The stabilizability of heat equations with time-dependent coefficients

In this paper, we study the stabilizability of heat equations with time-dependent coefficients. The instability of the systems is illustrated by special solutions. The boundary feedback stabilization results are established by the backstepping method where the growth order of the kernel function depends on time.     

The “Fingerprint” of a freshwater microalga Scenedesmus sp. LX1: Visualizing the composition of its soluble algal products

The composition of soluble algal products was visualized by a fingerprint analytical method.     

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.     

Two-step Estimation for Longitudinal Data When the Working Correlation Matrix is a Linear Combination of Some Known Matrices

Acta Mathematicae Applicatae Sinica, English Series - The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE...     

A 2-dimensional gradual period photonic heterostructure possessing omnidirectional band gap in visible range made by holography

A 2-dimensional gradual period photonic heterostructure was made with holography by use of non-uniform swelling effect of dichromated gelatin during processing. In this structure, the symmetric point group of triangle lattice was debased to C_2V from C_6V. Theoretical analysis and experimental results show that omnidirectional band gap in visible range can be achieved with this kind of heterostructure made by low refractive index materials.     

Two Bisupporting Keggin-Type POM-Based Hybrids Decorated by [Zn(phen)2]2+ Fragments

Two bisupporting Keggin-type polyoxoanion-based hybrids decorated by [Zn(phen)₂]²⁺ complexes, [Zn(phen)₂]₂(PW ₁₁ ^VI W^VO₄₀) (1) and K[Zn(phen)₂(H₂O)]₂(OH) (SiW₁₂O₄₀)·H₂O (2) (phen = 1,10′-phenanthroline), have been hydrothermally synthesized, and characterized by elemental analysis, IR spectra, UV–Vis spectrum, X-ray photoelectron spectroscopy (XPS), thermogravimetric analysis, and single-crystal X-ray diffraction. The structural analyses reveal that compound 1 consists of a 0D bisupporting Keggin-type heteropoly blue cluster obtained by using reductant glucose, which is grafted by two [Zn(phen)₂]²⁺ fragments; compound 2 presents a 1D infinite chain, which is constructed from bisupporting [SiW₁₂O₄₀]^4? polyoxoanions decorated by [Zn(phen)₂(H₂O)]²⁺ fragments and K⁺ ions. Additionally, the electrochemical behaviors of two compounds were studied.     

Application of supercritical fluid extraction coupled with counter–current chromatography for extraction and online isolation of unstable chemical components from Rosa damascena

Supercritical fluid extraction (SFE) coupled with high‐speed counter‐current chromatography (HSCCC) was successfully used for the extraction and online isolation of the unstable compounds from Rosa damascene in a single extraction and separation operation in two stages. The solvent systems of SFE/HSCCC were optimized with the help of multiexponential function model. At the first stage, the upper phase of the solvent system of n‐butanol–tert‐butyl methyl ether–acetonitrile–0.1% aqueous TFA (1.7:1.0:0.8:4.0, v/v/v/v) was used as both the SFE entrainer and the HSCCC stationary phase, and the target compounds were eluted with the corresponding lower phase to separate the hydrophobic compounds. At the second stage, the upper phase of the solvent system of n‐hexane–ethyl acetate–methanol–water (3.2:1.0:2.8:2.6, v/v/v/v) was used as both the SFE entrainer and the HSCCC stationary phase, followed by elution with the corresponding lower phase to separate the moderate hydrophobic compounds. Six compounds including formononetin, delphinidin, cyaniding, 5,6,4′‐trihydroxy‐7,8‐dimethoxy flavone, 5,3′‐dihydroxy‐7,8‐dimethoxy flavone, and 5‐hydroxy‐6,7,8,3′,4′‐pentamethoxy flavone were successfully separated in one extraction–separation operation within 300 min. The targeted compounds were identified by MS and NMR spectroscopy. This research has opened up great prospects for industrial application of SFE/HSCCC to the extraction and separation of unstable compounds.     

Atom-Economic Route to Densely Functionalized Thiophenes via Base-Catalyzed Rearrangement of 5-Propargyl-2H-thiopyran-4(3H)-ones

An atom-economic route to densely functionalized thiophenes has been developed via base-catalyzed rearrangement of 5-propargyl-2H-thiopyran-4(3H)-ones involving tandem retro-thio Michael addition, propargyl isomerization, and intramolecular thio-addition to allenes.