Sparse optimization on measures with over-parameterized gradient descent

Mathematical Programming - Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks...     

Comments on Salem polynomials

Archiv der Mathematik - We strengthen a sufficient condition, due to R.S. Vieira, for a (reciprocal) polynomial $$R(x)=(x-\alpha _{1})(x-\alpha _{1}^{-1})\cdots (x-\alpha _{s})(x-\alpha...     

Synthesis,characterization, and transport properties of Nafion-polypyrrole membrane for direct methanol fuel cell (DMFC) application

Journal of Solid State Electrochemistry - Due to their distinctive chemical, electronic, and environmental properties, polypyrrole is used as a blocking barrier for methanol leakage in direct...     

Theoretical and experimental investigations of complexation with BF3.Et2O effects on electronic structures,energies and photophysical properties of Anil and tetraphenyl (hydroxyl) imidazol

The novel compounds (E)‐2‐(((4‐hydroxyphenyl)imino)methyl)phenol, Tetraphenyl (hydroxyl) imidazole and their corresponding Boron difluoride complexes were synthesized and characterized by spectroscopic techniques. Density functional theory calculations at B3LYP‐D3/6–311++G (d, p) level of theory were performed for the geometric parameters. The MEP surface studies were used to understand the behavior of molecules in terms of charge transfer and to determine how these molecules interact. We used the GIAO and the B3LYP‐D3 with a 6–311++ G (d, p) basis set to simulate the (¹H‐NMR and ¹⁹F‐NMR) and the IR spectra, respectively. The corresponding calculated results are in good agreement with the experimental data. The stability of the molecule arising from hyperconjugation interaction and charge delocalization were analyzed using NBO analysis. FMOs revealed the occurrence of charge transfer within the molecule. The complexation using BF₃.Et₂O was also found to have remarkable effects on the electrochemical properties of the studied molecules, where (b) and (d) present lower chemical stability, higher reactivity and higher polarizability than (a) and (c), respectively. Moreover, the energy gap of (a) and (c) decreased after complexation using BF₃.Et₂O, indicating the reliability of the electrochemical evaluation of LUMO and HOMO energy levels. These values are the factors explaining the possible charge transfer interaction within the molecule. The absorption and emission spectra of the model compound were also simulated and compared to experimental observations in the DMF solvent. The results of DFT calculations supported the structural and spectroscopic data and confirmed the structure modification of frontier molecular orbitals for BF₂ complexes as well as tunable potentials and energy levels.     

k-Hankel Gabor Transform and Its Applications to the Theory of Localization Operators

Analysis Mathematica - We introduce and study the k-Hankel Gabor transform. We investigate the localization operators for this transform. In particular, we study their trace class properties and we...     

An effective method for the reduction of the device utilization amount in experimental realization of a fractional-order system

This study focuses on the experimental realization of the fractional-order FitzHugh–Nagumo (FHN) neuron model. Firstly, a second-order approximation function is included to the FHN neuron model to satisfy the fractional-order definition. Since these approximation functions can meet the response of the ideal system only in a limited frequency band, the identification of their center frequency is very critical. Thus, the center frequency ‘ω_c’ of this second-order approximation functions is swept until getting the spiking responses of this neuron model for the first time in this study. After the center frequency is determined, this approximation function is transferred into the ‘z’ domain by employing the Tustin discretization operator. This achieved discrete defined and fractional-order FHN neuron model becomes suitable for implementation on the digital platforms. To verify the proficiency of the proposed sweeping process experimentally, the fractional-order FHN model in ‘z’ domain is implemented on the FPGA platform. After these applications, the order of the approximation function is reduced to one. Once this followed frequency sweeping process is repeated for the first-order approximation, the fractional-order FHN neuron model, which is built by this least-order approximation function, is also implemented with the FPGA. Therefore, the reductions of the device utilization amounts by using this least-order approximation function and the importance of the specific frequency identification process are seen clearly.

     

How do molecular interactions affect fluorescence behavior of AIEgens in solution and aggregate states?

Molecular interactions are crucial in diverse fields of protein folding,material science,nanotechnology,and life origins.Although mounting experimental research controls luminescent behavior by adjusting molecular interactions in light-emitting materials,it remains elusive to correlate microscopic molecular interactions with macroscopic luminescent behavior directly.Here,we synthesized three red luminogens with subtle structural variation and investigated the influence of molecular interactions on their luminescent behavior in solution and aggregate states.Our results indicate that strongπ-πand D-A interactions in both dilute solution(between luminogen and solvent molecules)and aggregate(between luminogens)states cause the redshift in emission,while weak interactions(e.g.,Van der Waals,C–H…π,and C–H…F interactions)enhance the quantum yield.This work provides a thoughtful investigation into the complicated influence of various molecular interactions on luminescent behavior.     

Frustrated Lewis Pair Chemistry Enables N2 Borylation by Formal 1,3-Addition of a B−H Bond in the Coordination Sphere of Tungsten

The first example of a formal 1,3-B−H bond addition across the M−N≡N unit of an end-on dinitrogen complex has been achieved. The use of Piers’ borane HB(C₆F₅)₂ was essential to observe this reactivity and it plays a triple role in this transformation: 1) electrophilic N₂-borylation agent, 2) Lewis acid in a frustrated Lewis pair-type B−H bond activation, and 3) hydride shuttle to the metal center. This chemistry is supported by NMR spectroscopy and solid-state characterization of products and intermediates. The combination of chelate effect and strong σ donation in the diphosphine ligand 1,2-bis(diethylphosphino)ethane was mandatory to avoid phosphine dissociation that otherwise led to complexes where borylation of N₂ occurred without hydride transfer.