Ordinary Space Research Articles

Joint Probability Densities on Riemannian Manifolds are Symmetric Tensor Densities

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially, we develop a binary data matrix to record the values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle-oriented coordinate and the generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar fields in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of the cumulative probability function defined on Riemannian manifolds also give the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and give the formal definition of joint probabilities by partial derivatives of the cumulative distribution function. The equivalence between the symmetrized covariant derivative and the generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

Wave Function and Information

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e., its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called “quantum potential” in this context is briefly discussed.

On stability behaviors of 5D M-theory black objects

Using N = 2 supergravity formalism, we investigate certain behaviors of five-dimensional black objects from the compactification of M-theory on a Calabi–Yau three-fold. The manifold has been constructed as the intersection of two homogeneous polynomials of degrees (ω + 2, 1) and (2, 1) in a product of two weighted projective spaces given by WP4(ω,1,1,1,1)×P1 . First, we determine the allowed electric charge regions of the BPS and non BPS black holes obtained by wrapping M2-branes on appropriate two cycles in such a proposed Calabi–Yau three-fold. After that, we calculate the entropy of these solutions which takes a maximal value corresponding to ω = 1 defining the ordinary projective space P4 . For generic values of ω, we show that the non BPS states are unstable. Then, we conduct a similar study of five-dimensional black strings. Concerning the allowed magnetic charge regions of the BPS and non BPS black stringy solutions derived from M5-branes on dual divisors, we calculate the tension taking a minimal value for P4 . By determining the recombination factor, we show that the non-BPS black string states are stable in the allowed regions in the magnetic charge space.

We created space to reclaim time … and that time made extra(ordinary) space

ABSTRACT Within the concept of extra-space, this article aims to explore the meaning, relevance and consequences of the project HODO and the installation ‘The Resting Assembly’ as part of the official Portuguese student representation at the Prague Quadrennial 2023. In close relation to the cultural context of the project, the underlying ideas of time, space, and place are used to develop the methodological approaches, aims, intentions and decisions that guided the project. Based on these relationships, the article proposes to understand this project under the category of event which guides a way of thinking about scenographic contexts toward their amplification in contemporary practices, while furthering the theoretical dimension of the project. The article intends to describe how the idea that a specific (manifest expression of) time, its suspension or the act of pausing, is initiated by this project/object/performance as a form of agency and aesthetic reflection, contributing to an interrelation between time and space. In this sense, the project is studied as a space–time entity that can open up new possibilities in the Portuguese context of artistic creation and research in the field of scenography.

Behaviors of black holes and black strings in M-theory on Calabi–Yau manifolds

In this work, we reconsider the study of black holes and black strings in the compactification of M-theory on a Calabi–Yau three-fold, considered as a complete intersection of hypersurfaces in a product of weighted projective spaces given by [Formula: see text]. Using the [Formula: see text] supergravity formalism in five dimensions, we examine the BPS and non-BPS solutions by wrapping M-branes on appropriate cycles in such a Calabi–Yau geometry. For the black hole case, we compute certain thermodynamical quantities. In particular, we calculate the entropy taking a maximal value corresponding to the ordinary projective space [Formula: see text] with [Formula: see text]. Using extended black hole entropies, we evaluate the temperature involving a minimal value for [Formula: see text]. Then, we approach the stability of the non-BPS black holes via the recombination factor. In the allowed electric charge regions, we show that such states are unstable. For the black string solutions, we calculate the tension taking a minimal value corresponding to [Formula: see text]. Computing the recombination factor, we show that the associated non-BPS black string states are stable in the allowed magnetic charge regions of the moduli space.

Novel Approaches Characterizing Separation in Fuzzy Topology with Quasi-Coincidence

Fuzzy sets were introduced by Zadeh in 1965, and three years later, Chang defined fuzzy topological spaces. Fuzzy topological spaces are families of fuzzy sets that satisfy the three classical axioms of topology. In this paper, we introduce and study some new notions of To separation axioms in fuzzy topological spaces using the quasi-coincident relation for fuzzy sets. Every ordinary (crisp) topological space vacuously satisfies the condition of being quasi-To. We define the quasi-separation axioms for fuzzy topological spaces, as quasi-To, quasi-T1, Quasi-T2. We have introduced and studied some new notions of To separation axioms in fuzzy topological spaces using the quasi-coincident relation for fuzzy sets. These quasi-separation axioms are weaker than the corresponding classical To separation axioms, but they are still useful for characterizing and studying fuzzy topological spaces.

VISUAL INTEGRATION OF SCULPTURE IN FORMING THE IMAGE OF THE CITY

This work examines the issue of the phenomenon of modern sculpture and its influence on the formation of urban space. It has been established that Ukrainian sculpture is a young art that has undergone changes of generations and aesthetic views. Modern sculpture, creating new and modifying existing cultural and symbolic images of settlements, plays an extremely important role in creating the effect of authenticity of urban space, strengthens its cultural, artistic and historical meaning, is a kind of effective means of actualizing cultural memory. It is renewed not only according to the laws of the internal logic of classical fine art, but also inspired by external tectonic factors. 
 The image of the city creates, first of all, spiritual and scientific life, forming its cultural, artistic and intellectual states, a certain level of quality of the social dimension - aspirations and needs of residents, culture and art, consciousness and language. 
 It is small urban sculpture designed to create or emphasize the uniqueness and originality of each specific place, designed to awaken imagination and emotions. After all, it is precisely through it that the connection between architecture and fine art is possible, which aestheticizes the environment and life of a person, appealing to his feelings and thinking at the same time, brings variety and harmony, which are so necessary for a person. 
 As you know, a small plastic form attracts a person with its proportionality: it makes you want to approach it, touch it, take a picture. It is an integral and sometimes decisive part of the communication between the city and the person. It is the sculptures that make the city understandable, pleasant and accessible to people. A small urban sculpture can transform an ordinary space or strengthen existing advantages and place accents in a saturated historical center.

Ritual Sweat Bath in a Cross-Cultural Perspective

AbstractThis article traces differences and similarities in the ritual sweat bath usage through a comparative perspective that includes contemporary practice in Poland and the central and the north American traditions that inform it. I argue that there exist continuity and consistency of representations related to sweat bathing across time and space, which can be identified by the metaphors designating certain elements of the ritual. The bathhouse from a cross-cultural perspective can be considered a sacred and liminal space, a gateway that enables the transcending of ordinary space–time dimension and interaction with primordial creation–destruction forces. Fertility appears as only one aspect of these ambivalent forces. It manifests itself in the main metaphors of the Mother Earth’s womb and death–rebirth process in ritual’s contemporary descriptions in Poland. The similarities in the way the sweat bath experience is conceptualised reveal the influence of particulr elements of the ritual that induce specific bodily sensations, intrinsically related to the human organism conditions.

Bundle theoretic descriptions of massless single-particle state spaces; how do we perceive a moving quantum particle

Recently, a bundle theoretic description of massive single-particle state spaces, which is better suited for Relativistic Quantum Information Theory than the ordinary Hilbert space description, has been suggested. However, the mathematical framework presented in that work does not apply to massless particles. It is because, unlike massive particles, massless particles cannot assume the zero momentum state and hence the mass shell associated with massless particles has non-trivial cohomology. To overcome this difficulty, this paper suggests a new framework that can be applied to massless particles. Applications to the cases of massless particles with spin-1 and 2, namely photon and graviton, will reveal that the field equations, the gauge conditions, and the gauge freedoms of Electromagnetism and General Relativity naturally arise as manifestations of an inertial observer’s perception of the internal quantum states of a photon and a graviton, respectively. Finally, we show that gauge freedom is exhibited by all massless particles, except those with spin-0 and 1/2.

A review of the effect of the light environment of the VDT workspace on the "learning to learn" effect of video game training.

In recent years, the role of video games in enhancing brain plasticity and learning ability has been verified, and this learning transfer is known as the "learning to learn" effect of video game training. At the same time, against the background of healthy lighting, the influence of non-visual effects of light environment on the human rhythmic system has been gradually confirmed. As a special operation form of Visual Display Terminal (VDT) operation, video game training has a high dependence on VDT equipment and the VDT screen, and the background usually has a huge difference in brightness. Compared with the light environment of ordinary operation space, the light environment of VDT operation space is more complex. This complex light environment's non-visual effects cause human emotions, alertness, fatigue, cognitive ability, and other changes, which may affect the efficiency of the "learning to learn" effect of video game training. This article focuses on the impact of the light environment in the VDT workspace on the "learning to learn" effect of video game training. It first traces the factors that trigger the "learning to learn" effect of video game training, that is, the improvement of people's attention, perception, and cognitive ability. Then, the influencing mechanism and the evaluation method of the VDT workspace space light environment on the human rhythm system are discussed based on the basic theory of photobiological effect. In addition, the VDT display lighting light time pattern, photophysical properties, regulation, and protection mechanism on the human rhythm system are studied to demonstrate the VDT workspace light environment's special characteristics. Finally, combined with the progress of artificial lighting technology and the research results of health lighting, given the "learning to learn" effect of video game training, some thoughts on the design of the light environment of the workplace and future research directions are presented.

Compositional PLS biplot based on pivoting balances: an application to explore the association between 24-h movement behaviours and adiposity

Movement behaviour data are compositional in nature, therefore the logratio methodology has been demonstrated appropriate for their statistical analysis. Compositional data can be mapped into the ordinary real space through new sets of variables (orthonormal logratio coordinates) representing balances between the original compositional parts. Geometric rotation between orthonormal logratio coordinates systems can be used to extract relevant information from any of them. We exploit this idea to introduce the concept of pivoting balances, which facilitates the construction and use of interpretable balances according to the purpose of the data analysis. Moreover, graphical representation through ternary diagrams has been ordinarily used to explore time-use compositions consisting of, or being amalgamated into, three parts. Data dimension reduction techniques can however serve well for visualisation and facilitate understanding in the case of larger compositions. We here develop suitable pivoting balance coordinates that in combination with an adapted formulation of compositional partial least squares regression biplots enable meaningful visualisation of more complex time-use patterns and their relationships with an outcome variable. The use and features of the proposed method are illustrated in a study examining the association between movement behaviours and adiposity from a sample of Czech school-aged girls. The results suggest that an adequate strategy for obesity prevention in this group would be to focus on achieving a positive balance of vigorous physical activity in combination with sleep against the other daily behaviours.

Quantum formalism of interference as confinement in spatially structured Lorentzian wells

Non-paraxial interference has recently been explained as light energy confinement in spatially structured Lorentzian wells. This theory describes, in the same way, single particle interference in ordinary space too. Such an alternative thought is discussed here in the framework of a quantum formalism, which introduces confinement operators and density matrices of space states for the first time. Therefore, Lorentzian wells are characterized as the base states of space, which are excited by the geometric potential to produce interference. Geometrical uncertainty and space entanglement are discussed as novel features that approach the proposed theory in the quantum context. This formalism provides insight into the role of space in interference.

Optical phase of recursional hybrid visco ferromagnetic electromagnetic microscale

In this paper, we construct new optical hybrid normalization shapes of Lorentz fields with hybrid frames in ordinary space. Then, we demonstrate some descriptions for hybrid visco ferromagnetic H2-magnetic normalized optimistic solidity. We construct a hybrid normalized visco ferromagnetic H2-magnetic hybrid visco ferromagnetic microbeam model with a hybrid frame. Finally, we obtain an optical hybrid normalized visco ferromagnetic H2-electrical hybrid visco ferromagnetic microscale beam.

On quasi focal curves with quasi frame in space

In this study, we firstly characterize focal curves by considering quasi frame in the ordinary space. Then, we obtain the relation of each quasi curvatures of curve in terms of focal curvatures. Finally, we give some new conditions with constant quasi curvatures in the ordinary space.

Confinement and spatial entanglement: phenomenology of a new interference principle

Recently, the novel confinement principle in spatially-structured Lorentzian wells was reported to describe in a unified way the interference of classical waves and singular quantum particles in a causal framework in ordinary space. The phenomenology derived from this principle offers significant advantages over the conventional classical and quantum formalisms of interference founded on wave superposition. This paper presents a conceptual analysis of such a principle and its main implications indicating its fundamental differences from the standard descriptions.

Spatial filtering in a 6D hybrid-Vlasov scheme to alleviate adaptive mesh refinement artifacts: a case study with Vlasiator (versions 5.0, 5.1, and 5.2.1)

Abstract. Numerical simulation models that are used to investigate the near-Earth space plasma environment require sophisticated methods and algorithms as well as high computational power. Vlasiator 5.0 is a hybrid-Vlasov plasma simulation code that is able to perform 6D (3D in ordinary space and 3D in velocity space) simulations using adaptive mesh refinement (AMR). In this work, we describe a side effect of using AMR in Vlasiator 5.0: the heterologous grid approach creates discontinuities due to the different grid resolution levels. These discontinuities cause spurious oscillations in the electromagnetic fields that alter the global results. We present and test a spatial filtering operator for alleviating this artifact without significantly increasing the computational overhead. We demonstrate the operator's use case in large 6D AMR simulations and evaluate its performance with different implementations.

New Concepts of To Separation Axioms in Fuzzy Topology

Fuzzy set was introduced by Zadeh in his classical paper of 1965. Three years later, Chang gave the definition of fuzzy topology, which is a family of fuzzy set satisfying the three classical axioms. In this paper, we have introduced and studied some new notions of To separation axioms in fuzzy topological spaces by using quasi-coincident relation for fuzzy set. Every ordinary (crisp) topological space vacuously satisfies condition of being quasi-To. In this paper concept of quasi coincident relation used to introduce and investigate some quasi separation axioms such as To, T1, & T2. Concerning quasi-To space in the general frame work of fuzzy topological spaces.

Principal infty -bundles and smooth string group models

We provide a general, homotopy-theoretic definition of string group models within an infty -category of smooth spaces and present new smooth models for the string group. Here, a smooth space is a presheaf of infty -groupoids on the category of cartesian spaces. The key to our definition and construction of smooth string group models is a version of the singular complex functor, which assigns to a smooth space an underlying ordinary space. We provide new characterisations of principal infty -bundles and group extensions in infty -topoi, building on work of Nikolaus, Schreiber and Stevenson. These insights allow us to transfer the definition of string group extensions from the infty -category of spaces to the infty -category of smooth spaces. Finally, we consider smooth higher-categorical group extensions that arise as obstructions to the existence of equivariant structures on gerbes. These extensions give rise to new smooth models for the string group, as recently conjectured in joint work with Müller and Szabo.

A decade of time crystals: Quo vadis?

Ten years ago, the new era of time crystals began. Time crystals are systems that behave in the time dimension like ordinary space crystals do in space dimensions. We present a brief history of a decade of research on time crystals, describe current research directions, indicate challenges, and discuss some future perspectives for condensed matter physics in the time domain.

On a coupled fixed point theorem for a mapping satisfying a contraction of rational type in partially ordered S-metric space

In this paper, the concept of S-metric is used as a generalizion of the ordinary metric space to obtain a coupled fixed point result for a mapping satisfying a contraction of rational type in partially ordered S-metric space. Since such results has already been proved in ordinary metric space, similar procedure was followed in stating and proving our result in the setting of S-metric space. The result presented here modify and generalize the existing result of Circ et al (2012) which was stated in partially ordered metric space.