Extremes of projections of functional time series on data–driven basis systems

The paper is concerned with the extreme behavior of projections of time series of functions onto data-driven basis systems, for example, on the estimated functional principal components. The coefficients of these projections, called the scores, encode the shapes of the curves. Within the framework of functional data analysis, the extreme shapes are those corresponding to multivariate extremes of the scores. The scores are not directly observable, and must be computed from the data. Even for iid Gaussian functions, they form a triangular array of dependent non–Gaussian vectors. Thus, even though the extreme behavior of the population scores of Gaussian functions follows from well–known results, it is not clear what the extreme behavior of their approximations computed from the data is. We clarify these issues for Gaussian functions and for more general functional time series whose projections are in the Gumbel domain of attraction.     

How is cultural influence manifested in the formation of mathematics textbooks? A comparative case study of resource book series between Shanghai and England

Focusing on issues about the development of mathematics textbooks from a cultural perspective, this study examined a widely-used curriculum resource series, One Lesson One Exercise, published in China, and its adapted English series, published in the UK, to explore how cultural influence is manifested in the two series of resource books. For the study we established a conceptual framework classifying culture into six types in relation to people’s beliefs, values and ways of interacting about them, for data collection and analysis. The results indicate that there exist considerable differences between the Chinese and the English series that are related to cultural factors. It appears that, to a large extent, culture plays an essential role in the development of mathematics textbooks. Concerning the different types of culture, the results show that most adaptations between the Chinese series and the English series are related to ‘ways of behaving and customs’ and ‘artifacts, flora and fauna’, followed by ‘identities’ and ‘geography’, and the least are related to ‘organisations’ and ‘history’. Based on the study, we argue that the relevance and importance of culture to the development of mathematics textbooks must not be underestimated, and more research in this direction is needed.     

An aggregate deformation homotopy method for min-max-min problems with max-min constraints

In this paper, the constrained min-max-min problem, which is an essentially nonsmooth and nonconvex problem, is considered. Based on a twice aggregate function with a modification, an aggregate deformation homotopy method is established. Under some suitable assumptions, a smooth path from a randomly given point to a solution of the generalized KKT system is proven to exist. By numerically tracing the smooth path, a globally convergent algorithm for some solution of the problem is given. Some numerical results are given to show the feasibility of the method.     

Sharp constants in weighted trace inequalities on Riemannian manifolds

In this paper, we establish some sharp weighted trace inequalities ${W^{1,2}(\rho^{1-2 \sigma}, M) \hookrightarrow L^{\frac{2n}{n-2 \sigma}}(\partial M)}$ on n + 1 dimensional compact smooth manifolds with smooth boundaries, where ρ is a defining function of M and ${\sigma \in (0,1)}$ . This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.     

Performance of Extrinsic Fabry–Perot Interferometer Based on Graded-Index Lenses for a Fabry–Perot Cavity with Surface Errors

Interference contrast is an important parameter for extrinsic Fabry–Perot interferometer (EFPI) based on graded index (GRIN) lenses. It determines the signal-to-noise ratio (SNR) and the measurement accuracy. We discuss the influence of Fabry–Perot (FP) cavity surface errors, which are inevitable in controlling the interference contrast during the manufacturing procedure. Our theoretical analysis and results of numerical simulations demonstrate that the surface errors diminish the interference contrast — the larger the surface error, the smaller the interference contrast. The results obtained contribute to the EFPI application in fiber sensors.     

Silver nanowires for photonics applications

Although silver nanowires as plasmonic components have been investigated extensively in both theoretical and experimental studies, a systematic study is still lacking. In this work, a review is given to explain some basic features of experimentally prepared nanowires and their optical properties in different situations, such as waveguides, resonators, and antennas. The review also lists several possible applications of nanowires for enhanced light‐emitting, photonic device fabrication, sensors, lasers, and nonlinear optics. Combined with the merits of both nanowires and surface plasmon polaritons, silver nanowires are certain to show their potential in photonics in the near future.     

Simulation of resonant tunneling devices: origin of the I–V multi-peak behavior

Multi-peak behavior of the $I$ – $V$ curves of an AlAs/GaAs/AlAs double-barrier resonant tunneling diode combined with a layer of InAs quantum dots (QDs) is simulated. Our simulation results show that the coupling between the energy level in the emitter quantum well (quantum dot) layer and that in the central quantum well is the key point in understanding the origin of the $I$ – $V$ multi-peak behavior. The embedded designed QD layer at the emitter spacer can enhance this effect. The effects of device temperature on the $I$ – $V$ characteristics are also obtained. Our results provide the physical basis for understanding and utilizing the multi-peak behavior of $I$ – $V$ curves in designing resonant tunneling devices.     

Guiding Uniform Li Plating/Stripping through Lithium–Aluminum Alloying Medium for Long‐Life Li Metal Batteries

The uncontrolled growth of Li dendrites upon cycling might result in low coulombic efficiency and severe safety hazards. Herein, a lithiophilic binary lithium–aluminum alloy layer, which was generated through an in situ electrochemical process, was utilized to guide the uniform metallic Li nucleation and growth, free from the formation of dendrites. Moreover, the formed LiAl alloy layer can function as a Li reservoir to compensate the irreversible Li loss, enabling long‐term stability. The protected Li electrode shows superior cycling over 1700 h in a Li|Li symmetric cell.     

Impact of neutral and acidic species on cycloalkenes nucleation

Non-covalent hydrogen bond interactions between the π cloud of cycloalkenes and three atmospheric common nucleation precursors (H₂S, H₂O, and MeOH) have been investigated using DFT and CCSD(T). The structures and the energies of the 1:1 and 1:2 adducts were computed with the B3LYP-D3 method. The analysis of the investigated electronic properties and geometric parameters shows that cyclohexene is a stronger hydrogen bond acceptor than cyclopentene, then followed by 1,4-cyclohexadiene and 1,3-cyclohexadiene. Comparable red shifts of the OH-/SH-stretching vibrational frequencies were noticed for the studied clusters. Increasing the ring size enhances the hydrogen bond interaction, and increasing the π delocalization decreases the hydrogen bond interactions. This is further confirmed by Bader’s quantum theory of atoms in molecules. The nonadditivity effects were observed in the trimolecular complexes. All the complexes were analyzed by energy decomposition analysis to divide the interaction energy into individual components. Furthermore, the dipole moments and atmospheric implications were also investigated.