Manganese oxides(MNO_(x)),as low-toxicity and high-abundance catalysts,have been demonstrated to hold great promise for application in advanced oxidation processes(AOPs).However,further application of this material is...Manganese oxides(MNO_(x)),as low-toxicity and high-abundance catalysts,have been demonstrated to hold great promise for application in advanced oxidation processes(AOPs).However,further application of this material is restricted due to its unsatisfactory oxidant activation efficiency.Fortunately,recently remarkable research on deep activation mechanisms and modification of MNO_(x)have been undertaken to improve its reactivity.Herein,modification enhancement mechanisms of MNO_(x)to efficiently degrade various organic contaminants were discussed and highlighted,including metal doping,coupling with other metal oxides,composite with carbonaceous material,and compounding with other support.The activation mechanisms of different MNO_(x)and derivative-modified material(such as doped MNO_(x),metal oxide-MNO_(x)hybrids,and MNO_(x)-carbonaceous material hybrids)were summarized in great details,which was specifically categorized into both radical and non-radical pathways.The effects of pH,inorganic ions,and natural organic matter on degradation reactions are also discussed.Finally,future research directions and perspectives are presented to provide a clear interpretation on the MNO_(x)initiated AOPs.展开更多
In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hi...In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative.First,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis techniques.Second,the optimal control of the proposed problem is presented by using Balder’s theorem.Finally,an example is demonstrated to illustrate the obtained theoretical results.展开更多
We present a generalization of the linear one-dimensional diffusion equation by combining the fractional derivatives and the internal degrees of freedom. The solutions are constructed from those of the scalar fraction...We present a generalization of the linear one-dimensional diffusion equation by combining the fractional derivatives and the internal degrees of freedom. The solutions are constructed from those of the scalar fractional diffusion equation. We analyze the interpolation between the standard diffusion and wave equations defined by the fractional derivatives. Our main result is that we can define a diffusion process depending on the internal degrees of freedom associated to the system.展开更多
基金the National Natural Science Foundation of China(Nos.52170088 and 52070133)for financial support。
文摘Manganese oxides(MNO_(x)),as low-toxicity and high-abundance catalysts,have been demonstrated to hold great promise for application in advanced oxidation processes(AOPs).However,further application of this material is restricted due to its unsatisfactory oxidant activation efficiency.Fortunately,recently remarkable research on deep activation mechanisms and modification of MNO_(x)have been undertaken to improve its reactivity.Herein,modification enhancement mechanisms of MNO_(x)to efficiently degrade various organic contaminants were discussed and highlighted,including metal doping,coupling with other metal oxides,composite with carbonaceous material,and compounding with other support.The activation mechanisms of different MNO_(x)and derivative-modified material(such as doped MNO_(x),metal oxide-MNO_(x)hybrids,and MNO_(x)-carbonaceous material hybrids)were summarized in great details,which was specifically categorized into both radical and non-radical pathways.The effects of pH,inorganic ions,and natural organic matter on degradation reactions are also discussed.Finally,future research directions and perspectives are presented to provide a clear interpretation on the MNO_(x)initiated AOPs.
文摘In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative.First,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis techniques.Second,the optimal control of the proposed problem is presented by using Balder’s theorem.Finally,an example is demonstrated to illustrate the obtained theoretical results.
基金This work has been partially supported by the Project "The Sciences of Complexity (ZiF,Bielefeld Universitat),the Comision Interministerial de Ciecia y Tecnologia of Spain(grant PB98-0850) and the European Project COSIC of SENS(HPRN-CT-2000-00158)
文摘We present a generalization of the linear one-dimensional diffusion equation by combining the fractional derivatives and the internal degrees of freedom. The solutions are constructed from those of the scalar fractional diffusion equation. We analyze the interpolation between the standard diffusion and wave equations defined by the fractional derivatives. Our main result is that we can define a diffusion process depending on the internal degrees of freedom associated to the system.
