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1. Computer‐Assisted 3D Structure Elucidation (CASE‐3D): The Structural Value of ² J _CH in Addition to ³ J _CH Coupling Constants

   https://doi.org/10.1002/ange.201915103  

   Koos, Martin R. M.; Navarro‐Vázquez, Armando; Anklin, Clemens; Gil, Roberto R. (January 2020, Angewandte Chemie)

   Abstract We present a method to use long‐range CH coupling constants to derive the correct diastereoisomer from the molecular constitution of small molecules. A set of 79²J_CHand³J_CHvalues collected from a single HSQMBC experiment on a sample of strychnine were used in the CASE‐3D (computer‐assisted 3D structure elucidation) protocol. In addition to the most commonly used³J_CHcoupling constants, the subset of 32²J_CHvalues alone showed an excellent degree of configuration selection. The study is mainly based on comparison of DFT‐calculated^2,3J_CHvalues with experimental ones, critical for the case of²J_CH. But the configuration selection also works well using³J_CHvalues predicted from a semi‐empirical Karplus‐based equation limited to H−C−C−C fragments. The robustness, shown using strychnine as a proof of concept, makes theJ‐based CASE‐3D analysis a viable option for the application in fields such as peptide and carbohydrate research, organic synthesis, natural‐product identification and analysis, as well as medicinal chemistry. 

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2. On the Energy‐Dependent Deep ( L  < 3.5) Penetration of Radiation Belt Electrons

   https://doi.org/10.1029/2022GL101921  

   Mei, Yang; Li, Xinlin; Zhao, Hong; Sarris, Theodore; Khoo, Lengying; Hogan, Benjamin; O’Brien, Declan; Califf, Sam (May 2023, Geophysical Research Letters)

   Abstract Deep penetration of outer radiation belt electrons to lowL(<3.5) has long been recognized as an energy‐dependent phenomenon but with limited understanding. The Van Allen Probes measurements have clearly shown energy‐dependent electron penetration during geomagnetically active times, with lower energy electrons penetrating to lowerL. This study aims to improve our ability to model this phenomenon by quantitatively considering radial transport due to large‐scale azimuthal electric fields (E‐fields) as an energy‐dependent convection term added to a radial diffusion Fokker‐Planck equation. We use a modified Volland‐Stern model to represent the enhanced convection field at lowerLto match the observations of storm time values ofE‐field. We model 10–400 MeV/G electron phase space density with an energy‐dependent radial diffusion coefficient and this convection term and show that the model reproduces the observed deep penetrations well, suggesting that time‐variant azimuthalE‐fields contribute preferentially to the deep penetration of lower‐energy electrons. 

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3. On the extension of the FKG inequality to n functions

   https://doi.org/10.1063/5.0065285  

   Lieb, Elliott H.; Sahi, Siddhartha (April 2022, Journal of Mathematical Physics)

   The 1971 Fortuin–Kasteleyn–Ginibre inequality for two monotone functions on a distributive lattice is well known and has seen many applications in statistical mechanics and other fields of mathematics. In 2008, one of us (Sahi) conjectured an extended version of this inequality for all n > 2 monotone functions on a distributive lattice. Here, we prove the conjecture for two special cases: for monotone functions on the unit square in [Formula: see text] whose upper level sets are k-dimensional rectangles and, more significantly, for arbitrary monotone functions on the unit square in [Formula: see text]. The general case for [Formula: see text], remains open. 

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4. Reciprocity maps with restricted ramification

   Sharifi, Romyar T. (August 2022, Transactions of the American Mathematical Society)

   We compare two maps that arise in study of the cohomology of global fields with ramification restricted to a finite set S of primes. One of these maps, which we call an S-reciprocity map, interpolates the values of cup products in S-ramified cohomology. In the case of p-ramified cohomology of the pth cyclotomic field for an odd prime p, we use this to exhibit an intriguing relationship between particular values of the cup product on cyclotomic p-units. We then consider higher analogues of the S-reciprocity map and relate their cokernels to the graded quotients in augmentation filtrations of Iwasawa modules. 

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5. A new phenological metric for use in pheno‐climatic models: A case study using herbarium specimens of Streptanthus tortuosus

   https://doi.org/10.1002/aps3.11276  

   Love, Natalie_L_Rossington; Park, Isaac_W; Mazer, Susan_J (July 2019, Applications in Plant Sciences)

   PremiseHerbarium specimens have been used to detect climate‐induced shifts in flowering time by using the day of year of collection (DOY) as a proxy for first or peak flowering date. Variation among herbarium sheets in their phenological status, however, undermines the assumption thatDOYaccurately represents any particular phenophase. Ignoring this variation can reduce the explanatory power of pheno‐climatic models (PCMs) designed to predict the effects of climate on flowering date. MethodsHere we present a protocol for the phenological scoring of imaged herbarium specimens using an ImageJ plugin, and we introduce a quantitative metric of a specimen's phenological status, the phenological index (PI), which we use inPCMs to control for phenological variation among specimens ofStreptanthus tortuosus(Brassicaceeae) when testing for the effects of climate onDOY. We demonstrate that includingPIas an independent variable improves model fit. ResultsIncludingPIinPCMs increased the modelR²relative toPCMs that excludedPI; regression coefficients for climatic parameters, however, remained constant. DiscussionOur protocol provides a simple, quantitative phenological metric for any observed plant. IncludingPIinPCMs increasesR²and enables predictions of theDOYof any phenophase under any specified climatic conditions. 

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