Integral Representation and Explicit Formula at Rational Arguments for Apostol–Tangent Polynomials

The Fourier series expansion of Apostol–tangent polynomials is derived using the Cauchy residue theorem and a complex integral over a contour. This Fourier series and the Hurwitz–Lerch zeta function are utilized to obtain the explicit formula at rational arguments of these polynomials. Using the Lipschitz summation formula, an integral representation of Apostol–tangent polynomials is also obtained.

Analysis and Examination of the Sunni Commentators’ Views in Explaining the Temporal Extent of the Infallibility of the Prophets (PBUTH)

Sunni commentators have different views on the temporal extent of the infallibility of the prophets. While Some Ash'arites have expressed absolute infallibility, the Mu'tazilites believe that the Prophets (Peace Be Upon Them) have been infallible since the start of their prophethood. This study, by referring to Sunni interpretations, seeks analytical-critical processing of the method of Sunni commentators using the necessary tools and resources in expressing the time limit of the infallibility of the Prophets (PBUTH). Examination of the interpretators comments following verses about the infallibility of the prophets (PBUTH) shows that the opinon of the Sunni commentators on the fallibility of the Prophets before prophethood, lack using appropriate tools and is a claim without reason, and the cause of differences in views about the infallibility of the prophets after prophethood, is paying no attention to rational arguments and favoring religious beliefs by interpreting verses in order to prove one's opinion and imposing the mental background of the interpreter on the verses.

A few remarks on the values of the Bernoulli polynomials at rational arguments and some relations with ζ(2k + 1)

A problem posed by Lehmer in 1938 asks for simple closed formulae for the values of the even Bernoulli polynomials at rational arguments in terms of the Bernoulli numbers. We discuss this problem based on the Fourier expansion of the Bernoulli polynomials. We also give some necessary and sufficient conditions for ζ(2k + 1) be a rational multiple of π2k+1.

Internally Inconsistent, Self-Refuting, and Self-Undermining Views

In Chapter 8, the author articulates two more principles of epistemic irrationality, one that applies to self-refuting views and one that applies to self-undermining views. A self-refuting view is one that says, or in an indirect way communicates, “I am not true nor approximately true nor true enough.” A self-undermining view is one that says, or in an indirect way communicates, “It is not epistemically rational to believe me to be true or approximately true or true enough.” The author uses Grice’s idea of a conversation implicature and the Apel-Habermas idea of a performative contradiction to explain and formulate three presuppositions of making an argument and uses them to explain why any arguments for a behaviorist or eliminative materialist position are self-undermining. He then proposes an Epistemic Anthropic Principle: when scientists present arguments for a scientific theory, the theory must be compatible with the possibility of making rational arguments for it.

عید الاضحیٰ کی قربانی سے پہلے اور اُس کے بعد کے مراسمِ عبودیت ( جاوید احمد غامدی صاحب کے موقف کا ایک تنقیدی مطالعہ)

Jāvaid Aḥmad Ghāmidī, a contemporary Muslim modernist scholar, holds that the three established rituals of ḥajj and ‘umrah can be regarded as independent rituals in religion, which he categorises asnadhar (votive offering). The ritual is performed by fulfilling three conditions: 1) abstaining from removing body hair, 2) refraining from clipping nails, and 3) trimming or shaving the head. According to Ghāmidī, all believers can perform this rite, without any spatio-temporal restriction, as a supererogatory act. The Prophet (P.B.U.H.), he believes, encouraged Muslims to voluntarily observe it on the occasion of ‘īd al-aḍḥā. This is inferred by combining the information found in two Prophetic narrations, one reported by Umm Salamah and the other by ‘Abd Allah b. ‘āmr. In Ghāmidī’s view, all believers whether or not they are offering the animal sacrifice may offer such nadhar. For doing so, they would follow the two aforestated restrictions from the beginning of Dhū al-Ḥijjah (the twelfth month of the Islamic calendar) and trim or shave their heads on the ‘Īd day after the animal has been slaughtered (if they are to offer the sacrifice) orin anytime during the day (if they are not to offer the sacrifice). This last act is seen as a token of the completion of their votive offering to God. After a careful discussion of Ghāmidī’s view, this article concludes that the religious and rational arguments put forward by Ghāmidī are insufficient to relate the three rites (separately mentioned in the above Prophetic narrations) to the corresponding rites of ḥajj and ‘umrah and generalize them, out of the context, as one standalone ritual.

EXPERIENCES FROM STARTING AND RUNNING A SOFTWARE COMPANY WITHIN THE CONTEXT OF DESIGN RESEARCH

This paper deals with the story and experiences of setting up a new start-up company with the ambition to scale using a software-based product. The paper is written by researchers for researchers interested in doing the same thing. The paper concludes that it can be very beneficial for research as the startup-can be seen as a data collection machine, but to set up a start-up company, comes with unforeseen problems along the way. A few of them involves: Do not rely on rational arguments (only), when marketing your product. Expect long lead-times. Work with multiple threads and secure funding early to ensure that you can finance your startup. Finally, you need to be committed, and you have to have a strategy to manage both your research and your commercial activities.

Scientific data, ecological conversion and transformative affect

Scientific data supporting rational arguments for human-made causes of climate and environmental changes might be persuasive in some contexts. Law, policy, activism and The Earth Charter similarly appear insufficient to change attitudes and behaviours. Even biblical and theological arguments fail to move some Christians beyond apathy and climate denial. Decades of ecological theology and calls for ecological conversion suggest that appeals to reason and facts are limited without an affective epistemology that join knowledge and experience to produce worldview transformation through emotions, such as awe.Contribution: Departing from appeal to scientific data and arguments alone, the primary claim is that ecological conversion is not singularly a rational act. For broader engagement and action to mitigate climate and environmental degradation, experiential and affective encounter with nature promise wider participation and transformation.

ENLIGHTENED TRADITIONALISM: RATIONAL ARGUMENTS IN FAVOR OF THE SPIRITUAL AND PHILOSOPHICAL CURRENT OF THOUGHT

В политике часто встречается применение слишком емких, широко трактуемых понятий, к таковым можно отнести «традиционализм». В предметном разговоре использовать его проблематично, поскольку приверженцы разных традиций наполняют этот термин своим смыслом и ожидания оппонента могут быть не оправданы. Одной из задач науки является создание своеобразной картотеки, где каждая научная мысль и мнение учитывается, и между ними выстраивается взаимосвязь. В статье автором дается собственное определение понятия «традиционализм», что не исключает его схожесть с иными воззрениями. Традиционализм рассмотрен через историю европейской политической мысли с позиции идеологии. Изложенные в статье мысли частично совпадают с идеями разных политических течений: коммунистов, националистов, социалистов, консерваторов, религиозных организаций. Рассматривая просвещенный традиционализм, автором приведены рациональные аргументы в пользу духовно-философского течения мысли.

Theological principles of communicative (Takfiri) thought

Looking at the calamities that have inflicted on the Islamic society by its atheistic currents, it is indispensable to confront and fight against it radically. Getting acquainted with the principles of the criticism of the aforementioned currents is of great importance. Among the contemporary seditions that have led to the separation of the Muslim ummah is the excommunication (Takfir) of Muslims by each other in which one religion is accused of blasphemy by another school and they have to hear the most severe and most vulgar words and ultimately due to an imaginary crime of blasphemy and shirk, they will be slaughtered by the claimant. However, the process of excommunication, as it should be, does not emphasize on the debate and assumes that the insistence on excommunication and sins of other religions is to revive the tradition and to destroy heresy (Bid’ah); therefore it is necessary for Islamic researchers who consider fairness in their scientific discussions to understand the basics of the excommunicative movement to defend the legitimacy of Islam and Shi'ism and also protect them from falling into the trap of fallacies. Accordingly, the present article seeks to clarify the principles of excommunicative thought criticism in terms of Quranic verses, Hadith, Sirah Mutawatir (successive conducts) and rational arguments. Determining the position of conflict on matters such as intercession and resort (Tawassul) to prophets and imams while addressing issues such as the attribution of shirk to Shia, non-adherence to the well-known sirah of Salaf of blessing and visiting the tombs, and the need to pay attention to good heresy (Bid’ah) in the form of a superior controversy are considered the principles of excommunicative (Takfiri) thought criticism.