Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Interlayer Engineering of Molybdenum Trioxide toward High‐Capacity and Stable Sodium Ion Half/Full Batteries

Orthorhombic molybdenum trioxide (MoO₃) is one of the most promising anode materials for sodium‐ion batteries because of its rich chemistry associated with multiple valence states and intriguing layered structure. However, MoO₃ still suffers from the low rate capability and poor cycle induced by pulverization during de/sodiation. An ingenious two‐step synthesis strategy to fine tune the layer structure of MoO₃ targeting stable and fast sodium ionic diffusion channels is reported here. By integrating partially reduction and organic molecule intercalation methodologies, the interlayer spacing of MoO₃ is remarkably enlarged to 10.40 Å and the layer structural integration are reinforced by dimercapto groups of bismuththiol molecules. Comprehensive characterizations and density functional theory calculations prove that the intercalated bismuththiol (DMcT) molecules substantially enhanced electronic conductivity and effectively shield the electrostatic interaction between Na⁺ and the MoO₃ host by conjugated double bond, resulting in improved Na⁺ insertion/extraction kinetics. Benefiting from these features, the newly devised layered MoO₃ electrode achieves excellent long‐term cycling stability and outstanding rate performance. These achievements are of vital significance for the preparation of sodium‐ion battery anode materials with high‐rate capability and long cycling life using intercalation chemistry.     

Precise Extraction of Charge Carrier Mobility for Organic Transistors

Unreliable mobility values, and particularly greatly overestimated values and severely distorted temperature dependences, have recently hampered the development of the organic transistor field. Given that organic field‐effect transistors (OFETs) have been routinely used to evaluate mobility, precise parameter extraction using the electrical properties of OFETs is thus of primary importance. This review examines the origins of the various mobilities that must be determined for OFET applications, the relevant extraction methods, and the data selection limitations, which help in avoiding conceptual errors during mobility extraction. For increased precision, the review also discusses device fabrication considerations, calibration of both the specific gate‐dielectric capacitance and the threshold voltage, the contact effects, and the bias and temperature dependences, which must actually be handled with great care but have mostly been overlooked to date. This review serves as a systematic overview of the OFET mobility extraction process to ensure high precision and will also aid in improving future research.     

Direct Transformation of Arenols Based on C—O Activation

In the view of substrate availability, atomic efficiency and cost, directly using arenols as coupling partners in cross‐coupling, would be one of the most attractive goals. Up to date, many efforts have been made to activate the C—O bond of phenols with different strategies, for example, through in‐situ formed intermediates, through a catalytic reductive dearomatization‐condensation‐rearomatization sequence or catalytic deoxygenation. In this review, we summarized recent advances in cross‐couplings of arenols as the electrophiles via C—O activation.     

Polypyrrole Shell@3D‐Ni Metal Core Structured Electrodes for High‐Performance Supercapacitors

Three‐dimensional (3D) nanometal films serving as current collectors have attracted much interest recently owing to their promising application in high‐performance supercapacitors. In the process of the electrochemical reaction, the 3D structure can provide a short diffusion path for fast ion transport, and the highly conductive nanometal may serve as a backbone for facile electron transfer. In this work, a novel polypyrrole (PPy) shell@3D‐Ni‐core composite is developed to enhance the electrochemical performance of conventional PPy. With the introduction of a Ni metal core, the as‐prepared material exhibits a high specific capacitance (726 F g^?1 at a charge/discharge rate of 1 A g^?1), good rate capability (a decay of 33 % in C_sp with charge/discharge rates increasing from 1 to 20 A g^?1), and high cycle stability (only a small decrease of 4.2 % in C_sp after 1000 cycles at a scan rate of 100 mV s^?1). Furthermore, an aqueous symmetric supercapacitor device is fabricated by using the as‐prepared composite as electrodes; the device demonstrates a high energy density (≈21.2 Wh kg^?1) and superior long‐term cycle ability (only 4.4 % and 18.6 % loss in C_sp after 2000 and 5000 cycles, respectively).     

Polyvinylpyrrolidone and graphene-modified hematite nanoparticles for efficient electrocatalytic oxidation of p-nitrophenol

Journal of Solid State Electrochemistry - Polyvinylpyrrolidone (PVP) and graphene (G)-modified iron oxides (Fe2O3-PVP-G) are prepared by a simple hydrothermal reaction. Their morphology and...     

Specific emitter identification for satellite communication using probabilistic neural networks

Electromagnetic signal emitted by satellite communication (satcom) transmitters are used to identify specific individual uplink satcom terminals sharing the common transponder in real environment, which is known as specific emitter identification (SEI) that allows for early indications and warning (I&W) of the targets carrying satcom furnishment and furthermore the real time electromagnetic situation awareness in military operations. In this paper, the authors are the first to propose the identification of specific transmitters of satcom by using probabilistic neural networks (PNN) to reach the goal of target recognition. We have been devoted to the examination by exploring the feasibility of utilizing the Hilbert transform to signal preprocessing, applying the discrete wavelet transform to feature extraction, and employing the PNN to perform the classification of stationary signals. There are a total of 1000 sampling time series with binary phase shift keying (BPSK) modulation originated by five types of satcom transmitters in the test. The established PNNs classifier implements the data testing and finally yields satisfactory accuracy at 8 dB(±1 dB) carrier to noise ratio, which indicates the feasibility of our method, and even the keen insight of its application in military.