Epoché as the Breakthrough of the Natural Attitude

The following contribution aims to interpret the methodical device of Husserl’s epochéin light of the concept of breakthrough.Since the epochéis a theoretical device directed towards the suspension of the natural attitude,I will first attempt to define the concept of natural attitude.Subsequently,I will seek to understand the rich meaning of the concept of epoché.Finally,I will explore how this element is related to the concept of breakthrough.In other words,I will endeavour to clarify how the epochédetermines a breakthrough of the natural attitude,which is not to be understood as“annihilation”or“destruction”but as a traversal.

Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions

We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method.Based on the off-diagonal Bethe ansatz solutions,we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries.By taking a quasi-classical limit,we give explicit closed-form expression of the Bethe states of the Gaudin model.From the numerical simulations for the small-size system,it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1)symmetry.Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant.This fact enables us to recover the Bethe states of the Gaudin model with the U(1)symmetry.These results provide a basis for the further study of the thermodynamic limit,correlation functions,and quantum dynamics of the Gaudin model.

Arranging Electronic Localization of PtCu Nanoalloys to Stimulate Improved Oxygen Electroreduction for High-Performance Fuel Cells

Developing exceptionally durable and efficient oxygen reduction reaction(ORR)catalysts is of paramount importance to the widespread commercialization of proton exchange membrane fuel cells(PEMFCs)but is still challenging.Herein,PtCu nanoalloys rooted on nitrogen-doped carbon nanosheets(PtCuNC-700)with fully exposed PtCu nanoalloys and strong metal–support interaction were developed.Benefiting from its structural and compositional merits,PtCuNC-700 showcases superior ORR activity and stability with a specific activity of 1.05mA cm^(−2)and mass activity of 0.45 A mgPt^(−1),4.2-fold and 3.7-fold higher than Pt/C(0.25 mA cm^(−2)and 0.12 A mgPt^(−1)),respectively.Moreover,PtCuNC-700 exhibits first-class performance in H2/air PEMFC assessment and delivers a peak power density of 929.7 mW cm^(−2)and excellent cycling stability up to 30,000 cycles.Theoretical calculations disclose that the synergistic effect of alloying Pt with Cu combined with the strong interaction between PtCu nanoalloys and nitrogen-doped carbon nanosheets can effectively modify the local electron configuration and density of states of Pt sites approaching the Fermi level.Hence,the PtCu-alloy catalysts realized here diminish the energy barrier for ORR and accelerate their reaction kinetics.This work provides a reliable and effective approach to boost the activity and stability of Pt alloy-based ORR electrocatalysts in PEMFCs.

Decrypting the Influence of Axial Coordination on the Electronic Microenvironment of Co-N_(5)Site for Enhanced Electrocatalytic Reaction

Metal porphyrins are star molecules that possess welldefined coordination metal centers for versatile catalytic reactions.However,most previous work has focused on the correlations between in-plane symmetric configuration of metal-N_(4)sites and their catalytic performance.Addressing the catalytic contribution of additional axial coordination to such symmetric configuration remains a challenge.Theoretical calculations revealed that axially anchoring an extra pyridine on the tetra-coordinated cobalt porphyrin(Co-N4)to construct penta-coordinated cobalt porphyrin(Co-N_(5))renders cobalt a higher electron density,thereby favoring the rate-determining O_(2)adsorption/activation and reducing the oxygen electroreduction barrier.Therefore,a well-defined Co-N_(5)site is rationally introduced into the azo-linked polymer framework for a fundamental structure-catalytic performance correlation study.As-prepared Co-N_(5)catalyst exhibits a 26 mV positive shift in half-wave potential compared with the pyridine-free Co-N_(4)counterpart,discloses a markedly higher power density(141.4 mW cm^(−2)),and possesses better long-term durability(over 160 h cycles)in a Zn-air battery.Moreover,such a Co-N_(5)catalyst also showcases potential applications for CO_(2)reduction with high CO_(2)-to-CO conversion faradic efficiency and better selectivity than the Co-N_(4)counterpart because coordination of the fifth pyridine evokes electronic localization that suppresses a competitive side reaction.This work proves the positive electrocatalytic contribution of axial penta-coordination on well-defined metalporphyrin-based catalysts and offers atomic understanding of the structure-performance correlation on single atom catalysts for future catalyst design.

Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies

In this paper we present how nonlinear stochastic Itˆo differential equations arising in the modelling of perturbed rigid bodies can be solved numerically in such a way that the solution evolves on the correct manifold.To this end,we formulate an approach based on Runge-Kutta–Munthe-Kaas(RKMK)schemes for ordinary differ-ential equations on manifolds.Moreover,we provide a proof of the mean-square convergence of this stochastic version of the RKMK schemes applied to the rigid body problem and illustrate the effectiveness of our proposed schemes by demonstrating the structure preservation of the stochastic RKMK schemes in contrast to the stochastic Runge-Kutta methods.