Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Peculiar Photoinduced Electron Transfer in Porphyrin–Fullerene Akamptisomers

Porphyrin–fullerene dyads are promising candidates for organic photovoltaic devices. The electron-transfer (ET) properties of the molecular devices depend significantly on the mutual position of the donor and acceptor. Recently, a new type of molecular isomerism (akamptisomerism) has been discovered. In the present study, we explore how photoinduced ET can be modulated by passing from one akamptisomer to another. To this aim, four akamptisomers of the quinoxalinoporphyrin–[60]fullerene complex are selected for computational study. The most striking finding is that, depending on the isomer, the porphyrin unit in the dyad can act as either electron donor or electron acceptor. Thus, the stereoisomeric diversity allows one to change the direction of ET between the porphyrin and fullerene moieties. To understand the effect of akamptisomerism on the photoinduced ET processes, a detailed analysis of initial and final states involved in the ET is performed. The computed rate for charge separation is estimated to be in the region of 1–10 ns⁻¹. The formation of a long-living quinoxalinoporphyrin anion radical species is predicted.     

Charge-Transfer versus Charge-Separated Triplet Excited States of [ReI(dmp)(CO)3(His124)(Trp122)]+ in Water and in Modified Pseudomonas aeruginosa Azurin Protein

A computational investigation of the triplet excited states of a rhenium complex electronically coupled with a tryptophan side chain and bound to an azurin protein is presented. In particular, by using high-level molecular modeling, evidence is provided for how the electronic properties of the excited-state manifolds strongly depend on coupling with the environment. Indeed, only upon explicitly taking into account the protein environment can two stable triplet states of metal-to-ligand charge transfer or charge-separated nature be recovered. In addition, it is also demonstrated how the rhenium complex plus tryptophan system in an aqueous environment experiences too much flexibility, which prevents the two chromophores from being electronically coupled. This occurrence disables the formation of a charge-separated state. The successful strategy requires a multiscale approach of combining molecular dynamics and quantum chemistry. In this context, the strategy used to parameterize the force fields for the electronic triplet states of the metal complex is also presented.     

Extended phase diagram of La1-xCaxMnO3 by interfacial engineering

The interfacial enhanced ferromagnetism in maganite/ruthenate system is regarded as a promising path to broaden the potential of oxide-based electronic device applications. Here, we systematically studied the physical properties of LaLa_1-xCa_xMnO₃/SrRuO₃ superlattices and compared them with the LaLa_1-xCa_xMnO₃ thin films and bulk compounds. The LaLa_1-xCa_xMnO₃/SrRuO₃ superlattices exhibit significant enhancement of Curie temperature (T_C) beyond the corresponding thin films and bulks. Based on these results, we constructed an extended phase diagram of LaLa_1-xCa_xMnO₃ under interfacial engineering. We considered the interfacial charge transfer and structural proximity effects as the origin of the interface-induced high T_C. The structural characterizations revealed a pronounced increase of B-O-B bond angle, which could be the main driving force for the high T_C in the superlattices. Our work inspires a deeper understanding of the collective effects of interfacial charge transfer and structural proximity on the physical properties of oxide heterostructures.     

Graph-like compacta: Characterizations and Eulerian loops

A compact graph-like space is a triple $\left(X,V,E\right)$, where $X$ is a compact, metrizable space, $V\subseteq X$ is a closed zero-dimensional subset, and $E$ is an index set such that $X⧹V\cong \text{◂+▸}E\times \left(0,1\right)$. New characterizations of compact graph-like spaces are given, connecting them to certain classes of continua, and to standard subspaces of Freudenthal compactifications of locally finite graphs. These are applied to characterize Eulerian graph-like compacta.     

非齐度量测度空间上Morrey-Herz空间上的广义分数次积分算子及其交换子

设(χ,d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间,对于引进的一类非齐度量测度空间上的Morrey-Herz空间,利用非齐度量测度空间的特征,证明了广义分数次积分算子及其交换子在非齐度量测度空间上MorreyHerz空间的有界性.     

Approaching the Integer‐Charge Transfer Regime in Molecularly Doped Oligothiophenes by Efficient Decarboxylative Cross‐Coupling

A library of symmetrical linear oligothiophene was prepared employing decarboxylative cross‐coupling reaction as the key transformation. Thiophene potassium carboxylate salts were used as cross‐coupling partners without the need of co‐catalyst, base, or additives. This method demonstrates complete chemoselectivity and is a comprehensive greener approach compared to the existing methods. The modularity of this approach is demonstrated with the preparation of discreet oligothiophenes with up to 10 thiophene repeat units. Symmetrical oligothiophenes are prototypical organic semiconductors where their molecular electrical doping as a function of the chain length can be assessed spectroscopically. An oligothiophene critical length for integer charge transfer was observed to be 10 thiophene units, highlighting the potential use of discrete oligothiophenes as doped conduction or injection layers in organic electronics applications.     

The differentiation operator in the space of uniformly convergent Dirichlet series

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half-planes for each . The properties of the formal inverse of the differentiation are also investigated.