Stability of Multiplier Ideal Sheaves

Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.     

Characterization and gas adsorption of a novel three‐dimensional metal–organic framework (MOF) generated from a new polydentate fluorene‐bridged ligand

A polydentate ligand bridged by a fluorene group, namely 9,9‐bis(2‐hydroxyethyl)‐2,7‐bis(pyridin‐4‐yl)fluorene (L), has been prepared under solvothermal conditions in acetonitrile. Crystals of the three‐dimensional metal–organic framework (MOF) poly[[[μ₃‐9,9‐bis(2‐hydroxyethyl)‐2,7‐bis(pyridin‐4‐yl)fluorene‐κ³N:N′:O]bis(methanol‐κO)(μ‐sulfato‐κ²O:O′)nickel(II)] methanol disolvate], {[Ni(SO₄)(C₂₇H₂₄N₂O₂)(CH₃OH)]·2CH₃OH}_n, (I), were obtained by the solvothermal reaction of L and NiSO₄ in methanol. The ligand L forms a two‐dimensional network in the crystallographic bc plane via two groups of O—H…N hydrogen bonds and neighbouring two‐dimensional planes are completely parallel and stack to form a three‐dimensional structure. In (I), the Ni^II ions are linked by sulfate ions through Ni—O bonds to form inorganic chains and these Ni‐containing chains are linked into a three‐dimensional framework via Ni—O and Ni—N bonds involving the polydentate ligand L. With one of the hydroxy groups of L coordinating to the Ni^II atom, the torsion angle of the hydroxyethyl group changes from that of the uncoordinated molecule. In addition, the adsorption properties of (I) with carbon dioxide were investigated.     

Solution combustion synthesis,energy and environment: Best parameters for better materials

Solution combustion synthesis (SCS) is a worldwide used methodology for the preparation of inorganic ceramic and composite materials with controlled properties for a wide number of applications, from catalysis to photocatalysis and electrocatalysis, from heavy metal removal to sensoristics and electronics. The high versatility and efficiency of this technique have led to the introduction of many variants, which allowed important optimization to the prepared materials. Moreover, its ecofriendly nature encouraged further studies about the use of sustainable precursors for the preparation of nanomaterials for energy and environment, according to the concept of circular economy. On the other hand, the large variety of expressions to define SCS and the often-contradictory definitions of the SCS parameters witnessed a scarce consciousness of the potentiality of this methodology. In this review article, the most important findings about SCS and the selection criteria for its main parameters are critically reviewed, in order to give useful guidelines to those scientists who want to use this methodology for preparing materials with improved or new functional properties. This review aims as well (i) to bring more clarity in the SCS terminology (ii) to increase the awareness of the SCS as a convenient tool for the synthesis of materials and (iii) to propose a new perspective in the SCS, with special attention to the use of ecofriendly procedures. Part of the review is also dedicated to precautions and limitations of this powerful methodology.     

Generalized gradient approximation adjusted to transition metals properties: Key roles of exchange and local spin density

Perdew-Burke-Ernzerhof (PBE) and PBE adapted for solids (PBEsol) are exchange-correlation (xc) functionals widely used in density functional theory simulations. Their differences are the exchange, μ, and correlation, β, coefficients, causing PBEsol to lose the Local Spin Density (LSD) response. Here, the μ/β two-dimensional (2D) accuracy landscape is analyzed between PBE and PBEsol xc functional limits for 27 transition metal (TM) bulks, as well as for 81 TM surfaces. Several properties are analyzed, including the shortest interatomic distances, cohesive energies, and bulk moduli for TM bulks, and surface relaxation degree, surface energies, and work functions for TM surfaces. The exploration, comparing the accuracy degree with respect experimental values, reveals that the found xc minimum, called VV, being a PBE variant, represents an improvement of 5% in mean absolute percentage error terms, whereas this improvement reaches ~11% for VVsol, a xc resulting from the restoration of LSD response in PBEsol, and so regarded as its variant.     

Molecular structure,vibrational spectroscopic and chemical reactivity of nematogenic p-n-alkylbenzoic acids: A comparative computational analysis

Molecular structure and vibrational spectroscopic studies of higher homologous series nematogenic p-n-alkylbenzoic acids (nBAC) that have 6 (6BAC) and 7 (7BAC) carbon atoms in the alkyl chain have been investigated using the Density Functional Becke3-Lee-Yang-Parr (B3LYP) level with the basis set 6-31++G (d.p) and Hartree Fock (HF) with the same basis set. The observed vibrational spectra has been resolved and assigned in detail for comparision with both the molecules. These results indicate that DFT and HF values are slightly different at both the levels. A comparision of chemical reactivity such as HOMO (E_H), LUMO (E_L) energies, energy gap (E_g), ionization energy (I), electron affinity (A), electro negativity (χ), chemical hardness (η), electronic chemical potential (μ), electrophilicity index (ω), and softness (S) has been made. It has been observed that the decrement has occurred in the energy band gap value of isolated molecule with increment in alkyl chain length. This provides valuable information regarding enhancing the stability of liquid crystal materials by maintaining the conductivity.     

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The novel heteronuclear complexes [{cis-PtCl (NH₃)(μ-pyrazine)ZnCl (terpy)}](ClO₄)₂ (Pt-L1-Zn) and [{cis-PtCl (NH₃)(μ-4,4′-bipyridyl)ZnCl (terpy)}](ClO₄)₂ (Pt-L2-Zn) (where terpy = 2,2′:6′,2′′-terpyridine, L1 = pyrazine, L2 = 4,4′-bipyridyl) were synthesized and characterized. The pK_a values were determined, and based on them it was established that the π-acceptor ability of the pyrazine bridging ligand is more affective on lower pK_a values. The kinetic measurements of the substitution reactions with biologically relevant ligands, such as guanosine-5′-monophosphate (5′-GMP), inosine-5′-monophosphate (5′-IMP) and glutathione (GSH), were studied at pH 7.4. The reactions were followed under pseudo-first-order conditions by UV–Vis spectrophotometry. The order of reactivity of the investigated biomolecules for the first reaction is 5′-GMP > 5′-IMP > GSH, while for the second is 5′-IMP > GSH. Pt-L1-Zn complex is more reactive than Pt-L2-Zn. The cytotoxic activity of heteronuclear Pt-L1-Zn and Pt-L2-Zn complexes was determined on human colorectal cancer cell line (HCT-116) and human breast cancer cell line (MDA-MB-231). Both complexes significantly reduced cell viability on tested cell lines and exerted significant cytotoxic effects, with better effect on HCT-116 cells than cisplatin, especially after 72 hr (IC₅₀ < 0.52 μM). The Pt-L2-Zn complex showed higher activity against human breast cancer cells (MDA-MB-231) than cisplatin after 72 hr. The higher reactivity toward DNA constituent and significant cytotoxic activity may be attributed to the different geometry, Lewis acidity of different metal centers, as well as, to choice of bridging ligands.     

Environmentally Stable Polymer Gels with Super Deformability and High Recoverability Enhanced by Sub‐5 nm Particles in the Nonvolatile Solvent

It remains challenging to satisfy the combined performances for hydrogels with excellent mechanical behavior, high deformability, and super recoverability under harsh environmental conditions. In this study, we first established a strong polymer network via the crosslinking of polymer chains on the surfaces of sub‐5‐nm calcium hydroxide nanospherulites in ethylene glycol solvent. The organic gel expressed excellent mechanical properties such as a recoverable compressive engineering stress of 249 MPa and an elongation stress of 402 KPa, which was attributed to the uniform nanosized crosslinking structure as characterized by SEM. Moreover, the nonvolatile solvent remained in the gel, meaning that the sample can resist a wide temperature range of ?56 to 100 °C without losing the elastic properties. This novel organic gel could provide promising routes to develop the ideal elastic carriers for wearable devices, smart skin sensors, and damping materials. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 713–721     

Markov shifts and topological entropy of families of homoclinic tangles

The existence of a homoclinic orbit in dynamical systems implies chaotic behaviour with positive entropy. In this work, we determine explicitly the Markov shifts associated to certain Smale horseshoe homoclinic orbits which allow us to compute a lower bound for the topological entropy that such a system can have. It is done associating a heteroclinic orbit which belongs to the same isotopy class and then determining the Markov partition of the dynamical core of an end periodic mapping.     

Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.     

Air-Stable Hexagonal Bipyramidal Dysprosium(III) Single-Ion Magnets with Nearly Perfect D6h Local Symmetry

Eight-coordinated Dy^III centres with D_6h symmetry are expected to act as high-performance single-molecule magnets (SMMs) due to the simultaneous fulfilment of magnetic axiality and a high coordination number (a requisite for air stability). But the experimental realization is challenging due to the requirement of six coordinating atoms in the equatorial plane of the hexagonal bipyramid; this is usually too crowded for the central Dy^III ion. Here a hexaaza macrocyclic Schiff base ligand and finetuned axial alkoxide/phenol-type ligands are used to show that a family of hexagonal bipyramidal Dy^III complexes can be isolated. Among them, three complexes possess nearly perfect D_6h local symmetry. The highest effective magnetic reversal barrier is found at 1338(3) K and an open hysteresis temperature of 6 K at the field sweeping rate of 1.2 mT s⁻¹; this represents a new record for D_6h SMMs.