This paper introduces the new novel four-parameter Weibull distribution named as the Marshall–Olkin alpha power Weibull distribution. Some statistical properties of the distribution are examined. Based on Type-I censored and Type-II censored samples, maximum likelihood estimation, maximum product spacing, and Bayesian estimation for the MOAPW distribution parameters are discussed. Numerical analysis using real data sets and Monte Carlo simulation are accomplished to compare various estimation methods. This novel model’s supremacy upon some famous distributions is explained using two real data sets (...) and it is shown that the MOAPW model can achieve better fits than other competitive distributions. (shrink)

Modelling data in applied areas particularly in reliability engineering is a prominent research topic. Statistical models play a vital role in modelling reliability data and are useful for further decision-making policies. In this paper, we study a new class of distributions with one additional shape parameter, called a new generalized exponential-X family. Some of its properties are taken into account. The maximum likelihood approach is adopted to obtain the estimates of the model parameters. For assessing the performance of these estimators, (...) a comprehensive Monte Carlo simulation study is carried out. The usefulness of the proposed family is demonstrated by means of a real-life application representing the failure times of electronic components. The fitted results show that the new generalized exponential-X family provides a close fit to data. Finally, considering the failure times data, the Bayesian analysis and performance of Gibbs sampling are discussed. The diagnostics measures such as the Raftery–Lewis, Geweke, and Gelman–Rubin are applied to check the convergence of the algorithm. (shrink)

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.

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)

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)

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)

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)

Для специалистов, интересующихся проблемами этики.

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.

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.

Let A be an infinite Δ₂⁰ set and let K be creative: we show that K≤Q A if and only if K≤Q₁ A. (Here ≤Q denotes Q-reducibility, and ≤Q₁ is the subreducibility of ≤Q obtained by requesting that Q-reducibility be provided by a computable function f such that Wf(x)∩ Wf(y)=∅, if x \not= y.) Using this result we prove that A is hyperhyperimmune if and only if no Δ⁰₂ subset B of A is s-complete, i.e., there is no Δ⁰₂ subset (...) B of A such that \overline{K}≤s B, where ≤s denotes s-reducibility, and \overline{K} denotes the complement of K. (shrink)

It is proved that if 1 $\langle \mathscr{D}_{2n}, \leq, P\rangle$ and $\langle \mathscr{D}_{2n}, \leq, P\rangle$ are not elementary equivalent where P is the predicate P(a) = "a is a Π 0 1 e-degree".

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.

We show that the _sQ_-degree of a hypersimple set includes an infinite collection of \(sQ_1\) -degrees linearly ordered under \(\le _{sQ_1}\) with order type of the integers and each c.e. set in these _sQ_-degrees is a hypersimple set. Also, we prove that there exist two c.e. sets having no least upper bound on the \(sQ_1\) -reducibility ordering. We show that the c.e. \(sQ_1\) -degrees are not dense and if _a_ is a c.e. \(sQ_1\) -degree such that \(o_{sQ_1}, then there exist (...) infinitely many pairwise _sQ_-incomputable c.e. _sQ_-degrees \(\{c_i\}_{i\in \omega }\) such that \((\forall \,i)\;(a. (shrink)

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 ${\mathbf 0}_e'$.

A Turing degreedis the degree of categoricity of a computable structure${\cal S}$ifdis the least degree capable of computing isomorphisms among arbitrary computable copies of${\cal S}$. A degreedis the strong degree of categoricity of${\cal S}$ifdis the degree of categoricity of${\cal S}$, and there are computable copies${\cal A}$and${\cal B}$of${\cal S}$such that every isomorphism from${\cal A}$onto${\cal B}$computesd. In this paper, we build a c.e. degreedand a computable rigid structure${\cal M}$such thatdis the degree of categoricity of${\cal M}$, butdis not the strong degree of categoricity (...) of${\cal M}$. This solves the open problem of Fokina, Kalimullin, and Miller [13].For a computable structure${\cal S}$, we introduce the notion of the spectral dimension of${\cal S}$, which gives a quantitative characteristic of the degree of categoricity of${\cal S}$. We prove that for a nonzero natural numberN, there is a computable rigid structure${\cal M}$such that$0\prime$is the degree of categoricity of${\cal M}$, and the spectral dimension of${\cal M}$is equal toN. (shrink)

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.

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.

ḥeleḳ rishon. Sheʼelot u-teshuvot be-ʻinyanim shonim mi-toratenu ha-ḳedoshah shebi-khetav ṿeshe-be-ʻal peh -- ḥeleḳ sheni. Leḳet mikhtavim u-maʼamarim le-ḥizuḳ ṿe-hitʻorerut ba-ʻavodat ha-Shem yitbarakh -- ḥeleḳ shelishi. Leḳet mikhtavim me-a.m. ṿe-r. ha-Rav Ḥayim Shaʼul z. l.l. h.h. Grainiman baʻal ha-ḥidushim u-veʼurim".

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.

Although the effectiveness of some tobacco programs and policies has been clearly demonstrated in reducing the overall population smoking prevalence, the health benefits are not equally distributed across all socio-economic classes; a situation that clearly runs against the equalitarian ethos of most modern states. In this article, we evaluate the benefits of using Sen’s Capability Approach as a theory of social justice to guide public health program and policy development in a way that would prevent the further increase of inequalities (...) in health outcomes. Starting from four consensual goals of tobacco control practice (i.e. that individuals live a smoke-free life, that smokers quit smoking, that non-smokers are protected from exposure to second-hand smoke and that smoking cessation support is accessible) we found that besides the standard interventions (e.g. education on the harms of smoking, policies to reduce exposure to SHS) an iniquity-proof tobacco control program needs also to address the lack of options of underprivileged people in affordable smoke-free settings and in leisure activities. We conclude that an ethical tobacco prevention program needs to address the broader social determinants of health such as the socio-economic policies that put a strain on people’s capacity to shun or quit smoking. (shrink)

In this paper we develop the elementary theory of modules in the category Sh of sheaves over right-sided idempotent quantales. The main ingredient is the construction of a logic sound for Sh . As an application we prove that in Sh , a finitely generated projective module is free , a result that is relevant to the study of representation of non-commutative C ∗ -algebras.

The article explores the private nature of subjectivity in programs of integration the phenomenology with naturalism. It is considered if their tools are relevant for the phenomenological, rather than naturalistic way of subjectivity’s explaining. Justification of the key ideas is provided with the help of such concepts as “body image”, “body scheme”, (Sh. Gallagher), “ontological significance” (L. Baker), “experience”, “cognitive niches” (F. Varela), “transparent body” (T. Fuchs). Based on the traditional phenomenology of E. Husserl, it is shown that a set (...) of approaches that integrate phenomenology and naturalism within the framework of “first-person philosophy” can be characterized as a phenomenology without a phenomenological subject. It is shown that the phenomenological nature of the self-perspective in integrative programs is more likely to be understood as the qualification and privacy of subjectivity, while the transcendental aspect of the unobservable and biased consciousness is practically not taken into account. The article concludes that the logic of some projects of integration of phenomenology and naturalism overlook this transcendental peculiarity of consciousness, its fundamentally unobserved character. The classical phenomenological approach emphasizes on the extra-natural, biased, and non-empirical nature of consciousness. The role and significance of the phenomenological approach is not limited to the idea of “what-is-likeness” and privacy of subjective states. Phenomenology, which preserves the idea of the subject, means a radical break with the ontology of things and, in general, with the ontology of something objective at all. (shrink)

The paper analysis the strategies and concepts developed in the world in modern directions: innova- tive economy, digital economy, artificial intelligence, Industry 4.0 and others. The problem is to determine the initial fundamental parameters of order and their prospects in the global world, the definition and principles of artificial intel- ligence systems, its structure and important aspects and principles of future science and technology in analysis and synthesis based on synergetic approaches, innovative, information, converged technologies, taking into account the design (...) of future and viable and safe and sustainable development in the context of Industry 4.0, digital economy and Society 5.0. The general scheme of the integrated model of sustainable and socio-humanitarian development in the global system is proposed, which the authors call the noosphere model of sustainable and safe development as an important fundamental platform for the design and creation of AIS. In the XXI century education, science and innova- tive technologies becomes the «basis» of the spiritual and material reproduction of man, transforming the society of the XXI century into an educational society, ensures compliance with the law of advanced development of human quality, quality of social intelligence and quality of educational systems in society. noosphere evolution. Industry 4.0 is the next stage in the digitalization of production technologies with the accelerated introduction of new developments and cyberphysical systems, which is changing business models. Accordingly, Industry 4.0 as a separate segment of digital manufacturing technologies takes its place among other digital sectors. The analysis of the Strategies and Concepts developed in the world in modern directions: innovative economy, digital economy, artificial intelli- gence, Industry 4.0 and others is carried out in the work. The problem is to determine the initial fundamental para- meters of order and their prospects in the global world, the definition and principles of artificial intelligence systems, its structure and important aspects and principles of future science and technology in analysis and synthesis ba- sed on synergetic approaches, innovative, information, converged technologies, taking into account the design of future and viable and safe and sustainable development in the context of Industry 4.0, DE and Society 5.0. The main scientific and technological factors in the 21st century will be the development of: Artificial Intelligence, Nano Technologies, Bio-Media Technologies, Cognitive Technologies and Socio-Humanitarian Technologies. More specifically – this is the modern development of Innovative Technologies: «NBIC SH». Therefore, it is necessary to note the importance of taking into account the principle of I2K2+SH, ie: Intellectualization, Integration, Convergence, Coevolution and Socio- humanitarian technologies. It is important and necessary to take into account modern principles of designing a su- stainable and secure AIS and solving the problem of Harmonization between 2 worlds: Real and Virtual, especially in their hybridization. Our immediate future is a hybrid nonlinear world. Note that digitalization, artificial intelligence and robotics will be the main drivers of global economic growth by 2030E. An important paradigm and platform is the Integrated System: for Industry 4.0, DE and AI, taking into account the complex principle of I2K2+SH. If the transition of the Ukrainian economy to an innovative one does not take place in the next 3-5 years, Ukraine will remain in the backyard of civilization. (shrink)

-- -- ḫelek 2. Mikhtav 73-mikhtav 143 -- ḫelek 3. Mikhtav 144-mikhtav 206 --.

[ḥeleḳ 1]. Al hilkhot meḳaḥ ṭaʻut, onaʼah u-matanah, Ḥ m. 227-249 -- ḥeleḳ 2. ʻAl Hilkhot avedah u-metsiʼah, hefḳer, periḳah u-ṭeʻinah, genevah u-gezelah, Ḥ. m. 259-275, 348-377.