Topological Concepts Research Articles

Soft Complete Continuity and Soft Strong Continuity in Soft Topological Spaces

In this paper, we introduce soft complete continuity as a strong form of soft continuity and we introduce soft strong continuity as a strong form of soft complete continuity. Several characterizations, compositions, and restriction theorems are obtained. Moreover, several preservation theorems regarding soft compactness, soft Lindelofness, soft connectedness, soft regularity, soft normality, soft almost regularity, soft mild normality, soft almost compactness, soft almost Lindelofness, soft near compactness, soft near Lindelofness, soft paracompactness, soft near paracompactness, soft almost paracompactness, and soft metacompactness are obtained. In addition to these, the study deals with the correlation between our new concepts in soft topology and their corresponding concepts in general topology; as a result, we show that soft complete continuity (resp. soft strong continuity) in soft topology is an extension of complete continuity (resp. strong continuity) in soft topology.

Topological Considerations in Biomolecular Condensation.

Biomolecular condensation and phase separation are increasingly understood to play crucial roles in cellular compartmentalization and spatiotemporal regulation of cell machinery implicated in function and pathology. A key aspect of current research is to gain insight into the underlying physical mechanisms of these processes. Accordingly, concepts of soft matter and polymer physics, the thermodynamics of mixing, and material science have been utilized for understanding condensation mechanisms of multivalent macromolecules resulting in viscoelastic mesoscopic supramolecular assemblies. Here, we focus on two topological concepts that have recently been providing key mechanistic understanding in the field. First, we will discuss how percolation provides a network-topology-related framework that offers an interesting paradigm to understand the complex networking of dense 'connected' condensate structures and, therefore, their phase behavior. Second, we will discuss the idea of entanglement as another topological concept that has deep roots in polymer physics and important implications for biomolecular condensates. We will first review some historical developments and fundamentals of these concepts, then we will discuss current advancements and recent examples. Our discussion ends with a few open questions and the challenges to address them, hinting at unveiling fresh possibilities for the modification of existing knowledge as well as the development of new concepts relevant to condensate science.

1. On the Importance of the Institutional Aspect of the University in the Context of Historical Development of Technologies of Knowledge

Abstract This paper* discusses role and importance of the institutional aspect of the University in a context of historical development of technologies of knowledge. Through an analysis of similarities between subsequent technological innovations that transformed how knowledge was created, shared and stored, this paper shows that each time there was an institutional ‘answer’ to these developments. It is further argued that currently another such technological innovation is unfolding and that despite similarities it poses an unprecedented challenge, as it puts the institution itself into question. This paper discusses what the institutional character means for the University by highlighting the role it plays in making a place, thus connecting the institution to a concept of place and topology. Some further political consequences of this technological challenge to the institution and place are also discussed here.

Entropies of the Y-Junction Type Nanostructures

Recent research on nanostructures has demonstrated their importance and application in a variety of fields. Nanostructures are used directly or indirectly in drug delivery systems, medicine and pharmaceuticals, biological sensors, photodetectors, transistors, optical and electronic devices, and so on. The discovery of carbon nanotubes with Y-shaped junctions is motivated by the development of future advanced electronic devices. Because of their interaction with Y-junctions, electronic switches, amplifiers, and three-terminal transistors are of particular interest. Entropy is a concept that determines the uncertainty of a system or network. Entropy concepts are also used in biology, chemistry, and applied mathematics. Based on the requirements, entropy in the form of a graph can be classified into several types. In 1955, graph-based entropy was introduced. One of the types of entropy is edge-weighted entropy. We examined the abstract form of Y-shaped junctions in this study. Some edge-weight-based entropy formulas for the generic view of Y-shaped junctions were created, and some edge-weighted and topological index-based concepts for Y-shaped junctions were discussed in the present paper.

Topological quantum devices: a review.

The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.

Flexible Interlinking Converter With Enhanced FRT Capability for On-Board DC Microgrids

In this paper, a flexible interlinking dc/dc converter with enhanced FRTC is proposed to satisfy the advanced requirements of modern on-board DC MGs; the topology uses a non-isolated switched capacitor-type multilevel converter in combination with a cascaded step up/down converter to facilitate the incorporation of various types of energy storage and/or production units in a DC MG. Overall, a high voltage conversion ratio between the dc bus of the MG and the power unit is achieved. The proposed configuration facilitates the CCM operation of both the power unit and the DC MG and it is characterized by bidirectional power flow capability, enhanced FRTC, zero switching losses for the multilevel converter, limited complexity of the control scheme (compared to the counterpart multilevel solutions) and low real-time communication demands, corresponding so to the increasing flexibility needs of the EMS of modern MGs. The mathematical analysis and the dynamic performance of the control scheme of the proposed topology concept are evaluated via MATLAB/Simulink simulations and real-time CHIL tests, with the use of a 1202 dSPACE platform and an external dsPIC30F4011 microcontroller.

The Parallax View between Merleau-Ponty and Lacan

Since Narcissus sees himself seeing himself, i.e., comes to self-consciousness and plunges into self-destruction under the gaze, thinkers have problematized the Delphic maxim of “knowing thyself” from a visual perspective. In this trend, psychoanalysis joins the self-criticism of phenomenology in subverting the “myth” of the self-reflective consciousness. Whereas Lacan relegates the mirror stage to the Imaginary and interprets the gaze as objet a to account for the split in the subject, Merleau-Ponty overcomes the narcissistic enclosure of the tacit cogito by appealing to the self’s abandonment to the gaze of the other in an open-circuit of the reversible flesh. Through the lens of the topological concept of parallax, this study illuminates the fundamental distinctions between these two perspectives and proposes a promising future of psychoanalytic phenomenology.

Kulturowe czynniki postaw wobec „czwartej przyrody” w przestrzeni miejskiej

Cultural factors of attitudes towards "nature of the fourth kind” in urban space The return of spontaneous plants to the city is now considered a valuable process helping to balance degraded urban ecosystems (Kowarik, Körner 2005, Jakubowski 2019, 2020). However, research on public attitudes towards the “nature of the fourth kind” in the city and peri-urban areas shows that they are not unequivocally positive and are accompanied by conflicting feelings (Hunziker 1995, Bauer 2005, Sonti 2019). Addressing the issue of ambivalence associated with new wilderness, the article proposes its cultural interpretation. Firstly, it contextualises ambivalence as a contemporary form of the “numinous” experience (Otto 1999) that arises in encounters with the life dynamics of spontaneous plants that escape human control. Secondly, it identifies archetypal spatial figures of Western urban culture, namely wall and parcel, as cultural factors shaping attitudes toward the new wilderness both at the level of “situations” and “ideologies” (Kłoskowska 1973). Thirdly, it aims to reorient the view of new wilderness in the city with the use of the topological concept of “figuration” (Lash 2012) and the idea of thinking together with plants (Haraway 2016). The above issues are presented against the backdrop of two questions: about the politics guiding research on the social perception of the new wilderness and about the possibility of developing a more nuanced understanding of the “nature of the fourth kind” concept that goes beyond the scale of the wastelands by taking into account the micro-perspective of the mobile urban subject and the unconventional creativity of plants.

N-refined Neutrosophic Fuzzy of Some Topological Concepts

In this paper, we present and study some concepts in topological space by using two tools in fuzzy theory which namely fuzzy and neutrosophic concepts. n-refined neutrosophic fuzzy topological space have been studied by n-refined neighborhood, n-refined compact set and other notions. Finally, some definitions, examples and new results have been presented in this paper.

EXPLICIT DIGITAL MODELS OF LINEAR COMPLEXES

It is obvious that the interoperability of existing digital models is insufficient. Current research on model view definitions and on their semantic enrichment addresses the issue of good interpretation of the results of existing models to improve interoperability. The alternative research presented in this paper is not concerned with interpretation. Instead, the influence of modifications in the geometric and topological concepts of the digital models themselves on their interoperability is investigated. The geometric and topological attributes of the models are made as explicit as possible. Two-dimensional line drawings are replaced by three-dimensional linear complexes to reduce the need for implicit information. The topology of a complex is described with topological tables containing all elements of the model, thus replacing the geometric neighborhood concept of the industry foundation classes. A highly efficient algorithm for the construction of new topological tables of large buildings is presented. The difficulties encountered in modifying existing topological tables are analyzed and solved. Topological and geometric aspects of linear complexes that cannot be treated explicitly with topological tables are identified and presented.

Soft functions via soft semi ω -open sets

In this paper, we introduce the concepts of soft semi \( \omega \)-continuous, soft \(\omega \)-irresolute, and soft semi \(\omega \) -irresolute functions by using soft semi \(\omega \)-open sets. We characterize them and discuss their main properties with the help of examples. We investigate under what conditions the restriction of soft semi \( \omega \)-continuous, soft \(\omega \)-irresolute, and soft semi \(\omega \) -irresolute functions are respectively soft semi \(\omega \)-continuous, soft \( \omega \)-irresolute, and soft semi \(\omega \)-irresolute. Also, we investigate under what conditions the composition of two soft semi \(\omega \) -continuous, soft \(\omega \)-irresolute, and soft semi \(\omega \)-irresolute functions are respectively soft semi \(\omega \)-continuous, soft \(\omega \) -irresolute, and soft semi \(\omega \)-irresolute. In addition to these, we examine the connection between the new classes of soft functions and their corresponding general topological concepts.

Exploiting extraordinary topological optical forces at bound states in the continuum.

Polarization singularities and topological vortices in photonic crystal slabs centered at bound states in the continuum (BICs) can be attributed to zero amplitude of polarization vectors. We show that such topological features are also observed in optical forces within the vicinity of BIC, around which the force vectors wind in the momentum space. The topological force carries force topological charge and can be used for trapping and repelling nanoparticles. By tailoring asymmetry of the photonic crystal slab, topological force will contain spinning behavior and shifted force zeros, which can lead to three-dimensional asymmetric trapping. Several off-Γ BICs generate multiple force zeros with various force distribution patterns. Our findings introduce the concepts of topology to optical force around BICs and create opportunities to realize optical force vortices and enhanced reversible forces for manipulating nanoparticles and fluid flow.

Graded human sensitivity to geometric and topological concepts

In a seminal study, Dehaene et al. (2006) found evidence that adults and children are sensitive to geometric and topological (GT) concepts using a novel odd-one-out task. However, performance on this task could reflect more general cognitive abilities than intuitive knowledge of GT concepts. Here, we developed a new 2-alternative forced choice (2-AFC) version of the original task where chance represents a higher bar to clear (50% vs. 16.67%) and where the role of general cognitive abilities is minimized. Replicating the original finding, American adult participants showed above-chance sensitivity to 41 of the 43 GT concepts tested. Moreover, their performance was not strongly driven by two general cognitive abilities, fluid intelligence and mental rotation, nor was it strongly associated with mathematical achievement as measured by ACT/SAT scores. The performance profile across the 43 concepts as measured by the new 2-AFC task was found to be highly correlated with the profiles as measured using the original odd-one-out task, as an analysis of data sets spanning populations and ages revealed. Most significantly, an aggregation of the 43 concepts into seven classes of GT concepts found evidence for graded sensitivity. Some classes, such as Euclidean geometry and Topology, were found to be more domain-specific: they “popped out” for participants and were judged very quickly and highly accurately. Others, notably Symmetry and Geometric transformations, were found to be more domain-general: better predicted by participants’ general cognitive abilities and mathematical achievement. These results shed light on the graded nature of GT concepts in humans and challenge computational models that emphasize the role of induction.

Modular Multi-Input DC/DC Converter for EV Fast Charging

In this paper, a modular multi-input, single output DC/DC converter is proposed to enhance the energy management of a fast-charging station for electric vehicles (EVs). The proposed bidirectional converter can work in different modes of operation with fewer components and a modular design to extend the input power sources and increase the charging power rate. The converter has several merits compared to the conventional converters, such as centralizing the control, reducing power devices, and reducing power conversion stages. By using MATLAB/Simulink, the converter was tested in many operation modes and was used to charge a Nissan Leaf EV’s battery (350 V, 60 Ah) from hybrid sources simultaneously and individually in power up to (17 kW). In addition, it was tested on a hardware scale at a low power rate (100 W) for the validation of the simulation work and the topology concept. In addition, its different losses and efficiency were calculated during the different operation modes.

Topological nodal line phonons: Recent advances in materials realization

The topological phenomenon has been extensively studied in condensed matter physics and has attracted much attention in many different fields. Like electrons, phonons can also be studied using critical theorems and topology concepts, giving impetus to the birth of topological phonons. Among the topological phonons, the topological nodal line phonons in crystalline materials have emerged as a new area of rapid development in both experiment and theory. Researchers have been hunting for realistic materials with nodal line phonons for the last four years. To date, however, a timely review of recent advances in topological nodal line phonons, and especially their material realization, is still lacking. Considering the classification of the nodal line states, in this review, we will first review the identification of the materials hosting the nodal line phonons with different degeneracies, different types of dispersion, and different geometric shapes in theory. Moreover, we will review and discuss the reasons for the appearance of the nodal line phonons from the viewpoint of symmetry. Second, we will review the case where the nodal line appears in the projected surface phonon states instead of the bulk phonon states. Third, we will review the experimental material realization of nodal line phonons. Finally, we will present a summary, outlook, and additional notes. We believe that this review will contribute to a more advanced understanding of topological nodal line phonons in solid materials and will offer new perspectives on this rapidly expanding field.

On some weaker forms of soft continuity and their decomposition theorems

In this paper, we employ soft \(\omega ^{0}\)-open sets to establish four new classes of soft functions in STSs: soft \(\omega ^{0}\) -continuity, soft weak \(\omega ^{0}\)-continuity, soft \(w^{\ast }\) -continuity, and soft \(w^{\ast }\)-\(\omega ^{0}\)-continuity. We show that soft weak \(\omega ^{0}\)-continuity and soft \(w^{\ast }\)-\(\omega ^{0}\) -continuity are distinct notions, each of which is strictly weaker than soft \(\omega ^{0}\)-continuity. Furthermore, we get a soft \(\omega ^{0}\) -continuity decomposition theorem via both weak \(\omega ^{0}\)-continuity and soft \(w^{\ast }\)-\(\omega ^{0}\)-continuity. In addition, we demonstrate that soft \(w^{\ast }\)-continuity is precisely between soft continuity and soft \( w^{\ast }\)-\(\omega ^{0}\)-continuity. We further show that soft \(w^{\ast }\) -continuity and soft weak continuity are distinct concepts. In addition, we develop a soft continuity decomposition theorem via soft \(w^{\ast }\) -continuity and soft weak continuity. Finally, we examine the connection between our new soft topological ideas and their corresponding topological concepts. Include keywords, mathematical subject classification numbers as needed.

Bipolar Soft Limit Points in Bipolar Soft Generalized Topological Spaces

The concept of soft set theory can be used as a mathematical tool for dealing with problems that contain uncertainty. Then, a new mixed mathematical model called the bipolar soft set is created by merging soft sets and bipolarity, which gave the concept of a binary model of grading. Bipolar soft set is characterized by two soft sets, one of which provides positive information and the other negative. Bipolar soft generalized topology is a generalization of bipolar soft topology. The importance of limit points in all branches of mathematics cannot be ignored. It forms one of the most significant and fundamental concepts in topology. On this basis, the derived set concept is required in the establishment and continuation of some properties. Accordingly, the limit point in bipolar soft generalized theory is defined. In this paper, we present the notion of bipolar soft generalized limit points. We explained the relation between the bipolar soft generalized derived and the bipolar soft generalized closure set. Added to that, we discussed some structures of a bipolar soft generalized topological space such as: <img src=image/13428354_01.gif>-interior point, <img src=image/13428354_01.gif>-exterior point, <img src=image/13428354_01.gif>-boundary point, <img src=image/13428354_01.gif>-neighborhood point and basis on <img src=image/13428354_02.gif>. Finally, we give comparisons among these concepts of bipolar soft generalized topological spaces (<img src=image/13428354_02.gif>) by using bipolar soft point (<img src=image/13428354_03.gif>). Each concept introduced in this paper is explained with clear examples.

Design of a higher-order nodal-line semimetal in a spring-shaped acoustic topological crystal

The concept of higher-order topology has prompted the development of topological insulators, and a series of theoretical and experimental schemes have been proposed and realized to demonstrate higher-order hinge or corner states. While these ideas thrive in topological semimetals such as higher-order Dirac or Weyl semimetals, other degeneracy types such as nodal lines or nodal loop semimetals still remain to be fully exploited. In this work we consider a setup that hosts an acoustic springlike higher-order nodal-line semimetal protected by a screw-rotational symmetry. The underlying sandwich architecture is engineered with different coupling modes between different layers to construct a specific space group configuration, which enables the emergence of higher-order nodal lines in momentum space. Numerical calculations of the band dispersion show that nodal lines in opposite directions result in linked double hinge arcs. A corresponding topological invariant index is introduced to characterize the different topological phases. Furthermore, a propagation simulation of hinge and surface waves in a multilayer sample is performed that matches well with theoretical computations. Our work thus presents a higher-order nodal-line semimetal in an acoustic crystal and may receive practical applications in manufacturing sonic devices.

Magnetic hopfions in solids

Hopfions are an intriguing class of string-like solitons, named according to a classical topological concept classifying three-dimensional direction fields. The search for hopfions in real physical systems has been ongoing for nearly half a century, starting with the seminal work of Faddeev. However, so far, realizations in bulk solids are missing. Here, we show that hopfions appear as emergent particles of the classical Heisenberg model with competing exchange interactions. This requires going beyond the model approach used in prior work and deriving a general micromagnetic energy functional directly from a spin-lattice Hamiltonian. We present a definite parameter space in which the existence of hopfions is possible. This opens a concrete vista to combine computational approaches such as density functional theory with material informatics to find magnetic crystals that can host hopfions. As proof of principle, we show how zero-field hopfions can be visualized by the means of off-axis electron holography in a transmission electron microscope.

Topological Data Analysis of m-Polar Spherical Fuzzy Information with LAM and SIR Models

The concept of m-polar spherical fuzzy sets (mPSFS) is a combination of m-polar fuzzy sets (mPFS) and spherical fuzzy sets (SFS). An mPSFS is an optimal strategy for addressing multipolarity and fuzziness in terms of ordered triples of positive membership grades (PMGs), negative membership grades (NMGs), and neutral grades (NGs). In this study, the innovative concept of m-polar spherical fuzzy topology (mPSF-topology) is proposed for data analysis and information aggregation. We look into the characteristics and results of mPSF-topology with the help of several examples. Topological structures on mPSFSs help with both the development of new artificial intelligence (AI) tools for different domain strategies and the study of different kinds of uncertainty in everyday life problems. These strategies make it possible to recognise and look into a situation early on, which helps professionals to reduce certain risks. In order to address various group decision-making issues in the m-polar spherical fuzzy domain, one suggestion has been to apply an extended linear assignment model (LAM) along with the SIR method known as superiority and inferiority ranking methodology in order to analyze road accident issues and dispute resolution. In addition, we examine the symmetry of optimal decision and perform a comparative study between the research carried out using the suggested methodology and several existing methods.