Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Fused N-Heterocycles with Contiguous Stereogenic Centers Accessed by an Asymmetric Catalytic Cascade Reaction of Tertiary Enamides

We report in this article a cascade reaction strategy for the synthesis of complex N-heterocyclic compounds with contiguous and tetrasubstituted stereogenic carbons. Under the sequential catalysis of a chiral binol–Ti complex and BF₃, cyclopentanone-derived tertiary enamides undergo an enantioselective enamine addition to ketone carbonyls followed by diastereoselective trapping of the resulting acyliminiums by electron-rich aryl moieties to furnish four- and five-membered ring-fused N-heterocyclic products as the sole diastereomers in high yields with up to 99 % ee.     

Synthesis,Crystal Structures,and Catalytic Properties of Dioxomolybdenum(VI) Complexes Derived from 4-Chloro-2-{[4-Diethylamino-2-Hydroxybenzylidene]amino}phenol

Russian Journal of Coordination Chemistry - Two new dioxomolybdenum(VI) complexes, [MoO2L(EtOH)] (I) and [MoO2L(Sal)] (II), where L is the dianionic form of...     

Assembly of ϵ-Keggin Polyoxometalate from Molecular Crystal to Zeolitic Octahedral Metal Oxide

Zeolitic octahedral metal oxides are inorganic crystalline microporous materials with adsorption and redox properties. New ϵ-Keggin nickel molybdate–based zeolitic octahedral metal oxides have been synthesized. ³¹P NMR spectroscopy shows that reduction of Mo^VI-based molybdates forms an ϵ-Keggin polyoxometalate that immediately transfers to the solid phase. Investigation of the formation process indicates that a low Ni concentration, insoluble reducing agent, and long synthesis time are the critical factors for obtaining the zeolite octahedral metal oxides rather than the ϵ-Keggin polyoxometalate molecule. The synthesized zeolitic nickel molybdate with Na⁺ is used as the adsorbent, which effectively separates C₂ hydrocarbon mixtures.     

1,10-Phenanthroline: A versatile ligand to promote copper-catalyzed cascade reactions

Ligand-promoted copper-catalyzed cascade reactions have become a robust tool for the synthesis of cyclic compounds. Although numerous ligands have been developed, this review focuses on the introduction of commercially available 1,10-phenanthroline-promoted copper-catalyzed cascade reactions in recent years. Moreover, based on original articles, this review highlights product yields in the presence and absence of the ligand, and the possible mechanistic role of the ‘copper/1,10-phenanthroline’ catalytic system.     

Light Hydrocarbon Separations Using Porous Organic Framework Materials

Light hydrocarbons (C₁–C₃) are used as basic energy feedstocks and as commodity organic compounds for the production of many industrially necessary chemicals. Due to the nature of the raw materials and production processes, light hydrocarbons are generated as mixtures, but the high-purity single-component products are of vital importance to the petrochemical industry. Consequently, the separation of these C₁–C₃ products is a crucial industrial procedure that comprises a significant share of the total global energy consumption per year. As a complement to traditional separation methods (distillation, partial hydrogenation, etc.), adsorptive separations using porous solids have received widespread attention due to their lower energy costs and higher efficiency. Extensive research has been devoted to the use of porous materials such as zeolites and metal-organic frameworks (MOFs) as solid adsorbents for these key separations, owing to the high porosity, tunable pore structures, and unsaturated metal sites present in these materials. Recently, porous organic framework (POF) materials composed of organic building blocks linked by covalent bonds have also shown excellent properties in light hydrocarbon adsorption and separation, sparking interest in the use of these materials as adsorbents in separation processes. This Minireview summarizes the recent advances in the use of POFs for light hydrocarbon separations, including the separation of mixtures of methane/ethane, methane/propane, ethylene/ethane, acetylene/ethylene, and propylene/propane, while highlighting the relationships between the structural features of these materials and their separation performances. Finally, the difficulties, challenges, and opportunities associated with leveraging POFs for light hydrocarbon separations are discussed to conclude the review.     

Global Regularity of 3D Nonhomogeneous Incompressible Micropolar Fluids

This paper is concerned with the global well-posedness of strong and classical solutions for the 3D nonhomogeneous incompressible micropolar equations with vacuum. We prove that the problem (1.1)–(1.5) has a unique global strong/classical solution \((\rho,u,w)\), provided \(\mu_{1}\) is sufficiently large, or \(\|\rho_{0}\|_{L^{\infty}}\) or \(\|\rho_{0}^{1/2}u_{0}\| ^{2}_{L^{2}}+\|\rho_{0}^{1/2}w_{0}\|^{2}_{L^{2}}\) is small enough.