Structure Of Space Research Articles

Completeness and Geodesic Distance Properties for Fractional Sobolev Metrics on Spaces of Immersed Curves

We investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we consider are Sobolev metrics of possible fractional-order q∈[0,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q\\in [0,\\infty )$$\\end{document}. We establish the critical Sobolev index on the metric for several key geometric properties. Our first main result shows that the Riemannian metric induces a metric space structure if and only if q>1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q>1/2$$\\end{document}. Our second main result shows that the metric is geodesically complete (i.e., the geodesic equation is globally well posed) if q>3/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q>3/2$$\\end{document}, whereas if q<3/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q<3/2$$\\end{document} then finite-time blowup may occur. The geodesic completeness for q>3/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q>3/2$$\\end{document} is obtained by proving metric completeness of the space of Hq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^q$$\\end{document}-immersed curves with the distance induced by the Riemannian metric.

Strong and Weak Convergence Theorems for the Split Feasibility Problem of (β,k)-Enriched Strict Pseudocontractive Mappings with an Application in Hilbert Spaces

The concept of symmetry has played a major role in Hilbert space setting owing to the structure of a complete inner product space. Subsequently, different studies pertaining to symmetry, including symmetric operators, have investigated real Hilbert spaces. In this paper, we study the solutions to multiple-set split feasibility problems for a pair of finite families of β-enriched, strictly pseudocontractive mappings in the setup of a real Hilbert space. In view of this, we constructed an iterative scheme that properly included these two mappings into the formula. Under this iterative scheme, an appropriate condition for the existence of solutions and strong and weak convergent results are presented. No sum condition is imposed on the countably finite family of the iteration parameters in obtaining our results unlike for several other results in this direction. In addition, we prove that a slight modification of our iterative scheme could be applied in studying hierarchical variational inequality problems in a real Hilbert space. Our results improve, extend and generalize several results currently existing in the literature.

PnP-GA+: Plug-and-Play Domain Adaptation for Gaze Estimation Using Model Variants.

Appearance-based gaze estimation has garnered increasing attention in recent years. However, deep learning-based gaze estimation models still suffer from suboptimal performance when deployed in new domains, e.g., unseen environments or individuals. In our previous work, we took this challenge for the first time by introducing a plug-and-play method (PnP-GA) to adapt the gaze estimation model to new domains. The core concept of PnP-GA is to leverage the diversity brought by a group of model variants to enhance the adaptability to diverse environments. In this article, we propose the PnP-GA+ by extending our approach to explore the impact of assembling model variants using three additional perspectives: color space, data augmentation, and model structure. Moreover, we propose an intra-group attention module that dynamically optimizes pseudo-labeling during adaptation. Experimental results demonstrate that by directly plugging several existing gaze estimation networks into the PnP-GA+ framework, it outperforms state-of-the-art domain adaptation approaches on four standard gaze domain adaptation tasks on public datasets. Our method consistently enhances cross-domain performance, and its versatility is improved through various ways of assembling the model group.

Full‐scale measurements of thunderstorm outflows in the Northern Mediterranean

AbstractDownbursts are severe wind systems originating from thunderstorm clouds, and their strong horizontal outflows can pose serious hazards to natural and built environments. In the context of the activities of the European project THUNDERR—Detection, simulation, modelling and loading of thunderstorm outflows to design wind‐safer and cost‐efficient structures—a comprehensive database of full‐scale downburst measurements was built. All records were acquired by bi‐ or tri‐axial ultrasonic anemometers installed in the main ports of the High Tyrrhenian Sea, namely Genova, Livorno and La Spezia, within the European projects ‘Wind and Ports’ and ‘Wind, Ports and Sea’. The very limited space and time structure of downburst outflows makes the available records in nature inadequate for developing models that could be used in the atmospheric science and engineering communities. The database described herein represents a step forward in attempting to fill this gap. The downburst nature of all events contained in the dataset was verified through detailed meteorological analyses, including comparisons with radar and satellite images and lightning recordings. The wind speed records associated with the events detected by the anemometric network are made publicly available through the online repository Zenodo and can be reused for multiple purposes. The dataset is expected to convey an important impulse towards the physical characterization and modelling of downburst winds and their codification into design tools for the assessment of wind loading and its effects on structures and infrastructure. Furthermore, it could serve as a promising, essential tool for researchers and risk‐related insurance companies.

Capsicum leaf protein-based bionanocomposite films for packaging application: Effect of corn starch content on film properties

The addition of corn starch (CS) enhances the interfacial adhesion of the film-forming liquids (FFLs), weakening the internal relative molecular motion. As a result, the rheological properties and zeta potential values of the FFLs were affected. A tight spatial network structure between capsicum leaf protein (CLP), lignocellulose nanocrystals (LNCs) and CS can be formed through intermolecular entanglement and hydrogen bonding interactions. The crystallinity, thermal degradation temperature, tensile strength and water contact angle of the protein-based bionanocomposite films (PBBFs) increased with increasing CS addition. This is due to the transformation of the secondary space structure of the CLP inside the PBBFs and the increase in cohesion. However, the excessive addition of CS forms aggregated clusters on the surface of PBBFs, which increases the surface roughness of PBBFs and causes more light scattering. Therefore, the brightness and yellowness values of the PBBFs increase, and the transmittance decreases.

Spatial Gradient Differences in the Cooling Island Effect and Influencing Factors of Urban Park Green Spaces in Beijing

Urban park green spaces exhibit significant cool island effects, which can effectively mitigate the urban heat environment. Clarifying the characteristics and differences in the cool island effects of urban parks across different spatial gradients within cities is instrumental in identifying potential issues and optimizing the structure and resource allocation of park green spaces in a scientifically rational manner. This study focuses on parks within the central urban area of Beijing, utilizing remote sensing image interpretation and land surface temperature (LST) inversion to extract relevant characteristics of park green spaces and the park cool island intensity (PCI) index. Various mathematical and statistical methods including correlation analysis, regression analysis, and cluster analysis are employed to conduct comparative studies across three gradients: within the 3rd ring road, between the 3rd and 5th ring roads, and outside the 5th ring road. The analysis reveals that both park green space characteristics and urban heat island effects exhibit spatial gradient differences, collectively influencing the cool island effects of urban park green spaces. PCI gradually decreases across the three spatial gradients. Cluster analysis identifies four distinct types of parks with different cool island effect characteristics, highlighting the need for optimization and improvement in over half of the parks. Various indicators of park green space characteristics show different correlations with PCI, with variations in correlation strength and thresholds across gradients. The fitting effects of regression equations for each characteristic indicator and PCI gradually worsen from within the 3rd ring road to outside the 5th ring road, with different factors playing important roles across gradients. This study enhances our understanding of the cool island effects of urban park green spaces and facilitates the proposition of differentiated optimization management strategies for urban park green space planning and system construction in different regions.

Residential urban heritage space identification, delimitation, and potential assessment model based on space syntax

In the era of post-modernization, profound transformations in urban spaces have led to significant shifts in the spatial composition paradigms of contemporary urban heritage. Research on this process is crucial for elucidating the spatial pathways and compositional changes in the modernization transformation of urban heritage. This study aims to establish identification indicators and assessment systems for the spatial structure of urban residential environments exhibiting historical characteristics and heritage potential through a comparative analysis of residential urban heritage spatial paradigms in historic cities in China and Japan. First, grounded in space syntax theory, this study selected residential urban heritage in Suzhou&amp;rsquo;s Pingjiang Historic District and Uji&amp;rsquo;s Nakauji District as research cases. Utilizing road network data, this study analyzed the Life Integration (Int.VR1000) and Global Integration (Int.VR5000) of urban heritage spaces, thereby constructing a spatial topology system for heritage spaces. Second, the study employed urban spatial entropy indicators, such as architectural density entropy, spatial morphology entropy, and function mixing entropy, to quantitatively describe the spatial structure, consequently establishing a heritage space morphological structure indicator system. Finally, spatial clustering methods are used to integrate the spatial topology system with the morphological structure indicator system, resulting in a feature model for residential urban heritage spaces. The research results indicate that the transformation path of residential space paradigms is mainly influenced by spatial topology, affecting the structure of residential heritage spaces in three aspects: functional layout, building density, and spatial form. This phenomenon, in turn, impacts population distribution and the migration of living spaces. However, at the same time, the &amp;ldquo;resistance effect&amp;rdquo; of street and lane spaces and the limitations of architectural forms on spatial functions have protected the integrity and authenticity of the internal space.

Mapping semantic space: Exploring the higher-order structure of word meaning

Multiple representation theories posit that concepts are represented via a combination of properties derived from sensorimotor, affective, and linguistic experiences. Recently, it has been proposed that information derived from social experience, or socialness, represents another key aspect of conceptual representation. How these various dimensions interact to form a coherent conceptual space has yet to be fully explored. To address this, we capitalized on openly available word property norms for 6339 words and conducted a large-scale investigation into the relationships between 18 dimensions. An exploratory factor analysis reduced the dimensions to six higher-order factors: sub-lexical, distributional, visuotactile, body action, affective and social interaction. All these factors explained unique variance in performance on lexical and semantic tasks, demonstrating that they make important contributions to the representation of word meaning. An important and novel finding was that the socialness dimension clustered with the auditory modality and with mouth and head actions. We suggest this reflects experiential learning from verbal interpersonal interactions. Moreover, formally modelling the network structure of semantic space revealed pairwise partial correlations between most dimensions and highlighted the centrality of the interoception dimension. Altogether, these findings provide new insights into the architecture of conceptual space, including the importance of inner and social experience, and highlight promising avenues for future research.

The separability problem in molecular quantum systems: Information-Theoretic framework for Atoms in Molecules.

Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three-dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X-Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms-In-Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts. We have uncovered information-theoretical justifications for employing some of the most prevalent AIM schemes in the field of Chemistry, including Hirshfeld (stockholder partitioning), Bader's (topological dissection), and the quantum approach (Hilbert's space definition). In the first approach we have applied the generalized principle of minimum relative entropy derived from Sharma-Mittal relative entropy, avoiding the need for an arbitrary selection of reference promolecular atoms. Within the realm of topological-information partitioning, we have demonstrated that the Fisher information of Bader's atoms conform to a comprehensive theory based on the Principle of Extreme Physical Information. For the quantum approach we have presented information-theoretic justifications for conducting Löwdin symmetric transformations on the density matrix to form atomic Hilbert spaces.

Structural and Vibrational Properties of Carboxylates Intercalated into Layered Double Hydroxides: A Joint Computational and Experimental Study.

Layered double hydroxides (LDHs) are fascinating clay-like materials that display versatile properties, making them an extremely fertile playground for diverse applications, ranging from bio-compatible materials to the pharmaceutical industry to catalysis and photocatalysis. When intercalating organic and bio-organic species between the inorganic layers, such materials are named hybrid LDHs. The structure-property relation in these systems is particularly relevant, since most of the properties of the materials may be fine-tuned if a comprehensive understanding of the microscopic structure in the interlamellar space is achieved, especially with respect to the reorganization under water uptake (swelling). In this work, we combined experiments and simulations to rationalize the behavior of LDHs intercalating three carboxylates, the general structure of which can be given as [Mg4Al2(OH)12]A2-·XH2O (with A2- = succinate, aspartate, or glutamate and X representing increasing water content). Following this strategy, we were able to provide an interpretation of the different shapes observed for the experimental water adsorption isotherms and for the evolution of the infrared carboxylate band of the anions. Apart from small differences, due to the different reorganization of the conformational space under confinement, the behavior of the two amino acids is very similar. However, such behavior is quite different in the case of succinate. We were able to describe the different response of the anions, which has a significant impact on the isotherm and on the size of the interlamellar region, in terms of a different interaction mechanism with the inorganic layer.

Multiplicity structure of the arc space of a fat point

Multiplicity structure of the arc space of a fat point

Current state of the political culture of Afghanistan

The article is devoted to one of the important issues of the development of the political space, political system, political life, and ideological and cultural structure of modern Afghan society. The article attempts to analyze and discuss various aspects of the current state of the political culture of Afghanistan. The main attention is paid to the attitude of citizens to politics and the political regime of the Taliban (organization banned in Russia). Afghanistan’s current political culture is based on the models and values of the Taliban government. They rely on traditionalist political models. The implementation of modern political processes, such as elections, is not far from being able to question the power of representatives. It can be argued that political culture is the link between people and political power. The main task of political culture is to include people in the political system of society and political activities. Political culture is a system of political knowledge, attitudes, beliefs, and values, as well as political activities of political subjects. For example, political culture manifests itself differently in different social groups and communities, political movements, and individuals. The study of the current state of the political culture of Afghanistan allows us to conclude that today the level of conflict is quite high, the mood of the Afghan society is at a disorganized level. A controversial political culture prevails in Afghan society. This conflict can be seen in social differences, institutional weakness, society’s distrust of functioning authority, and cultural differences. 

Orientation Relationship of the Intergrowth Al13Fe3 and Al13Fe4 Intermetallics Determined by Single-Crystal X-ray Diffraction

In the Al-Fe binary system, the Al13Fe3 phase as well as the Al13Fe4 phase has similar icosahedral building blocks like those appearing in quasicrystals. Therefore, it is of vital importance to clarify the formation process of these two phases. Coexistence of the Al13Fe3 and Al13Fe4 phases was discovered from the educts obtained with a nominal atomic ratio of Al/Fe of 9:2 by high-pressure sintering for the first time. Firstly, single crystal X-ray diffraction (SXRD) combined with a scanning electron microscope (SEM) with energy dispersive X-ray spectroscopy (EDX) measurement capabilities were adopted to determine the detailed crystal structures of both phases, which were sharply refined with regard to Al13Fe3 and Al13Fe4. Secondly, the orientation relationship between Al13Fe3 and Al13Fe4 was directly deduced from the SXRD datasets and the coexistence structure model was consequently constructed. Finally, seven pairs of parallel atomic planes and their unique orientation relations were determined from the reconstructed reciprocal space precession images. In addition, the real space structure model of the intergrowth crystal along with one kind of interfacial atomic structure were constructed from the determined orientation relations between two phases.

\'C}iri{\'c} Contraction with Graphical Structure of Bipolar Metric Spaces and Related Fixed Point Theorems

We present the novel concept of graphical bipolar metric-type space in this article, which combines the notions of graph theory with fixed point theory. We prove that Every bipolar metric space is a graphical bipolar metric space but the converse is not true in general. Various concepts like covariant mapping, contravariant mapping, and Cauchy bisequence are also discussed within the context of graphical bipolar metric-type spaces. Furthermore, in this study, we show that fixed point results exist in graphical structures of bipolar metric spaces and a series of examples are provided to support the main results within the realm of the graph structure.

On some objections to the powers-BSA

Abstract This paper responds to Friend's (2023) critique of the Powers-BSA, a view according to which laws of nature are efficient descriptions of how modally laden properties (powers) are possibly distributed in spacetime. In the course of this response, the paper discusses the nature of scientific and metaphysical explanation, the aim of science, and the structure of modal space.

Function theory off the complexified unit circle: Fréchet space structure and automorphisms

Motivated by recent work on strict deformation quantization of the unit disk and the Riemann sphere, we study the Fréchet space structure of the set of holomorphic functions on the complement \(\Omega:=\{(z,w)\in \hat{\mathbb{C}}^2\colon z\cdot w\not=1\}\) of the complexified unit circle \(\{(z,w) \in \hat{\mathbb{C}}^2 \colon z\cdot w=1\}\). We also characterize the subgroup of all biholomorphic automorphisms of \(\Omega\) which leave the canonical Laplacian on \(\Omega\) invariant.

Highly localized horseshoe ripplons and solitons in positive dispersion media

In this study, we systematically review various ripplon solutions to the Kadomtsev–Petviashvili equation with positive dispersion (KP1 equation). We show that there are mappings that allow one to transform the horseshoe solitons and curved lump chains of the KP1 equation into circular solitons of the cylindrical Korteweg–de Vries (cKdV) equation and two-dimensional solitons of the cylindrical Kadomtsev–Petviashvili (cKP) equation. Then, we present analytical solutions that describe new nonlinear highly localized ripplons of a horseshoe shape. Ripplons are two-dimensional waves with an oscillatory structure in space and a decaying character in time; they are similar to lumps but non-stationary. In the limiting case, the horseshoe ripplons reduce to solitons decaying with time and having bent fronts. Such entities can play an important role in the description of strong turbulence in plasma and other media.

Flutter analysis of a rigid-flexible coupled composite space structure with momentum wheels under thermal load

The communication and observation spacecraft generally consists of the spacecraft body, the composite connecting beams, the working payload and the CMG/momentum wheel for integrated attitude-vibration control. When such complex space structure operates in near-Earth orbit, the sudden change in thermal load may cause a solar flux shock to the structure, which is likely to excite the flutter motion of the structure. The flutter mechanism of a rigid-flexible coupled composite space structure configured with the momentum wheel is investigated. In this study, the heat conduction equation of the composite beam appendage is derived. Then, the dynamic equations of the system influenced by the momentum wheel and composite material parameters are obtained based on the Kane's equations. Using the Routh–Hurwitz stability criterion, the stability boundaries of the flexible appendage are obtained for different composite material parameters, different operating conditions of the momentum wheel, and different attitude angular velocities. Finally, the flutter behavior is analyzed based on the dynamic response of the flexible structure and the flutter stability boundaries are verified.

Analysis of Ingress Into the Downstream Wheel Space of a 1.5-Stage Turbine By Full Circumference and Single Blade Passage Large-Eddy Simulations

Abstract The flow in a 1.5-stage axial turbine is investigated by large-eddy simulations. The focus is on the ingress in the downstream wheel space. Two setups are considered. In the first, the full 360 deg annulus is included on a computational mesh with approx. 1 billion mesh cells. The second setup includes a single blade passage in a 22.5 deg segment. The computational mesh has approx. 75 million mesh cells accordingly. The flow fields in the downstream wheel space differ strongly. In the 22.5 deg setup, the disk pumping effect is much more pronounced than in the 360 deg setup and the fluid bulk rotates in the direction of the rotor rotation. In the 360 deg setup, the fluid rotates in the opposite rotor direction and the velocities feature a deflection at intermediate radii. The differences are caused by the instantaneous flow fields. In the upstream wheel space of the 360 deg setup, two large-scale rotating vortex structures are predicted, which create four pressure peaks that propagate downstream. They interact with the second stator and create a rotating flow structure in the downstream wheel space, which generates alternating ingress and egress. Due to their spatial extent, none of these structures can exist in the 22.5 deg setup. The results show that for the investigated combination of turbine geometry and operating condition, the analysis of the downstream wheel space requires the detailed prediction of the unsteady flow phenomena in the upstream wheel space, i.e., it cannot be performed using the 22.5 deg setup.

АРХИТЕКТУРНО-ГРАДОСТРОИТЕЛЬНОЕ РАЗВИТИЕ УЛИЦЫ СИМФЕРОПОЛЬСКОЙ В ГОРОДЕ ЕВПАТОРИЯ

Abstract. The relevance of the development of Simferopolskaya Street in the city of Yevpatoria, Republic of Crimea, is due to the increased need to improve the quality of the coastal urban environment. Recently, the western part of the Crimean coast has been gaining increasing interest among tourists. One of the most popular tourist cities is Evpatoria. The main architectural and urban planning problems of the coastal zone in the area of the street have been identified. Simferopolskaya: obsolescence of low-rise residential buildings, unattractive aesthetic appearance of the facades of buildings and structures, lack of an embankment and comfortable landscaping of the territory. Currently, in the improvement of the territory under consideration, there is no single architectural style - a harmonious appearance of the street. The work analyzes theoretical and practical materials related to the object of research, and analyzes world analogues. Scientific principles and practical recommendations for the reconstruction of Simferopolskaya Street with the adjacent seaside area - the embankment and the beach - are proposed. To test the research results, an experimental design model was developed.&#x0D; Subject: Reconstruction of the territory within the boundaries of Simferopolskaya Street in the city of Evpatoria, landscaping.&#x0D; Materials and methods: During the study, an analysis of projects of world analogues was used. To identify the historical pattern of development of the territory, a comparative analysis of coastal territories of the Soviet period and at present is used. In the process of selecting materials on the topic of publication and analysis of the urban planning situation, the following methods were used: deduction, theoretical analysis and synthesis, the method of analogy, field surveys, photographic recording, critical and urban planning analysis, experimental design.&#x0D; Results: To increase the duration of the holiday season and increase the attractiveness of the study area, the main indicators have been identified: the formation of an identifying architectural image of the coastal strip of Simferopolskaya Street in the city of Evpatoria, attracting investors to implement projects, expanding the scope of services provided to tourists.&#x0D; It is proposed to apply the developed scientific principles for the development of the street and adjacent coastal areas:&#x0D; - the principle of integrity of the structure of space;&#x0D; - ecological principle;&#x0D; - principle of investment attractiveness;&#x0D; - the principle of increasing positive factors in the use and development of existing building functions and territory;&#x0D; - the principle of preservation and renewal;&#x0D; - the principle of continuity;&#x0D; - the principle of architectural and artistic expressiveness and functional diversity.&#x0D; The formation and transformation of urban public recreational zones of coastal areas must have a well-thought-out strategy for the systematic, phased implementation of work on the construction of facilities and improvement of coastal areas. To comply with the above principles, it is necessary to develop a strategy or concept for the development of the territory and adhere to it when reconstructing the territory.&#x0D; Conclusions: Based on the results of the analysis of global and domestic design and reconstruction of embankments, current trends in the formation of urban recreational zones of coastal territories were identified, which should also be applied to the city of Evpatoria:&#x0D; 1) development of pedestrian traffic infrastructure through the development of the coastal strip as a system of pedestrian spaces in contact with the shoreline of water bodies;&#x0D; 2) the maximum possible distance of water bodies from intense traffic flows, giving preference to pedestrian spaces;&#x0D; 3) improvement of the green zone as an infrastructure of coastal areas, by forming an integral, continuous strip or islands of greenery;&#x0D; 4) the formation within the boundaries of coastal territories of a multifunctional system that unites recreational areas and public spaces, the interaction of pedestrian, green, and water infrastructures as a single whole;&#x0D; 5) development of coastal areas as complex objects of urban culture.&#x0D; The practical application of the developed principles and recommendations embedded in the experimental design model - the concept of reconstruction of the seaside street of Simferopol in the city of Yevpatoria will contribute to the qualitative development of the urban environment.