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In this article, we considered the pseudo-parabolic equation with Caputo-Fabrizio fractional derivative. This equation has many applications in different fields, such as science, technology, and so on. In this article, we gave the formula of mild solution, which is represented in the form of Fourier series by some operators . In the linear case, we investigated the continuity of the mild solution with respect to the fractional order. For the nonlinear case, we investigated the existence and uniqueness of a global solution. The main proof technique is based on the Banach fixed point theorem combined with some Sobolev embeddings. For more detailed, we obtained two other interesting results: the continuity of mild solution with respect to the derivative order and the convergence of solution as the coefficient k approaches to zero.

Elucidating the impact of heteroatoms in graphitic carbon nitrides (g‐C3N4) is of utmost importance to rationalize materials. Hence, in this study, oxygen‐doped g‐C3N4 containing trace amounts of halogen in the structures for piezo‐photosynthesis of hydrogen peroxides (H2O2) is fabricated. The findings reveal that oxygen atoms may be inserted into g‐C3N4 in‐plane structures, while halogen atoms tend to become intercalated between g‐C3N4 layers. Furthermore, the presence of ammonium molten salts (NH4X) during the synthesis alters the concentration of mono and cluster vacancies of carbon and nitrogen in the materials, certifying by positron annihilation spectroscopy (PAS). These defective contributions will be meaningfully accelerate catalytic performance by providing trapping states. Additionally, the decomposition of generated H2O2 can produce highly oxidative hydroxyl radicals, inducing degradations on the catalyst's structures and unexpectedly decreasing catalytic outcomes. From the mechanistic view, different reduction and oxidation channels will be play a pivotal role in generating H2O2. Moreover, the influence of ultrasound and light is also carefully investigated in the work to gain more insights into how the catalysts are triggered to improve catalytic performance. Thus, this study highlights the importance of carefully characterizing structures of g‐C3N4 to precisely understand the catalytic properties, benefiting catalytic design and development. [ABSTRACT FROM AUTHOR]

In this paper, we are interested to study a mild solution of the Love equation. This type of equation has many applications in physics. Under various assumptions of the Cauchy data, we obtain the regularity of the mild solution. We also obtain the continuity of the mild solution concerning the parameter. We show that the mild solution of the Love equation converges to the mild solution of the wave equation. Our work may be the first paper on the mild solution of the Love equation. [ABSTRACT FROM AUTHOR]

The combination of two dielectric-magnetic components in the same composite has been shown to significantly improve the effectiveness of electromagnetic (EM) shielding and microwave absorption (MWA) because they have both a combination of high dielectric and magnetic losses and good impedance matching. The novel Bi1/2(Na0.8K0.2)1/2TiO3/Fe3O4 (BNKT/Fe3O4) composite has been successfully synthesized by a two-step method with wide effective absorption bandwidth (EAB = 16 GHz) in the high-frequency (2-18 GHz). It was evident that the MWA efficiency of the BNKT/Fe3O4 composite has been significantly improved compared with pure Bi1/2(Na0.8K0.2)1/2TiO3 or Fe3O4 materials. In addition, the BNKT/Fe3O4 composite could achieve reflection loss (RL = -39.41 dB, ~99.99% at 10.16 GHz) with a sample thickness optimal (d = 4.7 mm). This work shows that the novel BNKT/Fe3O4 composite has excellent MWA properties, all contributing to a potential candidate in the electromagnetic wave absorption and shielding fields. [ABSTRACT FROM AUTHOR]

Sustainability in catalysis is increasingly becoming the primary target in academic and industrial studies. Regarding the material perspective, designing heterojunction nanocatalysts to produce small molecules, such as hydrogen peroxide (H2O2), has been an attractive research theme in recent decades. Nonetheless, most reported materials suffer from a complicated synthetic process with various steps and using unbenign solvents, hindering practical applications on an industrial scale. This study proposed a facile one-step way to fabricate heterostructured CdS/g-C3N4 nanocatalysts to produce H2O2 from water and oxygen under light and ultrasound irradiation. The results showed that the formation of H2O2 mainly relies on oxygen radical species. Oxygen is initially converted into superoxide via excited electrons from CdS, followed by the formation of singlet oxygen from the oxidation process in g-C3N4 sites. Interestingly, the formation of H2O2 in an inert atmosphere is associated with the in situ evolution of oxygen from water oxidation due to the suitable electronic band position of g-C3N4 to drive multioxidation reactions. Charge transfer characterizations illustrate the S-scheme mechanism in the catalytic process, giving a better understanding of the charge transportation phenomenon, thus providing a critical pathway in designing and developing heterojunction materials for catalysis with easier catalyst preparation and operation processes. [ABSTRACT FROM AUTHOR]

Hydrogen peroxide (H2O2) can be considered as one of the world's indispensable chemicals. However, the synthetic process can prompt several severe environmental and human health issues. However, solar H2O2 production may provide opportunities to mitigate such issues. Graphitic carbon nitride (g‐C3N4) has emerged as one promising material for photocatalytic applications due to its unique properties. Although tremendous efforts in engineering g‐C3N4 have been proposed to improve catalytic results, the materials obtained still have some issues. Additionally, the mechanisms behind the production of H2O2 by using such materials are not yet fully understood. Herein, we conducted a literature survey reviewing the production of H2O2 using g‐C3N4‐based materials. The essential aspects of and current challenges in photocatalytic H2O2 generation are discussed, which may provide insight for researchers to overcome barriers and develop sustainable methods for H2O2 production. [ABSTRACT FROM AUTHOR]

Hydrogen peroxide (H2O2) can be considered as one of the world's indispensable chemicals. However, the synthetic process can prompt several severe environmental and human health issues. However, solar H2O2 production may provide opportunities to mitigate such issues. Graphitic carbon nitride (g‐C3N4) has emerged as one promising material for photocatalytic applications due to its unique properties. Although tremendous efforts in engineering g‐C3N4 have been proposed to improve catalytic results, the materials obtained still have some issues. Additionally, the mechanisms behind the production of H2O2 by using such materials are not yet fully understood. Herein, we conducted a literature survey reviewing the production of H2O2 using g‐C3N4‐based materials. The essential aspects of and current challenges in photocatalytic H2O2 generation are discussed, which may provide insight for researchers to overcome barriers and develop sustainable methods for H2O2 production. [ABSTRACT FROM AUTHOR]