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1. Born and inverse Born series for scattering problems with Kerr nonlinearities

   https://doi.org/10.1088/1361-6420/ad07a5  

   DeFilippis, Nicholas; Moskow, Shari; Schotland, John C (November 2023, Inverse Problems)

   Abstract We consider the Born and inverse Born series for scalar waves with a cubic nonlinearity of Kerr type. We find a recursive formula for the operators in the Born series and prove their boundedness. This result gives conditions which guarantee convergence of the Born series, and subsequently yields conditions which guarantee convergence of the inverse Born series. We also use fixed point theory to give alternate explicit conditions for convergence of the Born series. We illustrate our results with numerical experiments. 

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2. Born again universe

   https://doi.org/10.1103/PhysRevD.97.044003  

   Graham, Peter W.; Kaplan, David E.; Rajendran, Surjeet (February 2018, Physical Review D)
3. Inverse Born Series

   https://doi.org/10.1515/9783110560855-012  

   Moskow, Shari and (June 2019, The Radon Transform, The First 100 Years and Beyond)

   We present a survey of recent results on the inverse Born series. The convergence and stability of the method are characterized in Banach spaces. Applications to inverse problems in various physical settings are described. 

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4. Born‐digital biodiversity data: Millions and billions

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   Kays, Roland; McShea, William J.; Wikelski, Martin; Zurell, Damaris (May 2020, Diversity and Distributions)
5. Chemical bonding and Born charge in 1T-HfS2

   https://doi.org/10.1038/s41699-021-00226-z  

   Neal, S. N.; Li, S.; Birol, T.; Musfeldt, J. L. (December 2021, npj 2D Materials and Applications)

   null (Ed.)

   Abstract We combine infrared absorption and Raman scattering spectroscopies to explore the properties of the heavy transition metal dichalcogenide 1T-HfS 2 . We employ the LO–TO splitting of the E u vibrational mode along with a reevaluation of mode mass, unit cell volume, and dielectric constant to reveal the Born effective charge. We find $${Z}_{{\rm{B}}}^{* }$$ Z B *  = 5.3 e , in excellent agreement with complementary first-principles calculations. In addition to resolving the controversy over the nature of chemical bonding in this system, we decompose Born charge into polarizability and local charge. We find α  = 5.07 Å 3 and Z *  = 5.2 e , respectively. Polar displacement-induced charge transfer from sulfur p to hafnium d is responsible for the enhanced Born charge compared to the nominal 4+ in hafnium. 1T-HfS 2 is thus an ionic crystal with strong and dynamic covalent effects. Taken together, our work places the vibrational properties of 1T-HfS 2 on a firm foundation and opens the door to understanding the properties of tubes and sheets. 

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