Restricted testing conditions for the multilinear maximal operator

Restricted testing conditions were considered recently. For the maximal operator, Hytönen, Li and Sawyer [8] first obtained parental testing condition. Later, they [9] showed that it suffices to restrict testing to doubling cubes. Chen and Lacey [3] gave a similar restricted testing condition. In our paper, we discuss a version of the latter in the multilinear setting.

     

Nacre-Inspired,Liquid Metal-Based Ultrasensitive Electronic Skin by Spatially Regulated Cracking Strategy

The realization of liquid metal-based wearable systems will be a milestone toward high-performance, integrated electronic skin. However, despite the revolutionary progress achieved in many other components of electronic skin, liquid metal-based flexible sensors still suffer from poor sensitivity due to the insufficient resistance change of liquid metal to deformation. Herein, a nacre-inspired architecture composed of a biphasic pattern (liquid metal with Cr/Cu underlayer) as “bricks” and strain-sensitive Ag film as “mortar” is developed, which breaks the long-standing sensitivity bottleneck of liquid metal-based electronic skin. With 2 orders of magnitude of sensitivity amplification while maintaining wide (>85%) working range, for the first time, liquid metal-based strain sensors rival the state-of-art counterparts. This liquid metal composite features spatially regulated cracking behavior. On the one hand, hard Cr cells locally modulate the strain distribution, which avoids premature cut-through cracks and prolongs the defect propagation in the adjacent Ag film. On the other hand, the separated liquid metal cells prevent unfavorable continuous liquid-metal paths and create crack-free regions during strain. Demonstrated in diverse scenarios, the proposed design concept may spark more applications of ultrasensitive liquid metal-based electronic skins, and reveals a pathway for sensor development via crack engineering.     

Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

Nonlinear Dynamics - The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative...     

Magnetically Guidable Proteinaceous Adhesive Microbots for Targeted Locoregional Therapeutics Delivery in the Highly Dynamic Environment of the Esophagus

The esophagus is a tubular-shaped muscular organ where swallowed fluids and muscular contractions constitute a highly dynamic environment. The turbulent, coordinated processes that occur through the oropharyngeal conduit can often compromise targeted administration of therapeutic drugs to a lesion, significantly reducing therapeutic efficacy. Here, magnetically guidable drug vehicles capable of strongly adhering to target sites using a bioengineered mussel adhesive protein (MAP) to achieve localized delivery of therapeutic drugs against the hydrodynamic physiological conditions are proposed. A suite of highly uniform microparticles embedded with iron oxide (IO) nanoparticles (MAP@IO MPs) is microfluidically fabricated using the genipin-mediated covalent cross-linking of bioengineered MAP. The MAP@IO MPs are successfully targeted to a specific region and prolongedly retained in the tubular-structured passageway. In particular, orally administered MAP@IO MPs are effectively captured in the esophagus in vivo in a magnetically guidable manner. Moreover, doxorubicin (DOX)-loaded MAP@IO MPs exhibit a sustainable DOX release profile, effective anticancer therapeutic activity, and excellent biocompatibility. Thus, the magnetically guidable locomotion and robust underwater adhesive properties of the proteinaceous soft microbots can provide an intelligent modular approach for targeted locoregional therapeutics delivery to a specific lesion site in dynamic fluid-associated tubular organs such as the esophagus.     

Exact solutions of an asymmetric double well potential

Journal of Mathematical Chemistry - The analytical solutions of an asymmetric double well potential $$V(x)=a\, x^2-b\, x^3+c\, x^4$$ are found to be a triconfluent Heun function $$H_{T}(\alpha ,...     

Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

Fabricating Dual-Atom Iron Catalysts for Efficient Oxygen Evolution Reaction: A Heteroatom Modulator Approach

Understanding the thermal aggregation behavior of metal atoms is important for the synthesis of supported metal clusters. Here, derived from a metal–organic framework encapsulating a trinuclear Fe^III₂Fe^II complex (denoted as Fe₃) within the channels, a well-defined nitrogen-doped carbon layer is fabricated as an ideal support for stabilizing the generated iron nanoclusters. Atomic replacement of Fe^II by other metal(II) ions (e.g., Zn^II/Co^II) via synthesizing isostructural trinuclear-complex precursors (Fe₂Zn/Fe₂Co), namely the “heteroatom modulator approach”, is inhibiting the aggregation of Fe atoms toward nanoclusters with formation of a stable iron dimer in an optimal metal–nitrogen moiety, clearly identified by direct transmission electron microscopy and X-ray absorption fine structure analysis. The supported iron dimer, serving as cooperative metal–metal site, acts as efficient oxygen evolution catalyst. Our findings offer an atomic insight to guide the future design of ultrasmall metal clusters bearing outstanding catalytic capabilities.     

Anti-Markovnikov Hydroamination of Racemic Allylic Alcohols to Access Chiral γ-Amino Alcohols

A ruthenium-catalyzed formal anti-Markovnikov hydroamination of allylic alcohols for the synthesis of chiral γ-amino alcohols is presented. Proceeding via an asymmetric hydrogen-borrowing process, the catalysis allows racemic secondary allylic alcohols to react with various amines, affording enantiomerically enriched chiral γ-amino alcohols with broad substrate scope and excellent enantioselectivities (68 examples, up to >99 % ee).     

The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.