The Relativity of Indeterminacy

A long-standing tradition, largely present in both the physical and the philosophical literature, regards the advent of (special) relativity—with its block-universe picture—as the failure of any indeterministic program in physics. On the contrary, in this paper, we note that upholding reasonable principles of finiteness of information hints at a picture of the physical world that should be both relativistic and indeterministic. We thus rebut the block-universe picture by assuming that fundamental indeterminacy itself should also be regarded as a relative property when considered in a relativistic scenario. We discuss the consequence that this view may have when correlated randomness is introduced, both in the classical case and in the quantum one.

Some New Variants of Relative Regularity via Regularly Closed Sets

Every topological property can be associated with its relative version in such a way that when smaller space coincides with larger space, then this relative property coincides with the absolute one. This notion of relative topological properties was introduced by Arhangel’skii and Ganedi in 1989. Singal and Arya introduced the concepts of almost regular spaces in 1969 and almost completely regular spaces in 1970. In this paper, we have studied various relative versions of almost regularity, complete regularity, and almost complete regularity. We investigated some of their properties and established relationships of these spaces with each other and with the existing relative properties.

Intersectoral Relations of Civil Law with the Right to Subsoil Use (Mining Law) in the Context of the Russian Federation Arctic Zone Development

The need to develop the doctrine of intersectoral relations between civil law and the right to subsoil use is substantiated. The author highlights the main directions of intersectoral interaction and the impact of civil law and the right to subsoil use, including ownership of the subsoil, the ownership of the extracted minerals, mining waste, the right to own geological information, relative property obligations between the state and the subsoil user, protective legal relations.

Peculiarities of property management of subsidiary companies established by the joint-stock companies with state participation (on the example of “Russian Railways” JSC)

The relevance of this topic is substantiated by the insufficient coverage within scientific literature of the questions of legal regime of property of subsidiary companies with state participation in share capital, and management of state property transferred to such economic entities. The majority of research on the topic of property management of legal entities with state participation is structured through the prism of the efficiency of usage of state property, leaving outside the scope property sphere of subsidiary companies, which is also of considerable interest. The object of this article is the process of property management in the joint-stock companies with state participation, while the subject is the relations between the state-owned joint-stock company and its subsidiaries in the property sphere. Special attention is given to the practice of “Russian Railways” JSC (100% of which belongs to the Russian Federation) that is one of the largest private owners of real estate in Russia , and consolidates significant volume of money, shares and other movable property, which makes “Russian Railways” JSC and its subsidiary companies a fruitful ground for studying the topic at hand. The article underlines the need for identification of boundaries of the corporate and economic control of the parent company over its subsidiary, the absence of which in the current legislation can lead to a relative property autonomy of the subsidiaries of large joint-stock companies with state participation. Therefore, the author proposes mechanisms for improvement of legislation.

A VON NEUMANN ALGEBRA CHARACTERIZATION OF PROPERTY (T) FOR GROUPOIDS

For an arbitrary discrete probability-measure-preserving groupoid $G$, we provide a characterization of property (T) for $G$ in terms of the groupoid von Neumann algebra $L(G)$. More generally, we obtain a characterization of relative property (T) for a subgroupoid $H\subset G$ in terms of the inclusions $L(H)\subset L(G)$.

On the large-scale geometry of diffeomorphism groups of 1-manifolds

We apply the framework of Rosendal to study the large-scale geometry of the topological groups {\operatorname{Diff}_{+}^{k}(M^{1})} , consisting of orientation-preserving {C^{k}} -diffeomorphisms (for {1\leq k\leq\infty} ) of a compact 1-manifold {M^{1}} ( {=I} or {\mathbb{S}^{1}} ). We characterize the relative property (OB) in such groups: {A\subseteq\operatorname{Diff}_{+}^{k}(M^{1})} has property (OB) relative to {\operatorname{Diff}_{+}^{k}(M^{1})} if and only if {\sup_{f\in A}\sup_{x\in M^{1}}\lvert\log f^{\prime}(x)|<\infty} and {\sup_{f\in A}\sup_{x\in M^{1}}|f^{(j)}(x)|<\infty} for every integer j with {2\leq j\leq k} . We deduce that {\operatorname{Diff}_{+}^{k}(M^{1})} has the local property (OB), and consequently a well-defined non-trivial quasi-isometry class, if and only if {k<\infty} . We show that the groups {\operatorname{Diff}_{+}^{1}(I)} and {\operatorname{Diff}_{+}^{1}(\mathbb{S}^{1})} are quasi-isometric to the infinite-dimensional Banach space {C[0,1]} .

Relative Inner Amenability and Relative Property Gamma

Let $H$ be a proper subgroup of a discrete group $G$. We introduce a notion of relative inner amenability of $H$ in $G$, we prove some equivalent conditions and provide examples coming mainly from semidirect products, as well as counter-examples. We also discuss the corresponding relative property gamma for pairs of type II$_1$ factors $N\subset M$ and we deduce from this a characterization of discrete, icc groups which do not have property (T).

Relative Property

Most historians of slavery in the Americas treat masters of color who owned their own kin as an oddity, a scribal error, or as a topic to evade. Most others conclude that ruthlessly capitalistic owners reserved such behavior for slaves unrelated to them, and owned their own kin as slaves in name only, with the intention of providing protection and eventual manumission. This article considers several cases of close-kin ownership, particularly in Suriname, and explores the role of coercive economy in families emerging from enslavement, arguing that the capitalistic values of slaveholding pervaded families approaching freedom, often informing both their economic behavior and their interpersonal relations.