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For functions f1, . . ., fn on a set D, we characterize their linear independence with an invertible matrix from their values at n distinct points in D. With the matrix, the pointwise convergence of a sequence {gk} of functions in the span{f1, · · ·, fn} is shown to be equivalent to those of the sequences of the coordinates of gks in the span. When fis are bounded, a pointwise convergent sequence {gk} must uniformly converge to a function in the span. It turns out that the limit of a convergent sequence {gk} inherits the continuity, differentiability, and integrability of fis. Furthermore the (pointwise or uniform) convergence of a sequence of solutions of an n-th order constant coefficients linear differential equation is completely determined by that of the sequence of relevant initial conditions. [ABSTRACT FROM AUTHOR]

The results of the latest demographic forecasts from the world's leading specialized centers (United Nations Population Division, the Wittgenstein Center for Demography and Global Human Capital, the Institute for Health Metrics and Evaluation) are considered, demonstrating a certain bias in favor of individual countries and their calculation methods. The second part of this article provides a description of a digital twin of the planet's demographic system constructed by a Chinese−Russian team and implemented in China's national supercomputer center. In addition, the results of some calculations carried out using this tool are described. [ABSTRACT FROM AUTHOR]

Spiking neural network (SNN) is a brain-inspiredmodel withmore spatio-temporal information processing capacity and computational energy efficiency. However, with the increasing depth of SNNs, the memory problem caused by the weights of SNNs has gradually attracted attention. In this study, we propose an ultra-low latency adaptive local binary spiking neural network (ALBSNN) with accuracy loss estimators, which dynamically selects the network layers to be binarized to ensure a balance between quantization degree and classification accuracy by evaluating the error caused by the binarized weights during the network learning process. At the same time, to accelerate the training speed of the network, the global average pooling (GAP) layer is introduced to replace the fully connected layers by combining convolution and pooling. Finally, to further reduce the error caused by the binary weight, we propose binary weight optimization (BWO), which updates the overall weight by directly adjusting the binary weight. This method further reduces the loss of the network that reaches the training bottleneck. The combination of the above methods balances the network's quantization and recognition ability, enabling the network to maintain the recognition capability equivalent to the full precision network and reduce the storage space bymore than 20%. So, SNNs can use a small number of time steps to obtain better recognition accuracy. In the extreme case of using only a one-time step, we still can achieve 93.39, 92.12, and 69.55% testing accuracy on three traditional static datasets, Fashion-MNIST, CIFAR-10, and CIFAR-100, respectively. At the same time, we evaluate our method on neuromorphic N-MNIST, CIFAR10-DVS, and IBM DVS128 Gesture datasets and achieve advanced accuracy in SNN with binary weights. Our network has greater advantages in terms of storage resources and training time. [ABSTRACT FROM AUTHOR]

Being motivated by Dini's Theorem, the uniform convergence of a sequence of functions is characterized by that of another decreasing sequence of functions. This result allows us to describe the uniform convergence of a sequence of measurable functions on a closed interval in terms of that of a decreasing sequence of Lebesgue integrable functions. For a sequence of continuous functions on a compact set, its uniform convergence is further characterized by the pointwise convergence of another decreasing sequence of continuous functions. It also turns out that the uniform convergence of a sequence of Riemann integrable functions on a closed interval can be determined by that of another decreasing sequence of Riemann integrable functions. As applications, characterizations for a uniformly convergent series of functions have been presented and one fixed point theorem has been established. [ABSTRACT FROM AUTHOR]

Given a decreasing sequence {an} of nonnegative terms, we prove that there exist subsequences {nk} of {n} such that ∑∞k=1(nk+1-nk)ank and ∑∞n=1an have the same convergence. In particular, ∑∞n=1an converges if and only if ∑∞k=1 qkaqk converges for any natural number q > 1. Using this result, the ratio test is also extended. One example further shows that the new extended ratio test is applicable to discussing the convergence of a p-series for which the ratio test fails. [ABSTRACT FROM AUTHOR]

Taming interfacial electronic effects on Pt nanoparticles modulated by their concomitants has emerged as an intriguing approach to optimize Pt catalytic performance. Here, we report Pt nanoparticles assembled on vacancy-abundant hexagonal boron nitride nanosheets and their use as a model catalyst to embrace an interfacial electronic effect on Pt induced by the nanosheets with N-vacancies and B-vacancies for superior CO oxidation catalysis. Experimental results indicate that strong interaction exists between Pt and the vacancies. Bader charge analysis shows that with Pt on B-vacancies, the nanosheets serve as a Lewis acid to accept electrons from Pt, and on the contrary, when Pt sits on N-vacancies, the nanosheets act as a Lewis base for donating electrons to Pt. The overall-electronic effect demonstrates an electron-rich feature of Pt after assembling on hexagonal boron nitride nanosheets. Such an interfacial electronic effect makes Pt favour the adsorption of O2 alleviating CO poisoning and promoting the catalysis. [ABSTRACT FROM AUTHOR]

Although perovskites have been widely used in catalysis, tuning of their surface termination to control reaction selectivity has not been well established. In this study, we employed multiple surface-sensitive techniques to characterize the surface termination (one aspect of surface reconstruction) of SrTiO3 (STO) after thermal pretreatment (Sr enrichment) and chemical etching (Ti enrichment). We show, by using the conversion of 2-propanol as a probe reaction, that the surface termination of STO can be controlled to greatly tune catalytic acid/base properties and consequently the reaction selectivity over a wide range, which is not possible with single-metal oxides, either SrO or TiO2. Density functional theory (DFT) calculations explain well the selectivity tuning and reaction mechanism on STO with different surface termination. Similar catalytic tunability was also observed on BaZrO3, thus highlighting the generality of the findings of this study. [ABSTRACT FROM AUTHOR]

Under some new conditions,we present several equivalent (and sufficient) conditions for weak sharp solutions of variational inequalities in Hilbert spaces and give a finite convergence result for a class of algorithms for solving variational inequalities. [ABSTRACT FROM AUTHOR]

For a lower semicontinuous function f on a Banach space X, we study the existence of a positive scalar &emu; such that the distance function dS associated with the solution set S of f(x) ≤ 0 satisfies. [ABSTRACT FROM AUTHOR]

An unexpected oxygen-assisted reduction of cationic Au species by CO was found on a Au/SiO2 catalyst at room temperature and the produced metallic Au species plays an essential role in CO oxidation on Au/SiO2. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) photocatalysts have attracted considerable research interest in the past decades due to their unique optical, physical and chemical properties. Constructing 2D/2D heterojunctions with large interface area has been considered as an effective approach to enhance the transfer rate and the separation efficiency of the charge carriers, leading to dramatic increase in the photocatalytic performance of the photocatalysts. Here, the state-of-the-art progress on heterojunctions based on 2D materials is reviewed, including the photocatalysis principles using 2D heterojunctions, the categories of 2D heterojunctions and their application in different photocatalytic reactions, and the theoretical studies of the 2D heterojunctions. Moreover, the advantages and disadvantages of the 2D heterojunctions are also discussed. Finally, the ongoing challenges and opportunities for the future development of 2D photocatalysts with built-in heterojunctions are proposed. [ABSTRACT FROM AUTHOR]

An innovative multiple-step rapid thermal annealing (RTA) technique was developed for obtaining high hole concentration in the nonpolar a-plane Mg-delta-doped AlGaN films grown on semi-polar r-plane sapphire substrates with metal organic chemical vapor deposition. The structural, optical, and electrical properties of the nonpolar a-plane p-AlGaN epi-layers were characterized with high-resolution x-ray diffraction, photoluminescence spectra, and Hall effect measurement. The characterization results demonstrated that the dissociation efficiency of the Mg–H bonds in the nonpolar a-plane p-AlGaN films could be improved significantly with the multiple-step RTA process. In fact, a hole concentration as high as 1.9  ×  1018 cm−3 was achieved with the multiple-step RTA technique, which was 35%, 9%, and 23% higher than those obtained with conventional one-step, two-step, and the recently renovated two-step RTA methods, respectively. [ABSTRACT FROM AUTHOR]

MgN/AlGaN insertion layers were applied for the first time to the growth of nonpolar a-plane AlGaN epilayers by metal organic chemical vapor deposition technology. The full width at half maximum of the X-ray rocking curve for the a-plane AlGaN epilayers was reduced by approximately 50.6% and the root-mean-square roughness value of the surface was reduced by 74% by applying the MgN/AlGaN insertion layers with an optimized number of insertion pairs. These results reveal that the compressive strain within the a-plane AlGaN epilayers was effectively reduced, leading to significant improvements in crystalline quality and surface morphology. These improvements are very helpful in fabricating high-quality AlGaN-based ultraviolet light-emitting diodes. [ABSTRACT FROM AUTHOR]

Nonpolar a-plane AlGaN epi-layers were grown on a semi-polar r-plane sapphire substrate with an innovative two-way pulsed-flows metal organic chemical vapor deposition growth technology. A root-mean-square value of 1.79 nm was achieved, and the relative light transmittance of the a-plane AlGaN epi-layer was enhanced by 36.9%. These results reveal that the innovative growth method is able to improve the surface morphology and reduce the defect density in nonpolar a-plane AlxGa1–xN epi-layers, particularly those with an Al composition greater than 0.5, which are key materials for the fabrication of nonpolar AlGaN-based high light emission efficiency deep-ultraviolet light-emitting diodes. [ABSTRACT FROM AUTHOR]

A reformed flow-rate-modulation technology was developed for the metalorganic vapor phase epitaxy (MOVPE) growth of the N-polar GaN epitaxial layers. To improve the crystalline quality of the N-polar GaN epitaxial layers, a GaN nucleation layer was grown at relatively low temperature with carefully-controlled pulsed supply of Ga source and showed diverse morphology with atomic force microscope (AFM). Furthermore, the electrical and optical properties of the grown N-polar GaN epitaxial layers were investigated extensively by means of Hall effect, photoluminescence (PL), and X-ray rocking curve (XRC) measurements. The characterization results revealed that as compared with the N-polar GaN epitaxial layer grown over the conventional GaN nucleation layer which was deposited with continuous supply of both N and Ga sources, the electrical and optical properties of the N-polar GaN epitaxial layer grown with optimized supply of Ga source for the GaN nucleation layer were significantly improved. [ABSTRACT FROM AUTHOR]

Ultra-thin PtxFey-nanowires (PtxFey-NWs) with a diameter of 2-3 nm were successfully prepared through a solution-phase reduction method at Pt-Fe compositions from 1:1 to 2:1. The carbon supported PtxFey-NWs (PtxFey-NWs/C) demonstrated higher oxygen reduction reaction (ORR) activity and better electrochemical durability than conventional Pt/C catalyst. After 1000 cycles of 0-1.3 V (versus RHE), the relative electrochemical surface area (ECSA) of Pt2Fe1-NW/C dropped down to 46%, which was two times better than Pt/C catalyst, and the mass activity at 0.85 V (versus RHE) for Pt1Fe1-NW/C was 39.9 mA mg [?] 1-Pt, which is twice that for Pt/C (18.6 mA mg [?] 1-Pt). [ABSTRACT FROM AUTHOR]