A novel tert-butyl hydroperoxide tetrasubstituted cobalt phthalocyanine (CoPc(OC₁₀H₁₄N)₄) was synthesized by the classical phthalonitrile method. Subsequently, the cobalt phthalocyanine (CoPc) was immobilized on the multi-walled carbon nanotubes (MWCNTs) by ultrasonic impregnation method to obtain CoPc(OC₁₀H₁₄N)₄/MWCNTs composites. The obtained composites were characterized by Fourier transform infrared spectra (FT-IR), X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscope (SEM) and diffuse reflectance spectra (DRS) techniques. Using tert-butyl hydroperoxide (TBHP) as an environmentally friendly oxidant, CoPc(OC₁₀H₁₄N)₄/MWCNTs composites can be used as effective catalysts for the epoxidation of styrene. The effects of various variables, such as the mass ratio of CoPc(OC₁₀H₁₄N)₄/MWCNTs, reaction time, temperature, molar ratio of substrate/oxidant and the amount of catalyst on the catalytic capability were evaluated. The conversion of styrene reached 97.15%, and the epoxidation product achieved the selectivity of 84.44% under the optimal reaction conditions.

Hollow transition metal oxides have important applications in the degradation of organic pollutants by a photo-Fenton-like process. Herein, uniform, highly dispersible hollow CuFe₂O₄/C nanospheres (denoted as CFO/C-PNSs) were prepared by a one-pot approach. Scanning electron microscope (SEM) and transmission electron microscope (TEM) images verified that the CFO/C-PNS catalyst mainly presents hollow nanosphere morphology with a diameter of 250 ± 30 nm. Surprisingly, the photodegradation test results revealed that CFO/C-PNSs had an excellent photocatalytic performance in the elimination of various organic contaminants under visible light through the efficient Fenton catalytic process. Due to the unique hollow structure formed by the assembly of ultra-small CFO/C subunits, the catalyst exposes more reaction sites, improving its photocatalytic activity. More importantly, the resulting magnetically separable CFO/C-PNSs exhibited excellent stability. Finally, the possible photocatalytic reaction mechanism of the CFO/C-PNSs was proposed, which enables us to have a clearer understanding of the photo-Fenton mechanism. Through a series of characterization and analysis of degradation behavior of CFO/C-PNS samples over antibiotic degradation and Cr(VI) reduction, •OH radicals generated from H₂O₂ decomposition played an essential role in enhancing the reaction efficiency. The present work offered a convenient method to fabricate hollow transition metal oxides, which provided impetus for further development in environmental and energy applications. Highlights: Novel hollow CuFe₂O₄/C nanospheres were prepared by a facile and cost-effective method. CuFe₂O₄/C exhibited excellent photo-Fenton-like performance for antibiotic degradation. Outstanding photocatalytic performance was attributed to the specific hollow cavity-porous structure. A possible mechanism for H₂O₂ activation over hollow CuFe₂O₄/C nanospheres was detailed and discussed.

Sparse signal recovery arises from many applications. However, deterministic algorithms often require significant time, especially for large-scale systems. Hence, stochastic algorithms like the Stochastic Iterative Hard Thresholding Algorithm (StoIHT) were proposed to address large-scale problems. In this letter, we propose using the stochastic Polyak step size method to design step sizes and provide theoretical convergence analysis. Experimental results suggest that our algorithm demonstrates comparable performance to StoIHT in sparse signal recovery, albeit employing only half of the effective passes.