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The integrated industrial control systems require a reliable communication among each part of control systems. The limitation of network topology comprises the low latency of data transmission. The network algorithm topologies are sometimes failed to ensure the faulttolerant network design even if they offer it. Therefore, this works investigates a Node Insertion Algorithm (NIA) and Ant Colony Optimization (ACO) in order to solve the Travelling Salesman Problem (TSP) for network topologies in a communication network. The NP Non deterministic (polynomial time)-hardness based of TSP leads to the impossibility of polynomial time algorithm to solve an exponentially increasing amount of communication addresses. TSP itself is a well-known solution method known in the graph theory which is based on approximation algorithm. Therefore, this work also presents a comparison between the NIA and ACO for 200 nodes of network topologies. The results show that NIA is superior than ACO in terms of resulting ring's cost and computation duration. Three topologies are tested and it is observable that NIA requires only 14.88 seconds to finish the computation in which the resulting ring's length reaches 164019 units. Therefore, the achievement of the NIA can be applied for logical and physical nodes for a reliable connection in an industrial topology network. [ABSTRACT FROM AUTHOR]

Non-Hermitian topology is a recent hot topic in condensed matters. In this paper, we propose a novel platform drawing interdisciplinary attention: rock–paper–scissors (RPS) cycles described by the evolutionary game theory. Specifically, we demonstrate the emergence of an exceptional point and a skin effect by analyzing topological properties of their payoff matrix. Furthermore, we discover striking dynamical properties in an RPS chain: the directive propagation of the population density in the bulk and the enhancement of the population density only around the right edge. Our results open new avenues of the non-Hermitian topology and the evolutionary game theory. [ABSTRACT FROM AUTHOR]

This paper presents the ways that reflective questions were used to develop pre-service mathematics teachers' understanding of metric and topological spaces. In particular, the purpose of developing PSTs' understanding of metric and topological spaces is that understanding these mathematical concepts leads to PSTs' understandings on how to teach and learn geometrical figures in mathematics classes after completion of their degree programs. This paper details the interpretation of the PSTs' reflections on metric and topological spaces. From PSTs' reflections, it was found that reflective questions helped individual PSTs to develop their understanding of matric and topological spaces, including giving the meaning of metric and topological spaces, and relating with real objects available in their daily environment. The findings have implications in teaching and learning metric and topological spaces.

In this work, a bibliometric analysis of the investigations of the last 54 years focused on the teaching of topology and its applications in the learning of other areas of knowledge was carried out. The articles that appear in the SCOPUS database were taken into account under the search criteria of the words topology and teaching, connected with the Boolean expression AND in the search field ABS. As a result, 329 articles were obtained which, based on the PRISMA methodology, were reduced to 74 papers. In them publication trends, impact of publications, citation frequencies, among others, were compared. In addition, its use was identified for learning topology at different levels of training, areas of knowledge where this discipline is most applied and strategies used to teach these applications.

This paper provides an account of the topological and its description of contemporary culture and use as a research methodology, a topological lens, generally, and in education research specifically. Some commentary is proffered on the relationships between the topological and the topographical, between relations and locations. A critical account is then provided on each of the papers in the special issue on the topological in education research and the specific contributions of each. The editors of the special issue make the important point that the topological is a spatio-temporal phenomenon, not just a spatial one. The topological does not exist in time and space, but rather constructs both and they change in a conjoint manner. As such, a topological lens rejects a construction of space as static and of time (and the temporal) as simply linear and chronological. The topological has been facilitated and articulated by and through practices of commensuration, datafication and digitalisation, flows and scapes, global connectivities and new relations, mobilities of various kinds and multiple networks. The paper argues that much greater emphasis has been given to the spatial in topological research; that is, there has been some neglect of the temporal in the spatio-temporal character of topologies.

• We compare the performance of global metrics and their local variants in the identification of expert-selected milestone papers on two distinct citation datasets. • We obtain a family of local variants of PageRank (LeaderRank) with a tunable degree of locality and find they can generate highly correlated scores with the scores by the original metrics. • The local variants of PageRank (LeaderRank) perform similarly well as the original global PageRank (LeaderRank) algorithms in the identification of seminal papers. • The local variants of PageRank (LeaderRank) perform significantly better than local metrics such as citation count, h-index and semi-local centrality. • Compared to network-based global metrics, the proposed local estimates provide a better trade-off between performance and computational efficiency. Recent works aimed to understand how to identify "milestone" scientific papers of great significance from large-scale citation networks. To this end, previous results found that global ranking metrics that take into account the whole network structure (such as Google's PageRank) outperform local metrics such as the citation count. Here, we show that by leveraging the recursive equation that defines the PageRank algorithm, we can propose a family of local impact metrics. Our results reveal that the obtained PageRank-based local metrics outperform the citation count and other local metrics in identifying the seminal papers. Compared with global metrics, these local metrics can reach similar performance in the identification of seminal papers in shorter computational time, without requiring the whole network topology. Our findings could help to better understand the nature of groundbreaking research from citation network analysis and find practical applications in large-scale data. [ABSTRACT FROM AUTHOR]

This document is a special issue of the journal Axioms titled "Topology and Functional Analysis" in honor of María Jesús Chasco's 65th birthday. It includes papers on topological groups, topological semi-groups, and topological vector spaces, highlighting the interaction between topology and functional analysis. The papers cover various topics such as factorization of groups into thin subsets, extensions of characters defined on subgroups, distinguished subgroups of compact Abelian groups, preservation of min-subgroup structure under aggregation functions, bounded sets in topological spaces subject to the action of a monoid, and the distinguished property in tensor products and weak* dual spaces. María Jesús Chasco is recognized for her contributions to mathematics, particularly in the field of duality in topological groups. [Extracted from the article]

In an interplay between the Fundamental Theorem of Arithmetic and topology, this paper presents material for a capstone seminar that expands on ideas from number theory, analysis, and linear algebra. It is designed to generate an immersive way of learning in which students discover new connections between familiar concepts, create definitions, and investigate non-standard questions. The ideas are arranged as a series of questions for students to explore, with expositions to the instructor on how to guide them in looking for answers. The investigations culminate in a satisfying outcome: that partition topologies are the same as unique factorization topologies, those that satisfy our topological version of the Fundamental Theorem of Arithmetic.

As critical posthumanist and (new) materialist scholarship become more established in educational research, a reconsideration of methodological approaches suited to a radical relational onto-epistemology is required. A popular figuration adopted by researchers to help think and do such research is the Deleuze-Guattarian "rhizome." Coming to terms with "how" rhizomic styled research (rhizo research) is undertaken and "what" it can yield however, can be challenging. In this paper, a study involving a "Zombie Apocalypse Survival Course" run at a human pathology museum becomes an animated example of rhizo research. Through it we demonstrate how infusing this research with an "analytic of lines" (derived from Deleuze-Guattarian rhizomatics) provides for a practice of research that has the power to shift the ontological and epistemological positions that continue to define qualitative research in education and bring understudied, ethico-political dimensions of it into view.

With the continuous development of new energy power generation and smart grid, Power Electronic Transformer (PET) has a good prospect for development because of its remarkable advantages. Based on the topology of AC/DC/AC, the modulation strategy with dual-PWM (Pulse Width Modulation) is adopted to control the operation of power electronic transformers in this paper. The PET structure consists of three units: importation portion, isolation portion and output portion. Model building and analyzing both at the input and output terminals are achieved step by step. And the simulation of the whole PET system with dual-PWM is accomplished with MATLAB/ Simulink. The simulation results show the control system stability and output voltage regulation precision are improved with feed-forward voltage decoupling vector control system. The correctness and effectiveness of the control strategy are demonstrated through the simulation. PETs play an important role in enhancing power supply reliability for Power Grid and promoting the new energy power generation development. [ABSTRACT FROM AUTHOR]

New grid equipment startup programs are widely used in various countries to regulate the commissioning of new equipment; these programs have unique differences in terms of strictness, information asymmetry, and complexity relative to other types of startup programs. With respect to rule-based generation methods, because the method of revising the rules weakens their migration ability, it is difficult to adapt these methods to the status quo of high-speed power grid construction; moreover, most of the current generation methods based on deep learning improve upon the rule-based methods but do not eliminate the rules of the constraints. Therefore, this paper presents a fusion topology for generating a new grid equipment startup scheme, which generates the scheme from end to end. The method utilizes the powerful processing capabilities of the GATv2 model and the ERNIE-GEN model for topology and text, respectively. The device type-based coding strategy and the scheme complexity-based self-attention layer selection strategy are used in the GATv2-based device identification model to address information asymmetry and complexity variability, and the device information modification strategy is applied to solve the strictness variability problem in the ERNIE-GEN-based scheme generation model. Finally, through the testing and verification of field data from four types of new equipment startup schemes in real power grids, it is verified that the method can effectively generate new equipment startup schemes for power grids, and the reasonableness and efficiency of the three strategies are verified through ablation experiments, which verify that the method can effectively generate new equipment startup schemes for power grids that meet the requirements of real power grids. [ABSTRACT FROM AUTHOR]

Optimizing the configuration of acquisition terminals can maximize the observability and state estimation accuracy of the distribution grid achieving comprehensive perception of the distribution grid. However, the existing optimization configuration methods typically target a single topology structure. For regional distribution grids with dynamic topology changes, it cannot meet the observability requirements of all their topologies. In this regard, this paper proposes an optimal configuration scheme for regional distribution grid acquisition terminals considering dynamic observability. Firstly, the regional distribution grid considering the change of contact switch is modeled. Based on the observation redundancy and state estimation accuracy, the dynamic observability index of regional distribution grid is proposed. Then, a multi-objective optimal configuration model of acquisition terminal is constructed with the objective function of maximizing dynamic observability and minimizing configuration cost. Finally, the effectiveness of the proposed approach is validated with the simulation model. [ABSTRACT FROM AUTHOR]

Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences.

The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second- order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs. Two practical factors, external disturbance and Markov switching topology, are considered in this paper to better match actual situations. Besides, T-S fuzzy technology is used to approximate the unknown nonlinearity of MASs. Then, by using boundary control scheme with collocated measurements, two theorems are obtained to ensure the finite-time H∞ deployment of first-order and second-order agents, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper analyzes, designs and implements a reconfigurable phase-shifted full-bridge (PSFB) converter. It adopts the topology of the traditional PSFB converter and incorporates clamping circuits to solve some fundamental problems of conventional topology. In addition, auxiliary switches are employed for output reconfiguration, which allows expanding the output voltage range without compromising the system efficiency. Single pole double throw (SPDT) mechanical switches are used to realize series and parallel connections. In this paper, the characterization of the PSFB converter with clamping circuit and its design considerations are discussed. A 10 kW prototype with a power density of 0.485 W/cm3, 900 V input voltage and 400/800 V nominal output voltage was manufactured. The experimental results validated the analysis and confirmed the high conversion efficiency for a wide load range; an efficiency of 96.69% was obtained for the full load condition. [ABSTRACT FROM AUTHOR]

Distributed in-network processing has garnered much attention due to its capability to estimate the unknown parameter of interest from noisy measurements based on a set of cooperating sensor nodes. In previous studies, distributed in-network processing mainly focused on short-distance communication systems, wherein sensor nodes collect certain parameters of interest within their maximum communication distance. In addition, the estimation of certain parameter vectors of interest from noisy measurements, relying heavily on training signals, is achieved with a non-blind distributed estimation algorithm. However, in some applications, acquiring knowledge of training signals beforehand is difficult. Therefore, it is necessary to perform distributed estimation algorithms for receivers without training signals, a concept known as blind distributed estimation. In this paper, the generalized Sato algorithm is used to design the blind equalizer for the signal estimation. In addition, we consider extending the short-distance communication system to a long-distance communication system for an unmanned aerial vehicle (UAV) cooperating with sensor nodes in the wireless sensor network (WSN). In this scenario, the data signal is transmitted from a UAV to the WSN and is received by sensor nodes. However, the performance of the blind equalizer is susceptible to the transmission channel in long-distance communication systems. Here, we present a network topology reconfiguration approach to address the issue of distributed blind equalization. The objective of the proposed method is to discard the influence of ill-channels on the other sensor nodes by detecting ill-channels and redesigning the sensor node weights. Through computer simulation experiments, we evaluated the performance of the blind equalizer using the average mean square error (MSE) and average symbol error rate (SER). In the results of the computer simulation experiments, the blind equalizer using the proposed method outperformed the conventional methods in terms of prediction accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

Disjoint paths are defined as paths between the source and destination nodes where the intermediate nodes in any two paths are disjoint. They are helpful in fault-tolerance routing and securing message distribution in the network. Several research papers were proposed to solve the problem of finding disjoint paths for a variety of interconnection networks such as Hypercube, Generalized Hypercube, Mesh, Torus, Gaussian, Eisenstein–Jacobi, and many other topologies. In this research, we have developed a general algorithm that constructs maximal node-to-node disjoint paths for symmetric networks where all paths are shortest. The algorithm presented in this paper outperforms other algorithms in finding not only the disjoint paths but shortest and maximal disjoint paths with a complexity of O (n 2) . In addition, we have simulated the proposed algorithm on different networks. The solution of unsolved problem in Cube-Connected-Cycles is given in the simulation results. [ABSTRACT FROM AUTHOR]

This paper introduces a topology optimization approach based on the virtual element method (VEM), incorporating uncertainties. The objective of this optimization process is to design an optimal material layout for problems governed by linear elasticity equations to minimize the volume while satisfying probabilistic compliance constraints. The VEM is used to solve the boundary value problem in reliability-based topology optimization (RBTO). In the comparison between the VEM and the standard finite element method (FEM), a key difference emerges in the absence of explicitly defined shape functions tied to discrete degrees of freedom in VEM. Unlike FEM, VEM directly constructs the discrete bilinear form and load linear form without the need for computing shape function derivatives within the elements. This flexibility accommodates meshes with intricate geometries and arbitrarily shaped elements. The paper discusses the computational efficiency of VEM RBTO and explores the geometric impact of tessellations on converged topologies, demonstrating reduced susceptibility to checkerboard patterns compared to conventional quadrilateral elements. Additionally, the single-loop approach is examined, showcasing comparable accuracy to the first-order/second-order reliability methods (FORM/SORM) of RBTO using VEM. Numerical results for several problems that demonstrate the feasibility of the proposed method are presented. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a scenario in which protected and unprotected services coexist in an elastic optical network under dynamic traffic. In the investigated scenario, unprotected services can reuse the reserved idle bandwidth to provide protection to the protected services. Under this scenario, we propose a new heuristic algorithm that enables such reuse as well as define and introduce a new assignment problem in elastic optical networks, named a Transmission Spectrum Assignment (T-SA) problem. In this paper, we consider a scenario in which services may be routed using the multipath routing approach. Additionally, protection using bandwidth squeezing is also considered. We assess our proposal through simulations on three different network topologies and compare our proposal against the classical protection approach, in which bandwidth reuse is not allowed. For the simulated range of network loads, the maximum (minimum) blocking probability reduction obtained by our proposal is approximately 48% (10%) in the European topology, 46% (7%) in the NSFNET topology, and 32% (6%) in the German topology. [ABSTRACT FROM AUTHOR]

Distributed photovoltaics (DPVs) are widely distributed and the output is random, which brings challenges to the safe operation of the distribution network, so the construction of photovoltaic aggregations can effectively participate in the flexible regulation of the power system. At present, the extraction of DPV clustering features is not sufficient, only considering the output characteristics of PVs. Certain PVs under some nodes may have a more pronounced regulation effect, but they may be ignored in the clustering process. To address the above problems, this paper proposes a DPV aggregation approach considering the distribution network topology. It combines the voltage sensitivity and the power curve and regards them as clustering features to form the DPV aggregation with the highest average voltage sensitivity participating in voltage regulation. The simulation on the IEEE 33-node system verifies that the proposed aggregation approach can select DPV aggregation more suitable for voltage regulation, and make full use of the aggregation to realize the optimal voltage regulation effect. [ABSTRACT FROM AUTHOR]

This paper examines the concepts and practical applications of the spanning tree protocol (STP). It also covers per-VLAN spanning tree (PVST), multiple spanning tree (MST), and rapid STP (RSTP). Moreover, practical scenarios are presented to help the reader understand the concepts and implementations of these protocols. This study analyzes protocols using seven metrics. All protocols have been evaluated using these metrics in both small and big topology scenarios to obtain the best results. In addition, all metrics are mentioned in the introduction chapter, and the way used to apply tests on the metrics is described in the methodology chapter. Based on the experiments, different STPs performance are compared, including STP, RSTP, PVST, and MST. In summary, findings show that STP is easy to use and performs well overall, but it consistently has high latency issues. RSTP is suitable for small networks and has quick convergence, but it cannot handle as much load as STP. PVST performed the best in the experiments, as it demonstrated high scalability and the ability to handle a lot of pressure, although it requires strong hardware. However, MST did not perform as well as expected, as it struggled with delay problems and high jitter. In conclusion, it is recommended to use RSTP for simple networks that require fast convergence with dependable delay and capacity, or STP for networks that require good scaling and bandwidth. PVST is an excellent option for those who can afford high-performance hardware, while MST is suitable for simple networks or those with outdated hardware. [ABSTRACT FROM AUTHOR]

In the search for efficient renewable energy solutions, grid-connected photovoltaic (PV) systems have become a key technology. This paper delves into optimizing these systems through a thorough comparison of various PV array and boost converter topologies, employing advanced Maximum Power Point Tracking (MPPT) algorithms. Utilizing simulations, the research scrutinizes diverse configurations of PV arrays, including series and parallel, in conjunction with different boost converter designs. The focus is on enhancing power output in different irradiation conditions. Key performance metrics, such as efficiency, tracking precision, and system stability, are rigorously evaluated. The comparative analysis primarily hinges on two MPPT techniques: the Perturb and Observe (P&O) method and the Particle Swarm Optimization (PSO) algorithm. This investigation not only provides critical insights into the optimal selection of PV array and boost converter configurations for grid-connected systems but also underscores the superiority of intelligent algorithms like PSO in enhancing operational efficacy. Results demonstrate a remarkable 99% efficiency and energy output advantage of the parallel PV array configuration compared to the series configuration. [ABSTRACT FROM AUTHOR]

This paper is concerned with the well-posedness and asymptotic behavior of solutions for the following extensible beam equation with non-local energy damping u tt + Δ 2 u - κ ϕ (‖ ∇ u ‖ 2 ) Δ u - φ (‖ Δ u ‖ 2 + ‖ u t ‖ 2) Δ u t + f (u) = h. More specifically, this is a complementary work to the paper by Sun and Yang (Discrete Contin Dyn Syst Ser B 27(6):3101–3129, 2022), where the authors consider this model assuming the hypothesis that φ ∈ C 1 (R +) with non-degenerate condition φ (s) > 0 , s ∈ R + . They prove the existence of strong global and exponential attractors and their robustness on the perturbed extensibility parameter κ . In this paper assuming φ (s) ⪆ γ s q which contemplates the degenerate condition φ (0) = 0 , we prove the existence of weak and regular solutions to the problem proposed and employing the method given in Temam (Springer-Verlag, New York, 1998) we show that the dynamic system (X , S t) given by the weak solutions of the problem has a compact global attractor in the weak topology of the phase space X. This class of nonlinear beams arising in connection with models for flight structures with non-local energy damping is proposed by Balakrishnan and Taylor (Proceedings Damping 89, Flight Dynamics Lab and Air Force Wright Aeronautical Labs, WPAFB, 1989). [ABSTRACT FROM AUTHOR]

The report of the 20th National Congress of the Communist Party of China pointed out that it is necessary to accelerate the construction of digital China, and actively develop equipment intelligence, digitalization, and high‐end equipment manufacturing. With the construction of a new round of digital China, the safety of digital technology and high‐end equipment is particularly important for power grid. Transformer is an important link of power grid operation. The destructive thermal failure of transformer has become a hot research issue in the power industry. At the same time, there are more and more power electronic equipment in the power grid, which makes the regulation and control more and more complicated. Taking a 1000 kVA oil‐immersed transformer as an example, the magnetic, current, and thermal multi field coupling numerical analysis method is first used to simulate and analyse the operation status of the transformer. By comparing the simulation results with the monitoring data results, the error of the results is controlled within 5%. Finally, the multi‐state characteristic parameters of the transformer are monitored through sensors, and the numerical simulation analysis results are integrated with the state monitoring results to build a transformer thermal life loss assessment system. The method in this paper can evaluate and analyse the running state of transformer in real time, which is of great significance for the power company to formulate the treatment measures. [ABSTRACT FROM AUTHOR]

This paper gives an overview of area, power, delay for four different 64-bit adders. The design metrics in VLSI are low area and delay alongside low power designs. Adder is one of the necessary components of almost every kind of digital and high-performance systems such as FIR filters, digital signal processors and microprocessors etc. Different types of adders are carry tree adder, carry save adder, carry look ahead adder and carry select adder. In this work we have designed, simulated and synthesized these adder topologies and compared the results in cadence tool. [ABSTRACT FROM AUTHOR]

This paper presents two methods of shaping the mesh topology of lightweight structures as spherical domes. The two given methods of dividing the initial face of the polyhedra determine the obtained structures, which differ in the way of connecting the nodal points. These points were obtained by applying the algorithm for calculating spherical coordinates presented in the paper, which were then converted to the Cartesian system using transformation formulas. Two models of dome structures are presented, based on a 4608-hedron according to the first division method, and on a 4704-hedron, using the second proposed method with numerical analysis. Thus, the novelty of this paper is an implementation of the formulas and algorithms from geodesic domes based on the regular dodecahedron to the regular octahedron, which has not been presented so far. The choice of the shape of the structure has impacts on sustainable development, dictated by structural and visual considerations, leading to the design of a light structure with low consumption of construction material (steel), which can undoubtedly be helpful when making the final structure shape. In addition, according to this research, it can be concluded that using the first method to create a geodesic dome mesh is more straightforward, safer, and requires less design experience. [ABSTRACT FROM AUTHOR]

In this paper, the problem of broadband vibration suppression of power-driven-damper vehicle "inerter-spring-damper" (ISD) suspension is studied. The suspension can effectively inherit the low-frequency vibration suppression effect of ISD suspension and the high-frequency vibration suppression effect of the power-driven-damper control strategy. Based on the structural method, this paper proposes four suspensions with different structures. The optimal structure and parameters are obtained by using pigeon-inspired optimization. The results show that, based on the optimal structure, the Root-Mean-Square (RMS) of body acceleration and the RMS of suspension working space are reduced by 23.1% and 6.6%, respectively, compared to the traditional passive suspension. The influence of the damping coefficient on the dynamic performance of the power-driven-damper vehicle ISD suspension is further studied. The vibration suppression characteristics of the proposed suspension are simulated and analyzed in both the time domain and frequency domain. It is shown that the power-driven-damper vehicle ISD suspension can effectively reduce vibrations across a wide frequency range and significantly improve body acceleration and suspension working space, thereby enhancing the ride comfort. [ABSTRACT FROM AUTHOR]

The present paper studies digital topological rough set structures associated with Khalimsky (K -, for brevity) topology. We further explore their properties related to topological (closure and interior) operators. In addition, we find that the K -topological rough set structures have their own features different from certain theoretical properties of the H -rough set structure in [9] w.r.t. the topological operators. More precisely, whereas the H -rough set structure is a topological operator, K -topological concept approximations are proved not to be topological operators. Thus, this paper proposes an alternative approach to the K -topological concept approximations so that we finally have new types of topological operators. Furthermore, it appears that this new ones are smoothly matched with the earlier H -rough set structure from the viewpoint of topological operators. Therefore, they can facilitate the study of continuous-oriented or digital-oriented rough sets, which can be used in applied sciences without any limitations of the cardinalities of the universe and a target set. Besides, they can support certain decision rules with no restriction to anything continuous or discrete (or digital). In addition, we introduce the notion of K -definability of a target subset of a universal set and write an algorithm for estimating the roughness of the above new concept approximations. In this paper each set need not be finite and a covering is locally finite. [ABSTRACT FROM AUTHOR]

Metamaterials are usually designed using biomimetic technology based on natural biological characteristics or topology optimization based on prior knowledge. Although satisfactory results can be achieved to a certain extent, there are still many performance limitations. For overcoming the above limitations, this paper proposes a rapid metamaterials design method based on the generation of random topological patterns. This method realizes the combined big data simulation and structure optimization of structure-electromagnetic properties, which makes up for the shortcomings of traditional design methods. The electromagnetic properties of the proposed metamaterials are verified by experiments. The reflection coefficient of the designed absorbing metamaterial unit is all lower than −15 dB over 12–16 GHz. Compared with the metal floor, the radar cross section (RCS) of the designed metamaterial is reduced by a minimum of 14.5 dB and a maximum of 27.6 dB over the operating band. The performance parameters of metamaterial obtained based on the random topology design method are consistent with the simulation design results, which further verifies the reliability of the algorithm in this paper. [ABSTRACT FROM AUTHOR]

The term "MANET," which stands for "Mobile Adhoc Network," refers to an ad hoc wireless network incorporating routing mechanism atop an ad hoc link layer network. These networks consist of wirelessly linked mobile nodes that self- configure and self-heal. Due to frequent changes in network architecture, MANET nodes have the freedom to move. Each node in the network serves as a router, forwarding traffic to specified nodes. Broadcast algorithms in wireless ad hoc networks typically follow two main approaches: static and dynamic. In the static approach, local algorithms proactively determine each node's status based on local topology information and a globally known priority function. This paper reveals that existing local broadcast algorithms based on the static approach fail to achieve a satisfactory approximation factor for the optimum solution to an NP-hard problem. However, it is demonstrated that a constant approximation factor is attainable when relative position information is available. The hybrid broadcast method dynamically determines each node's state "on-the-fly," ensuring complete delivery and maintaining a consistent value approaching the ideal outcome as closely as possible. [ABSTRACT FROM AUTHOR]

In this paper, the discovery of the Jones polynomial will be discussed, emphasizing the way in which it illustrated the remarkable unity between distinct parts of mathematics, each with its own language, but initially without a dictionary. [ABSTRACT FROM AUTHOR]

In the last decade, the Poincaré conjecture has probably been the most famous statement among all the contributions of Poincaré to the mathematics community. There have been many papers and books that describe various attempts and the final works of Perelman leading to a positive solution to the conjecture, but the evolution of Poincaré's works leading to this conjecture has not been carefully discussed or described, and some other historical aspects about it have not been addressed either. For example, one question is how it fits into the overall work of Poincaré in topology, and what are some other related questions that he had raised. Since Poincaré did not state the Poincaré conjecture as a conjecture but rather raised it as a question, one natural question is why he did this. In order to address these issues, in this paper, we examine Poincaré's works in topology in the framework of classifying manifolds through numerical and algebraic invariants. Consequently, we also provide a full history of the formulation of the Poincaré conjecture which is richer than what is usually described and accepted and hence gain a better understanding of overall works of Poincaré in topology. In addition, this analysis clarifies a puzzling question on the relation between Poincaré's stated motivations for topology and the Poincaré conjecture. [ABSTRACT FROM AUTHOR]

Isolated bidirectional DC–DC converters are becoming increasingly important in various applications, particularly in the electric vehicle sector, due to their ability to achieve bidirectional power flow and their safety features. This paper aims to review the switch strategies and topologies of isolated bidirectional DC–DC converters, with a specific focus on their applications in the field of electric vehicles. From the perspective of topology, PWM-type isolated bidirectional DC–DC converters, dual active bridge converters, and resonant-type isolated bidirectional DC–DC converters constitute the three main categories of these converters. The paper further examines the traditional switch strategies of these converters and discusses how specific switch technologies, such as single-phase shift, expanding-phase shift, double-phase shift, and triple-phase shift, can enhance the overall performance of isolated bidirectional DC–DC converters. The paper meticulously examines the characteristics of each topology and control scheme, as well as their typical use cases in practical applications. Particularly, the paper delves into the applications of isolated bidirectional DC–DC converters in the electric vehicle sector and draws conclusions regarding their potential and trends in future electric vehicle technology. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in finding sufficient conditions, which ensure the existence of solutions to a weak (pessimistic) bilevel optimization problem (S) in a topological sequential setting. To this aim, we consider an approach of (S) by means of a family of regularized perturbed bilevel optimization problems (Sn) of (S). Unlike (S), such problems (Sn) have the privilege to admit solutions under mild assumptions. Using the notion of variational convergence, after establishing stability results, we prove the existence of solutions to problem (S). [ABSTRACT FROM AUTHOR]

Tensegrity structures, which consist of tension cables and compression rods, are widely used in various fields. It is particularly important to find the tensegrity with definite geometric configuration for the following research and application. This paper presents a traversal topology-finding method for tensegrity structures based on dynamic programming algorithm and ground structure method. After the designer has given the cable topology, the dynamic programming is adopted to realize the traversal selection of the rod. In order to reduce the traversal space and realize the constraint of rod length type, the rod is classified according to length. Compared with existing topology-finding methods, the algorithm can not only output all feasible topologies but also incorporate structural constraints, such as rod length type and prestressed stability, into the calculation process. Four tensegrity numerical examples illustrate the feasibility and effectiveness of the topology-finding method. [ABSTRACT FROM AUTHOR]

The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism. [ABSTRACT FROM AUTHOR]

In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine's notions of generalized closed sets and Maki's  Λ  sets. The methods used in this investigation are described in my previous work, where a unified concept of general closedness is presented. From a methodology point of view, the present concept is symmetric to the previous. In generalizing open subsets, one can use the two methods. According to the first one, the family of Levine's generalization is used as some base to build the family of closed subsets of the new topology. In the second method, the family of open subsets is extended, in the same way, as the family of closed subsets in the classic Levine's method. The results obtained in this general conception easily extend and imply well-known theorems of this area of investigation. In the literature on this issue, many versions of generalizations of  Λ -sets have been investigated. The tools used in this paper enabled us to prove that there exist at most 10 generalizations of these types, and we show the relationships between them in the graph. As a result, it turns out that some generalizations investigated in the literature are trivial. [ABSTRACT FROM AUTHOR]

The popularity of the average current mode (ACM) controlled boost type power factor correction (PFC) topologies is increasing due to their suitability for power quality problems. Proportional-Integral (PI) controller method is generally used in ACM controlled boost PFC circuits which include two controllers. However, the most important complexity of ACM controlled PFC circuits is tuning the coefficients of the PI controllers optimally. Therefore, this paper proposes the optimal tuning of PI coefficients used in ACM controlled boost PFC circuits using different meta-heuristics algorithms. First, the proposed ACM controller-based boost PFC topology is analyzed in MATLAB/Simulink software by using variable loads. Then the simulation results of the Cuckoo Optimization Algorithm (COA) based ACM controlled boost PFC converter are compared with the results determined via Ziegler-Nichols (ZN), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Imperialistic Competitive Algorithm (ICA), and Invasive Weed Optimization (IWO). Finally, the experimental verification of the topology has been done using a 600 W prototype and eZdsp F28335. As COA showed better results among other evolutionary algorithms used in this paper, we used COA parameters to observe the performance of the proposed tuning method. The experimental studies have been done under different load variations similar to the simulation studies. [ABSTRACT FROM AUTHOR]

This paper addresses L-fuzzy topologies induced by L-G-filters and studies the categorical relations between L-G-filter spaces and L-fuzzy topological spaces. Three functors from the category of L-G-filter spaces to the category of Lfuzzy topological spaces are obtained. Having introduced the concept of monotone L-fuzzy topologies, the study inquires into the sum, subspace, product, quotient and the lattice structure of such topologies. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to obtain a symmetrical step-down topology with lower equivalent capacity and wider step-down range under the condition of the same output. Two new symmetrical step-down topologies of star-connected autotransformers are proposed in this paper. Taking the equivalent capacity as the main parameter, the obtained topologies are modeled and analyzed in detail. Design/methodology/approach: This paper adopts the research methods of design, modeling, analysis and simulation verification. First, the star-connected autotransformer is redesigned according to the design objective of symmetrical step-down topology. In addition, the mathematical model of two topologies is established and a detailed theoretical analysis is carried out. Finally, the theoretical results are verified by simulation. Findings: Two symmetrical star-connected autotransformer step-down topologies are designed, the winding configurations of the corresponding topology are presented, the step-down ranges of these three topologies are calculated and the influence of step-down ratio on the equivalent capacity of autotransformer are analyzed. Through analysis, the target step-down topologies are obtained when the step-down ratio is [1.1, 5.4] and [1.1, 1.9] respectively. Research limitations/implications: Because the selected research object is only a star-connected autotransformer, the research results may lack generality. Therefore, researchers are encouraged to further study the topologies of other autotransformers. Practical implications: This paper includes the implications of the step-down ratio on the equivalent capacity of autotransformers and the configuration of transformer windings. Originality/value: The topologies designed in this paper enable star-connected autotransformer in the 12-pulse rectifier to be applied in step-down circumstances rather than situations of harmonic reduction only. At the same time, this paper provides a way that can be used to redesign the autotransformer in other multi-pulse rectifier systems, so that those transformers can be used in voltage regulation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a Cartan calculus on the homology of free loop spaces which is introduced by Kuribayashi, Wakatsuki, Yamaguchi and the author [ Cartan calculi on the free loop spaces , Preprint, arXiv:2207.05941, 2022]. In particular, it is proved that the Cartan calculus can be described by the loop product and the loop bracket in string topology. Moreover, by using the descriptions, we show that the loop product behaves well with respect to the Hodge decomposition of the homology of free loop spaces. [ABSTRACT FROM AUTHOR]

Recent technological advances have renewed the research interest in current-source inverters (CSIs). Nonetheless, CSI research still falls behind its voltage-source counterpart with regards to topologies, modulation, and control. Acknowledging the above, this paper presents a novel single-phase five-level CSI topology. The proposed circuit utilises eight switches and two inductors for the generation of five distinct output levels while maintaining low output voltage THD and d v / d t . Furthermore, by offsetting the inductor currents from a binary 1:2 to a trinary 1:3 ratio, the proposed inverter can generate seven current levels at its output. The inverter offers built-in short-circuit protection and can boost a low input DC voltage to a higher peak AC output voltage. These merits, alongside an electrolytic-capacitor-free design, simple current balancing mechanism, and fault-tolerant characteristics, make it a promising candidate for PV module-integrated inverter (MII) systems. The current topology utilises two inductors but is fully functional with single-inductor operation. The paper provides a functional analysis of the inverter topology alongside the inverter switching states and corresponding conduction paths. A detailed analysis of the inductor current dynamics as well as a current-balancing algorithm for dual- and single-inductor operations are given. The theoretical analysis of the proposed circuit and its functional operation are verified using simulations and experimental results carried out on a laboratory prototype. [ABSTRACT FROM AUTHOR]