Universal Space Research Articles

Computably and punctually universal spaces

We prove that the standard computable presentation of the space C[0,1] of continuous real-valued functions on the unit interval is computably and punctually (primitively recursively) universal. From the perspective of modern computability theory, this settles a problem raised by Sierpiński in the 1940s.We prove that the original Urysohn's construction of the universal separable Polish space U is punctually universal. We also show that effectively compact, punctual Stone spaces are punctually homeomorphically embeddable into Cantor space 2ω; note that we do not require effective compactness be primitive recursive. We also prove that effective compactness cannot be dropped from the premises by constructing a counterexample.

Традиционные духовные ценности как глокальная основа интерпретации аксиологических концептов в кинодискурсе

The article studies multimodal verbal, visual and auditory mechanisms of contamination of universal, global and national value spaces in the aspect of dominant axiological concepts’ interpretation of regional film discourse. Film discourse can be considered as the most representative field for the shift of value dominants, combining various semiotic code systems for the most effective implementation of the perlocutionary effect, pursuing the main goal of transforming the conceptual and value space of the recipient. As part of the analysis of the key methods of glocalization of axiologems, a complex of methods of the hermeneutic and interpretative approach was used, including contextual, linguacultural, etymological, linguaaxiological, discursive and modal methods. The polymodal and polycode nature of the empirical material requires systematic consideration of ways to intensify traditional spiritual values in their verbalization. The key method of contaminating tradition and innovation in modifying the content of axiological concepts is a constitutive link to global, universal components shared by other ethnonational communities. Such an association occurs in the context of the expansion of the positive and negative spaces of the described concept deportation, which is significant both for the Karachay-Balkarian linguaculture under consideration and for many peoples of the USSR. The concept represents a whole precedent world, including individual concepts for concretizing values and anti-values in a situational and local rethinking. The key axiological concepts in the translation of traditional values and anti-values of the deportation are recognized as jashau (“life”), as a global axiologeme, with the concept of elum/ajal (“death”) leveled out and thrown to the periphery; as well as private locally interpreted concepts bilim (“knowledge”), syy/namys (“dignity/honor”), kishilik (“courage”), azatlyk (“freedom”). The overtones of universal perception in the generalized content of these concepts make it possible to create a glocalized space of interpretation that reflects common values and meanings in the ethno-national linguistic consciousness.

International Legal Outer Space Policy of the United States of America

The new outer space natural resources policy of the United States, outlined between 2015 and 2020 by national legislation (including the U.S. Space Resource Exploration and Exploitation Act of 2015 and the U.S. Executive Order of April 6, 2020) and in 2020 also by the U.S.-initiated separate international Artemis Aсcords, is meant to be consistent with the universal Outer Space Treaty of 1967, the basic source of international space law. This policy, which opens access for private investors to natural resources of celestial bodies under the American legislation has commanded a wide international attention not only because of the exhilarating data on the high density of deposits of precious metals and other highlydemanded natural resources on some asteroids, but also because of the question raised during the workings of the UN Committee on the Peaceful Uses of Outer Space: does this policy violate the US obligations under international law according to which the use of outer space, including celestial bodies, constitutes "the province of all mankind"? Or is it more rational for other states to create a similar international format of selective cooperation in order to be among the first to exploit the wealth of nearby celestial bodies without devoting political efforts to collectively establish international offense committed by the United States? Can a national legal and international legal response of Russia, China and other states, which are not subordinated to the United States, supported by their technological and industrial outer space infrastructure applicable to the outer space natural resources activities, become an effective incentive to negotiate a universal special international legal regime? It appears to be feasible since it is necessary to ensure conflict-free and, consequently, economically stable outer space natural resources activities corresponding to the national interests of the majority of states even with different international legal positions.

Incomplete preferences or incomplete information? On Rationalizability in games with private values

I propose a notion of Rationalizability, called Incomplete Preference Rationalizability, for games with incomplete preferences. Under an appropriate topological condition, the incomplete preference rationalizable set is non-empty and compact. I argue that incomplete orderings can be used to model incomplete information in strategic settings. Drawing on this connection, I show that in games with private values the sets of incomplete preference rationalizable actions, of belief-free rationalizable actions (Battigalli et al., 2011; Bergemann and Morris, 2017), and of interim correlated rationalizable actions (Dekel et al., 2007) of the universal type space coincide.

Geometry of universal embedding spaces for almost complex manifolds

Geometry of universal embedding spaces for almost complex manifolds

The world of “worlds” in the dimensions of semiosis With the example of the linguacultural space of Kyiv

The relevance of the article is due to the constant dynamics of the lexicon as a manifestation of the essential property of the language and, in particular, of the phenomenon of the development of semantics of the name world (світ), which became one of the most frequently used notional units of the Ukrainian language in the 21st century. The purpose of the study is to identify the peculiar features of the semantization process of the lexeme world (світ) using the example of the linguacultural space of Kyiv taking into account various dimensions of semiosis. The study is also aimed at establishing the factors that influenced the nominative activity of the unit and determining its linguo-pragmatic vector. The subject matter of the study is the nominative-referential and pragmatic potential of the name world (світ), recorded in mass media texts and Kyiv ergonymicon. To achieve the goal, the following methods and techniques were used: component analysis of the word, distributive analysis, analysis of dictionary definitions, the descriptive method, results of associative experiments, the constructive method, contextual analysis, content analysis, and techniques of quantitative analysis. The novelty of the study is determined by the complex multifaceted approach to elucidating the semantization process of the name world (світ), carried out on the basis of semiotics and linguacultural studies. As a result of the study of the semantics of numerous common and proper nominals with the world component, it was concluded that the reference of these nominations was affected by the actualization of the nuclear semes ‘limit’, ‘sphere’, ‘totality’, ‘completeness of volume’ (‘межа’, ‘сфера’, ‘сукупність’, ‘повнота обсягу’), and in addition, by the potential evaluative seme. Emphasis is placed on the general tendency towards the nomination of various semiotic spheres by units with spatial semantics. One of the main factors of the nominative activity of the name has been determined as the sound-symbolic and iconic nature of the sign, which ensures its euphony and aesthetic appeal, which, in its turn, is especially significant for ‘commercial’ names and advertising texts. Attention is paid to defining the specifics of comprehension and interpretation of knowledge and ideas about the world and their arrangement in mental space. On the comparison basis of the concept WORLD (СВІТ) as a Ukrainian linguacultural dominant with the universal domain SPACE (ПРОСТІР), the axiological cognitive features of ‘comprehensiveness’, ‘infinity’, ‘matter’, ‘cognition’ (‘всеосяжність’, ‘безмежність’, ‘матерія’, ‘пізнання’), which determine the linguo-pragmatic vector of nominations, have been allocated. Prospects for further research are seen in the study of the functional and pragmatic properties of the name world (світ) in different speech registers.

Three Ritual Steps between India and Iran

Abstract The use of triadic patterns is a well-known modality occurring in some Indo-Iranian mythological contexts. This fact has been considered as a phenomenon too generic, and its presence just noted as an unimportant evidence. But, in reality, this procedure, despite its potentially perplexing background, produces some symbolic implications, whose frequent occurrence should be better observed. For instance, within the Vedic and Brāhmaṇic framework, Viṣṇu makes three steps in order to enlarge the universal space, and for this reason this god is also called Trivikrama-, “Having Three Steps”. The present sequence, with its space-time implications, finds a correspondence in the disposition of the Vedic altar of Fire, which needs three footsteps of ground. Even more fitting and pertinent are the inevitable speculations emerging from the ritual meaning of the pebbles or stones called svayamātr̻ṇṇā, “naturally perforated”, placed by the Adhvaryu in the first, third and fifth layer of the brick-altar of the Agnicayana. They have a patent cosmological identity (see, e.g., ŚB 8.7.3.9–10). Within the Iranian context, references to the number three are equally relevant and not just meaningless. Three are the main steps of the soul of the dead after their meeting with the daēnā-, explicitly corresponding to three different cosmic levels, while the vara- of Yima, and the baršnūmgāh, a place of ritual purification, are divided in three parts, and in any case everything connected with them follows a triadic basis with multiples or submultiples of “three”, or again with fractions with an expressed denominator “three”. The act of piling up the perforated stones on the three layers of the Vedic fire altar presents deep cosmological implications, strictly connected also with the holes through which an imaginary column arises. The act of piling up (cinute) resounds the action to be performed by the soul in the Mazdean choreography of the afterlife, when the bridge (pərətu-) allowing the crossing of the intermediate space (that links earth and heaven) is piled up (by one who is cinuuaṇt-, presumably the soul itself). But piling the bricks and tending the fire are ritual performative actions expressed with the same verb and with actions, which inevitably resonate, as in the image of the third prince appearing within the afterlife choreography presented as a vision to the Sasanian Great Priest Kerdir. These occurrences, already focused on in past studies, evoke direct correspondences in ritual procedures emphasizing a definitive transition into another status, so that any triplication or any trifold implement has a special force and completeness.

Uniqueness and homogeneity of non-separable Urysohn universal ultrametric spaces

We first introduce the new notion of petaloid ultrametric spaces, which is intended to be a standard class of non-separable Urysohn universal ultrametric spaces. Next we prove that all petaloid spaces are isometric to each other and homogeneous for all finite subspaces (and compact subspaces). Moreover, we show that the following spaces are petaloid, and hence they are isometric to each other and homogeneous: (1) The space of all continuous functions, whose images contain the zero, from the Cantor set into the space of non-negative real numbers equipped with the nearly discrete topology, (2) the space of all continuous ultrametrics on a zero-dimensional infinite compact metrizable space, (3) the non-Archimedean Gromov–Hausdorff space, and (4) the space of all maps from the set of non-negative real numbers into the set of natural numbers whose supports are finite or decreasing sequences convergent to the zero.

Universal spaces for asymptotic dimension via factorization

AbstractThe main goal of this paper is to construct universal spaces for asymptotic dimension by generalizing to the coarse context an approach to constructing universal spaces for covering dimension using a factorization result due to Mardesic.

A Universal Space for the Bourbaki-Complete Spaces and Further Examples

In this paper it is provided an explicit embedding for complete metric spaces having a star-finite base of its uniformity into the universal space kappa ^{omega _0} times mathbb {R}^{omega _0}, where kappa ge omega _0 is the cellularity of the space and kappa ^{omega _0} is the Baire space of weight kappa . From this result, similar embeddings for general Bourbaki-complete uniform spaces as well as for metric spaces are derived. In particular, these embeddings partially preserve the uniform structure of the original space. Several examples of Bourbaki-complete metric spaces having no star-finite base for its metric uniformity are constructed.

VSpace: A browser-based vowel synthesiser

Two-formant representation of the universal vowel space is a foundational model in phonetics (Fant & Risberg 1963; Traunmüller & Lacerda 1983), but tools for rapid synthesis of vowel sounds corresponding to points in the vowel space are limited. Stand-alone applications such as the Formant Synthesizer Demo (Beskow, 2000) provide this functionality, and rich tools for formant synthesis are available in Praat (Boersma and Weenink, 2023), Matlab (Rabiner et al., 2023) and other platforms, but these tools are not universally accessible, while web-based speech synthesis tools (e.g., Thapen, 2017) do not typically allow systematic manipulation or quantification of key acoustic parameters. VSpace is a browser-based formant synthesizer developed using the Tone.js Web Audio framework. A universal vowel space is represented as a trapezoid scaled to typical male, female or child speaker formant ranges. Clicking on any point generates a vowel sound corresponding to the first and second formant frequencies selected, synthesized with typical F3 and F4 frequencies excited by a selectable source signal. IPA symbols corresponding to typical formant frequencies for language-specific vowel phonemes may be superimposed on the vowel space. Key synthesis parameters are configurable through the web interface to allow exploration of the acoustic consequences for vowel perception.

The Preservice Teachers’ Approaches Toward Incorrect Probability Problems

Identifying the mistakes in student responses and being able to manage the solution process are among the fundamental skills that should be acquired by the pre-service teachers. This skill is important in probability, about which students have a great number of misconceptions. The aim of this study was to determine the misconceptions in the student answers given by the researcher about probability and to examine the solution explanations of the preservice teachers. In this context, the student answers containing five wrong solutions were examined. Case study, one of the qualitative research methods, was used. Forty-two third grade preservice mathematics teachers participated in the study. A task-based interview was used in the study. The findings revealed that the participants were able to recognize simple and discrete probability problems more easily and provided correct solutions; however, they had difficulty in determining the universal space independent events and failed to detect the mistakes in the student answers successfully. As a result of the research, it was concluded that the importance attached to procedural knowledge should also be given to conceptual knowledge, what a concept means as well as what it does not mean should be explained, open-ended questions that will increase the power of reasoning should be used instead of typical problems, and more effective learning should be carried out by using different teaching methods and techniques.

COWORKING SPACE DI KOTA PONTIANAK DENGAN PENDEKATAN PRINSIP FLEKSIBILITAS DALAM ARSITEKTUR

The freelancer profession in the current era is in great demand by many people. In the world of freelancing, income and place of work are not fixed. Most freelancers have little business capital in leveraging skills and building relationships. In addition, freelancers do not have a limit on working time, but are free to determine where to work. Freelancer activity facilities in Pontianak City do not support convenience. They are active in cafes or coffee shops with a low level of privacy. Freelancers and other creative industry players need a place that is comfortable for their activities, both working, socializing, and collaborating in running their business. They need a container that fits their activities, namely coworking space. Coworking space is a multifunctional workplace that combines various commercial functions, such as offices, meetings, culinary, entertainment, and others. For this reason, it is necessary to design a coworking space in Pontianak City. The purpose of a coworking space is to accommodate various work activities, both individually and in groups, along with their supporting activities. The design method used is flexibility in architecture, including adaptable and universal space. The steps used are looking for problems, identifying, collecting data, analyzing, conveying ideas, selecting ideas, designing products, and evaluating. The expected result is a flexible spatial plan inside and outside the coworking space, adapting to the dynamics of freelancers and other users.

Экосистема инновационных сред территории: дополнительное образование и предпринимательство

In the article, based on part of the conclusions of a qualitative study of the acceleration infrastructure of universities and the concept of social ecosystems, the hypothesis of the concept of innovative environments in the region is formulated. Starting from the organizational weakness of small and medium-sized businesses, the secondary nature of the acceleration infrastructure of universities, and its incorrect orientation to "entrepreneurship" with mandatory access to startups, the structural insufficiency of the innovation environment of the region is stated. The solution to this problem is supposed to be within the framework of the formation of the socio-technical infrastructure of the ecosystem of innovative environments that ensure the continuity of training, education, research and project activities, and the employment of students. Based on the idea of the role of organizational infrastructure in the functioning of socio-cultural communities or environments, as well as on the changes resulting from the "digital" nature of this infrastructure, the main features of the regional innovation ecosystem are conceptualized. It is an organizational and meaningful association of existing subjects of innovative activity, the core of which is the education system (school – college – university), around which a platform of "additional education" is formed with the participation of business and scientific institutions as the main "consumers" of graduates. The cell of the environment is a small working group of students under the mentorship of a teacher, which undergoes a variable design and research trajectory under the supervision of "consumers". The event part of the environment necessarily includes not only project and educational work directly but also a cultural and leisure component. The problem of using the results of research and development is supposed to be solved by either bringing groups into the space of existing business ecosystems (technoparks, etc.) or by using the institute of venture studios acting as operators of such sites. Such an ecosystem should be a universal educational space organized by a "package of services" and included in the "package of social services" of the territory, the variability of which is provided by the function of participating "consumers", as well as a combination of educational, research, cultural, and leisure programs. The testing of the provisions laid down was carried out in the spring and summer of 2023 during the competitive program of the Innovation Promotion Fund.

Proper Equivariant Stable Homotopy Theory

This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective ‘proper’ alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from equivariant cells with compact isotropy groups; the adjective ‘genuine’ indicates that the theory comes with appropriate transfers and Wirthmüller isomorphisms, and the resulting equivariant cohomology theories support the analog of an R O ( G ) R O(G) -grading. Our model for genuine proper G G -equivariant stable homotopy theory is the category of orthogonal G G -spectra; the equivalences are those morphisms that induce isomorphisms of equivariant stable homotopy groups for all compact subgroups of G G . This class of π ∗ \pi _* -isomorphisms is part of a symmetric monoidal stable model structure, and the associated tensor triangulated homotopy category is compactly generated. Consequently, every orthogonal G G -spectrum represents an equivariant cohomology theory on the category of G G -spaces. These represented cohomology theories are designed to only depend on the ‘proper G G -homotopy type’, tested by fixed points under all compact subgroups. An important special case of our theory are infinite discrete groups. For these, our genuine equivariant theory is related to finiteness properties in the sense of geometric group theory; for example, the G G -sphere spectrum is a compact object in our triangulated equivariant homotopy category if the universal space for proper G G -actions has a finite G G -CW-model. For discrete groups, the represented equivariant cohomology theories on finite proper G G -CW-complexes admit a more explicit description in terms of parameterized equivariant homotopy theory, suitably stabilized by G G -vector bundles. Via this description, we can identify the previously defined G G -cohomology theories of equivariant stable cohomotopy and equivariant K-theory as cohomology theories represented by specific orthogonal G G -spectra.

К вопросу о герменевтике мультикультурализма в условиях высокой скорости информационного обмена

The All-Russian academic conference “The Nature and Specifics of Multiculturalism in Conditions of High-Speed Information Exchange” was first held at the Institute of Oriental Studies, RAS in 2023. It opened for discussion a number of fundamental issues that go beyond the theory of paradigm shifts and scientific revolutions and represent a fundamentally new expansion of universal knowledge space in the domain of cyberculture. The expansion of screen civilization is accompanied by the spread of a new type of multiculturalism. The Department of Comparative Cultural Studies of the IOS RAS invited researchers in humanities from different national academic centers to reflect on the implication of digital reality for the current epistemological transition and the hermeneutics of multiculturalism.

GAN Prior Based Null-Space Learning for Consistent Super-resolution

Consistency and realness have always been the two critical issues of image super-resolution. While the realness has been dramatically improved with the use of GAN prior, the state-of-the-art methods still suffer inconsistencies in local structures and colors (e.g., tooth and eyes). In this paper, we show that these inconsistencies can be analytically eliminated by learning only the null-space component while fixing the range-space part. Further, we design a pooling-based decomposition (PD), a universal range-null space decomposition for super-resolution tasks, which is concise, fast, and parameter-free. PD can be easily applied to state-of-the-art GAN Prior based SR methods to eliminate their inconsistencies, neither compromise the realness nor bring extra parameters or computational costs. Besides, our ablation studies reveal that PD can replace pixel-wise losses for training and achieve better generalization performance when facing unseen downsamplings or even real-world degradation. Experiments show that the use of PD refreshes state-of-the-art SR performance and speeds up the convergence of training up to 2~10 times.

REFLECTION OF THE "THREE WORLDS" CONCEPT OF GRIGORY SKOVORODA IN THE PHILOSOPHICAL LYRICS OF ARSENY TARKOVSKY

The article is devoted to the reflection of the "three worlds" concept of Grigory Skovoroda in the philosophical lyrics of Arseny Tarkovsky, who considered the Ukrainian thinker his spiritual teacher. His religious and mystical concept provides for the mutual harmonious interaction of the macrocosm (Universe), microcosm (man) and the symbolic world of the Bible. Using the example of selected poems, the artistic content and poetic structure of images of macro- and microcosm are analyzed. The spatial element of the chronotope in Tarkovsky’s poetry is very revealing. In some cases, it directly correlates with the category of the microcosm. One of its most representative manifestations is the space of the steppe. It retains all the signs of a traditionally self-sufficient geographic landscape with its characteristic realities, and at the same time appears as a universal spiritual space that imparts a sense of inner freedom. The holistic spatial perspective of the macrocosm unfolds both horizontally (steppe and other topoi) and vertically: from the earth to the sky and further to the stars. Tarkovsky’s microcosm, like Skovoroda’s, has a religious and ethical connotation. It is represented by highly suggestive images of a lyrical hero, who gazes intently at the world around him, feeling an integral part of it. Not only is the microcosm likened to the macrocosm, but the great world is organically humanized in the process of active interaction. Tarkovsky’s awareness of the harmonious relationship between the Universe and the man is often realized through biblical contexts, both evident and concealed.

C∗-irreducibility of commensurated subgroups

Given a commensurated subgroup $\Lambda$ of a group $\Gamma$, we completely characterize when the inclusion $\Lambda\leq \Gamma$ is $C^*$-irreducible and provide new examples of such inclusions. In particular, we obtain that $\rm{PSL}(n,\mathbb{Z})\leq\rm{PGL}(n,\mathbb{Q})$ is $C^*$-irreducible for any $n\in \mathbb{N}$, and that the inclusion of a $C^*$-simple group into its abstract commensurator is $C^*$-irreducible. The main ingredient that we use is the fact that the action of a commensurated subgroup $\Lambda\leq\Gamma$ on its Furstenberg boundary $\partial_F\Lambda$ can be extended in a unique way to an action of $\Gamma$ on $\partial_F\Lambda$. Finally, we also investigate the counterpart of this extension result for the universal minimal proximal space of a group.

The scheme of monogenic generators II: local monogenicity and twists

This is the second paper in a series of two studying monogenicity of number rings from a moduli-theoretic perspective. By the results of the first paper in this series, a choice of a generator $$\theta $$ for an A-algebra B is a point of the scheme $${\mathcal {M}}_{B/A}$$ . In this paper, we study and relate several notions of local monogenicity that emerge from this perspective. We first consider the conditions under which the extension B/A admits monogenerators locally in the Zariski and finer topologies, recovering a theorem of Pleasants as a special case. We next consider the case in which B/A is étale, where the local structure of étale maps allows us to construct a universal monogenicity space and relate it to an unordered configuration space. Finally, we consider when B/A admits local monogenerators that differ only by the action of some group (usually $${\mathbb {G}}_m$$ or $$\textrm{Aff}^1$$ ), giving rise to a notion of twisted monogenerators. In particular, we show a number ring A has class number one if and only if each twisted monogenerator is in fact a global monogenerator $$\theta $$ .