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Topology - Science topic

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Publications related to Topology (10,000)
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Article
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In chemical graph theory, numerical encoding of chemical structure associated with topological indices is growing immensely. Prediction of the characteristics specified by the molecule's chemical structure is a salient feature of these topological indices. In this paper, we obtained the-polynomial of the two-dimensional Boron Kagome Lattice. Some t...
Article
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Topological descriptors/indices are very significant in the study of intrinsic properties of chemical graphs and nanostructures. These indices are used to extract information from the symmetry of molecular graphs and are based on some of the graph invariants such as the vertex degree, distance, and spectrum. This article computes reverse degree-bas...
Article
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Topological Indices serve as mathematical models for the QSPR/QSAR study, which provides the optimum theoretical analysis for expensive practical drug discovery experiments. In this paper, some of the degree-based topological indices concerning the vertices at distance 2 are obtained for alkane groups. And then, some physiochemical properties of Al...
Article
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As an innovative planar artificial structure, elastic metasurface exhibits great potential in the application fields of vibration and noise control. By virtue of the superior performance of compact/ultra-thin configuration, easy-fabrication and richer physics, metasurfaces are expected to make up for the deficiency of traditional meta-materials. Ho...
Conference Paper
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In this paper we report on the recent progress of development of the unified framework for small-scale and large-scale topology. Firstly, we introduce the notion of spatial sets and spatial maps which simultaneously generalise the existing notions of spaces such as topological spaces, uniform spaces, bornological spaces and coarse spaces. After rec...
Article
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The past decades have witnessed the flourishing of non-Hermitian physics in non-conservative systems, leading to unprecedented phenomena of unidirectional invisibility, enhanced sensitivity and more recently the novel topological features such as bulk Fermi arcs. Among them, growing efforts have been invested to an intriguing phenomenon, known as t...
Article
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Parallel mechanisms (PMs) of the 3-CCC class exhibit many attractive features, such as decoupled motion, degenerated singularity, simple forward-kinematics relations and high dexterity, making them promising in many applications. However, in order to simplify the analysis, existing research mainly focuses on its several subclasses, leading to drawb...
Article
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Quantum oscillation is an important phenomenon in low temperature transport studies of topological materials. In three-dimensional topological insulators, Dirac semimetals, Weyl semimetals, and other topological nontrivial materials, the topologically nontrivial band structure will add a phase correction to the quantum oscillation patterns, which i...
Article
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Topological semimetals represent a new class of topological materials, which are highly desirable for both physics frontier and electronics applications owing to their nontrivial band structures and topologically protected surface states. The large-area fabrication of high-quality topological semimetal films is the prerequisite step to realize thei...
Conference Paper
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The analytical studies on the sound absorption characteristics of a homogeneous Double Leaf Micro Perforate Panel (DL-MPP) absorber with non-circular perforations are presented in this study. The DL-MPP's sound absorption coefficient is calculated using an equivalent electro-acoustical model. The performance of the DL-MPP with Non-Circular perforat...
Method
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Unraveling the morphological complexity of two-dimensional macromolecules allows researchers to design and fabricate high-performance, multifunctional materials. Here, we present a protocol based on statistical learning to resolve morphological complexity utilizing geometrical, topological, and physical features extracted from the strain energy hea...
Article
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Mooring is a widely used stationkeeping approach for floating structures. The main contribution of this paper is to propose a novel localization scheme, which provides additional real-time position references and estimates the unknown anchor positions to a moored structure simultaneously using tension measurements from the mooring monitoring system...
Research
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A Mobile ad hoc network is self-configuring infrastructure having less network of mobile device (laptops, smart-phones, sensors, etc.) connected by wireless link. This type of network is separate network. Security is a primary issue in order to provide secure communication in aggressive environment. There are still some challenges associated with M...
Article
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In [18], Tallafha and Khalil introduced a new type of uniform space which is a mixture of topology and analysis, namely semi-linear uniform spaces. In this paper, we continue and extend this study by presenting a new generalization of a semi-linear uniform space, namely weak semi-linear uniform spaces. Then we present the concept of proximinal sets...
Article
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Topological states of matter and their corresponding properties are classical research topics in condensed matter physics. Quite recently, the application of materials that feature these states has been extended to the field of electro- chemical catalysis and become an emerging research topic that is receiving increasing interest. In particular, se...
Preprint
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Discoveries of tetraquarks not only enrich the hadronic spectrum but also provide more platforms to understand quantum chromodynamics. We study the production processes of hidden-charm and open-charm tetraquarks in $B$ decays by analyzing their topological amplitudes. Relations between different channels are found, which confront tests by experimen...
Article
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Suitable space vector modulation (SVM) with reduced high-frequency common-mode voltages (HF-CMVs) for grid-connected current-source inverters (CSIs) have not been well investigated yet. In this study, the potential of active zero-state SVM (AZS-SVM) to suppress high frequency common-mode voltages (HF-CMVs) is revealed and theoretically analyzed, wh...
Article
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We study the suppression of the conductance quantization in quantum spin Hall systems by a combined effect of electronic interactions and edge disorder, that is ubiquitous in exfoliated and chemical vapor deposition grown two-dimensional (2D) materials. We show that the interplay between the electronic localized states due to edge defects and elect...
Article
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We simulate the smallest building block of the Sachdev-Ye-Kitaev (SYK) model, a system of four interacting Majorana modes. We propose a 1D Kitaev chain that has been split into three segments, i.e., two topological segments separated by a non-topological segment in the middle, hosting four Majorana Zero Modes at the ends of the topological segments...
Article
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We provide a detailed study of topological and combinatorial properties of sectionable tournaments. This class forms an inductively constructed family of tournaments grounded over simply disconnected tournaments, those tournaments whose fundamental groups of acyclic complexes are non-trivial. When T is a sectionable tournament, we fully describe th...
Article
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In this paper, the most suited analog-to-digital (A/D) converters (ADCs) for Internet of Things (IoT) applications are compared in terms of complexity, dynamic performance, and energy efficiency. Among them, an innovative hybrid topology, a digital–delta (Δ) modulator (ΔM) ADC employing noise shaping (NS), is proposed. To implement the active build...
Article
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Axial-flux permanent-magnet (AFPM) motors are a kind of important motor with compact structure, high power density and high torque density. In this review, the progress of AFPM motors and their key technologies are analyzed and described, with emphasis on the topological structures, design and optimization methods and control techniques. Based on t...
Article
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Topological data analysis (TDA) is an emergent field of data analysis. The critical step of TDA is computing the persistent Betti numbers. Existing classical algorithms for TDA are limited if we want to learn from high-dimensional topological features because the number of high-dimensional simplices grows exponentially in the size of the data. In t...
Article
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The article deals with the correspondence between soft ideal topological spaces and ideal topological ones. Investigation of soft ideal topological spaces is based on methods of general topology, and the application of results for soft omega open and strongly soft omega open sets is given.
Article
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It is known that transitive Anosov diffeomorphisms have a unique measure of maximal entropy (MME). Here we discuss the converse question. Transitivity of Anosov diffeomorphisms can be reached under suitable hypotheses on Lyapunov exponents on the set of periodic points and the structure of the MME. In another way, assuming together the uniqueness o...
Article
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New structures in the form of multiple optical bottles (OBs), produced by the chirped Airy-Gaussian vortex beams (CAGVBs) in free space, are derived numerically and experimentally. By selecting appropriate parameters, multiple OB structures with different sizes, different locations, and amounts of individual 'bottles' in them are produced. These ch...
Preprint
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Quantum gravity and time. Early publication: https://openreview.net/forum?id=HzlR0EoDTB
Article
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This paper discusses the containment control problem of nonlinear multiagent systems with unknown disturbance and switching topology. The novel model of nonlinear multiagent systems is given and the dynamic functions of this model are considered to be continuous. Utilizing the approximation capability of the neural networks to estimate the unknown...
Preprint
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We study, for a continuous linear operator $T$ on an F-space $X$, when the direct sum operator $T\oplus T$ is recurrent on $X\oplus X$. In particular: we establish the analogous notion, for recurrence, to that of (topological) weak-mixing for transitivity/hypercyclicity, namely quasi-rigidity; and we construct a recurrent but not quasi-rigid operat...
Preprint
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This article considers consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. It is considered the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in a given region, which can...
Preprint
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The Bloch Sphere visualization of the possible states of a single qubit has proved a useful pedagogical and conceptual tool as a one-to-one map between qubit states and points in a 3-D space. However, understanding many important concepts of quantum mechanics, such as entanglement, requires developing intuitions about states with a minimum of two q...
Article
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The particle motion associated to the α-relaxation in supercooled liquids is still challenging scientists due to its difficulty to be probed experimentally. By combining synchrotron techniques, we report the existence of microscopic structure-dynamics relationships in Pt 42.5 Cu 27 Ni 9.5 P 21 and Pd 42.5 Cu 27 Ni 9.5 P 21 liquids which allows us t...
Article
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This study aims to find discontinuous and continuous approaches to reducing the size of planar truss structures with a specified shape and topology. The member’s section area has assumed to be a decision variable, and the objective function is to minimize their weight. The member stresses and node displacements are the constraints that must maintai...
Article
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Tandem cylinder flow comprises several different flow regimes. Within the reattachment regime, the development of the gap shear layers is of utmost importance to the flow, but has received little attention so far. Through direct numerical simulations at $Re = 10^{4}$ , for a gap ratio of 3.0, we have discovered that the shear layers are significant...
Preprint
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This paper presents a Temporal Graph Neural Network (TGNN) framework for detection and localization of false data injection and ramp attacks on the system state in smart grids. Capturing the topological information of the system through the GNN framework along with the state measurements can improve the performance of the detection mechanism. The p...
Article
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In this paper, we use a geometric technique developed by González-Prieto, Logares, Muñoz, and Newstead to study the G-representation variety of surface groups of arbitrary genus for G being the group of upper triangular matrices of fixed rank. Explicitly, we compute the virtual classes in the Grothendieck ring of varieties of the G-representation v...
Article
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Spatial organization of chromatin plays a critical role in genome regulation. Previously, various types of affnity mediators and enzymes have been attributed to regulate spatial organization of chromatin from a thermodynamics perspective. However, at the mechanistic level, enzymes act in their unique ways and perturb the chromatin. Here, we constru...
Preprint
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We establish the existence of multiple solutions for Gierer-Meinhardt system involving Neumann boundary conditions. The approach combines the methods of sub-supersolution and Leray-Schauder topological degree.
Preprint
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We use the long-wavelength effective theory of black branes (blackfold approach) to perturbatively construct holographic duals of the vacua of the $\mathcal{N}=1$* supersymmetric gauge theory. Employing the mechanism of Polchinski and Strassler, we consider wrapped black five-brane probes with D3-brane charge moving in the perturbative supergravity...
Preprint
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Motivated by applications in medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be effici...
Preprint
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This expository article supplies the mathematical background underpinning the braid representation calculator introduced in arXiv:2212.00831; those representations describe the sets of logic gates available to a topological quantum computer for processing encoded qubits. Assuming little background in category theory, we first recall the notion of a...
Research Proposal
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Renewable energies have become a core and essential part of current and future grids thanks to power electronics converters, which enable this wide spread of renewable energy systems and ease their integration into DC or AC grids. Power electronics topologies designed for renewable energy integration are designed to be compact, cost less and exhibi...
Preprint
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The $su(2)$ coherent-state path-integral technique is employed to study lattice electrons strongly coupled to a quantum spin background. In the large-spin limit it is replaced with its classical counterpart that breaks the time-reversal symmetry. The fermions propagating through a classical large-spin texture may then exhibit the topological Hall e...
Article
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Inference of species networks from genomic data under the Network Multispecies Coalescent Model is currently severely limited by heavy computational demands. It also remains unclear how complicated networks can be for consistent inference to be possible. As a step toward inferring a general species network, this work considers its tree of blobs, in...
Article
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In this paper, a consensus tracking protocol for nonlinear agents is presented, which is based on the Nonlinear Dynamic Inversion (NDI) technique. Implementation of such a technique is new in the context of the consensus tracking problem. The tracking capability of nonlinear dynamic inversion (NDI) is exploited for a leader-follower multi-agent sce...
Preprint
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The introduction of non-orthogonal electric and magnetic fields in the QCD vacuum enhances the weight of topological sectors with a nonzero topological charge. For weak fields, there is a linear response for the expectation value of the topological charge. We study this linear response and relate it to the QCD correction to the axion-photon couplin...
Preprint
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Intersection cohomology is a way to enhance classical cohomology, allowing us to use a famous result called Poincar\'e duality on a large class of spaces known as stratified pseudomanifolds. There is a theoretically powerful way to arrive at intersection cohomology by classifying sheaves that satisfy what are called Deligne axioms. We stablish an a...
Article
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Metasurfaces have emerged as game-changing technology ranging from microwaves to optics. This article provides a roadmap to the evolution of electromagnetic metasurfaces with a focus on their synthesis techniques, materials used for their design and their recent and futuristic applications. A broad classification is provided, and the design princip...
Preprint
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Here we present an analysis of the evolution of Majorana corner modes realizing in a higher-order topological superconductor (HOTSC) on a square lattice under the influence of local Coulomb repulsion. The HOTSC spectral properties were considered in two regimes: when the intensities of many-body interactions are either weak or strong. The weak regi...
Article
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Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies that appear for the first time at five loops. Explicitly, we open the loops into connected trees and group th...
Preprint
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We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct topological states with opposite signs of the valley Hall index, and separated by a heterojunction. In the practical cir...
Article
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Entanglement is one of the most fundamental features of quantum systems. In this work, we obtain the entanglement spectrum and entropy of Floquet noninteracting fermionic lattice models and build their connections with Floquet topological phases. Topological winding and Chern numbers are introduced to characterize the entanglement spectrum and eige...
Article
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Recently, the theory of Complex Networks gives a modern insight into a variety of applications in our life. Complex Networks are used to form complex phenomena into graph-based models that include nodes and edges connecting them. This representation can be analyzed by using network metrics such as node degree, clustering coefficient, path length, c...
Article
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Generative models for structure-based molecular design hold considerable promise for drug discovery, with the potential to speed up the hit-to-lead development cycle while improving the quality of drug candidates and reducing costs. Data sparsity and bias are, however, the two main roadblocks to the development of three-dimensionally aware models....
Preprint
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We investigate the effects of random onsite disorder on higher-order Thouless pumping of noninteracting fermionic Benalcazar-Bernevig-Hughes (BBH) model. The interplay of disorderinduced topological phase transition and delocalization-localization transition is extensively explored. The higher-order Thouless pumping is characterized by the quantize...
Preprint
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We consider a dimer lattice of the Fermi-Pasta-Ulam-Tsingou (FPUT) type, where alternating linear couplings have a controllably small difference, and the cubic nonlinearity ($\beta$-FPUT) is the same for all interaction pairs. We use a weakly nonlinear formal reduction within the lattice bandgap to obtain a continuum, nonlinear Dirac-type system. W...
Article
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We continue our research plan of developing the theory of small and locally small spaces, proposing this theory as a realisation of Grothendieck’s idea of tame topology on the level of general topology. In this paper, we develop the theory of Heyting small spaces and prove a new version of Esakia Duality for such spaces. To do this, we notice that...
Preprint
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We propose a mechanism with a low activation energy for lipid translocation, based on a change of topology of the membrane of a protocell. The inner and outer layers are connected and form toroidal nanoholes stabilised by repulsive electrostatic forces for small radius and attractive elastic forces for large radius. Thanks to these holes, the energ...
Preprint
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Topological Data Analysis (TDA) is a well-established field derived to give insight into the geometric structure of real-world data. However, many methods in TDA are computationally intensive. The method that computes the respective Betti number has been shown to obtain a speed-up from translating the algorithm into a quantum circuit. The quantum c...
Thesis
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We propose the construction of a boundary map to analyse and compute the boundary of an invariant set of a specific set-valued mapping F(M) := B_ε(f(M)) for M ⊂ R^d, d ≥ 2, ε > 0 and some diffeomorphism f. The core of this thesis builds on a result where the outward unit normal bundle of a continuously differentiable boundary of an invariant set is...
Preprint
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V.V.Grushin and V.P.Palamodov proved in 1962 that it is impossible to place in $R^3$ uncountably many pairwise disjoint polyhedra each homeomorphic to the Moebius band. We generalize this result in two directions. First, we give a generalization of this result to tame subsets in $R^N$, $N\geqslant 3$. Second, we show that in case of $R^3$ the theor...
Article
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Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT), in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2...
Preprint
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A two-dimensional (2D) model of topological insulator with N-stacked Su-Schrieffer-Heeger (SSH) chains is proposed. This study considers a basic model with all the fundamental symmetries (particle-hole, chiral, and time-reversal) preserved. This model is topologically trivial irrespective of the topological property of the individual SSH chain. In...
Article
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Inductive power transfer (IPT) technology is widely used in autonomous underwater vehicles (AUVs) to achieve safety and flexibility. However, the eddy current loss (ECL) will be generated in the seawater due to the high-frequency alternating current in the transmitter and receiver. An underwater IPT system with a series-none (SN) compensation topol...
Article
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Quantum spin Hall insulators (QSHIs) based on HgTe and three-layer InAs/GaSb quantum wells (QWs) have comparable bulk band gaps of about 10–18 meV. The former, however, features a band gap vanishing with temperature, while the gap in InAs/GaSb QSHIs is rather temperature independent. Here, we report on the realization of a large inverted band gap i...
Preprint
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Following the recent preparation of infinitene (J. Am. Chem. Soc. 2022, 144, 862-871), a computational (ωB97XD/6-311G(d)) exploration of 42 isomeric compounds with 12 fused phenyl rings identified structures with linking number of zero (ring, saddle, and ribbon shapes), two (infinitene-like shape), and one (Möbius infinitene shape) is reported. An...
Article
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A Banach space X has property (K), whenever every weak* null sequence in the dual space admits a convex block subsequence (fn)n=1∞$(f_{n})_{n=1}^\infty$ so that ⟨fn,xn⟩→0$\langle f_{n},x_{n}\rangle \rightarrow 0$ as n→∞$n\rightarrow \infty$ for every weakly null sequence (xn)n=1∞$(x_{n})_{n=1}^\infty$ in X; X has property (μs)$(\mu ^{s})$ if every...
Conference Paper
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Frequency domain impedance of Li-ion batteries contains valuable information about the state of charge (SOC) and state of health (SOH). Normally, electrochemical impedance spectroscopy (EIS) is performed during the relaxation of battery cells. However, performing EIS during the batteries operation has been achieved through switching power converter...
Preprint
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The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in topological considerations, the algorithm makes key use of the geometry of the surface. We introduce data structures...
Article
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Path homology is a topological invariant for directed graphs, which is sensitive to their asymmetry and can discern between digraphs which are indistinguishable to the directed flag complex. In Erdős–Rényi directed random graphs, the first Betti number undergoes two distinct transitions, appearing at a low-density boundary and vanishing again at a...