On Integration in Partially Ordered Groups

A semitopological group (topological group) is a group endowed with a topology for which multiplication is separately continuous (multiplication is jointly continuous and inversion is continuous). In this paper we answer (Arhangel’skii et al., Math Maced 8:1–19, 2010, Problem 10.4), by showing that if (G, ·, τ) is a semitopological group and (G, τ) is homeomorphic to a product of Cech-complete spaces, then (G, ·, τ) is a topological group.

In this note, we firstly discuss some properties of spaces which are countably sieve-complete, densely q-complete and strongly Baire. By some known conclusions, we finally show that if G is a regular countably sieve-complete semitopological group then G is a topological group. If a regular semitopological group G has a dense subgroup which is countably sieve-complete (densely q-complete), then G is a topological group. If G is a regular countably sieve-complete semitopological group then G is a D-space if and only if G is paracompact. We point out that some conditions in Theorem 2.14 and Corollary 2.15 in [17] are not essential.

LetS be a uniform semigroup (this includes all topological groups and affine semigroups). We show that a certain space of uniformly continuous functions onS has a left invariant mean iffS has the fixed point property for uniformly continuous affine actions ofS on compact convex sets. This is closely related to but independent of the results of T. Mitchell in [13] and A. Lau in [10]. Interesting examples and consequences are given for the special cases of topological groups and affine convolution semigroups of probability measures on a locally compact semigroup or group.

In this paper, it is shown that every compact Hausdorff $K$-space has countable tightness. This result gives a positive answer to a problem posed by Malykhin and Tironi [‘Weakly Fréchet–Urysohn and Pytkeev spaces’, Topology Appl.104 (2000), 181–190]. We show that a semitopological group $G$ that is a $K$-space is first countable if and only if $G$ is of point-countable type. It is proved that if a topological group $G$ is a $K$-space and has a locally paracompact remainder in some Hausdorff compactification, then $G$ is metrisable.

The Ellis theorem and continuity in groups

Totally Lindelöf and totally ω-narrow paratopological groups

ABSTRACT. Some results of Mukherjea and Tserpes are generalized by showing that any sequentially compact, cancellative topological semigroup is a topological group. Hence, any countably compact, cancellative topological semigroup with any additional condition that would imply sequential compactness is also a topological group. Finally, it is shown that any w‐bounded, cancellative topological semigroup is also a topological group.

Contour Integrals and Vector Calculus on Fractal Curves and Interfaces

Countably compact sequential topological semigroup with two-sides cancellations is a topological group

We prove that the existence of a selective ultrafilter implies the existence of a countably compact Hausdorff group topology on the free Abelian group of size continuum. As a consequence, we show that the existence of a selective ultrafilter implies the existence of a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group).

The following study aims to compare the policies of European countries related to the treatment of international protection holders, especially in the initial moments of the integration process. The object of the analysis is the policy frameworks for integrating international protection holders and how these frameworks are reflected in the relevant policy documents. We compare 12 policies through the lens of Hartmut Esser’s theoretical model of social integration. In the study, we identify four main findings: (1) the EU definition of international protection holder integration is paradoxically best matched by the public policies of non-EU countries; (2) the labor market is still perceived as a key area in the integration process; (3) despite the declared two-way principle, the topic of removing barriers to integration is neglected; (4) the term community is used exclusively in relation to the local, neighborhood context, not in relation to (ethnic) “origin”.

In the formation of a common market within the framework of interstate associations (Unions), the goal of improving the health of the member states population can be achieved, among other things, by providing an unimpeded access to safe, effective and quality medicines (drugs). One of the elements is activities in the field of these medicinal products compounding. This review has been prepared by authors due to the lack of information in the Russian-language literature on the regulation of this area in the current legal systems of the BRICS countries.The aim of the work was to analyze the regulatory mechanisms and current approaches to the organization of activities in the field of medicinal products compounding, presented in the legislation of the BRICS interstate association (Union) member countries, including their structuring (systematization) in order to develop proposals for the convergence of these practices.Materials and мethods. PubMed, Google Scholar, elibrary.ru, and specialized databases of regulatory legal documents of the BRICS countries were used as search resources. The following keywords were used as search keywords: “drug”, “drug product”, “medicinal products compounding”, “pharmacy organization”, “medical organization”, “compounding”, “drug preparation”, “drug dilution (reconstitution)” in English, Portuguese, Spanish, Chinese and Arabic. The paper uses empirical, theoretical, quantitative tools, including the analysis of a wide list of relevant sources - regulatory legal documents governing the activities of compounding pharmacies in the BRICS countries.Results. The study presents key regulatory legal acts and documents, analyzes them and describes the main provisions of the legislative framework for the organization of activities in the field of medicinal products compounding. The identified peculiarities determine the need to rethink the current state of the Russian regulation of the medicinal products compounding sector. The study emphasizes the need to improve regulatory approaches in Russia. The BRICS countries can strive to develop the best practices and “gold” standards for the organization of this socially important activity in the field of medicinal products compounding. Such an approach can led to the creation of a unified good practice in compounding and dispensing of medicinal products. Conclusion. The authors of the study consider it advisable to carry out a further and more detailed elaboration of the convergence issues of regulatory practices of both health care systems and pharmaceutical industries in the BRICS member states. It has been proposed to develop and form a “Roadmap” (an action plan) for the development of the cooperation between the BRICS member states in the field of health care and pharmaceutical industry in order to intensify integration processes and build a modern model of the public health and drug market, including joint research and development by world-class scientific centers for technological development of the interstate association (Union) countries.

In this article a definition of integration is given, defining integration as a process whereby two or more actors form one new actor. There are many ways in which this may be brought about, and the process may have very different consequences, but conditions and consequences should not be confused with the definition. Three types of integration are then distinguished: territorial, organizational, and associational. These three types can be combined in many ways, and nations can be analyzed in terms of how these processes of integration are combined inside the nation. Corresponding reasoning may be used for the analysis of world integration. The three types of integration are then analyzed in terms of how they satisfy basic human and social needs. It is pointed out that whereas organizational and associational integration are complementary and always will satisfy some human needs, territorial integration depends very much on communication and will tend to disappear with in creasing communication. But organizational integration will lead to crises that can only be alleviated by means of associational integration, and vice versa. Hence, a general world trend of decreasing territorial integration and a pattern of dialectical change from organizational to associational and back again are predicted. The basic problem of a substitute for the decreasingly important territorial integration is then left unanswered.

Empirical and theoretical insights from the rich body of research on ‘integration’ in migration studies have led to increasing recognition of its complexity. Among European scholars, however, there remains no consensus on how integration should be defined nor what the processes entail. Integration has, moreover, been the subject of powerful academic critiques, some decrying any further use of the concept. In this paper we argue that it is both necessary and possible to address each of the five core critiques on which recent criticism has focused: normativity; negative objectification of migrants as ‘other’; outdated imaginary of society; methodological nationalism; and a narrow focus on migrants in the factors shaping integration processes. We provide a definition of integration, and a revised heuristic model of integration processes and the ‘effectors’ that have been shown to shape them, as a contribution to a constructive debate on the ways in which these challenges for empirical research can be overcome.

The process known as the differentiation of functions in the Calculus does not present the insurmountable difficulties one experiences in attacking the converse problem associated with the Integral Calculus. As is well known, there are many functions which we cannot integrate, and as the process of integration is really a summation, this means there are many areas which cannot be evaluated by exact methods. There are many cases in various branches of science in which it is required to determine the area of a closed curve obtained by plotting a series of observations. The engineer, for example, has to determine the areas of indicator and similar diagrams, the naval architect has to calculate volumes, and centres of gravity or buoyancy by approximate methods. The mathematician may be called upon to evaluate definite integrals which cannot be integrated directly, such as the elliptic integrals. The problem reduces simply to the consideration of the determination of the area between the curve y = f ( x ), the ordinates x = x 0 and x = x 0 + nh , and the axis of x ; and the first part of the paper will be devoted to the methods of obtaining empirical rules for approximation to the evaluation of such an area when f ( x ) cannot be directly integrated. In the second part, the mechanical methods of integration will be considered, including demonstrations with the different types of instruments illustrating these methods.