Order convergence in infinite-dimensional vector lattices is not topological

In this note, we show that the order convergence in a vector lattice $X$ is not topological unless $\dim X<\infty$. Furthermore, we show that, in atomic order continuous Banach lattices, the order convergence is topological on order intervals

Eclipses of the inner satellites of Jupiter observed in 2015

During the 2014-2015 campaign of mutual events, we recorded ground-based photometric observations of eclipses of Amalthea (JV) and, for the first time, Thebe (JXIV) by the Galilean moons. We focused on estimating whether the positioning accuracy of the inner satellites determined with photometry is sufficient for dynamical studies. We observed two eclipses of Amalthea and one of Thebe with the 1 m telescope at Pic du Midi Observatory using an IR filter and a mask placed over the planetary image to avoid blooming features. A third observation of Amalthea was taken at Saint-Sulpice Observatory with a 60 cm telescope using a methane filter (890 nm) and a deep absorption band to decrease the contrast between the planet and the satellites. After background removal, we computed a differential aperture photometry to obtain the light flux, and followed with an astrometric reduction. We provide astrometric results with an external precision of 53 mas for the eclipse of Thebe, and 20 mas for that of Amalthea. These observation accuracies largely override standard astrometric measurements. The (O-C)s for the eclipse of Thebe are 75 mas on the X-axis and 120 mas on the Y-axis. The (O-C)s for the total eclipses of Amalthea are 95 mas and 22 mas, along the orbit, for two of the three events. Taking into account the ratio of (O-C) to precision of the astrometric results, we show a significant discrepancy with the theory established by Avdyushev and Ban'shikova in 2008, and the JPL JUP 310 ephemeris.Comment: 7 pages, 10 figures, 4 table

Unbounded Convergence in the Convergence Vector Lattices: a Survey

on the occas'ion of hi,s 65th anniuersary Various convergences in vector lattices were historicalll' a subject of deep investigation v'hich stems from the begining of the 20th century in works of Riesz, Kantorovich, Nakano, !'ulikh, Zanen, a',d marl)/ other mathematicians. The stud,v of the unbounded order convergence had been initiated b5' Nakano in late 40th in connection with Birkhoff's ergodic theorem. The idea of Nakano $-as to define the almost everywhere convergence in terms of lattice operations without the direct use of measure theory. Many years later it was recognised that the unbounded order convergence is also rathe useful in probability theory. Since then. the idea of investigating of convergences by using their unbounded versions, have been exploited in several papers. For instance, unbounded convergences in vector lattices have attracted attention of many researchers in order to find nes' approaches to r,-arious problems of functional analysis, operator theorl', variational caicuius, theory of risk measures in mathematical finance, stochastic processes, etc. Some of those unbounded convergences, like unbounded norm convergence. unbounded multi-norm convergence. unbounded r-convergence are topological. Others are not topological in general, for example: the unbounded order convergence, the unbounded relative uniform convergence) various unbounded convergences in lattice-normed lattices, etc. Topological convergences are. as usual, more flexible for an investigation due to the compactness arguments, etc. The non-topological convergences axe more complicated in genelal, as it can be seen on an example of the a.e-convergence. In the present paper we present recent developments in convergence vector lattices with emphasis on reiated unbounded convergences. Special attention is paid to the case of con\rergence in lattice multi pseudo normed vector lattices that generalizes most of cases which were discussed in the literature in the last 5 vears

um-Topology in multi-normed vector lattices

Let be a separating family of lattice seminorms on a vector lattice X, then is called a multi-normed vector lattice (or MNVL). We write if for all . A net in an MNVL is said to be unbounded m-convergent (or um-convergent) to x if for all . um-Convergence generalizes un-convergence (Deng et al. in Positivity 21:963–974, 2017; Kandić et al. in J Math Anal Appl 451:259–279, 2017) and uaw-convergence (Zabeti in Positivity, 2017. doi: 10.1007/s11117-017-0524-7 ), and specializes up-convergence (Aydın et al. in Unbounded p-convergence in lattice-normed vector lattices. arXiv:1609.05301 ) and -convergence (Dabboorasad et al. in -Convergence in locally solid vector lattices. arXiv:1706.02006v3 ). um-Convergence is always topological, whose

Problem of Periodization of the World History in Soviet Social Science of the 1920s

The article is devoted to the development of the periodization of world history in Soviet social science of the 1920s. Various options for periodization that existed in the educational literature on this discipline in the specified period are considered. It is noted that Soviet social scientists abandoned the traditional division of history into Antiquity, the Middle Ages and the New Time and introduced a new approach to the periodization of world history: primitive (including one or two formations in different versions), feudalism, commercial capitalism and industrial capitalism. The methodological basis of this approach associated with the works of K. Marx, E. Meyer and M.N. Pokrovsky is revealed. A hypothesis is proposed according to which such an approach to world history meant the recognition by the Soviet social scientists of the non-linear nature of the historical process and the endowment of historical time with meaningful, class, characteristics. The author of the article believes that these processes in Soviet social science corresponded to a “temporal turn” in European thought of the first third of the twentieth century, characterized by the consideration of time as a process that has semantic content and depends on the subject. It is noted that, despite the return of the terms Antiquity, Middle Ages, and New Time in the 1930s, this periodization already included an idea of the class nature of historical time, which remained in Soviet science until the end of the existence of the USSR

Проблема периодизации всеобщей истории в «Кратком курсе экономической науки» А. А. Богданова

The article is devoted to the problem of periodization of universal history in the work "A Short Course in Economic Science" written by Alexander Bogdanov. It analyzes the changes in the periodization of the historical process in various editions of the work, identifies the intellectual sources of those changes and establishes a connection between the evolution of Bogdanov’s historical concept and the development of historical science in the late 19th and early 20th centuries. The main direction in the evolution of Bogdanov’s historical views was the transition from a linear progressive scheme of world history to a description of history as a complex non-linear process in which periods of development are combined with periods of decline and stagnation. Abandoning the idea of steady linear progress, Bogdanov also abandoned the strict correspondence between a specific economic form and a certain historical era and concluded that various economic forms could coexist. The changes in Bogdanov’s approaches to the question of the role of economic forms in the periodization of world historical process testify to his search for special features specifying various eras in the history of mankind and reflect a general interest in the substantial characteristics of time characteristic of the European intellectual space of the first third of the 20th century. © 2020, Perm State University. All rights reserved