We show that the e-degree 0'e and the map u ↦ u' are definable in the upper semilattice of all e-degrees. The class of total e-degrees ≥0'e is also definable.

[1] Sefer Orḥot Ḥayim leha-Rosh ʻim beʼur "ha-Shem orḥotenu" ... 2. Ḳunṭres Be-Shaʻar ha-melekh ʻal haḳdamat ha-Rambam, kolel tsiyunim u-meḳorim u-veʼurim be-divre ha-Rambam ṿeha-Raʼabad ... 3. Ḳunṭres Tashlum yefeh ʻenayim ʻal Seder Zeraʻim u-Ṭehorot, ʻeduyot, Tamid, Midot, Ḳenim ṿe-ʻod ṿe-hu tsiyunim ʻal mas. elu mi-Yerushalmi u-midrashim ... 4. Ḳunṭres Marʼot maḳom, ṿe-hu tsiyunim ʻal ha-meḳomot she-Rashi ṿe-Tos. meviʼim mirdrash o Yerushalmi ṿe-Tosefta ṿe-khu. ṿe-lo tsuyan meḳoro ... 5. Ḳunṭres Ṭeʻama de-ḳara, ṿe-hu ḳetsat ḥidushim ʻal ha-Torah ṿe-ʻal Neviʼim u-Khetuvim -- ḥeleḳ (...) 3. Heʻarot ʻal seder ha-Shas (ṿe-kholel gam ezeh ḳunṭresim). (shrink)

Excerptions from the lives of Shiite Imams as a model of Islamic ethics.

A law is one of the basic concepts of the dialectical materialist conception of determinism as a philosophical theory of the objective interrelationship and mutual conditioning of phenomena in the material and mental world. A law establishes a rigorously determined connection among circumstances, i.e., a totality of derivative components and conditions of their actions and results. By overlooking the existence of two different levels—the concept and the objective reality corresponding to it—some philosophers erroneously interpret Marx's theses concerning the approximateness of (...) the realization of the laws of society. Let us take, for example, Marx's thesis that "In general, in capitalist production general laws are realized in a very confused and approximate way, merely as a prevailing tendency, as a kind of average among constant fluctuations that is never solidly established."1 Some investigators see this as an objectively existing social law in itself, attributing to it an "inexactitude" of operation, variation, and approximation, instead of seeing it as a specific application of a particular law. They thus forget that Marx said, in the Foreword to the very first volume of Capital: "The question does not specifically have to do with a greater or lesser degree of development of the social antagonisms that derive from the natural laws of capitalist production, but rather lies in these laws themselves, these trends, which operate and are realized with iron necessity.". (shrink)

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)

We investigate strong versions of enumeration reducibility, the most important one being s-reducibility. We prove that every countable distributive lattice is embeddable into the local structure $L(\mathfrak D_s)$ of the s-degrees. However, $L(\mathfrak D_s)$ is not distributive. We show that on $\Delta^{0}_{2}$ sets s-reducibility coincides with its finite branch version; the same holds of e-reducibility. We prove some density results for $L(\mathfrak D_s)$ . In particular $L(\mathfrak D_s)$ is upwards dense. Among the results about reducibilities that are stronger than s-reducibility, (...) we show that the structure of the $\Delta^{0}_{2}$ bs-degrees is dense. Many of these results on s-reducibility yield interesting corollaries for Q-reducibility as well. (shrink)

Faults; religious aspects; Islam; Islamic daʻwah.

Orthogonality of all families of pairwise weakly orthogonal 1-types for ℵ0-categorical weakly o-minimal theories of finite convexity rank has been proved in 6. Here we prove orthogonality of all such families for binary 1-types in an arbitrary ℵ0-categorical weakly o-minimal theory and give an extended criterion for binarity of ℵ0-categorical weakly o-minimal theories . © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

We show that the Q-degree of a hyperhypersimple set includes an infinite collection of Q1-degrees linearly ordered under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\leq_{Q_1}}$$\end{document} with order type of the integers and consisting entirely of hyperhypersimple sets. Also, we prove that the c.e. Q1-degrees are not an upper semilattice. The main result of this paper is that the Q1-degree of a hemimaximal set contains only one c.e. 1-degree. Analogous results are valid for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...) \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^0}$$\end{document}s1-degrees. (shrink)

Muslim women; religious life; Islmic call.