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1. Tenth-order QED lepton anomalous magnetic moment: Eighth-order vertices containing a second-order vacuum polarization

   https://doi.org/10.1103/PhysRevD.85.033007  

   Aoyama, Tatsumi ; Hayakawa, Masashi ; Kinoshita, Toichiro ; Nio, Makiko ( February 2012 , Physical Review D)
2. Tenth-order QED contribution to lepton anomalous magnetic moment: Fourth-order vertices containing sixth-order vacuum-polarization subdiagrams

   https://doi.org/10.1103/PhysRevD.83.053002  

   Aoyama, Tatsumi ; Hayakawa, Masashi ; Kinoshita, Toichiro ; Nio, Makiko ( March 2011 , Physical Review D)
3. Second-order variational analysis in second-order cone programming

   https://doi.org/10.1007/s10107-018-1345-6  

   Hang, Nguyen T. ; Mordukhovich, Boris S. ; Sarabi, M. Ebrahim ( March 2020 , Mathematical Programming)
4. Inverting the variable fractional order in a variable-order space-fractional diffusion equation with variable diffusivity: analysis and simulation

   https://doi.org/10.1515/jiip-2019-0040  

   Zheng, Xiangcheng ; Li, Yiqun ; Cheng, Jin ; Wang, Hong ( April 2021 , Journal of Inverse and Ill-posed Problems)

   null (Ed.)

   Abstract Variable-order space-fractional diffusion equations provide very competitive modeling capabilities of challenging phenomena, including anomalously superdiffusive transport of solutes in heterogeneous porous media, long-range spatial interactions and other applications, as well as eliminating the nonphysical boundary layers of the solutions to their constant-order analogues.In this paper, we prove the uniqueness of determining the variable fractional order of the homogeneous Dirichlet boundary-value problem of the one-sided linear variable-order space-fractional diffusion equation with some observed values of the unknown solutions near the boundary of the spatial domain.We base on the analysis to develop a spectral-Galerkin Levenberg–Marquardt method and a finite difference Levenberg–Marquardt method to numerically invert the variable order.We carry out numerical experiments to investigate the numerical performance of these methods. 

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5. Order Matters: On the Impact of Swapping Order on an Entanglement Path in a Quantum Network

   https://doi.org/10.1109/INFOCOMWKSHPS54753.2022.9798254  

   Chang, Alena ; Xue, Guoliang ( May 2022 , The 1st International Workshop on Network Science for Quantum Communication Networks (NetSciQCom 2022))

   In this paper, we study the properties of path metrics of an entanglement path for a given entanglement swapping order of the path. We show how to efficiently compute the path metrics of an entanglement path for any given swapping order. We show that different entanglement swapping orders for the same path can lead to different expected throughputs. A key finding is that the binary operator corresponding to entanglement swapping along a path is not associative. We further show that the problem of computing an s-t path with maximum expected throughput under any entanglement swapping order does not have the subpath optimality property, which is a key property most path finding algorithms such as Dijkstra’s algorithm rely on. We use extensive simulations to validate our theoretical findings. 

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