Comparative study on composition, structure, and adsorption behavior of activated carbons derived from different synthetic waste polymers

The composition, structure, and adsorption behavior of activated carbons (ACs) derived from three different types of waste polymers, i.e., tire rubber (TR), polyvinyl chloride (PVC), and polyethyleneterephtalate (PET), by KOH activation were compared. The AC derived from PET exhibited the largest surface area (2831 m(2)/g) and pore volume (1.68 cm(3)/g) due to the homogenous aromatic composition of PET. The AC derived from PVC exhibited relatively lower surface area (2666 m(2)/g) but more narrowed pore size distribution (2-3 nm). The complex composition and high ash content of tire particles resulted in AC product with significantly lower surface area (398.5 m(2)/g) and heterogeneous pore width. Adsorption data of methylene blue (MB) were fitted well by Langmuir equation, indicating monolayer coverage on the ACs. The high oxygen content of PET-derived AC heavily affected its adsorption to MB and iodine. Due to the remarkable surface area and highly mesoporous structures, ACs based on both PET and PVC exhibited much higher adsorption capacities than that of TR and commercial coal-based AC (F400). This study demonstrates that the properties of ACs are highly dependent on their starting polymers and the potential of converting synthetic polymer waste into effective adsorbents for environmental remediation and cleanup.     

Γ-Convergence of 2D Ginzburg-Landau functionals with vortex concentration along curves

We study the variational convergence of a family of twodimensional Ginzburg-Landau functionals arising in the study of superfluidity or thin-film superconductivity as the Ginzburg-Landau parameter ε tends to 0. In this regime and for large enough applied rotations (for superfluids) or magnetic fields (for superconductors), the minimizers acquire quantized point singularities (vortices). We focus on situations in which an unbounded number of vortices accumulate along a prescribed Jordan curve or a simple arc in the domain. This is known to occur in a circular annulus under uniform rotation, or in a simply connected domain with an appropriately chosen rotational vector field. We prove that if suitably normalized, the energy functionals Γ-converge to a classical energy from potential theory. Applied to global minimizers, our results describe the limiting distribution of vortices along the curve in terms of Green equilibrium measures.     

关于“费尔马最后定理的证明”一文的评注

本文对“费尔马最后定理的证明”一文作出几点评注，主要结论是该证明仅仅是对费尔马最后定理的部分情形的证明，即并没有完全证明费尔马最后定理     

Cremer fixed points and small cycles

Let , , and let denote the sequence of convergents to the regular continued fraction of . Let be a function holomorphic at the origin, with a power series of the form . We assume that for infinitely many we simultaneously have (i) , (ii) the coefficients stay outside two small disks, and (iii) the series is lacunary, with for . We then prove that has infinitely many periodic orbits in every neighborhood of the origin.

     

High frequency characteristics of NiO/(FeCo/NiO)10 multilayers with exchange anisotropy

[NiO/Fe₆₅Co₃₅]₁₀ exchange-coupled multilayer films for high frequency applications are fabricated, and their static magnetic property and microwave permeability are studied systematically. Both exchange bias field and ferromagnetic resonance frequency of the multilayers increase with decreasing Fe₆₅Co₃₅ thickness, which means that the microwave properties such as permeability and FMR frequency can be controlled by changing Fe₆₅Co₃₅ thickness in the exchange-coupled films. Ferromagnetic resonance frequencies beyond 7 GHz of the films are measured and reported for the first time.     

Singular rational curves with points of nearly-maximal weight

In this article we study rational curves with a unique unibranch genus-g singularity, which is of κ-hyperelliptic type in the sense of [27]; we focus on the cases $\kappa =0$ and $\kappa =1$, in which the semigroup associated to the singularity is of (sub)maximal weight. We obtain a partial classification of these curves according to the linear series they support, the scrolls on which they lie, and their gonality.     

Synthesis and Structure of the Dimeric Copper(II) Complex Tetrakis[<Emphasis Type="Italic">N</Emphasis>-thiazol-2-yl-(4-methylphenyl)sulfonamidate]dicopper(II)

Abstract The coordination chemistry of the ligand N-thiazol-2-yl-toluenesulfonamidate towards the copper(II) ion has been investigated using an electrochemical synthesis method. The X-ray structure of this complex was elucidated and is discussed. The compound crystallised in the monoclinic crystal system, P2₁/c space group with a = 17.3888(9), b = 16.3003(9), c = 18.3679(9) ? and β = 114.3640(10)°. Four bidentate sulfathiazolato anions bridge two metal centers in a paddle-wheel fashion, with the nitrogen atoms as donors to give a dimeric species with a Cu···Cu distance of 2.7859(5) ?. Graphical Abstract The coordination chemistry of the ligand N-thiazol-2-yl-toluenesulfonamidate towards the copper(II) ion has been investigated using an electrochemical synthesis method. The X-ray structure of the product has been elucidated and is discussed. Sulfathiazolato anions act as bridging ligands to give a dimeric species with a Cu···Cu distance of 2.7859(5) ?.      

pH‐Dependent Degradation of Layered Black Phosphorus: Essential Role of Hydroxide Ions

The practical application of layered black phosphorus (LBP) is compromised by fast decomposition in the presence of H₂O and/or O₂. The role of H₂O is controversial. Herein, we propose a hydroxide ion (OH^?)‐initiated degradation mechanism for LBP to elucidate the role of H₂O. We found that LBP degraded faster in alkaline solutions than in neutral or acidic solutions with or without O₂. Degradation rates of LBP increased linearly from pH 4 to 10. Density functional theory (DFT) calculations showed that OH^? initiated the decomposition of LBP through breaking the P?P bond and forming a P?O bond. The detection of hypophosphite, generated from OH^? reacting with P atoms, confirmed the hypothesis. Protons acted in a way distinctive from OH^?, by inducing deposition/aggregation or forming a cation–π layer to protect LBP from degradation. This work reveals the degradation mechanism of LBP and thus facilitates the development of effective stabilization technologies.