Effective Power Series Computations

Foundations of Computational Mathematics - Let K be an effective field of characteristic zero. An effective tribe is a subset of $$K [[z_1, z_2, \ldots ]] = K \cup K {[}[z_1]] \cup K [[z_1, z_2]]...     

Synthesis,Crystal Structure,and Selected Properties of [Au(S2CNH2)2]SCN: A Precursor for Gold Macro-Needles Consisting of Gold Nanoparticles Glued by Graphitic Carbon Nitride

A new preparation route is developed for the synthesis of needle-like crystals of [Au(S₂CNH₂)₂]SCN, which avoids disproportionation of the Au^I salt used as a starting material. In the crystal structure, the two crystallographically independent Au^III centers are in a square-planar environment of two S₂CNH₂ ligands. The Hirshfeld surface analysis reveals the presence of noncovalent intermolecular S⋅⋅⋅S interactions, which are essential for the spatial arrangement of the molecules. Density functional theory (DFT) calculations including dispersion and damping corrections result in a unit cell volume very close to the value determined experimentally. Thermal decomposition in an inert atmosphere generates black needles with lengths of up to 500 μm. X-ray powder diffraction and pair distribution function analyses demonstrate that the needles are composed of nanosized crystals with a volume-weighted average domain size of 20(1) nm. According to results of X-ray photoemission experiments, the black needles are covered by a nitrogen-rich carbon nitride with composition near (CN)₂N. ¹³C solid-state NMR investigations indicate that two different carbon species are present, with signals corresponding well to heptazine units as in melon and triazine units as in poly(triazin imide) type compounds. Scanning transmission electron microscopy tomography evidences that the needles are composed of slightly elongated nanoparticles.     

Synthesis,Structure, Photophysical Properties,and Photostability of Benzodipyrenes

This work explores the syntheses, structures, photophysical properties, and photostability of benzodipyrenes (BDPs). BDPs were synthesized through an InCl₃-AgNTf₂-catalyzed, four-fold alkyne benzannulation reaction. The structures of BDP 4 a and its corresponding endoperoxide product were unambiguously confirmed by X-ray crystallography. The BDPs reported here can also be recognized as peri- and cata-benzannulated pentacenes with a non-functionalized central ring. Unlike the previous reported pentacene-based polycyclic aromatic hydrocarbons, the absorbances of the BDPs were blueshifted by ca. 40 nm relative to pentacene, even after extension of π-conjugation. The newly synthesized BDP products exhibit relatively good stability with half-lives as high as 4612 min in THF.     

Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

Janus Gold Nanostars–Mesoporous Silica Nanoparticles for NIR-Light-Triggered Drug Delivery

Janus gold nanostar–mesoporous silica nanoparticle ( AuNSt–MSNP ) nanodevices able to release an entrapped payload upon irradiation with near infrared (NIR) light were prepared and characterized. The AuNSt surface was functionalized with a thiolated photolabile molecule ( 5 ), whereas the mesoporous silica face was loaded with a model drug (doxorubicin) and capped with proton-responsive benzimidazole-β-cyclodextrin supramolecular gatekeepers ( N 1 ). Upon irradiation with NIR-light, the photolabile compound 5 photodissociated, resulting in the formation of succinic acid, which induced the opening of the gatekeeper and cargo delivery. In the overall mechanism, the gold surface acts as a photochemical transducer capable of transforming the NIR-light input into a chemical messenger (succinic acid) that opens the supramolecular nanovalve. The prepared hybrid nanoparticles were non-cytotoxic to HeLa cells, until they were irradiated with a NIR laser, which led to intracellular doxorubicin release and hyperthermia. This induced a remarkable reduction in HeLa cells viability.     

Temperature Effects on the Fracture Dynamics and Elastic Properties of Popgraphene Membranes

Popgraphene (PopG) is a new 2D planar carbon allotrope which is composed of 5–8–5 carbon rings. PopG is intrinsically metallic and possesses excellent thermal and mechanical stability. In this work, we report a detailed study of the thermal effects on the mechanical properties of PopG membranes using fully-atomistic reactive (ReaxFF) molecular dynamics simulations. Our results showed that PopG presents very distinct fracture mechanisms depending on the temperature and direction of the applied stretching. The main fracture dynamics trends are temperature independent and exhibit an abrupt rupture followed by fast crack propagation. The reason for this anisotropy is due to the fact that y-direction stretching leads to a deformation in the shape of the rings that cause the breaking of bonds in the pentagon-octagon and pentagon-pentagon ring connections, which is not observed for the x-direction. PopG is less stiff than graphene membranes, but the Young's modulus value is only 15 % smaller.     

Some trends in the theory of groups with finitely many normalizers

Ricerche di Matematica - This paper provides an account of results and methods from the theory of infinite groups admitting only finitely many normalizers of subgroups with a given property. Some...