The technical literature actively discusses ideas for creating digital twins to solve a wide range of problems that arise for enterprises of various kinds. Advances in the areas of information technology and the development of the necessary software really make it possible to obtain important new results through the creation of digital twins. This paper proposes the concept of building a network of digital twins, used to solve a number of actual problems in complex telecommunication systems. Two applications are considered (...) examples of such tasks. The first application is the organization of information feedback for enterprises involved in the life cycle of a telecommunication network: “elaboration of modernization principles, development of equipment, design, construction, and operation.” The second application is monitoring traffic, including its atypical behavior, in order to avoid the recurrence of erroneous actions in case of emergency situations. Another important feature of the digital twin network is that it will become an effective tool for conducting interdisciplinary research. (shrink)

Faults; religious aspects; Islam; Islamic daʻwah.

Working toward showing the decidability of the $\forall \exists $ -theory of the ${\Sigma ^0_2}$ -enumeration degrees, we prove that no so-called Ahmad pair of ${\Sigma ^0_2}$ -enumeration degrees can join to ${\mathbf 0}_e'$.

This paper provides a critical review of economic outcome metrics used in healthcare value assessment, emphasizing the evolving landscape of resource allocation, patient-centered approaches, and standardization efforts. With healthcare costs rising globally, the efficient allocation of limited resources is essential. Metrics like Quality-Adjusted Life Years (QALYs), Disability-Adjusted Life Years (DALYs), Incremental Cost-Effectiveness Ratios (ICERs), and Cost-Benefit Analysis (CBA) are central to guiding funding decisions, influencing insurance coverage, and shaping treatment prioritization. Emerging trends, such as the integration of artificial intelligence (AI) (...) and big data, are enhancing the precision of these assessments, while patient-centered metrics underscore the importance of patient satisfaction and quality of life. Additionally, there is a growing push for the standardization of these metrics to create consistent frameworks across diverse health systems. This paper explores case studies, practical applications, and future directions to provide insights into how healthcare systems can adopt more effective, globally aligned economic assessments. (shrink)

We show that if M is an r‐maximal set, A is a major subset of M, B is an arbitrary set and, then. We prove that the c.e. ‐degrees are not dense. We also show that there exist infinite collections of ‐degrees and such that the following hold: (i) for every i, j,, and,(ii) each consists entirely of r‐maximal sets, and(iii) each consists entirely of non‐r‐maximal hyperhypersimple sets.

Study and teaching of Islam with refererence to Qurʼan and Hadith.

We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and M1\A≡Q1,NM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus} A\equiv{}_{Q_{1,N}}M_{2}{\setminus} B}$$\end{document}, then M1\A≡mM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus}A\equiv{}_{m}M_{2}{\setminus} B}$$\end{document}. If M1 and M2 are r-maximal sets and M10,M11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0},\,M_{1}^{1}}$$\end{document} and M20,M21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{2}^{0},\,M_{2}^{1}}$$\end{document} are nontrivial splittings of M1 and M2, respectively, then M10≡Q1,NM20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{Q_{1,N}}M_{2}^{0}}$$\end{document} if and only if M10≡1M20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{1}M_{2}^{0}}$$\end{document}. From this result follows that if A and B are Friedberg splitting of an r-maximal set, then the Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degree of A contains only one c.e. 1-degree. (shrink)

Islamic philosophy - Congresses ; Sufism - Congresses.

1. Ḳlorshṭeln dem emes̀'n Toyrehdign 'ṿeg tsu a gliḳlikh leb' durkh arbeṭn af di mides̀ on darfn nutsn profesyonale ṭerapi. Ṿen darfn yo nutsn ṭerapi un ṿos iz der rikhṭiger tsugang dertsu. A breyṭe erḳlerung iber di yesoydes̀ fun Idishḳeyṭ.

Critical study of Ṣirāṭʹhā-yi mustaqīm, a book by ʻAbd al-Karīm Surūsh on religious pluralism and philosophy of religion.

It is proved that the (2p)-c. e. e-degrees are not elementarily equivalent to the (2p + 1)-c. e. e-degrees for each nonzero p ∈ ω. It follows that m-c. e. e-degrees are not elementarily equivalent to the n-c. e. e-degrees if 1 < m < n.

Collection of works on literature theory, translated into Mongolian language.

In this paper we study structural properties of n-c. e. Q-degrees. Two theorems contain results on the distribution of incomparable Q-degrees. In another theorem we prove that every incomplete Q-degree forms a minimal pair in the c. e. degrees with a Q-degree. In a further theorem it is proved that there exists a c. e. Q-degree that is not half of a minimal pair in the c. e. Q-degrees.

We show that the Δ0 2 enumeration degrees are dense. We also show that for every nonzero n-c. e. e-degree a, with n≥ 3, one can always find a nonzero 3-c. e. e-degree b such that b < a on the other hand there is a nonzero ωc. e. e-degree which bounds no nonzero n-c. e. e-degree.

We prove that the degree structures of the d.c.e. and the 3-c.e. Turing degrees are not elementarily equivalent, thus refuting a conjecture of Downey. More specifically, we show that the following statement fails in the former but holds in the latter structure: There are degrees f > e > d > 0 such that any degree u ≤ f is either comparable with both e and d, or incomparable with both.

Commentary on Quwaysinī's commentary on Akhḍarī's work titled the Sullam al-muawraq on logic.

Critical review of theory of re-enchantment by Darius Shayegan, a prominent thinker, cultural theorist and comparative philosopher.

Teachings of Muslim saints to earn bread by honest means.

al-Mujallad al-awwal. Muqaddimāt al-taḥqīq wa-muqaddimat al-Imām al-Zubaydī lil-Itḥāf -- al-mujallad al-thānī. Kitāb al-ʻIlm ilá nihāyat al-bāb al-thālith -- al-mujallad al-thālith. Tatimmat kitāb al-ʻilm min al-bāb al-rābiʻ ilá ākhir al-kitāb -- al-mujallad al-rābiʻ. Kitāb Qawāʻid al-ʻaqāʼid -- al-mujallad al-khāmis. Kitāb Asrār al-ṭahārah -- al-mujallad al-sādis. Kitāb Asrār al-ṣalāh ilá nihāyat shurūṭ al-jumʻah min al-bāb al-khāmis -- al-mujallad al-sābiʻ. Tatimmat kitāb asrār al-ṣalāh min ādāb al-jumʻah ilá ākhir al-kitāb -- al-mujallad al-thāmin. Kitābā Asrār al-zakāh wa-asrār al-ṣawm -- al-mujallad al- tāsiʻ. Kitāb asrār (...) al-ḥajj -- al-mujallad al-ʻāshir. Kitābā ādāb tilāwat al-Qurʼān wa-al-adhkār wa-al-daʻawāt -- al-mujallad al-ḥādī ʻashar. Kitābā tartīb al-awrād wa-tafḍīl iḥyāʼ al-layl wa-ādāb al-akl -- al-mujalladal-thānī ʻashar. Kitābā ādāb al-Nikāḥ wa-ādāb al-Kasb wa-al-maʻāsh -- al-mujallad al-thālith ʻashar. Kitāb al-Ḥalāl wa-al-ḥarām -- al-mujallad al-rābiʻ ʻashar. Kitāb al-Ulfah wa-al-ukhuwwah -- al-mujallad al-khāmis ʻashar. Kitābā ādāb al-ʻUzlah wa-ādāb al-Safar -- al-mujallad al-sādis ʻashar. Kitābā ādāb al-Samāʻ wa-al-wajd wa-al-Amr bi-al-maʻrūf wa-al-nahy ʻan al-munkar -- al-mujallad al-sābiʻ ʻashar. Kitābā ādāb al-maʻīshah wa-akhlāq al-nubūwah wa-sharḥ ʻajāʼib al-qalb -- al-mujallad al-thāmin ʻashar. Kitābā riyāḍat al-nafs wa-tahdhīb al-akhlāq wa-kasr al-shahwatayn -- al-mujallad al-tāsiʻ ʻashar. Kitābā āfāt al-lisān wa-dhamm al-ghaḍab -- al-mujallad al-ʻishrūn. Kitābā dhamm al-dunyā wa-dhamm al-bukhl -- al-mujallad al-ḥādī wa-al-ʻishrūn. Kitābā dhamm al-jāh wa-dhamm al-kibr wa-al-ʻajab -- al-mujallad al-thānī wa-al-ʻishrūn. Kitābā dhamm al-ghurūr wa-al-tawbah -- al-mujallad al-thālith wa-al-ʻishrūn. Kitābā al-ṣabr wa-al-shukr -- al-mujallad al-rābiʻ wa-al-ʻishrūn. Kitābā al-rajā wa-al-khawf -- al-mujallad al-khāmis wa-al-ʻishrūn. Kitāb al-zuhd wa-al-faqr -- al-mujallad al-sādis wa-al-ʻishrūn. Kitāb al-tawḥīd wa al-tawakkul -- al-mujallad al-sābiʻ wa-al-ʻishrūn. Kitāb al-maḥabbah wa-al-shawq wa-al-uns wa-al-riḍā -- al-mujallad al-thāmin wa-al-ʻishrūn. Kutub al-ikhlāṣ wa-al-nīyah wa-al-murāqabah wa-al-muḥāsabah wa-al-tafakkur -- al-mujallad al- tāsiʻ wa-al-ʻishrūn. Kitāb dhikr al-mawt wa-mā baʻdih ilá nihāyat al-bāb al-thāmin -- al-mujallad al-thalāthūn. Kitāb dhikr al-mawt wa-mā baʻdih ilá ākhar al-kitāb wa-yalīhi maṣādir al-taḥqīq. (shrink)

jild-i 1. Az ʻAbd al-Ḥamīd Kātib (59 Sh.) tā Abū al-Ḥasan Masʻūdī (336 Sh.) -- jild-i 2. Az Abū al-Ḥasan ʻĀmirī (291 Sh.) tā Abū al-Faz̤l Bayhaqī (465 Sh.) -- jild-i 3. Az Nāṣir Khusraw (383 Sh.) tā Sadīd al-Dīn ʻAwfī (616 Sh.) -- jild-i 4. Az Najm al-Dīn Rāzī (553 Sh.) tā Fakhr al-Muḥaqqiqīn (748 Sh.) -- jild-i 5. Az ʻUbayd Zākānī (670 Sh.) tā Jalāl al-Dīn Sayūṭī (884 Sh.) -- jild-i 6. Az Rūzbihān Khunjī (825 Sh.) tā Shaykh (...) Ḥurr ʻĀmilī (1071 Sh.) -- jild-i 7. Az ʻAlāmah Majlisī (1006 Sh.) tā Muḥammad Bāqir Shafaq (1223 Sh.) -- jild-i 8. Az Muḥammad Ṣādiq Marvazī (1147 Sh.) tā Mīrzā Fatḥʻalī Ākhūndzādah (1289 Sh.) -- jild-i 9. Az Mīrzā-yi Shīrāzī Avval (1194 Sh.) tā Ākhūnd Khurāsānī (1290 Sh.) -- jild-i 10. Az ʻAbd Allāh Māzandarānī (1219 Sh.) tā Saʻd Zaghlūl (1306 Sh.) -- jild-i 11. Az ʻImād al-ʻUlamāʼ Khalkhālī (1237 Sh.) tā ʻAbd al-ʻAzīz S̲aʻālibī (1323 Sh.) -- jild-i 12. Az Āyat Allāh Burūjirdī (1254 Sh.) tā Muḥammad Amīn Rasūlʹzādah (1333 Sh.) -- jild-i 13. Az ʻAbd al-Karīm Zanjānī (1263 Sh.) tā Amīn al-Ḥusaynī (1353 Sh.) -- jild-i 14. Az Jamālzādah (1274 Sh.) tā Mahdī Bāzargān (1373) -- jild-i 15. Az Muḥammad Ḥamīd Allāh (1286 Sh.) tā Muṭahharī (1358 Sh.) -- jild-i 16. Az Farīdūn Ādamīyat (1299 Sh.) tā Muṣṭafá Khumaynī (1356 Sh.) -- jild-i 17. Az Samīr Amīn (1310 Sh.) tā Ḥasan Ḥanafī -- jild-i 18. Az Sayyid Muḥammad Bāqir Ṣadr (1314 Sh.) tā Rāshid al-Ghanūshī -- jild-i 19. Az ʻAlī Awmlīl (1321 Sh.) tā Ṭāriq Ramaz̤ān. (shrink)

al-juzʼ 1. [Without special title] -- al-juzʼ 2. al-Masmūḥ wa-al-mamnūʻ fī firāsh al-zawjīyah.