Universal Space Research Articles

Time, observer, and consciousness

In today’s physics, opinions on what is time are different. Some physicists deny the existence of time, and others think that time has physical existence. Nevertheless, time was never directly perceived by senses. With our eyes, we perceive the flow of material changes, i.e., motion in space. Our recent proposal is that universal space is time-invariant in the sense there is no physical time which would be the fourth dimension of space. The model of space-time is replaced with the model of time-invariant space, where we perceive the flow of material changes. In past years, neuroscience has discovered that linear psychological time “past-present-future” has origin in neuronal activity of the brain. An observer is experiencing the flow of material changes in the frame of psychological time. With eyes, we do not perceive some physical time in which material changes run. The observer perceives a stream of changes that run in the time-invariant space. This stream of changes the observer experiences in the brain through the psychological liner time. In the universe, there is no linear time past‐present‐future, material changes run in time-invariant space. An observer only perceives changes (not time) and he experiences changes in the frame of psychological time. The observer (the subject) is beyond psychological time, and it does not change during a human lifetime. Observer can be understood as the function of consciousness.

Interpolatory tensorial reduced order models for parametric dynamical systems

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent and parameter-specific. The ROM exploits compressed tensor formats to find a low rank representation for a sample of high-fidelity snapshots of the system state. This tensorial representation provides ROM with an orthogonal basis in a universal space of all snapshots and encodes information about the state variation in parameter domain. During the online phase and for any incoming parameter, this information is used to find a reduced basis that spans a parameter-specific subspace in the universal space. The computational cost of the online phase then depends only on tensor compression ranks, but not on space or time resolution of high-fidelity computations. Moreover, certain compressed tensor formats enable to avoid the adverse effect of parameter space dimension on the online costs (known as the curse of dimension). The analysis of the approach includes an estimate for the representation power of the acquired ROM basis. We illustrate the performance and prediction properties of the ROM with several numerical experiments, where tensorial ROM’s complexity and accuracy is compared to those of conventional POD-ROM.

I. Kant: How is aesthetic possible?

The subject of the research is the ways of substantiating the fundamental concept of aesthetic science -- the category of aesthetic in Kant's philosophy. The author examines such aspects of the topic as the content of transcendental philosophy, in which the mind indulges in a purely aesthetic occupation, draws for himself the structure of the whole, the congruence of the conditions of the work of art of a priori fulfillment of feelings, understanding the category of beauty under the sign of aesthetic intention cogito, analysis of how the artist combines the aesthetic aspects of the thing in itself with the incommensurable worlds in the work art. The aesthetic exists in a kind of universal space, which is defined by the transcendental as the "last foundation". The main conclusions of the study is the statement that, by analogy with transcendental aesthetics, Kant admits an aesthetic of pure practical reason that is not identical to it, expressing the hope that in the future it will be possible to comprehend both as elements of the unity of the entire faculty of pure reason. The author's special contribution to the study of the topic is the search in the context of the philosophical interpretation of the concept of aesthetic pleasure, as it is carried out within the framework of Kant's moral philosophy. The novelty of the research lies in identifying the dramaturgy of the foundations of the aesthetic, which does not presuppose any of its scenario as a basis for building aesthetic thinking, in revealing how the system of aesthetic interactions and syntheses correlates with structures ideally initial in relation to the world and man, with absolute foundations, without which there is no aesthetics.

Lagrange Multivariate Polynomial Interpolation: A Random Algorithmic Approach

The problems of polynomial interpolation with several variables present more difficulties than those of one-dimensional interpolation. The first problem is to study the regularity of the interpolation schemes. In fact, it is well-known that, in contrast to the univariate case, there is no universal space of polynomials which admits unique Lagrange interpolation for all point sets of a given cardinality, and so the interpolation space will depend on the set Z of interpolation points. Techniques of univariate Newton interpolating polynomials are extended to multivariate data points by different generalizations and practical algorithms. The Newton basis format, with divided-difference algorithm for coefficients, generalizes in a straightforward way when interpolating at nodes on a grid within certain schemes. In this work, we propose a random algorithm for computing several interpolating multivariate Lagrange polynomials, called RLMVPIA (Random Lagrange Multivariate Polynomial Interpolation Algorithm), for any finite interpolation set. We will use a Newton-type polynomials basis, and we will introduce a new concept called Z , z -partition. All the given algorithms are tested on examples. RLMVPIA is easy to implement and requires no storage.

A study of universal elements in classes of bases of topological spaces

The universality problem focuses on finding universal spaces in classes of topological spaces. Moreover, in ``Universal spaces and mappings'' by S. D. Iliadis (2005), an important method of constructing such universal elements in classes of spaces is introduced and explained in details. Simultaneously, in ``A topological dimension greater than or equal to the classical covering dimension'' by D. N. Georgiou, A. C. Megaritis and F. Sereti (2017), new topological dimension is introduced and studied, which is called quasi covering dimension and is denoted by $\dim_{q}$. In this paper, we define the base dimension-like function of the type dim$_{q}$, denoted by {b} - {dim}$^{\rm I F}_{q}$, and study the property of universality for this function. Especially, based on the method of ``Universal spaces and mappings'' by S. D. Iliadis (2005), we prove that in classes of bases which are determined by {b} - {dim}$^{\rm I F}_{q}$ there exist universal elements.

The impact of effective tortuosity on carbonate acidizing and the validation of Damköhler and Péclet dimensionless phase space

Acid stimulation is one of the main methodologies to enhance well productivity and increase permeability lost by near-wellbore formation damage through matrix acidizing. The desired outcome of acidizing carbonate rocks is to form deep conductive flow channels called “wormholes”. The productivity enhancement depends on how deep these wormholes penetrate into the reservoir. The porous medium is characterized by three fundamental parameters which are anisotropic or isotropic porosity, permeability, and percolation. Here we test the hypothesis that effective tortuosity - a key parameter for microstructure characterization in porous media - has a significant effect on wormhole formation. Significant progress has been made by empirical work on carbonate acidizing to increase the stimulation efficiency, but further improvements are possible by developing a deeper understanding of the impact of effective tortuosity on wormhole initiation and development. We use Indiana limestone core-flooding experiments to inject diluted hydrochloric acid (HCl) at different acid concentrations and injection rates. Effective tortuosity was calculated for the tight Indiana limestone and was compared with an earlier study on the highly porous Mount Gambier limestone to evaluate the effect of tortuosity on wormhole formation. Our results suggest that the inverse Damköhler and Péclet phase space, traditionally used for evaluating criteria for wormhole formation, needs to be extended by tortuosity as a third dimension to capture the effect of microstructure for the initiation of wormhole phenomenon. Incorporating this extension will improve the prediction of wormhole initiation conditions for all carbonate rock types by using a universal dimensionless phase space.

A Compactification of the Universal Moduli Space of Principal G-Bundles

Let G be a semisimple linear algebraic group, rho :Ghookrightarrow text {SL}(V) a finite-dimensional faithful representation, gge 2 a natural number, and delta a positive rational number. We prove the existence of a compactification of the universal moduli space of semistable principal G-bundles over overline{text {M}}_{g}, provided that delta is sufficiently large, having the following property: the fibers over singular curves are the moduli spaces of delta -semistable singular principal G-bundles.

Domain adaptation for epileptic EEG classification using adversarial learning and Riemannian manifold

The epileptic electroencephalography (EEG) classification technique has been extensively adopted in epilepsy diagnosis and management due to its powerful capacity in distinguishing brain dysfunction. Since EEG patterns vary significantly from patient to patient, conventional studies usually perform the training and testing processes on the same subject. However, the challenging issue regarding domain shift among different individuals remains unsolved, which leads to low popularization of clinical application. To alleviate such problem, a domain adaptation model is proposed in this paper. This method intends to learn the universal feature space between different patients via constructing an adversarial autoencoder. By performing an adversarial training procedure, the aggregated posterior of the embedding space is matched with a Riemannian manifold-based prior that contains cross-domain information. This variational inference process can increase the generalization ability while circumventing the overfitting to source domains. Moreover, a distance measure is developed to align the distributions among various domains using the Riemannian mean. It can make the extracted features present higher domain adaptability by minimizing domain gaps in hidden space. Two common classification tasks, seizure prediction and seizure detection, are utilized for model evaluation. In the tests performed on the CHB-MIT scalp EEG dataset, the proposed model achieves a sensitivity of 82.2%, a false alarm rate (FPR) of 0.13 h−1 for seizure prediction and a sensitivity of 86.4%, an FPR of 0.08 h−1 for seizure detection. Experimental results indicate that this method can effectively reduce the domain disparity compared with state-of-the-art baselines.

On the Carathéodory metric of universal Teichmüller space

In contrast to finite dimensional Teichmuller spaces, all non-expanding invariant metrics on the universal Teichmuller space coincide. This important fact found various applications. We give its new, simplified proof based on some deep features of the Grunsky operator, which intrinsically relate to the universal Teichmuller space. This approach also yields a quantitative answer to Ahlfors' question.

Cardinal-indexed classifying spaces for families of subgroups of any topological group

For G a topological group, existence theorems by Milnor (1956), Gelfand–Fuks (1968), and Segal (1975) of classifying spaces for principal G-bundles are generalized to G-spaces with torsion. Namely, any G-space approximately covered by tubes (a generalization of local trivialization) is the pullback of a universal space indexed by the orbit types of tubes and cardinality of the cover. For G a Lie group, via a metric model we generalize the corresponding uniqueness theorem by Palais (1960) and Bredon (1972) for compact G. Namely, the G-homeomorphism types of proper G-spaces over a metric space correspond to stratified-homotopy classes of orbit classifying maps.The former existence result is enabled by Segal's clever but esoteric use of non-Hausdorff spaces. The latter uniqueness result is enabled by our own development of equivariant ANR theory for noncompact Lie G. Applications include the existence part of classification for unstructured fiber bundles with locally compact Hausdorff fiber and with locally connected base or fiber, as well as for equivariant principal bundles which in certain cases via other models is due to Lashof–May (1986) and to Lück–Uribe (2014). From a categorical perspective, our general model EFκG is a final object inspired by the formulation of the Baum–Connes conjecture (1994).

An algebraic study of Volterra integral equations and their operator linearity

The algebraic study of special integral operators led to the notions of Rota-Baxter operators and shuffle products which have found broad applications such as iterated integrals. This paper carries out an algebraic study of general integral operators and equations, and shows that there are rich algebraic structures underlying Volterra integral operators and the corresponding equations. First Volterra integral operators are shown to produce a matching twisted Rota-Baxter algebra satisfying twisted integration-by-parts operator identities. In order to provide a universal space to express general integral equations, free operated algebras are then constructed in terms of bracketed words and rooted trees with decorations on the vertices and edges. Further explicit constructions of the free objects in the category of matching twisted Rota-Baxter algebras are obtained by a twisted and decorated generalization of the shuffle product, providing a universal space for separable Volterra equations. As an application of these algebraic constructions, it is shown that any integral equation with separable Volterra kernels is operator linear in the sense that the equation can be simplified to a linear combination of iterated integrals with the same kernels.

К вопросу об исторических и философских истоках цифровой реальности

The purpose of the study is to reveal the genesis of the concept of digital reality and its connection with the millennial Pyphagorean tradition in European philosophy and culture, based on the logic and dialectic of the number as a metaphysical entity. The article implements an attempt to historically and philosophically consider the phenomenon of digital reality: the conclusions of modern researchers are confirmed about the key importance of this philosophical tradition as a special system of thought, which defined modern ideological and scientific paradigms and contributed to the formation of the social model of post-industrial, information-digital society. Scientific novelty is to reveal a modern scientific understanding of the notion that numbers can materialize the world by reflecting reality and returning it to man through knowledge derived through the programming or construction of digital reality on the basis of symbolic-applied logic. As a result of the analysis of philosophical sources, it has been proved that information in our world can be considered as another kind of movement of matter, and the Internet is not only an "information technology" but a "social form", a "universal social space" that appeared not overnight – with the invention of "breakthrough" technology, but formed by centuries of cultivated scientific knowledge.

P-adic L-functions in universal deformation families

We construct examples of p-adic L-functions over universal deformation spaces for {{,mathrm{GL},}}_2. We formulate a conjecture predicting that the natural parameter spaces for p-adic L-functions and Euler systems are not the usual eigenvarieties (parametrising nearly-ordinary families of automorphic representations), but other, larger spaces depending on a choice of a parabolic subgroup, which we call ‘big parabolic eigenvarieties’.

FUNCTIONAL GROUPS OF PREMISES OF EXTRACURRICULAR EDUCATION INSTITUTIONS OF THE I-IV CITY PLANNING ORGANIZATION LEVELS

The main task of a modern extracurricular education institution (hereafter EEI) is to provide students with competencies in relation to a certain activity profile, which provides for the possibility of applying in practice the acquired skills and abilities. Extracurricular activities stimulate socialization and train teamwork skills by combining activities in the form of individual activities, group work, intergroup work.
 The relevance of this work is due to the need to study the qualitative composition and interrelationships of the minimum necessary and comfortable EEI functional groups of premises. This will allow more efficient spaces planning when creating new EEIs and modernizing existing ones by using the optimal list of premises and convenient functional connections between them, identifying appropriate options for the interior design of the building.
 The work is based on the research of Merilova I. A., who developed a model of formation of the EEIs educational network, consisting of four urban planning organization levels (system of EEI arrangement in accordance with the number of settlement inhabitants, population density, the radius of institutions accessibility and the number of pupils). For rural areas there are 3 urban organization levels: I - a small village without a school (built-in EEI), II - a village with a school (EEI integrated into the school building), III - district center, urban-type settlement (independent EEI building of district importance). For the urban environment, the researcher identifies 4 levels of EEI urban organization: I - apartment building or quarter (built-in EEI), II - neighborhood (EEI integrated into the school building structure), III - district EEI, IV - city level institution. Each subsequent level of urban planning organization provides an increasing radius of institution accessibility, an increasing number of students, more and more diverse learning profiles.
 The list of specific functional groups that have to be arranged in the EEI of a certain urban organization level directly depends on the profile of activity, the function of the educational institution. In general, the profiles of EEI activities can be divided into three areas: scientific and educational; sports and health; artistic.
 EEIs of I-IV urban organization levels are based on interrelations of the joint list of functional groups of premises: lobby group, administrative, economic, auxiliary at the main function, educational group of rooms. The specific list of premises of the educational functional group is determined by the area, profile of institution activity and its specific type. In accordance with the growth of the institution capacity and its throughput, the quantitative area indicators of groups of premises increase, but the composition of functional groups is little variable. In order to effectively use the premises, it is advisable to arrange universal learning spaces. In order to minimize the required EEI areas, it is possible to create certain zones using furniture and equipment, without allocating separate premises for them, which is especially relevant for EEI of I urban planning organization level. The common planning needs of EEI that are specialized in art and scientific-educational areas are noted, namely: the necessity of similar groups of premises arrangement, the similarity in approaches to the educational premise design, the possibility of the organization in universal educational premise of certain activity kinds both art, and scientific-educational areas (in case of requirement absence for specific equipment and arrangement).

APPROACHES TO THE FORMATION AND EXPEDIENCY OF ORGANIZATION OF UNIVERSAL STUDY PREMISES OF EXTRACURRICULAR EDUCATION INSTITUTION FOR DIFFERENT AGE CATEGORIES OF CHILDREN

The universal educational space of extracurricular educational institution has its specific features, in particular, it is universal only for one age category of users. Ergonomic parameters of primary school children, preschoolers, middle-aged and older children differ significantly. To determine the conformity of furniture to a certain height of the child, the concept of "growth group" or "growth group", "growth range" is used. The parameters of furniture for 6 groups are conditionally allocated. The ability to transform the space for different scenarios ensures its most efficient use. Transformations are possible, for example, through the use of movable partitions, mobile furniture and equipment, as well as technical devices.
 It is important to create in the learning space areas for individual, group and mass work, centers for independent work and for classes under the teacher or instructor guidance. Various internal space solutions of the environment enable and make more comfortable the processes of learning in groups, communication between groups, the ability to work in large associations, which contributes to the active children socialization.
 In accordance with the trends in the educational field, the requirements for educational environments are changing. Through competency and personal approaches that have become popular, the attention of designers should be focused on the possibility of forming the most diverse educational environment containing cells of different scales: for individual work, for individual work with counseling or assistance, for pair work, work in small groups (up to 4 people), in regular groups (up to 15-20 people) and mass work, horizontal and vertical communication (between students of the same age and different ages; between students and teachers; between students of the same learning profile and different profiles).
 The environment of the extracurricular education institution should be equipped in accordance with the ergonomic parameters of the users’ age categories. There are options for arranging separate educational facilities for each age category of users (option 1) and an option for arranging an environment with universal equipment that allows to adapt quickly to the children ergonomic parameters. Features of the universal learning room are the use of specific equipment (compared to option 1 increased in size and cost of desks and chairs that allow to adjust quickly the student's workplace to his/her ergonomic parameters), which complicates and somewhat limits the variability of furniture elements combinations in fixed room area (natural light enters the room up to a maximum of 6 meters), increases the area of the room. The effectiveness of each option should be assessed by expert in economic field, taking into account the intensity of premises usage, the area of the institution, its capacity, projected profits and expenses of the institution.

Concept of application of water electrolysis propulsion system as a component of a universal space platform for asteroid exploration mission

Concept of application of water electrolysis propulsion system as a component of a universal space platform for asteroid exploration mission

The universal Poisson deformation of hypertoric varieties and some classification results

In this paper, we study and describe the universal Poisson deformation space of hypertoric varieties concretely. In the first application, we show that affine hypertoric varieties as conical symplectic varieties are classified by the associated regular matroids (this is a partial generalization of the result by Arbo and Proudfoot). As a corollary, we obtain a criterion when two quiver varieties whose dimension vector have all coordinates equal to one are isomorphic to each other. Then we describe all 4- and 6-dimensional affine hypertoric varieties as quiver varieties and give some examples of 8-dimensional hypertoric varieties which cannot be raised as such quiver varieties. In the second application, we compute explicitly the number of all projective crepant resolutions of some 4-dimensional hypertoric varieties by using the combinatorics of hyperplane arrangements.

MEDIA DESIGN IN THE FORMATION OF INNOVATIVE CULTURAL AND ENTERTAINMENT BUILDINGS

The article is devoted to identifying the design features of innovative cultural and entertainment buildings using media architecture and design tools to develop methodological foundations for their formation. Criteria for differentiation of these objects have been determined. The article presents the main typological characteristics of cultural and entertainment buildings using the means of media architecture and design. The functional components of this type of architectural object and complex have been determined. Modern fundamental approaches and the main trends in urban planning, spatial organization and architectural and planning solutions of innovative cultural and entertainment buildings using media architecture and design are identified. The article analyzes foreign experience in designing innovative cultural and entertainment buildings using media architecture and design. Trends in the formation of their volumetric-spatial structure have been determined. The factors influencing the formation of innovative cultural and entertainment buildings and complexes in the urban environment are identified. The article provides definitions of the concepts of "media architecture" and "media facade". The methods of architectural and design formation of innovative cultural and entertainment buildings using the means of media architecture and design are revealed: the method of multi-functional structure, the method of integration with the environment, the method of using national traditions, the method of complexity, the method of flexibility and communicativeness of space, the method of accessibility and adaptability (setting up a universal space), the reception of stylistic unity. The perspective directions of formation and development trends of innovative architectural objects in the urban environment with the use of media design means are determined.

The fundamental groupoid as a topological groupoid: Lasso topology

This paper is devoted to study of a topology on the fundamental groupoid which makes it a topological groupoid and give up a functor from category of topological spaces to the category of topological groupoids. The resulting topological fundamental groupoid, denoted by πlX for a given space X is a generalization of the universal path space and also is a generalization of the topological fundamental group equipped by Lasso topology such that πlX(x)=π1l(X,x), for x∈X.

Singular principal bundles on reducible nodal curves

Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of δ \delta -semistable pseudo bundles on a nodal curve become, for large values of δ \delta , the moduli spaces of semistable singular principal bundles. The latter are reasonable candidates for degenerations and a potential basis for further developments as on irreducible nodal curves. In particular, we find a notion of semistability for principal bundles on reducible nodal curves. The understanding of the asymptotic behavior of δ \delta -semistability rests on a lemma from geometric invariant theory. The results allow for the construction of a universal moduli space of semistable singular principal bundles over the moduli space of stable curves. Due to recent work of Wilson, this universal moduli space has a close relation to the sheaf of algebras of conformal blocks.