/2, 1/3, 1/4 show the possibility of accretion onto asymptotically safe black hole. We formulate the accretion problem as Hamiltonian dynamical system and explain its phase flow in detail which reveals interesting results in asymptotically safe gravity theory.

Construction is dependent on accurate, timely and safe supply chain, otherwise whole project will be halted. Previously, it has found that most construction projects failed to complete on designated time that ultimately surges the cost as well. Although there are various approaches to deal with the situation, there is evidence that collaboration among stakeholders would reduce the risks and enhance the performance. Therefore, the aim of this study is to verify the relationship between the supply chain performance (SCP) with three stakeholder management approaches, namely supplier relationship (SR), customer relationship (CR), and risk and reward sharing (RRS). A total of 585 questionnaires were distributed using systematic probability sampling of listed construction organizations and only 258 responses were returned. The data were analyzed through the Smart PLS Software using two types of function i.e. PLS Algorithm and Bootstrapping. Based on the PLS Algorithm, the path coefficient results confirm that SR, CR, and RRS influence the SCP. It also has found that all three approaches have 56% of explaining power on SCP (R 2 value = 0.560). The bootstrapping function revealed that the three hypotheses supported and this confirmed the hypotheses are true. This study enhances the relationship among stakeholders beyond the traditional collaboration to risk and reward sharing simultaneously. This integration will provide a competitive position as all members share their expertise that will ultimately improve the quality and lead time and enrich the flexibility. Thus, it can be concluded that long-term success is heavily dependent on relationships with the suppliers, customers, risk and reward sharing. This study will help construction managers to understand the importance of good relationships while doing strategic decision making.