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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]

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 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]

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]

The Delaunay triangulation of a set of points P on a hyperbolic surface is the projection of the Delaunay triangulation of the set P ~ of lifted points in the hyperbolic plane. Since P ~ is infinite, the algorithms to compute Delaunay triangulations in the plane do not generalize naturally. Using a Dirichlet domain, we exhibit a finite set of points that captures the full triangulation. We prove that an edge of a Delaunay triangulation has a combinatorial length (a notion we define in the paper) smaller than 12 g - 6 with respect to a Dirichlet domain. To achieve this, we introduce new tools, of intrinsic interest, that capture the properties of length-minimizing curves in the context of closed curves. We then use these to derive structural results on Delaunay triangulations and exhibit certain distance minimizing properties of both the edges of a Delaunay triangulation and of a Dirichlet domain. The bounds produced in this paper depend only on the topology of the surface. They provide mathematical foundations for hyperbolic analogs of the algorithms to compute periodic Delaunay triangulations in Euclidean space. [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]

In recent years, with the development of low‐earth orbit broadband satellites, the combination of multi‐path transmission and software‐defined networking (SDN) for satellite networks has seen rapid advancement. The integration of SDN and multi‐path transmission contributes to improving the efficiency of transmission and reducing network congestion. However, the current SDN controllers do not support the multi‐path QUIC protocol (MPQUIC), and the routing algorithm used in current satellite networks based on minimum hop count struggles to meet the real‐time requirements for some applications. Therefore, this paper designs and implements an SDN controller that supports the MPQUIC protocol and proposes a multi‐objective optimization‐based routing algorithm. This algorithm selects paths with lower propagation delays and higher available bandwidth for subflow transmission to improve transmission throughput. Considering the high‐speed mobility of satellite nodes and frequent link switching, this paper also designs a flow table update algorithm based on the predictability of satellite network topology. It enables proactive rerouting upon link switching, ensuring stable transmission. The performance of the proposed solution is evaluated through satellite network simulation environments. The experimental results highlight that SDN‐MPQUIC significantly improves performance metrics: it reduces average completion time by 37.3% to 59.3% compared to QSMPS and by 52.8% to 72.4% compared to Disjoint for files with different sizes. Additionally, SDN‐MPQUIC achieves an average throughput improvement of 81.4% compared to QSMPS and 147.8% compared to Disjoint, while demonstrating a 26.3% lower retransmission rate than QSMPS. [ABSTRACT FROM AUTHOR]

Two-dimensional materials with unique properties have received much attention in recent years. Current research is exploring their potential applications in various fields. Acoustic topological insulators have been an emerging branch in the field of acoustic metamaterials in recent years. Its strong unidirectional transmission capability has potential applications in acoustic sensors, filters, and beamwaves. However, to realize a wide range of applications of acoustic topological materials, it is necessary to solve the problems of multi-band and wide bandgap. To this end, this paper proposes a jointly resonant acoustic topological insulator structure. The structure achieves multi-band filtering, and three filterable bandgaps can be obtained below 6200 Hz. Meanwhile, the total width of the three filterable bandgaps accounts for 65.5% at 6200 Hz and below. In this paper, the band structure is obtained by using the method of finite element simulation. The generation of topological phase transition induced by the rotation angle of the scatterer is analyzed. The pseudo-spin case of the valley hall effect is also analyzed from the point of view of acoustic energy flow, and the existence of edge states is verified. Finally, the unidirectional transport properties possessing backward scattering immunity are verified. The multi-band structure with a great bandwidth means that this work will have great potential for applications in filters. Also, since acoustic topologies based on the Valley hall effect do not possess strong defect immunity, this work proposes to utilize defect states as acoustic switches. [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]

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]

Thermo-elastic systems have a wide range of applications in various engineering fields. Traditional single-objective topology optimization (TO) design of thermos-elastic structures is difficult to achieve the combined optimum of multiple properties, and the non-periodic TO design of results are complex and difficult to fabricate. This paper introduces a multi-objective TO formulation based on density for designing thermo-elastic structures with periodic constraints, aiming to overcome the aforementioned issues. This paper assesses two competing weighted objective functions, the first function corresponds to structural and thermal compliance, while the second pertains to regional temperature and global stress. To solve the optimization issue, we utilize the p-norm function with a modified coefficient for evaluating the maximum temperature and stress values. Additionally, the adjoint variable method is employed to evaluate the sensitivity of various objectives, while the method of moving asymptotes (MMA) is used to update the design variables. Then the influence of different weight coefficients and subregion numbers regarding thermos-elastic coupled analysis is demonstrated through numerical examples. The results show that the complexity of the subregion features decreases as the number of subregions increases, and that changing both the number of subregions and the weighting coefficients results in changes in the overall structural performance. Finally, the geometric model is reconstructed using the TO results, and the structural performance is validated through the simulation of the reconstructed model. The results indicate that the TO results obtained by the method of this paper have predefined performance. [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]

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]

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 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]

The seminormalization of an algebraic variety X$X$ is the biggest variety linked to X$X$ by a finite, birational, and bijective morphism. In this paper, we introduce a variant of the seminormalization, suited for real algebraic varieties, called the R‐seminormalization. This object has a universal property of the same kind as the one of the seminormalization but related to the real closed points of the variety. In a previous paper, the author studied the seminormalization of complex algebraic varieties using rational functions that extend continuously to the closed points for the Euclidean topology. We adapt some of those results here to the R‐seminormalization, and we provide several examples. We also show that the R‐seminormalization modifies the singularities of a real variety by normalizing the purely complex points and seminormalizing the real ones. [ABSTRACT FROM AUTHOR]

A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade (Braunstein et al. in Phys Rev Lett 91(16):168701, 2003; Braunstein et al. in Int J Bifurc Chaos 17(07):2215–2255, 2007; Chen et al. in Phys Rev Lett 96(6):068702, 2006; Wu et al. in Phys Rev Lett 96(14):148702, 2006) is as follows: for a large class of random graph models with degree exponent τ ∈ (3 , 4) , distances in the minimal spanning tree (MST) on the giant component in the supercritical regime scale like n (τ - 3) / (τ - 1) . The aim of this paper is to make progress towards a proof of this conjecture. We consider a supercritical inhomogeneous random graph model with degree exponent τ ∈ (3 , 4) that is closely related to Aldous's multiplicative coalescent, and show that the MST constructed by assigning i.i.d. continuous weights to the edges in its giant component, endowed with the tree distance scaled by n - (τ - 3) / (τ - 1) , converges in distribution with respect to the Gromov–Hausdorff topology to a random compact real tree. Further, almost surely, every point in this limiting space either has degree one (leaf), or two, or infinity (hub), both the set of leaves and the set of hubs are dense in this space, and the Minkowski dimension of this space equals (τ - 1) / (τ - 3) . The multiplicative coalescent, in an asymptotic sense, describes the evolution of the component sizes of various near-critical random graph processes. We expect the limiting spaces in this paper to be the candidates for the scaling limit of the MST constructed for a wide array of other heavy-tailed random graph models. [ABSTRACT FROM AUTHOR]

This paper presents a preliminary study of a 25 kV–50 Hz railway substation power supply system. The control of a back-to-back converter based on modular multilevel converter (MMC) technology was investigated to fit with the power quality requirements of the application. One of the main challenges is the presence of constraining load conditions, under which the train circulation variability, low-frequency harmonics and critical power transients can notably decrease the power quality and lead to instability. In order to address this, cascaded controllers based on resonant controllers are proposed to ensure the desired performance. Furthermore, balancing voltage algorithms are added to avoid stress phenomena and additional losses in the studied power conversion interface. The paper presents the design of the control stages and demonstrates the robust performance of the system using a realistic loading condition of a railway substation. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to introduce the notion of stabilizers in L-algebras and develop stabilizer theory in L-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a CKL-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in CKL-algebra are ideals. Then by using the right stabilizers we produced a basis for a topology on L-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to advance the concept of region reaching control for a single robot to the study of region reaching consistency for uncertain fully‐actuated multi‐robot systems formulated by Lagrange dynamics. By introducing a directed network communication topology and utilizing the pinning‐like control methods, a distributed region reaching consensus control strategy is proposed. The desired region shape can be specified by selecting an appropriate potential objective function. A feature of the developed region reaching consensus algorithm is fully distributed, which is also an important generalization of pinning‐like set point tracking scheme based on the typical proportion‐integration‐differentiation control scheme. More importantly, the scope of consistency in this paper can be explicitly defined, which is different from traditional consistency control algorithms. Subsequently, numerical examples are presented to illustrate the performance of the designed controllers. [ABSTRACT FROM AUTHOR]

This paper introduces soft bitopological ordered spaces, combining soft topological spaces with partial order relations. The authors extensively investigate increasing, decreasing, and balancing pairwise open and closed soft sets, analyzing their properties. They prove that the collection of increasing (decreasing) open soft sets forms an increasing (decreasing) soft topology. The paper thoroughly examines increasing and decreasing pairwise soft closure and interior operators. Notably, it introduces bi--ordered soft separation axioms, denoted as PSTi (PSTi•, PSTi*, PSTi** --ordered spaces, i = 0, 1, 2, showcasing their interrelationships through examples. It explores separation axiom distinctions in bitopological ordered spaces, referencing relevant literature such as the work of El-Shafei et al. [5]. The paper investigates new types of regularity and normality in soft bitopological ordered spaces and their connections to other properties. Importantly, it establishes the equivalence of three properties for a soft bitopological ordered space satisfying the conditions of being TP*-soft regularly ordered: PST2--ordered, PST1-ordered, and PST0-ordered. It introduces the concept of a bi--ordered subspace and explores its hereditary property. The authors define soft bitopological ordered properties using ordered embedding soft homeomorphism maps and verify their applicability for different types of PSTi--ordered spaces, i = 0, 1, 2. Finally, the paper identifies the properties of being a TP*; (PP*)--soft T3--ordered space and a TP-soft T4-ordered space as a soft bitopological ordered property. [ABSTRACT FROM AUTHOR]

This paper presents the development of path-tracking control strategies for an over-actuated autonomous electric vehicle. The vehicle platform is equipped with four-wheel steering (4WS) as well as torque vectoring (TV) capabilities, which enable the control of vehicle dynamics to be enhanced. A nonlinear model predictive controller is proposed taking into account the nonlinearities in vehicle dynamics at the limits of handling as well as the crucial actuator constraints. Controllers with different actuation formulations are presented and compared to study the path-tracking performance of the vehicle with different levels of actuation. The controllers are implemented in a high-fidelity simulation environment considering scenarios of vehicle handling limits. According to the simulation results, the vehicle achieves the best overall path-tracking performance with combined 4WS and TV, which illustrates that the over-actuation topology can enhance the path-tracking performance during conditions under the limits of handling. In addition, the performance of the over-actuation controller is further assessed with different sampling times as well as prediction horizons in order to investigate the effect of such parameters on the control performance, and its capability for real-time execution. In the end, the over-actuation control strategy is implemented on a target machine for real-time validation. The control formulation proposed in this paper is proven to be compatible with different levels of actuation, and it is also demonstrated in this work that it is possible to include the particular over-actuation formulation and specific nonlinear vehicle dynamics in real-time operation, with the sampling time and prediction time providing a compromise between path-tracking performance and computational time. [ABSTRACT FROM AUTHOR]

Feature design, a basic geometric modeling and design method, is the basis of realizing the combination of design and manufacturing. Most of the existing topology optimization methods ignore the feature design, which leads to the separation of feature design and topology optimization. The advantages of topology optimization are limited in practical application. Based on the moving morphable components (MMC) method, this paper presents a feature-driven topology optimization method (FD-MMC), which realizes the combination of feature design and topology optimization. By transforming the pixels of engineering features into special components, the engineering features can be added to the process of optimization design, and the feature-driven topology optimization is realized. In addition, an innovative solution is proposed for the optimal splitting problem of large flat-plate parts based on the FD-MMC method. Finally, this paper also proposes an improved strategy for the shortcomings of FD-MMC method. [ABSTRACT FROM AUTHOR]

There are many methods for solving the topology optimization problem of single-material. It is a great challenge how to utilize existing methods or make appropriate improvements to solve multi-material topology optimization problems. In this paper, a multiple solid isotropic material with penalization model (SIMP) of variable density method is proposed to solve the problem of multi-material topology optimization. All candidate materials, including void material, are arranged in descending order of elastic modulus. The material conversion scheme of multiple SIMP is based on the elastic modulus of the candidate material after interpolation. The iterative criterion of multi-material topology optimization is derived from the Kuhn-Tucker condition using the guide-weight method. The innovation of this paper is to transform the multi-material topology optimization problem into multiple SIMP of the variable density method. Three examples show that it is effective and moderate to use the proposed method to solve the problem of multi-material topology optimization. [ABSTRACT FROM AUTHOR]

The famous Ascoli-Arzelà theorem served as a springboard for research into compactness in function spaces, particularly spaces of continuous functions. This paper investigates compact subsets of spaces of continuous functions endowed with topologies between the topology of pointwise convergence and the topology of uniform convergence. More precisely, this paper studies necessary and sufficient conditions for a subset to be compact in Cλ,u(X) for a locally-λ space X when λ ⊇ 퓕(X), for a hemi- λ λf-space X when λ ⊆ 퓟 퓢(X), and for a k-space X when λ ⊇ 퓚(X). This paper also studies that every bounded subset of Cλ,u(X) has compact closure for some classes of topological spaces X. [ABSTRACT FROM AUTHOR]

Single-phase converters are commonly used in small and medium power supply systems, but their inherent 2ω-ripple power has a significant impact on system performance, including maximum power point fluctuations in photovoltaic systems, low-frequency light flicker in light-emitting diode lighting systems, and the efficiency and lifetime of fuel cell systems. In this paper, we review the single-phase converter topologies with 2ω-ripple suppress and provide a comprehensive summary and comparison of power decoupling topologies. Power decoupling topology can be divided into passive power decoupling topology (PPDT) and active power decoupling topology (APDT). Among them, the PPDT does not need to add switching devices and has simple structure and convenient control. However, due to the volume and life of the energy storage element, the application place is also limited. The APDT needs to add an active power buffer to suppress the 2ω-ripple power. According to the different working modes of the active power buffer switch, the APDT can be divided into independent APDT and dependent APDT. The former operates independently in the original converter, while the latter needs to share switching devices or energy storage elements with the original converter. This paper systematically summarizes the existing single-phase converter circuit topologies for suppressing 2ω-ripple and their development process, aiming to provide classification and comparison for researchers and engineers to select the circuit topologies suitable for their specific applications. [ABSTRACT FROM AUTHOR]

The partial component consensus in mean‐square for delayed nonlinear multi‐agent systems (NMASs) with uncertain nonhomogeneous Markov switching (UNMS) topologies subjected to aperiodic denial‐of‐service (DoS) cyber‐attacks is investigated. Firstly, the partial component (ω$$ \omega $$‐dimensional) consensus of the system (n$$ n $$‐dimensional, 1≤ω≤n$$ 1\le \omega \le n $$) is considered in this paper. When ω=n$$ \omega =n $$, the partial component consensus degrades into identical consensus. Secondly, the communication topologies governed by uncertain nonhomogeneous Markov chains are random. Thirdly, the communication topologies suffer from aperiodic DoS cyber‐attacks. Then, in view of stochastic analysis technology, distributed control theory and Lyapunov stability theory, the partial component consensus conditions are obtained using permutation matrix and inequality scaling skills. Eventually, the correctness of the results is verified through an example. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic event‐triggered fixed‐time control scheme for the phase synchronization of Kuramoto networks with switching topology and stochastic coupling noise. To deal with the problems of switching topology and stochastic coupling noise, a multilayered control structure with a specially designed noise reduction layer is developed. The effectiveness is proved based on stochastic differential theory. To save communication resources and reduce control frequency, a dynamic event‐triggered mechanism is proposed. By introducing a dynamic variable into the triggering condition, the triggered instants are further reduced compared to the traditional static event‐triggered method. The synchronizing criteria and parameter conditions are established with stochastic Lyapunov stability theory. The analysis of Zeno behavior is also given. Finally, numerical simulation experiments are conducted to demonstrate the effectiveness of the proposed dynamic event‐triggered control scheme. [ABSTRACT FROM AUTHOR]

Parametric level set method (PLSM) using interpolation method, such as radial basis function (RBF) interpolation, exposes high computational cost and poor stability when solving structural topology optimization (STO) problems with large-scale nodes. However, the quasi-interpolation method can approximate the level set function (LSF) and its generalized functions without solving any system of linear equations. With this good property, this paper utilizes multiquadric (MQ) quasi-interpolation to parameterize the LSF and innovatively introduces it into the STO problem. Moreover, the MQ quasi-interpolation is utilized to compute the element density, which makes the level set band method (LSBM) more rigorous. The proposed methods were compared with the PLSM based on compactly supported radial basis functions (CSRBFs). The results show that the approximation accuracy, computational efficiency and stability of the evolution process of the proposed methods are better than those of CSRBFs when the shape parameter takes a suitable small value. [ABSTRACT FROM AUTHOR]

Neural networks have gained popularity for modeling complex non-linear relationships. Their computational efficiency has led to their growing adoption in optimization methods, including topology optimization. Recently, there have been several contributions toward improving derivatives of neural network outputs, which can improve their use in gradient-based optimization. However, a comparative study has yet to be conducted on the different derivative methods for the sensitivity of the input features on the neural network outputs. This paper aims to evaluate four derivative methods: analytical neural network's Jacobian, central finite difference method, complex step method, and automatic differentiation. These methods are implemented into density-based and homogenization-based topology optimization using multilayer perceptrons (MLPs). For density-based topology optimization, the MLP approximates Young's modulus for the solid isotropic material with penalization (SIMP) model. For homogenization-based topology optimization, the MLP approximates the homogenized stiffness tensor of a representative volume element, e.g., square cell microstructure with a rectangular hole. The comparative study is performed by solving two-dimensional topology optimization problems using the sensitivity coefficients from each derivative method. Evaluation includes initial sensitivity coefficients, convergence plots, and the final topologies, compliance, and design variables. The findings demonstrate that neural network-based sensitivity coefficients are sufficiently accurate for density-based and homogenization-based topology optimization. The neural network's Jacobian, complex step method, and automatic differentiation produced identical sensitivity coefficients to working precision. The study's open-source code is provided through a python repository. [ABSTRACT FROM AUTHOR]

Using attribute graphs for node embedding to detect community structure has become a popular research topic. However, most of the existing algorithms mainly focus on the network structure and node features, which ignore the higher-order relationships between nodes. In addition, only adopting the original graph structure will suffer from sparsity problems, and will also result in suboptimal node clustering performance. In this paper, we propose a hypergraph network embedding (HGNE) for community detection to solve the above problems. Firstly, we construct potential connections based on the shared feature information of the nodes. By fusing the original topology with feature-based potential connections, both the explicit and implicit relationships are encoded into the node representations, thus alleviating the sparsity problem. Secondly, for integrating the higher-order relationship, we adopt hypergraph convolution to encode the higher-order correlations. To constrain the quality of the node embedding, the spectral hypergraph embedding loss is utilized. Furthermore, we design a dual-contrast mechanism, which draws similar nodes closer by comparing the representations of different views. This mechanism can efficiently prevent multi-node classes from distorting less-node classes. Finally, the dual-contrast mechanism is jointly optimized with self-training clustering to obtain more robust node representations, thus improving the clustering results. Extensive experiments on five datasets indicate the superiority and effectiveness of HGNE. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce the structure space of uniformly strongly prime ideals of an ordered semigroup and to study the separation axioms and the compactness property. [ABSTRACT FROM AUTHOR]

The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian. Since the topological classification of such Hamiltonians depends on their symmetry classes, a primary issue we address is determining the requirement for the Lindbladian operators, under which the modular Hamiltonian can preserve its symmetry class during the dynamical evolution. We solve this problem for the fermionic Gaussian state and for the modular Hamiltonian being a quadratic operator of a set of fermionic operators. When these conditions are satisfied, along with a nontrivial topological classification of the symmetry class of the modular Hamiltonian, a topological transition can occur as time evolves. We present two examples of dissipation-driven topological transitions where the modular Hamiltonian lies in the AIII class with U (1) symmetry and the DIII class without U (1) symmetry. By a finite size scaling, we show that this density matrix topology transition occurs at a finite time. We also present the physical signature of this transition. [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]

Due to the low voltage and high randomness of renewable energy, high-performance grid-connected converters are needed. With the advantages of a high boost ratio, flexible design, and simple control, the Y-Source Converter (YSC) is widely concerned. However, there are a few drawbacks to the traditional Y-source converter, including significant switching stress, voltage voltage overshoot, and discontinuous current. To solve the problems above, a series of improved topologies are proposed. Moreover, the voltage gain, current ripple, and soft switching characteristics have also been optimized. So far, the existing literature lacks the collation and comparison of different topologies of Y-source, as well as the analysis of its evolution process. Therefore, this paper provides a comprehensive overview of Y-source converters' topologies. According to their features and applications, different topologies are classified and described, leading to guidance for the selection of YSCs under different scenarios. Meanwhile, the working principle, evolution process, and vital issues are analyzed. By revealing their deductive rules, valuable suggestions are provided for the future development of YSCs. [ABSTRACT FROM AUTHOR]

Conventional 5-level active neutral-point-clamped (5L-ANPC) topology and state-of-the-art 5-level hybrid active neutral-point-clamped (5L-HANPC) topology are popular for inverter applications. However, their dc-link voltage utilization is limited to only 50%. With the maximum voltage level generated by only half dc-link voltage, these inverters are not capable of boosting voltage in their ac output. To resolve these drawbacks, this paper proposes a family of four novel 5-level boost-active neutral-point-clamped (5L-BANPC) inverters. Without requiring any flying capacitors, the proposed topologies can generate five voltage levels by effectively using the dc-link capacitors. The dc-link voltage utilization of the proposed 5L-BANPC inverters is twice that of the 5L-ANPC and 5L-HANPC topologies. While generating the five-level ac output voltage, natural voltage balancing of both dc-link capacitors and voltage boosting are achieved. Ease of implementation is another noteworthy merit of the proposed 5L-BANPC inverters because they can be implemented using six widely available commercial half-bridge modules without requiring a dedicated circuit design. The operation of the proposed topologies is analyzed. Experimental results are presented for verification. [ABSTRACT FROM AUTHOR]

In this paper we characterize hyperbolic cosine transforms of (positive) Borel measures ν in terms of exponential convexity (Bernstein's terminology). The case of compactly supported measures ν is also considered. All of this is then applied to (bounded) composition operators C T , ρ : f ↦ f ∘ T on L 2 (R κ , μ ρ) with affine symbols T = A + a , where d μ ρ (x) = ρ (x) d x , ρ (x) = ψ (‖ x ‖) − 1 , ψ is a continuous positive real valued function and ‖ ⋅ ‖ is the Euclidean norm on R κ. The main result states that the map R κ ∋ a ↦ C I + a , ρ is continuous in the strong operator topology and has cosubnormal values if and only if ψ is the hyperbolic cosine transform of a compactly supported Borel measure (I is the identity transformation). The case of affine symbols T that are not translations is also discussed. [ABSTRACT FROM AUTHOR]

The paper presents a fault region identification method for the active distribution network (ADN) with limited PMU. First, PMU configuration and region division strategies are proposed based on the network topology. Next, the difference in three-phase current variations between the normal and fault regions of the ADN is analyzed. A multi-dimensional state monitoring matrix is built using the measured current data. The spectral norm ratio coefficient is constructed based on the 2-norm to lower the complexity of the multi-dimensional state monitoring matrix and quantify the difference in state changes before and after the fault occurs in each region. Then, the fault region is identified by combining each region's spectral norm ratio coefficient and the change of the current phase. Finally, an IEEE 33-node simulation model is created to simulate faults under different working conditions. According to the simulation results, the suggested approach is less impacted by fault type, neutral point grounding mode, and transition resistance. Furthermore, even if the communication does not match the rigorous synchronization requirements, the proposed method can still complete the fault identification of the distribution network correctly and has high robustness. [ABSTRACT FROM AUTHOR]

Network topology plays a key role in determining the characteristics and dynamical behaviors of a network. But in practice, network topology is sometimes hidden or uncertain ahead of time because of network complexity. In this paper, a robust-synchronization-based topology observer (STO) is proposed and applied to solve the problem of identifying the topology of complex delayed networks (TICDNs). In comparison to the existing literature, the proposed STO does not require any prior knowledge about the range of topological parameters and does not have strict limits on topology type. Furthermore, the proposed STO is suitable not only for networks with fixed coupling strength, but also for networks with adaptive coupling strength. Finally, a few comparison examples for TICDNs are used to verify the feasibility and efficiency of the proposed STO, and the results show that the proposed STO outperforms the other methods. [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 considers the secure distributed control consensus problem of linear multi‐agent systems (MASs) under switching topologies, subject to intermittent sequential scaling attacks, which was compelled to scaling factor, attack frequency, duration and cooperative‐competitive networks. First, the scenario of a fixed topology is considered, and a novel control protocol combined with a logarithmic quantizer and relative state measurements of neighbouring agents is discussed. The sighed graph is utilized to characterize the communication topology determined by the information flow directions and captured by the graph Laplacian matrix. After that, sufficient conditions for effectiveness of the developed control methods in guiding the MASs to secure bipartite leader‐following consensus are constructed. Second, the scenario of switching topologies is considered, and it is derived that the secure bipartite consensus will be achieved if the designed state feedback control protocol with the scaling factor, the attack duration, attack frequency and switching signal are selected properly. At last, to prove the effectiveness of the designed controllers, a simulation example depended on the real‐word actual military is introduced. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed optimization problem for a class of nonlinear uncertain multi-agent systems with unmeasured states, switched parameters, and directed communication topologies changing in the control process. To achieve the goal of optimizing the global objective function, a penalty function is constructed through making up of a sum of local objective functions and integrating consensus conditions of the multi-agent systems to utilize local and neighboring information. Radial basis function neural-networks and neural-networks state observer are applied to approximate the unknown nonlinear functions and obtain the unmeasured states, respectively. To avoid "explosion of complexity" and obtain derivatives for virtual control functions continuously, dynamic surface control technology is proposed to develop a distributed adaptive backstepping neural network control protocol to ensure that all the agents' outputs asymptotically reach consensus to the optimal solution of the global objective function. Simulations demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Nowadays, the Internet of Things (IoT) networks provide benefits to humans in numerous domains by empowering the projects of smart cities, healthcare, industrial enhancement and so forth. The IoT networks include nodes, which deliver the data to the destination. However, the network nodes' connectivity is affected by the nodes' removal caused due to the malicious attacks. The ideal plan is to construct a topology that maintains nodes' connectivity after the attacks and subsequently increases the network robustness. Therefore, for constructing a robust scale-free network, two different mechanisms are adopted in this paper. First, a Multi-Population Genetic Algorithm (MPGA) is used to deal with premature convergence in GA. Then, an entropy based mechanism is used, which replaces the worst solution of high entropy population with the best solution of low entropy population to improve the network robustness. Second, two types of Edge Swap Mechanisms (ESMs) are proposed. The Efficiency based Edge Swap Mechanism (EESM) selects the pair of edges with high efficiency. While the second ESM named as EESM-Assortativity, transforms the network topology into an onion-like structure to achieve maximum connectivity between similar degree network nodes. Further, Hill Climbing (HC) and Simulated Annealing (SA) methods are used for optimizing the network robustness. The simulation results show that the proposed MPGA Entropy has 9% better network robustness as compared to MPGA. Moreover, both the proposed ESMs effectively increase the network robustness with an average of 15% better robustness as compared to HC and SA. Furthermore, they increase the graph density as well as network's connectivity. [ABSTRACT FROM AUTHOR]

This paper presents the methodology and theoretical foundation of topology optimization (TO) Results Spaceframe Interpreter, an automatic TO results interpreter that generates a closely associated space frame consisting of welded structural tubing or rectangular bars. TO is a computational technique that uses a finite element (FE) formulation to identify the most weight-efficient structure within a design domain. Density-based TO results in structures that take organic forms and is usually a tedious and cumbersome process to generate a computer-aided-design (CAD) model to manufacture through conventional techniques. The optimal topology frequently resembles a space frame, which is well-known as being a rigid, lightweight structure. The methodology of the TO results interpreter leverages several techniques from volumetric image processing and has four primary processes. First, the results are obtained from commercial FE/TO software and mapped into a cubic grid of voxels. Second, junction locations are extracted and member connectivity that represents a frame is identified. Third, a sizing optimization is incorporated to determine appropriate sectional dimensions of the circular or rectangular space frame members. Fourth, the optimized space frame geometry is imported into a CAD design tool to automatically create a design model. The logic and are implemented within the frame extraction processes. The automated TO interpreter is designed to interact with commercial FE analysis and CAD systems. The interpreter is demonstrated on various spatial examples including aerospace and automotive applications. In each case, the welded space frame closely resembles the TO result, with nearly equivalent stiffness and mass. [ABSTRACT FROM AUTHOR]

Transparent thermal heaters based on metallic networks have gained considerable attention in the last few years as a result of their superior response time, low sheet resistance, and low cost of manufacturing. To increase the mechanical stability and reliability of the thermal heater, it is desirable to embed the metallic network in some form of matrix. Embedding the network, however, changes the nature of thermal conduction making both in‐plane and out‐of‐plane thermal conduction important for ensuring reliability and uniform thermal distribution. The performance of embedded thermal heaters is also significantly influenced by the geometry of the metallic network, both in terms of optical transparency and thermal performance. In this paper, a coupled electro‐thermal model and an electromagnetic model are developed to investigate the properties of an embedded metallic mesh in a polymer matrix. Infrared thermal imaging and ultraviolet‐visible spectrophotometry are used to quantify thermal transport and transparency in the system and to verify the performance of finite element models. A systematic study is then performed to assess the role of network topology both on in‐plane and out‐of‐plane thermal distribution and optical performance. According to numerical analysis, a structure‐property relationship is established which can provide desirable network configurations to optimize performance. [ABSTRACT FROM AUTHOR]

In this paper, we prove the multiplicity and concentration behavior of complex-valued solutions for the following Kirchhoff–Schrödinger equation with magnetic field - (a ε 2 + b ε [ u ] A / ε 2) Δ A / ε u + V (x) u = f (| u | 2) u , x ∈ R 2 , where ε > 0 is a small parameter, the nonlinearity f is involved in critical exponential growth in the sense of Trudinger–Moser inequality and both V : R 2 → R and A : R 2 → R 2 are continuous potential and magnetic potential, respectively. Imposing a local constraint of potential V(x) first introduced from del Pino and Felmer, we get the multiplicity of solutions by way of the relationship between the number of the solutions and the topology of the set with V attaining the minimum. Our strategy of main proof is based on the variational methods combined with the penalization technique, the Trudinger–Moser inequality and Ljusternik–Schnirelmann theory, and our result is still new even without magnetic effect. [ABSTRACT FROM AUTHOR]