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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]

This paper describes a flow control of the dye in the paper mill with the quasi-Z-source indirect matrix converter (QZSIMC) fed induction motor drive. More than a decade the voltage-source inverter (VSI) and current-source inverter (CSI) have been used to control the speed of the induction motor, which in turns controls the flow of dye. Recently, the matrix converter (MC) has been an excellent competitor for the VSI or CSI for its compactness. The voltage transfer ratio of the VSI, CSI, and MC has been limited to 0.866. Thus, the efficiency of these converters is less. To improve the voltage transfer ratio the quasi-Z-source network (QZSN) is to be used between voltage source and indirect MC (IMC). The modification in the shoot-through duty ratio of the QZSN varies the voltage transfer ratio greater than 0.866. Different voltage transfer ratios are needed for different voltage sag conditions. For a variation of the duty ratio of the QZSN, the fuzzy logic controller has been presented. To control the IMC vector control with space vector modulation has been presented. This paper proposes the implementation of QZSIMC adjustable speed drive for the flow control of dye in paper mill during different voltage sag conditions. A 4-kW prototype has been built and the effectiveness of the proposed system is verified with simulation results and experimental setup. Simulation is done in MATLAB, Simulink platform. Experimental setup is done with the aid of a TMS320F2812 (Texas Instrument) processor. The experimental results validate the maintenance of the speed of an induction motor at the set condition, thus controlling the perfect flow of dye in paper manufacturing technology. [ABSTRACT FROM AUTHOR]

The paper focuses on the sociological adaptation and development of the mental mapping method within the study of national identity. 'Mental map' is defined as a spatial image or model formed over time in the individual or collective consciousness, while the method of mental mapping is interpreted as a graphic representation of a certain area by an informant at the request of a researcher. The study is based on the empirical application of mental mapping to the analysis of national identity among Ukrainian students (n=942). The paper outlines methodological and theoretical specifics of mental mapping and indicates perspectives of this method in the context of a visual sociological paradigm.

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.

The Rock-Scissors-Paper is a game in which two players choose one out of three possible options: rock, scissors or paper. Rock breaks scissors, scissors cuts paper, and paper covers a rock. We use this game model to motive our students, with heterogeneous backgrounds, to obtain a basic knowledge of Complex Networks and Ecology. In particular, we analyze the behavior of the rock-scissors-paper model, a basic cyclic antagonist ecological model, played at different network topologies: random, scale-free and entangled. One of our main goals is that students scrutinize the topological properties determining optimal persistence of Biodiversity. In particular, our students have studied the extinction time of the 3 species when the size of the complex networks change, keeping the same properties in the nodes of the network. They have performed the simulations on networks with the same average degree = 4, and with an initial random distribution of the species (rock, scissor, paper). Substantially different behaviors can be found playing in the different topologies. We want the students to understand the influence of the network topology in the outcome of the game; and more general the relevance of the underlying network topology in Game Theory. [ABSTRACT FROM AUTHOR]

This paper offers a methodological framework to research data practices in education critically. Data practices are understood in the generic sense of the word here, i.e., as the actions, performances, and the resulting consequences, of introducing data-producing technologies in everyday educational situations. The paper first distinguishes between data infrastructures, datafication and data points as three distinct, yet interrelated, phenomena. In order to investigate their concrete doings and specificities, the paper proposes a topological methodology that allows disentangling the relational nature and interwovenness of data practices. Based on this methodology, the paper proceeds with outlining a methodical toolbox that can be employed in studying data practices. Starting from nascent work on digital education platforms as a worked example, the toolbox allows researchers to investigate data practices as consisting of four unique topological dimensions: the Interface of a data practice, its actual Usage, its concrete Design, and its Ecological embeddedness - IUDE.

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.

Microfluidic paper-based analytical devices ($\mu $ PADs) are a clean-room free, cost-effective, and self-pumping flow-based rapid prototyping technique, which is compatible with a varying range of fluids. Until now, $\mu $ PADs have been primarily fabricated using crayons, and plotting-machine and solid-ink printers. These devices can be easily employed for various detection schemes, such as electrical, electrochemical, and optical. The presence of a capillary effect in the chromatograph paper has made $\mu $ PADs independent of a passive device, such as pumps and valves. In this paper, an alternative and a novel method is proposed to achieve the $\mu $ PADs effortlessly using a 3-D printer (3DP), which has many advantages over the existing methods. For creating hydrophobic barriers for microchannel walls, polycaprolactone (PCL) filament was used with fused-deposition modeling (FDM) 3DP. PCL filaments were deposited on the chromatography paper followed by heating for determining the overall dimension and depth of the microchannel at which PCL melts and penetrates into this paper. The $\mu $ PADs are characterized and optimized for two parameters. First, fabrication parameters, such as heating temperature and time duration, were used for the creation of the hydrophobic barrier using a hot air oven. Second, the microchannel parameters, such as microchannel width, boundary thickness, chromatography paper grade, and microchannel source shape (rectangular, triangular, and circular) were used for the fluid-flow by measuring the time taken by fluid to travel a fixed length of the microchannel. After rigorous analysis, it was found that for the creation of the hydrophobic barrier, $\mu $ PADs heated between temperature 120°C to 150°C require 30 min. Under optimized conditions for the fluid flow, the chromatography paper grade 1441 with a triangular source microchannel was found to be best. This paper provides an alternate, simple, and optimized method toward the development of the application-specific $\mu $ PADs, such as the micro-viscometer, which, in turn, can be widely used to monitor various types of fluids including human bodily fluids. [ABSTRACT FROM AUTHOR]

The article informs that the first topology paper in China was published by Kiang Tsai-hai in 1931.

• 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]

The article looks into the structures of directed graphs through the Borromean rings and the game rock-paper-scissors. Topics discussed include the graph representations for the two-player game rock-paper-scissors (RPS(3)), in which in mathematics is referred to as a balanced tournament, for the five-weapon game (RPS(5)), and for the hexagonal pyramid. The isomorphism and automorphisms of graph are also mentioned.

Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical metamaterials. However, to make kirigami-inspired structures a reality requires controlling the topology of kirigami to achieve connectivity and rigidity. We address this question by deriving the maximum number of cuts (minimum number of links) that still allow us to preserve global rigidity and connectivity of the kirigami. A deterministic hierarchical construction method yields an efficient topological way to control both the number of connected pieces and the total degrees of freedom. A statistical approach to the control of rigidity and connectivity in kirigami with random cuts complements the deterministic pathway, and shows that both the number of connected pieces and the degrees of freedom show percolation transitions as a function of the density of cuts (links). Together, this provides a general framework for the control of rigidity and connectivity in planar kirigami. [ABSTRACT FROM AUTHOR]

This study is trying to address the critical need for efficient routing in Mobile Ad Hoc Networks (MANETs) from dynamic topologies that pose great challenges because of the mobility of nodes. The main objective was to delve into and refine the application of the Dijkstra's algorithm in this context, a method conventionally esteemed for its efficiency in static networks. Thus, this paper has carried out a comparative theoretical analysis with the Bellman-Ford algorithm, considering adaptation to the dynamic network conditions that are typical for MANETs. This paper has shown through detailed algorithmic analysis that Dijkstra's algorithm, when adapted for dynamic updates, yields a very workable solution to the problem of real-time routing in MANETs. The results indicate that with these changes, Dijkstra's algorithm performs much better computationally and 30% better in routing optimization than Bellman-Ford when working with configurations of sparse networks. The theoretical framework adapted, with the adaptation of the Dijkstra's algorithm for dynamically changing network topologies, is novel in this work and quite different from any traditional application. The adaptation should offer more efficient routing and less computational overhead, most apt in the limited resource environment of MANETs. Thus, from these findings, one may derive a conclusion that the proposed version of Dijkstra's algorithm is the best and most feasible choice of the routing protocol for MANETs given all pertinent key performance and resource consumption indicators and further that the proposed method offers a marked improvement over traditional methods. This paper, therefore, operationalizes the theoretical model into practical scenarios and also further research with empirical simulations to understand more about its operational effectiveness. [ABSTRACT FROM AUTHOR]

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]

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.

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 the paper, the novel topology of the resonant DC link three-level soft-switching inverter is proposed to reduce switching losses and improve the efficiency of three-level inverter at high switching frequency. Symmetrical auxiliary resonant circuits are set in the DC link of three-level hard-switching inverter. Moreover, the terminal voltage of the resonant capacitors between the DC buses periodically drops to zero via the resonance of auxiliary circuits. Furthermore, under such condition, the main switches of the three-level inverter would be operated, in order to achieve zero-voltage switching. Based on the equivalent circuits in different operating modes, the paper analyses the working process of the soft-switching inverter in detail. In addition, a 3 kW laboratory prototype of resonant DC link three-phase three-level soft-switching inverter is built. The experimental results show that the main switches and auxiliary switches of the inverter are operated under soft-switching conditions, and the efficiency is significantly improved compared with the three-level hard-switching inverter. Therefore, the proposed topology can effectively reduce switching losses and prove to be more practical in engineering. [ABSTRACT FROM AUTHOR]

In the framework of a 1D cyclic competition model, the Rock-Paper-Scissors model, where three kinds of generic agents are allowed to mutate, to interact and to move in space, we study the formation of stochastic patterns, where all the agents do coexist. We modelled the problem using an individual-based setting and we used the system size van Kampen expansion to deal with the Master Equation. We have hence been able to characterise the spatio-temporal patterns using the power spectrum of the fluctuations. We proved that such patterns are robust against the intrinsic noise and they can be found for parameter values beyond the ones fixed by the deterministic approach (mean field approximation). We complement such analytical results with numerical simulations based on the Gillespie algorithm. [ABSTRACT FROM AUTHOR]

Nowadays, the microgrid system is characterized by a diversification of power factors and a complex network structure. Existing studies on microgrid fault diagnosis and troubleshooting mostly focus on the fault detection and operation optimization of a single power device. However, for increasingly complex microgrid systems, it becomes increasingly challenging to effectively contain faults within a specific spatiotemporal range. This can lead to the spread of power faults, posing great harm to the safety of the microgrid. The topology optimization of the microgrid based on deep reinforcement learning proposed in this paper starts from the overall power grid and aims to minimize the overall failure rate of the microgrid by optimizing the topology of the power grid. This approach can limit internal faults within a small range, greatly improving the safety and reliability of microgrid operation. The method proposed in this paper can optimize the network topology for the single node fault and multi-node fault, reducing the influence range of the node fault by 21% and 58%, respectively. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the topological structure of semantic networks based on titles of papers published in scientific journals. It discusses its properties and presents some reflections on how the use of social and complex network models can contribute to the diffusion of knowledge. The proposed method presented here is applied to scientific journals where the titles of papers are in English or in Portuguese. We show that the topology of studied semantic networks are small-world and scale-free. [ABSTRACT FROM AUTHOR]

In this paper, we extend the interference channel with degraded message sets model by introducing multiple secondaries. The new model allows for multiple concurrent transmissions in a wireless network by employing dirty paper and superposition coding. We apply the proposed scheme to the communication between nodes in a wireless mesh network (WMN). The cases of different WMN. topologies are analyzed, and numerical results show that considerable capacity gains are achieved when using the proposed model with multiple secondaries. [ABSTRACT FROM AUTHOR]

Problem $$1$$ of (Bulman-Fleming et al. Commun Algebra 34:1291-1317, ) asks: what conditions on a pomonoid $$S$$ and a convex, proper right ideal $$K$$ , guarantee that $$S/K$$ has property $$(P_w)$$ ? This question was first answered in Proposition 3.2 of (Qiao and Li Semigroup Forum 77:306-315, ) and later in Lemma $$5$$ of (Kilp Semigroup Forum 86:592-602, ). In this note we first show, by counterexample, that the result of Qiao and Li is incorrect, and then demonstrate a condition equivalent to that of Kilp. [ABSTRACT FROM AUTHOR]

This manuscript describes three activities connecting the Tower of Hanoi puzzle to three familiar fractal forms. The first connects coin flipping, paper folding, and the Tower of Hanoi to the Dragon Curve. The second illustrates mathematician Ian Stewart's method for showing how the relationships between possible states of the Tower of Hanoi are related to stages in Sierpinski's Gasket. The final activity compares right-left moves of Tower of Hanoi disks to iterations of the Von Koch Curve. [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.

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have derived conclusions that are incorrect, trivial, or limited. [ABSTRACT FROM AUTHOR]

For a segmented dynamic wireless power transfer (DWPT) system, when electric vehicles (EVs) move over two adjacent transmitting coils, the received power fluctuates greatly and has some loss. Arming at this problem, this paper proposes a dual receiver segmented DWPT topology to reduce the received power fluctuation of the receiving coil passing through the rail junction during the moving process of the EV. Through magnetic field analysis in this paper, tuning the current phase difference between two adjacent transmitting coils to 180° can enhance the magnetic field. In this paper, a dual receiver series topology (DRST) is designed to pick up power, which consists of four fully controlled components and four diodes. According to EVs' real-time position, the segment DWPT system has three working modes and six working states under the control of DRST. Finally, experiments are carried out. Compared to the single-receiving-coil system, DRST is effective in improving the average output power from 2.007 to 5.657 W and significantly reducing the power fluctuation. [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]

Immediately following the commentary below, the previously published article by R. Thom is printed in its entirety: R. Thom, Ensembles et morphismes stratifyíes, Bulletin of the American Mathematical Society 75 (1969), no. 2, 240-284 (French). This is followed by the first publication of the 1970 lecture notes of J. Mather, Notes on topological stability. [ABSTRACT FROM AUTHOR]

Through tuning the conformations of N-donor ligands and the coordinative preferences of metal ions, three new metal–organic frameworks with different dimensionalities, namely, {[Co(L1)(bpp)(H2O)]·0.63H2O}n(1), [Ni(L1)(bpp)(H2O)(CH3OH)]n(2) and {Co2(L1)2(bpe)2(H2O)2}·(H2O)(CH3CN)}n(3) (H2L1 = 1,2-bis(4-carboxy-phenoxy)ethane, bpp = 1,3–bis(4-pyridyl)propane and bpe = 1,2–bis(4-pyridyl)ethene), have been synthesized and structurally characterized. Compound 1exhibits a 2D → 2D parallel interpenetrating motif containing two kinds of double helixes. Polymer 2displays 2D → 3D interpenetrating framework. Compound 3is composed of 3D unusual self-interpenetrating net with (4,6)-connected (54·68)(56·65·72·82) topology. This work evidently indicates that the effect of secondary ligands and geometric preferences of metal centers are critical in construction of polymeric arrangement. In addition, the stabilities of these compounds and the magnetic behaviour of 3are discussed. [ABSTRACT FROM AUTHOR]

It is shown that an approach earlier used by the author for classification of closed simply connected 6-manifolds (reduction to the problem of calculating certain bordism groups) can also be applied for easily obtaining the results by Barden (1965) on classification of closed simply connected 5-manifolds. Bibliography: 11 titles. [ABSTRACT FROM AUTHOR]

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]

In recent years, factorization combined with attribute information has played an important role in attribute community detection. However, previous studies focused more on connecting the original shallow topological and attribute data. They ignored the potential representation structure of the network. To solve the problem that shallow information cannot fully represent the network structure, this paper proposes an attribute node classification method based on Attribute Edges weights Fusion and graph Embedding Factorization, called AEFEF. First, AEFEF converts topological information and attribute information into corresponding matrices representing node associations. Then, AEFEF constructs a new adjacency matrix by increasing the weights of shared edges between the topology structure and attribute structure. This operation can strengthen the tightness between nodes. Second, to explore the potential community structure, feature embedding is obtained by factorizing the attribute similarity matrix. Meanwhile, the new adjacency matrix is designed as a weight matrix to make the feature embedding between related nodes more similar. Finally, semi Non-negative Matrix Factorization (NMF) is introduced to modify the feature embedding by converting the negative values into positive values. Then the embedding is factorized to generate the membership matrix. At the same time, the network with a rich structure is decomposed with topological data as the main component. Otherwise, attribute information is the main component of NMF used to increase the accuracy of node classification. AEFEF is compared with 10 state-of-the-art algorithms on 7 real network datasets. The results reveal that AEFEF can improve the precision of attribute community detection. [ABSTRACT FROM AUTHOR]

This paper addresses the high-frequency signal transmission problem of high-speed differential lines on four-layer printed circuit boards (PCBs). It establishes a mathematical model of high-speed differential lines in conjunction with modified Kron's methodology (MKM), a nontraditional circuit modeling method. The article builds the model through diakoptics of differential lines, then generates the corresponding topology maps, and finally creates the model through tensorial analysis of the network (TAN). The differential line model is simulated and optimized by HFSS. This paper mainly analyzes the influence of differential line spacing and grounding vias on the signal transmission of differential lines. Secondly, it analyzes the problem of multi-group differential line arrangement based on the above work. Finally, the experimental results obtained are consistent with the simulation ones. [ABSTRACT FROM AUTHOR]

The topological Dehn twists have several applications in mathematical sciences as well as in physical sciences. The interplay between homotopy theory and Dehn twists exposes a rich set of properties. This paper generalizes the Dehn twists by proposing the notion of pre-twisted space, orientations of twists and the formation of pointed based space under a homeomorphic continuous function. It is shown that the Dehn twisted homotopy under non-retraction admits a left lifting property (LLP) through the local homeomorphism. The LLP extends the principles of Hurewicz fibration by avoiding pullback. Moreover, this paper illustrates that the Dehn twisted homotopy up to a base point in a based space can be formed by considering retraction. As a result, two disjoint continuous functions become point-wise continuous at the base point under retracted homotopy twists. Interestingly, the oriented Dehn twists of a pre-twisted space under homotopy retraction mutually commute in a contractible space. [ABSTRACT FROM AUTHOR]