Iron(Ⅱ) phthalocyanines(FePc) supported on functionalized nanostructured carbon materials have been studied as electrocatalysts for the oxygen reduction reaction(ORR) in an alkaline medium. Herein, two types of carbo...Iron(Ⅱ) phthalocyanines(FePc) supported on functionalized nanostructured carbon materials have been studied as electrocatalysts for the oxygen reduction reaction(ORR) in an alkaline medium. Herein, two types of carbon nanotubes(CNTs) have been explored as support, Single-Walled Carbon Nanotubes and Herringbone Carbon Nanotubes(SWCNTs and h CNTs, respectively), both electrochemically modified with ortho-aminophenylphosphonic acid(2APPA), which provides phosphate axial coordinating ligands for the immobilization of FePc molecules. All the catalysts were prepared via a facile incipient wetness impregnation method. Comprehensive experimental analysis together with density functional theory(DFT) calculations has demonstrated both the importance of the five-coordinated Fe macrocycles that favor the interaction between the FePc and the carbon support, as well as the effect of the CNT structure in the ORR. FePc axial coordination provides a better dispersion, leading to higher stability and a favorable electron redistribution that also tunes the ORR performance by lowering the stability of the reaction intermediates. Interestingly, such improvement occurs with a very low content of metal(~1 wt% Fe),which is especially remarkable when h CNT support is employed. This work provides a novel strategy for the development of Fe-containing complexes as precious metal-free catalysts towards the ORR.展开更多
In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly the sums of the ...In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly the sums of the first k-Lucas numbers, and then for the even and the odd k-Lucas numbers. Later, we find the generating function of these numbers. Below we prove these same formulas for the alternated k-Lucas numbers. Then, we prove a relation between the k–Fibonacci numbers of indexes of the form 2rn and the k–Lucas numbers of indexes multiple of 4. Finally, we find a formula for the sum of the square of the k-Fibonacci even numbers by mean of the k–Lucas numbers.展开更多
Satellite constellations allow distributed tasks among multiple spacecraft,reducing mission time and enhancing objectives.Interest in constellations has increased due to reduced costs in satellite production and launc...Satellite constellations allow distributed tasks among multiple spacecraft,reducing mission time and enhancing objectives.Interest in constellations has increased due to reduced costs in satellite production and launch.A key step in constellation planning is its design,which determines the orbital distribution of the satellites.In this work,we apply the 2D Necklace Flower Constellations methodology to explore possible architectures for future missions around Titan.As a result of strong perturbations in regions near natural satellites and environmental restrictions on Titan,proposals for maintaining constellations to enhance data collection and prevent mutual collisions between the satellites involved are an important aspect to consider.Therefore,the proposed designs incorporate frozen orbits and repetition ground tracks in an initial dynamical model that includes the efects of the J2 and J3 perturbations.Analyses using a simplifed dynamic model,with a simple mean and a complete dynamic model,employing the IAS15 integrator from the Rebound package,show that,for the assumed perturbations,the proposed constellation confgurations maintain long-term ground-track coverage of the surface of Titan.The performance evaluation indicates that the methodology provides robust constellation geometries,supporting orbit control and mission feasibility for Titan exploration.展开更多
Local Fourier analysis(LFA)is a useful tool in predicting the convergence factors of geometric multigrid methods(GMG).As is well known,on rectangular domains with periodic boundary conditions this analysis gives the e...Local Fourier analysis(LFA)is a useful tool in predicting the convergence factors of geometric multigrid methods(GMG).As is well known,on rectangular domains with periodic boundary conditions this analysis gives the exact convergence factors of such met hods.When other boundary conditions are considered,however,this analysis was judged as been heuristic,with limited capabilities in predicting multigrid convergence rates.In this work,using the Fourier method,we extend these results by proving that such analysis yields the exact convergence factors for a wider class of problems,some of which can not be handled by the traditional rigorous Fourier analysis.展开更多
基金the Ministry of Science,Innovation and Universities of Spain for the FPU grant(FPU18/05127)MCI/AEI and FEDER,UE(PID2019-105923RB-I00,RTI2018-095291-B-I00 projects)for the financial support。
文摘Iron(Ⅱ) phthalocyanines(FePc) supported on functionalized nanostructured carbon materials have been studied as electrocatalysts for the oxygen reduction reaction(ORR) in an alkaline medium. Herein, two types of carbon nanotubes(CNTs) have been explored as support, Single-Walled Carbon Nanotubes and Herringbone Carbon Nanotubes(SWCNTs and h CNTs, respectively), both electrochemically modified with ortho-aminophenylphosphonic acid(2APPA), which provides phosphate axial coordinating ligands for the immobilization of FePc molecules. All the catalysts were prepared via a facile incipient wetness impregnation method. Comprehensive experimental analysis together with density functional theory(DFT) calculations has demonstrated both the importance of the five-coordinated Fe macrocycles that favor the interaction between the FePc and the carbon support, as well as the effect of the CNT structure in the ORR. FePc axial coordination provides a better dispersion, leading to higher stability and a favorable electron redistribution that also tunes the ORR performance by lowering the stability of the reaction intermediates. Interestingly, such improvement occurs with a very low content of metal(~1 wt% Fe),which is especially remarkable when h CNT support is employed. This work provides a novel strategy for the development of Fe-containing complexes as precious metal-free catalysts towards the ORR.
文摘In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly the sums of the first k-Lucas numbers, and then for the even and the odd k-Lucas numbers. Later, we find the generating function of these numbers. Below we prove these same formulas for the alternated k-Lucas numbers. Then, we prove a relation between the k–Fibonacci numbers of indexes of the form 2rn and the k–Lucas numbers of indexes multiple of 4. Finally, we find a formula for the sum of the square of the k-Fibonacci even numbers by mean of the k–Lucas numbers.
基金supported by Program CAPES-PDSE,process number 88881.982568/2024-01São Paulo Research Foundation(FAPESP)[grant number 2022/11783-5]+1 种基金supported by Grant PID2024-156002NB-I00 funded by MICIU/AEI/10.13039/501100011033/FEDER,UEthe Aragón Government and European Social Fund(E24_23R).
文摘Satellite constellations allow distributed tasks among multiple spacecraft,reducing mission time and enhancing objectives.Interest in constellations has increased due to reduced costs in satellite production and launch.A key step in constellation planning is its design,which determines the orbital distribution of the satellites.In this work,we apply the 2D Necklace Flower Constellations methodology to explore possible architectures for future missions around Titan.As a result of strong perturbations in regions near natural satellites and environmental restrictions on Titan,proposals for maintaining constellations to enhance data collection and prevent mutual collisions between the satellites involved are an important aspect to consider.Therefore,the proposed designs incorporate frozen orbits and repetition ground tracks in an initial dynamical model that includes the efects of the J2 and J3 perturbations.Analyses using a simplifed dynamic model,with a simple mean and a complete dynamic model,employing the IAS15 integrator from the Rebound package,show that,for the assumed perturbations,the proposed constellation confgurations maintain long-term ground-track coverage of the surface of Titan.The performance evaluation indicates that the methodology provides robust constellation geometries,supporting orbit control and mission feasibility for Titan exploration.
文摘Local Fourier analysis(LFA)is a useful tool in predicting the convergence factors of geometric multigrid methods(GMG).As is well known,on rectangular domains with periodic boundary conditions this analysis gives the exact convergence factors of such met hods.When other boundary conditions are considered,however,this analysis was judged as been heuristic,with limited capabilities in predicting multigrid convergence rates.In this work,using the Fourier method,we extend these results by proving that such analysis yields the exact convergence factors for a wider class of problems,some of which can not be handled by the traditional rigorous Fourier analysis.
