Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^con_(p,q,s) over Rⁿ or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rⁿ or a given cube of Rⁿ with finite side length.Furthermore, some VMO-H¹-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.     

Graphene Saturable Absorber Mirror for Mode-Locked Orange Pulse Laser

Journal of Russian Laser Research - We demonstrate a passively-mode-locked Pr3+: LuLiF4 laser operated at the 604 nm orange wave-length, using monolayer graphene as a saturable absorber. The...     

Reduced Density Matrix and Quantum Correlation in Two-Qubit Quantum Rabi Model

International Journal of Theoretical Physics - In this work, we give an analytical derivation of the reduced density matrix between two qubits in a cavity field, which is described by the quantum...     

Developing Flexible Quinacridone-Derivatives-Based Photothermal Evaporaters for Solar Steam and Thermoelectric Power Generation

Solar-driven interfacial vaporization by localizing solar-thermal energy conversion to the air−water interface has attracted tremendous attention. In the process of converting solar energy into heat energy, photothermal materials play an essential role. Herein, a flexible solar-thermal material di-cyan substituted 5,12-dibutylquinacridone (DCN−4CQA)@Paper was developed by coating photothermal quinacridone derivatives on the cellulose paper. The DCN−4CQA@Paper combines desired chemical and physical properties, broadband light-absorbing, and shape-conforming abilities that render efficient photothermic vaporization. Notably, synergetic coupling of solar-steam and solar-electricity technologies by integrating DCN−4CQA@Paper and the thermoelectric devices is realized without trade-offs, highlighting the practical consideration toward more impactful solar heat exploitation. Such solar distillation and low-grade heat-to-electricity generation functions can provide potential opportunities for fresh water and electricity supply in off-grid or remote areas.     

Fully asynchronous stochastic coordinate descent: a tight lower bound on the parallelism achieving linear speedup

Mathematical Programming - We seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent that achieves linear speedup. We focus on asynchronous coordinate...     

Interactions of the vector breathers for the coupled Hirota system with $$4\times 4$$ 4 × 4 Lax pair

Nonlinear Dynamics - In this paper, we investigate the interactions of the vector breathers for the coupled Hirota system with $$4\times 4$$ Lax pair. Firstly, we give the first-order breather...     

Designing Covalent Organic Frameworks with a Tailored Ionic Interface for Ion Transport across One-Dimensional Channels

A strategy based on covalent organic frameworks for ultrafast ion transport involves designing an ionic interface to mediate ion motion. Electrolyte chains were integrated onto the walls of one-dimensional channels to construct ionic frameworks via pore surface engineering, so that the ionic interface can be systematically tuned at the desired composition and density. This strategy enables a quantitative correlation between interface and ion transport and unveils a full picture of managing ionic interface to achieve high-rate ion transport. Moreover, the effect of interfaces was scaled on ion transport; ion mobility is increased in an exponential mode with the ionic interface. This strategy not only sets a benchmark system but also offers a general guidance for designing ionic interface that is key to systems for energy conversion and storage.     

Formation of Azulene-Embedded Nanographene: Naphthalene to Azulene Rearrangement During the Scholl Reaction

Incorporation of a non-hexagonal ring into a nanographene framework can lead to new electronic properties. During the attempted synthesis of naphthalene-bridged double [6]helicene and heptagon-containing nanographene by the Scholl reaction, an unexpected azulene-embedded nanographene and its triflyloxylated product were obtained, as confirmed by X-ray crystallographic analysis and 2D NMR spectroscopy. A 5/7/7/5 ring-fused substructure containing two formal azulene units is formed, but only one of them shows an azulene-like electronic structure. The formation of this unique structure is explained by arenium ion mediated 1,2-phenyl migration and a naphthalene to azulene rearrangement reaction according to an in-silico study. This report represents the first experimental example of the thermodynamically unfavorable naphthalene to azulene rearrangement and may lead to new azulene-based molecular materials.