By Grothendieck's anabelian conjectures, Galois representa-tions landing in outer automorphism group of the algebraic fundamen-tal group which are associated to hyperbolic smooth curves de ned over number- elds encode all the arithmetic information of these curves. The Goal of this paper is to develop an arithmetic Teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arith-metic information coming from all curves of the same topological type de ned over number- elds. We also introduce Hecke-Teichmuller Lie al-gebra which plays the role of Hecke algebra in the anabelian framework.

This paper deals with some of the most important and longstanding homological conjectures‎. ‎The framework which‎ ‎is of interest to us is that of a finite dimensional algebra over a field‎. ‎Auslander-Reiten conjecture‎, ‎finitistic dimension conjecture‎, ‎(Generalized) Nakayama conjecture‎, ‎and vanishing conjecture are discussed in separate sections and the interaction between them‎ ‎is studied‎. ‎As declared by the title‎, ‎the current paper will put an emphasis on the Auslander-Reiten conjecture.

The rise of Islamic rulers to translate the works of other nations in the early centuries of the appearance of Islam is known as the translation movement. The influence of this cultural phenomenon on the Muslims' thought is noteworthy and the Muslims' jurisprudential thought is not separated therefrom. In the Islamic jurisprudence, many of the proofs for inferring the verdicts are considered conjectures, while following the conjectures has been strongly condemned in the Holy Quran. This paradox has become a challenge in the course of acting on the basis of proofs of inference. The purpose of this paper is to identify the origin of this paradox and find a way out of it. This paper, which has been prepared by historical-analytical-descriptive method relying on library sources, claims that the above said paradox has happened as a result of the semantic evolution of the terms knowledge and conjecture due to the translation of sciences such as logic. The definitions and attitudes entered into the Islamic world through translation have been proposed initially by some Sunni theologians in opposition to Ahl al-Hadith; however, the views of some Shiite jurists have been affected by them as well.

In the traditional jurisprudence, it is said that there is a presumption in favor of the unreliability of conjectures (ẓ unû n), and only certain conjectures, buttressed with reliable evidence, are reliable or authoritative. Some contemporary intellectuals have challenged the unreliability of rational conjectures, believing that evidence adduced for the above claim in the traditional jurisprudence does not go through. In volumes 92 and 96 of Naqd va Nazar, an article was published by Hossein Kamkar in critique of Abolqasem Fanaei’s claim and in defense of the principle of the unreliability of rational conjectures. The critic tries to establish the principle of the unreliability of rational conjectures (the claim in traditional jurisprudence), responds to Abolqasem Fanaei’s objections, and raises objections against his arguments. In my view, the critic’s attempt to undermine Fanaei ’s arguments and defend the traditional jurisprudence fails, and the principle of reliability of rational conjectures (Fanaei’s claim) is flawless. Drawing on a rational-analytic method, the paper seeks to show the implausibility of the claim by the traditional jurisprudence to the effect that conjectures are unreliable, and indeed the contrary is plausible and reasonable; that is, the idea that the presumption is in favor of the reliability of all conjectures except in cases where there is conclusive evidence for their unreliability. The conclusion I draw from my consideration of the two papers by Hossein Kamkar is that his objections against Fanaei’s claim involve negligence of chains of transmissions and implications of hadiths and of the priority of rational evidence over transmitted evidence. I believe that the religious legislator could not rule out the reliability of rational conjectures, arguments adduced by Muslim jurists and scholars of principles of jurisprudence are not sufficiently cogent, and rational conjectures are like certitudes essentially reliable.

In this paper, we compute the images of some of the Z-basis elements under the anti-automorphism map  of the mod 2 Steenrod algebra A 2 and propose some conjectures based on our computations.

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Background: Medicalization of the natural lifelong socio-biological phenomena is one of the epitomes of challenges in front of modern societies. Empirical research findings have reveled that demand for some of the health care services is expanding, especially after commencement of the Health Transformation Plan (HTP) in Iran. Given the evidence about the precedents and probable streamline role of the sovereign market and consumers’ demands on the country’ s surging medicalization trend, this study was aimed at exploring the healthcare professionals’ (HCPs) prospects about the demand side portrayal of the phenomenon. Methods: Purposive and snowball sampling method were used to recruit a total of 31 key national informants to participate in 14 semi-structured interviews and 3 focus group discussions that were planned to acquire data and insights that were not accomplished during the interview sessions. The data were collected, transcribed, and analyzed from March 2016 to February 2017 using content analysis (inductive and deductive) approach to identify certain concepts and explore the underlying facts behind the discourses. The transcribed texts were indexed and codes were extracted and categorized into subthemes and themes. MAXQDA 12 software was used for better organizing and managing the data. Results: Data were organized in 4 categories and 10 subcategories. Factors relating to national/provincial health policies and plans, healthcare consumers, the public expectations about health care professionals’ affluence, and community context were considered as key sets of factors to infuriate unnecessary medicalization in Iran with the HTP having considerable role as a suitable platform to boost the incongruous phenomenon. Conclusions: The socio-cultural context and health policy making mechanisms could have a significant role in over utilization of health services and unrestrained medicalization in Iran. The dilemma should be regarded as a multidimensional embarrassment and until a multifaceted approach was not applied for its control, no major success could be expectable.

In recent years, inflationary models have been studied from different perspectives using different conditions. Now, in this paper, we want to investigate the inverse monomial Inflation$(IMI)$ on the brane. We limit our results to the potentials of the form $\frac{M^{4+\sigma}}{\phi^{\sigma}}$, where${M, \sigma}$are constants. We calculate some cosmological parameters and then we investigate the satisfaction of the model with some conjectures of the swampland program. We will check the model's compatibility with the refined dS swampland conjecture(RDSSC), further refining the de Sitter swampland conjecture (FRSDC), scalar weak gravity (SWGC), and strong scalar weak gravity conjecture (SSWGC). Despite the incompatibility with (DSC), We find a specific region of compatibility with other ones which means it satisfied the (FRDSSC) for example with (a=0.982873,\hspace{0.1cm} b=0.017127,\hspace{0.1cm} q=2.2). Also, the model is compatible with the (SWGC) with the ($\phi\leq \sigma+2$) condition and consistent with the (SSWGC) with the ($\phi \leq \sqrt{(\sigma+2)(\sigma+1)}$) condition. Since inverse monomial Inflation(IMI) on the brane could satisfy some swampland conjecture simultaneously, it has the potential to be a “real” inflation model of the universe.

Recognition of whether hadith transmitters are trustworthy, which is considered among necessary preliminaries of juristic deductions, is mostly dependent upon statements of rijal experts. In order to authenticate opinions of earlier rijal experts Muslim scholars have suggested some ways, such as authority of single report, that of testimony, that of expert’s opinion, or the Closure Proof each of which encountering some problems or, at least, some limitations and conditions in such a way that one cannot make acceptance of opinions of rijal experts dependent on them. While surveying and criticizing those ways, which presuppose that actualization of one of such designations is necessary for the departure from prohibition of acing on the basis of conjecture, the present essay proposes a perspective according to which actualization of a particular designation or causality of a specific factor plays no role in the authority of conjectures; rather, what causes departure from prohibition of acing on the basis of conjecture is that the opinion should reach a level that it could remove the wise’s state of perplexity in the position of action and propel them to the action. By authenticating such conjectures, which we call “conjectures authorized by the wise,” one can prove validity of most of statements of rijal experts concerning trustworthiness or otherwise of hadith transmitters.