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1. Anodic Olefin Coupling Reactions: Elucidating Radical Cation Mechanisms and the Interplay between Cyclization and Second Oxidation Steps

   https://doi.org/10.1002/tcr.202100118  

   Medcalf, Zach; Moeller, Kevin D. (June 2021, The Chemical Record)

   Abstract Anodic olefin coupling reactions generate new bonds and ring skeletons through a net two electron process that reverses the polarity of a known, electron‐rich functional group. While much of the early work on the mechanism of these reactions focused on the initial oxidation and cyclization steps of the process, the second oxidation step also plays a central role in determining the success of the reaction. Evidence supporting this observation is presented, along with evidence that optimization of this second oxidation step is not enough to pull a poor cyclization to the desired product. Successful cyclization reactions require optimization of both processes. 

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2. A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility

   https://doi.org/10.1090/mcom/3843  

   Hou, Dianming; Ju, Lili; Qiao, Zhonghua (November 2023, Mathematics of Computation)

   In this paper, we propose and analyze a linear second-order numerical method for solving the Allen-Cahn equation with a general mobility. The proposed fully-discrete scheme is carefully constructed based on the combination of first and second-order backward differentiation formulas with nonuniform time steps for temporal approximation and the central finite difference for spatial discretization. The discrete maximum bound principle is proved of the proposed scheme by using the kernel recombination technique under certain mild constraints on the time steps and the ratios of adjacent time step sizes. Furthermore, we rigorously derive the discrete $H^1$error estimate and energy stability for the classic constant mobility case and the $L^{\mathrm{\infty <\#comment/>}}$error estimate for the general mobility case. Various numerical experiments are also presented to validate the theoretical results and demonstrate the performance of the proposed method with a time adaptive strategy. 

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3. Asymptotic second moment of Dirichlet L -functions along a thin coset

   https://doi.org/10.1017/fms.2025.44  

   Garcia, Bradford; Young, Matthew P (January 2025, Forum of Mathematics, Sigma)

   Abstract We prove an asymptotic formula for the second moment of central values of DirichletL-functions restricted to a coset. More specifically, consider a coset of the subgroup of characters modulodinside the full group of characters moduloq. Suppose that$$\nu _p(d) \geq \nu _p(q)/2$$for all primespdividingq. In this range, we obtain an asymptotic formula with a power-saving error term; curiously, there is a secondary main term of rough size$$q^{1/2}$$here which is not predicted by the integral moments conjecture of Conrey, Farmer, Keating, Rubinstein, and Snaith. The lower-order main term does not appear in the second moment of the Riemann zeta function, so this feature is not anticipated from the analogous archimedean moment problem. We also obtain an asymptotic result for smallerd, with$$\nu _p(q)/3 \leq \nu _p(d) \leq \nu _p(q)/2$$, with a power-saving error term fordlarger than$$q^{2/5}$$. In this more difficult range, the secondary main term somewhat changes its form and may have size roughlyd, which is only slightly smaller than the diagonal main term. 

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4. Spectral diagonal ensemble Kalman filters

   https://doi.org/10.5194/npg-22-485-2015  

   Kasanický, I.; Mandel, J.; Vejmelka, M. (January 2015, Nonlinear Processes in Geophysics)

   A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the approximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles. 

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5. Isovector and flavor diagonal charges of the nucleon from 2+1+1 flavor QCD

   https://doi.org/10.22323/1.334.0131  

   Gupta, Rajan; Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Yoon, Boram; Jang, Yong-Chull; Lin, Huey-Wen (May 2019, The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018))

   We present high-statistics results for the isovector and flavor diagonal charges of the proton using 11 ensembles of 2+1+1 flavor HISQ fermions. In the isospin symmetric limit, results for the neutron are given by the $$u \leftrightarrow d$$ interchange. A chiral-continuum fit with leading order corrections was made to extract the connected and disconnected contributions in the continuum limit and at $$M_\pi=135$$~MeV. All results are given in the $$\overline{MS}$$ scheme at 2~GeV. The isovector charges, $$g_A^{u-d} = 1.218(25)(30)$$, $$g_S^{u-d} = 1.022(80)(60) $$ and $$g_T^{u-d} = 0.989(32)(10)$$, are used to obtain low-energy constraints on novel scalar and tensor interactions, $$\epsilon_{S}$$ and $$\epsilon_{T}$$, at the TeV scale. The flavor diagonal axial charges are: $$g_A^u \equiv \Delta u \equiv \langle 1 \rangle_{\Delta u^+} = 0.777(25)(30)$$, $$g_A^d \equiv \Delta d \equiv \langle 1 \rangle_{\Delta d^+} = -0.438(18)(30)$$, and $$g_A^s \equiv \Delta s \equiv \langle 1 \rangle_{\Delta s^+} = -0.053(8)$$. Their sum gives the total quark contribution to the proton spin, $$\sum_{q=u,d,s} (\frac{1}{2} \Delta q) = 0.143(31)(36)$$. This result is in good agreement with the recent COMPASS analysis $$0.13 < \frac{1}{2} \Delta \Sigma < 0.18$$. Implications of results for the flavor diagonal tensor charges, $$g_T^u = 0.784(28)(10)$$, $$g_T^d = -0.204(11)(10)$$ and $$g_T^s = -0.0027(16)$$ for constraining the quark electric dipole moments and their contributions to the neutron electric dipole moment are discussed. These flavor diagonal charges also give the strength of the interaction of dark matter with nucleons via axial and tensor mediators. 

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