Periods of generalized Fermat curves

Let $k,n\ge 2$ be integers. A generalized Fermat curve of type $(k,n)$ is a compact Riemann surface S that admits a subgroup of conformal automorphisms $H\le \text{Aut}(S)$ isomorphic to ${\mathbb{Z}}_k^n$, such that the quotient surface $S/H$ is biholomorphic to the Riemann sphere $\stackrel{?}{\mathbb{C}}$ and has $n+1$ branch points, each one of order k. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from algebraic topology and integration theory on Riemann surfaces, we find a set of generators for the first homology group of a generalized Fermat curve. Finally, with this information, we find a set of generators for the period lattice of the associated Jacobian variety.     

Hilbert’s Nullstellensatz for analytic trigonometric polynomials

This paper proves such a new Hilbert’s Nullstellensatz for analytic trigonometric polynomials that if ${\left\{f_j\right\}}_{j=1}^{n\ge 2}$ are analytic trigonometric polynomials without common zero in the finite complex plane $?$ then there are analytic trigonometric polynomials ${\left\{g_j\right\}}_{j=1}^{n\ge 2}$ obeying ${\sum }_{j=1}^{n\ge 2}{f}_j{g}_j=1$ in $?$, thereby not only strengthening Helmer’s Principal Ideal Theorem for entire functions, but also finding an intrinsic path from Hilbert’s Nullstellensatz for analytic polynomials to Pythagoras’ Identity on $?$.     

Analyticity of resonances and eigenvalues and spectral properties of the massless Spin–Boson model

We extend the method of Pizzo multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of dilated Hamiltonians and norm-bounds for the corresponding resolvent operators, in neighborhoods of resonances and eigenvalues. We apply our method to the massless Spin–Boson model assuming a slight infrared regularization. We prove that the resonance and the ground-state eigenvalue (and their eigenprojections) are analytic with respect to the dilation parameter and the coupling constant. Moreover, we prove that the spectrum of the dilated Spin–Boson Hamiltonian in the neighborhood of the resonance and the ground-state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground-state eigenvalue, respectively. Additionally, we provide norm-estimates for the resolvent of the dilated Spin–Boson Hamiltonian near the resonance and the ground-state eigenvalue. The topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past. However, to the best of our knowledge, this is the first time that it is addressed from the perspective of Pizzo multiscale analysis. Once the multiscale analysis is set up our method gives easy access to analyticity: Essentially, it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic. The type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime. The latter will be demonstrated in a forthcoming publication. The introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent (and different) from the method we apply to construct resonances.     

Macroscopic and microscopic electrical properties of a ferrofluid in a low frequency field

Using the complex dielectric permittivity measurements, in the frequency range 20 Hz – 2 MHz and at temperatures between (25–70) ^∘C, the polarizability (α), the electric modulus (M) and the electrical conductivity (σ), of a ferrofluid sample, were determined. The results enabled the computation of the thermal activation energy of electrical conduction, the obtained value being approximately equal, at 0.15 eV. By eliminating the losses arising from electrical conduction, we highlighted the existence of a Schwarz type dielectric relaxation, in the sample, at the frequency above 5 kHz. These results allowed, for the first time, the evaluation of the mechanical mobility, u, of the ions on the particle surface, resulting in a value of, $u=3.4\cdot {10}^8$ m/s N. Knowledge of macroscopic and microscopic electrical properties is useful in explaining the dielectric polarization mechanisms and relaxation processes of ferrofluids, and also in the use of ferrofluids in technological and biomedical applications.     

Local process-dependent structural and mechanical properties of extrusion blow molded high-density polyethylene hollow parts

Although applied for several decades, production of hollow plastic parts by extrusion blow molding (EBM) is still over-dimensioned. To overcome this issue, a thorough investigation of the process-structure-property relationship is required. In this study, the local process-structure-property relationship for high-density polyethylene EBM containers is analyzed with differential scanning calorimetry and dynamic mechanic analysis microindentation. Local process-dependent crystallinity and complex modulus data at various processing conditions are supplemented with wide-angle X-ray diffraction and transmission electron microscopy (TEM). The crystallinities and the complex moduli clearly show lower values close to the mold side than at the inner side and the middle of the cross-section, which reflects the temperature gradient during processing. Additionally, the orientation of the polymer chain (c-axis) reveals a low level of biaxiality with a slight tendency towards transverse direction. The biaxiality increases for low mold temperature and high draw ratio. Finally, biaxiality is confirmed with TEM, which reveals no preferred lamellar orientation.     

Generation and Stabilization of a Dinickel Catalyst in a Metal-Organic Framework for Selective Hydrogenation Reactions

Although many monometallic active sites have been installed in metal–organic frameworks (MOFs) for catalytic reactions, there are no effective strategies to generate bimetallic catalysts in MOFs. Here we report the synthesis of a robust, efficient, and reusable MOF catalyst, MOF-NiH, by adaptively generating and stabilizing dinickel active sites using the bipyridine groups in MOF-253 with the formula of Al(OH)(2,2′-bipyridine-5,5′-dicarboxylate) for Z-selective semihydrogenation of alkynes and selective hydrogenation of C=C bonds in α,β-unsaturated aldehydes and ketones. Spectroscopic studies established the dinickel complex (bpy⋅⁻)Ni^II(μ₂-H)₂Ni^II(bpy⋅⁻) as the active catalyst. MOF-NiH efficiently catalyzed selective hydrogenation reactions with turnover numbers of up to 192 and could be used in five cycles of hydrogenation reactions without catalyst leaching or significant decrease of catalytic activities. The present work uncovers a synthetic strategy toward solution-inaccessible Earth-abundant bimetallic MOF catalysts for sustainable catalysis.     

Tracking an FeV(O) Intermediate for Water Oxidation in Water

High-valent iron-oxo species are appealing for conducting O−O bond formation for water oxidation reactions. However, their high reactivity poses a great challenge to the dissection of their chemical transformations. Herein, we introduce an electron-rich and oxidation-resistant ligand, 2-[(2,2′-bipyridin)-6-yl]propan-2-ol to stabilize such fleeting intermediates. Advanced spectroscopies and electrochemical studies demonstrate a high-valent Fe^V(O) species formation in water. Combining kinetic and oxygen isotope labelling experiments and organic reactions indicates that the Fe^V(O) species is responsible for O−O bond formation via water nucleophilic attack under the real catalytic water oxidation conditions.     

Engineered Bacteria Labeled with Iridium(III) Photosensitizers for Enhanced Photodynamic Immunotherapy of Solid Tumors

Despite metal-based photosensitizers showing great potential in photodynamic therapy for tumor treatment, the application of the photosensitizers is intrinsically limited by their poor cancer-targeting properties. Herein, we reported a metal-based photosensitizer-bacteria hybrid, Ir-HEcN , via covalent labeling of an iridium(III) photosensitizer to the surface of genetically engineered bacteria. Due to its intrinsic self-propelled motility and hypoxia tropism, Ir-HEcN selectively targets and penetrates deeply into tumor tissues. Importantly, Ir-HEcN is capable of inducing pyroptosis and immunogenic cell death of tumor cells under irradiation, thereby remarkably evoking anti-tumor innate and adaptive immune responses in vivo and leading to the regression of solid tumors via combinational photodynamic therapy and immunotherapy. To the best of our knowledge, Ir-HEcN is the first metal complex decorated bacteria for enhanced photodynamic immunotherapy.     

A Dicyanomethyl Radical Conjugated with a Pyridylamino Group: Combining Radical-based Dynamic Covalent Chemistry and Coordination Chemistry

In this work, we aimed to develop a dicyanomethyl radical that undergoes both reversible C−C bond formation/dissociation and metal-ligand coordination reactions to combine dynamic covalent chemistry (DCC) based on organic radicals with coordination chemistry. We have previously reported a dicyanomethyl radical conjugated with a triphenylamine ( 1 ⋅) that exhibits a monomer/dimer equilibrium between the σ-bonded dimer ( 1₂ ). We designed and synthesized a novel dicyanomethyl radical with a pyridyl group as a coordination point ( 2 ⋅) by replacing the phenyl group of 1 ⋅ with a 3-pyridyl group. We showed that 2 ⋅ is also in an equilibrium with the σ-bonded dimer ( 2₂ ) in solution and has suitable thermodynamic parameters for application in DCC. 2₂ coordinates to PdCl₂ in a 2 : 2 ratio to selectively form a metallamacrocycle ( 2₂ )₂(PdCl₂)₂, and its structure was clarified by single crystal X-ray analysis. Variable-temperature NMR, ESR, and electronic absorption measurements revealed that ( 2₂ )₂(PdCl₂)₂ also undergoes the reversible C−C bond formation/dissociation reaction. Ligand-exchange experiment showed that 2₂ was liberated from ( 2₂ )₂(PdCl₂)₂ by the addition of another ligand with a higher affinity for Pd^II. This work demonstrated that DCC based on dicyanomethyl radicals works orthogonally to metal-ligand coordination reactions.