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A Course In Functional Analysis

ACCESS Metrics & More Article Recommendations ■ CONTENTS High-Throughput Nanopores 320 Nanopore Working Principle 320 Arrayed Nanopore Configurations 321 Machine-Learning Assisted Nanopore Readout 321 Integration Modalities for Nanopores 321 Nanopore-Confined Electrochemistry 322 High-Throughput Scanning Ion Conductance Microscopy 324 From Nanopore to Nanoprobe 324 High-Throughput SICM 324 High-Throughput Imaging 325 High-Throughput Single-Cell Manipulation and Measurements 326 SICM as an Electrochemical Probe 326 Applications in Material Sciences 327 Applications in Life Sciences 328 High-Throughput Scanning Electrochemical Cell Microscopy 329 Technical and Theoretical Developments 329 Electrochemical Measurements and Characterization 331 Popular Redox Reactions and Electrode Materials 331 Corrosion 332 Phase Formation 332 Two-Dimensional Materials 333 Photoelectrochemistry 335 Electrocatalysis: Single Particles and PseudoSingle-Crystal Screening of Structure−Activity 336 Battery Electrode Materials 339 Optical Microscopies in Electrochemistry 339 Overview of Operational Principles 339 Operational Principles 339 Methodologies for Quantitative Image Analysis 340 Converting Local Optical Information into an Electrochemically Relevant Signal 340 Computing and Automatized Image Analysis 340 Imaging Single Events 340 A Complement to Single Nanoobject Electrochemistry 340 Electron Transfer 341 Probing Concentration Profiles 341 Conversion 341 Growth and Dissolution 342 Catalysis and Motion 342 Competing Processes 343 Electrochemistry versus Physical Transformation 343 Competing Electrochemical Reactions 344 One versus Many 344 Seeing Collective Behaviors 344 How to Access Missing Pieces of Information 344 Hyphenation with Local Complementary Information 345 Other Electrochemical and Electronic HighThroughput Imaging Techniques 345 Conclusion 346 Author Information 347 Corresponding Authors 347 Authors 347 Author Contributions 347 Notes 347 Biographies 347 Acknowledgments 348 List of Abbreviations Used 348 References 349

https://pubs.acs.org/doi/pdf/10.1021/acs.analchem.2c05105

The New Era of High-Throughput Nanoelectrochemistry

Transition metal dichalcogenides (TMDs) intercalated with spin-bearing transition metal centers are a diverse class of magnetic materials where the spin density and ordering behavior can be varied by the choice of host lattice, intercalant identity, level of intercalation, and intercalant disorder. Each of these degrees of freedom alters the interplay between several key magnetic interactions to produce disparate collective electronic and magnetic phases. The array of magnetic and electronic behavior typified by these systems renders them distinctive platforms for realizing tunable magnetism in solid-state materials and promising candidates for spin-based electronic devices. This Perspective provides an overview of the rich magnetism displayed by transition metal-intercalated TMDs by considering Fe- and Cr-intercalated NbS2 and TaS2. These four exemplars of this large family of materials exhibit a wide range of magnetic properties, including sharp switching of magnetic states, current-driven magnetic switching, and chiral spin textures. An understanding of the fundamental origins of the resultant magnetic/electronic phases in these materials is discussed in the context of composition, bonding, electronic structure, and magnetic anisotropy in each case study.

Structure and Magnetism of Iron- and Chromium-Intercalated Niobium and Tantalum Disulfides.

In this paper, we expand the study of the multiplication operators on the Lipschitz space of a tree begun in Colonna and Easley (Integral Equ Oper Theory 68:391–411, 2010) by focusing on their adjoint acting on a certain separable subspace of the Lipschitz space whose dual is isometrically isomorphic to \(\mathbf L^1\). We then study the properties of two useful operators \(\nabla \) and \(\Delta \) and use them (along with the multiplicative symbol \(\psi \)) to define the Toeplitz operator \(T_\psi \) on the space \(\mathbf L^p\) for \(1\le p \le \infty \). We give conditions for its boundedness and study its point spectrum.

Some classes of operators with symbol on the Lipschitz space of a tree

Two-dimensional (2D) magnetic crystals hold promise for miniaturized and ultralow power electronic devices that exploit spin manipulation. In these materials, large, controllable magnetocrystalline anisotropy (MCA) is a prerequisite for the stabilization and manipulation of long-range magnetic order. In known 2D magnetic crystals, relatively weak MCA typically results in soft ferromagnetism. Here, we demonstrate that ferromagnetic order persists down to the thinnest limit of FexTaS2 (Fe-intercalated bilayer 2H-TaS2) with giant coercivities up to 3 T. We prepare Fe-intercalated TaS2 by chemical intercalation of van der Waals-layered 2H-TaS2 crystals and perform variable-temperature transport, transmission electron microscopy, and confocal Raman spectroscopy measurements to shed new light on the coupled effects of dimensionality, degree of intercalation, and intercalant order/disorder on the hard ferromagnetic behavior of FexTaS2. More generally, we show that chemical intercalation gives access to a rich synthetic parameter space for low-dimensional magnets, in which magnetic properties can be tailored by the choice of the host material and intercalant identity/amount, in addition to the manifold distinctive degrees of freedom available in atomically thin, van der Waals crystals.

Hard Ferromagnetism Down to the Thinnest Limit of Iron-Intercalated Tantalum Disulfide.

Tailoring electron transfer dynamics across solid-liquid interfaces is fundamental to the interconversion of electrical and chemical energy. Stacking atomically thin layers with a small azimuthal misorientation to produce moiré superlattices enables the controlled engineering of electronic band structures and the formation of extremely flat electronic bands. Here, we report a strong twist-angle dependence of heterogeneous charge transfer kinetics at twisted bilayer graphene electrodes with the greatest enhancement observed near the 'magic angle' (~1.1°). This effect is driven by the angle-dependent tuning of moiré-derived flat bands that modulate electron transfer processes with the solution-phase redox couple. Combined experimental and computational analysis reveals that the variation in electrochemical activity with moiré angle is controlled by a structural relaxation of the moiré superlattice at twist angles of <2°, and 'topological defect' AA stacking regions, where flat bands are localized, produce a large anomalous local electrochemical enhancement that cannot be accounted for by the elevated local density of states alone. 

/pdf/tunable-angle-dependent-electrochemistry-at-twisted-bilayer-2w0r8nr8.pdf

Tunable angle-dependent electrochemistry at twisted bilayer graphene with moiré flat bands

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determine estimates on the operator norm, and show there are no isometries.

Isaac M. Craig

Papers

Tunable angle-dependent electrochemistry at twisted bilayer graphene with moiré flat bands

Multiplication operators on weighted banach spaces of a tree

Structure and Magnetism of Iron- and Chromium-Intercalated Niobium and Tantalum Disulfides.

Hard Ferromagnetism Down to the Thinnest Limit of Iron-Intercalated Tantalum Disulfide.

Multiplication Operators on Weighted Banach Spaces of a Tree