Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.     

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form     

Philicity of Acetonyl and Benzoyl Radicals: A Comparative Experimental and Computational Study

In this work, the reactivities of acetonyl and benzoyl radicals in aromatic substitution and addition reactions have been compared in an experimental and computational study. The results show that acetonyl is more electrophilic than benzoyl, which is rather nucleophilic. A Hammett plot analysis of the addition reactions of the two radicals to substituted styrenes clearly support the nucleophilicity of benzoyl, but in the case of acetonyl, no satisfactory linear correlation with a single substituent-related parameter was found. Computational calculations helped to rationalize this effect, and a good linear correlation was found with a combination of polar parameters (σ⁺) and the radical stabilization energies of the formed intermediates. Based on the calculated philicity indices for benzoyl and acetonyl, a quantitative comparison of these two radicals with many other reported radicals is possible, which may help to predict the reactivities of other aromatic radical substitution reactions.     

Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

Facile Synthesis of Ultra-Small Few-Layer Nanostructured MoSe2 Embedded on N,P Co-Doped Bio-Carbon for High-Performance Half/Full Sodium-Ion and Potassium-Ion Batteries

Sodium/potassium-ion batteries (SIBs/PIBs) arouse intensive interest on account of the natural abundance of sodium/potassium resources, the competitive cost and appropriate redox potential. Nevertheless, the huge challenge for SIBs/PIBs lies in the scarcity of an anode material with high capacity and stable structure, which are capable of accommodating large-size ions during cycling. Furthermore, using sustainable natural biomass to fabricate electrodes for energy storage applications is a hot topic. Herein, an ultra-small few-layer nanostructured MoSe₂ embedded on N, P co-doped bio-carbon is reported, which is synthesized by using chlorella as the adsorbent and precursor. As a consequence, the MoSe₂/NP-C-2 composite represents exceedingly impressive electrochemical performance for both sodium-ion batteries (SIBs) and potassium-ion batteries (PIBs). It displays a promising reversible capacity (523 mAh g⁻¹ at 100 mA g⁻¹ after 100 cycles) and impressive long-term cycling performance (192 mAh g⁻¹ at 5 A g⁻¹ even after 1000 cycles) in SIBs, which are some of the best properties of MoSe₂-based anode materials for SIBs to date. To further probe the great potential applications, full SIBs pairing the MoSe₂/NP-C-2 composite anode with a Na₃V₂(PO₄)₃ cathode also exhibits a satisfactory capacity of 215 mAh g⁻¹ at 500 mA g⁻¹ after 100 cycles. Moreover, it also delivers a decent reversible capacity of 131 mAh g⁻¹ at 1 A g⁻¹ even after 250 cycles for PIBs.     

The Linear Optical Unambiguous Discrimination of Hyperentangled Bell States Assisted by Time Bin

A linear optical unambiguous discrimination of hyperentangled Bell states is proposed for two‐photon systems entangled in both the polarization and momentum degrees of freedom (DOFs) assisted by time bin. This unambiguous discrimination scheme can completely identify 16 orthogonal hyperentangled Bell states using only linear optical elements, where the function of the auxiliary entangled Bell state is replaced by time bin. Moreover, the possibility of extending this scheme for distinguishing hyperentangled Bell states in n DOFs is discussed, and it shows that $2^{n+k+1}$ hyperentangled Bell states in n ( $n\ge 2$) DOFs can be distinguished with k ( $k<n$) auxiliary entangled states of additional DOFs by introducing a time delay, which decreases the auxiliary entanglement resource required for unambiguous discrimination of hyperentangled Bell state. Therefore, this scheme provides a new way for distinguishing hyperentangled states with current technology, which will extend the application of discrimination of hyperentangled states via linear optics to other quantum information protocols besides hyperdense coding schemes in the future.     

Parallel Translation on K¨ahler Manifolds

In this paper, the author establishs a real-valued function on K¨ahler manifolds by holomorphic sectional curvature under parallel translation. The author proves if such functions are equal for two simply-connected, complete K¨ahler manifolds, then they are holomorphically isometric.     

Noise Reduction in Spur Gear Systems

This article lists some tips for reducing gear case noise. With this aim, a static analysis was carried out in order to describe how stresses resulting from meshing gears affect the acoustic emissions. Different parameters were taken into account, such as the friction, material, and lubrication, in order to validate ideas from the literature and to make several comparisons. Furthermore, a coupled Eulerian–Lagrangian (CEL) analysis was performed, which was an innovative way of evaluating the sound pressure level of the aforementioned gears. Different parameters were considered again, such as the friction, lubrication, material, and rotational speed, in order to make different research comparisons. The analytical results agreed with those in the literature, both for the static analysis and CEL analysis—for example, it was shown that changing the material from steel to ductile iron improved the gear noise, while increasing the rotational speed or the friction increased the acoustic emissions. Regarding the CEL analysis, air was considered a perfect gas, but its viscosity or another state equation could have also been taken into account. Therefore, the above allowed us to state that research into these scientific fields will bring about reliable results.