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1. Shrinking targets for the geodesic flow on geometrically finite hyperbolic manifolds

   https://doi.org/10.3934/jmd.2021014  

   Kelmer, Dubi; Oh, Hee (January 2021, Journal of Modern Dynamics)

   Let \begin{document}$$ \mathscr{M} $$\end{document} be a geometrically finite hyperbolic manifold. We present a very general theorem on the shrinking target problem for the geodesic flow, using its exponential mixing. This includes a strengthening of Sullivan's logarithm law for the excursion rate of the geodesic flow. More generally, we prove logarithm laws for the first hitting time for shrinking cusp neighborhoods, shrinking tubular neighborhoods of a closed geodesic, and shrinking metric balls, as well as give quantitative estimates for the time a generic geodesic spends in such shrinking targets. 

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2. Biocompatible Direct Deposition of Functionalized Nanoparticles Using Shrinking Surface Plasmonic Bubble

   https://doi.org/10.1002/admi.202000597  

   Moon, Seunghyun; Zhang, Qiushi; Huang, Dezhao; Senapati, Satyajyoti; Chang, Hsueh‐Chia; Lee, Eungkyu; Luo, Tengfei (June 2020, Advanced Materials Interfaces)

   Abstract Functionalized nanoparticles (NPs) are the foundation of diverse applications. Especially, in many biosensing applications, concentrating suspended NPs onto a surface without deteriorating their biofunction is usually an inevitable step to improve detection limit, which remains to be a great challenge. In this work, biocompatible deposition of functionalized NPs to optically transparent surfaces is demonstrated using shrinking bubbles. Leveraging the shrinking phase of bubble mitigates the biomolecule degradation problems encountered in traditional photothermal deposition techniques. The deposited NPs are closely packed, and the functional molecules are able to survive the process as verified by their strong fluorescence signals. Using high‐speed videography, it is revealed that the contracting contact line of the shrinking bubble forces the NPs captured by the contact line to a highly concentrated island. Such shrinking surface bubble deposition (SSBD) is low temperature in nature as no heat is added during the process. Using a hairpin DNA‐functionalized gold NP suspension as a model system, SSBD is shown to enable much stronger fluorescence signal compared to the optical‐pressure deposition and the conventional thermal bubble contact line deposition. The demonstrated SSBD technique capable of directly depositing functionalized NPs may significantly simplify biosensor fabrication and thus benefit a wide range of relevant applications. 

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3. Shrinking target problems for flows on homogeneous spaces

   https://doi.org/10.1090/tran/7783  

   Kelmer, Dubi; Yu, Shucheng (February 2019, Transactions of the American Mathematical Society)

   We study shrinking targets problems for discrete time flows on a homogeneous space Γ\G with G a semisimple group and Γ an irreducible lattice. Our results apply to both diagonalizable and unipotent flows and apply to very general families of shrinking targets. As a special case, we establish logarithm laws for cusp excursions of unipotent flows, settling a problem raised by Athreya and Margulis. 

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4. VALUES OF RANDOM POLYNOMIALS IN SHRINKING TARGETS

   https://doi.org/https://doi.org/10.1090/tran/8204  

   Kelmer, Dubi Yu (January 2020, Transactions of the American Mathematical Society)

   null (Ed.)

   Relying on the classical second moment formula of Rogers we give an effective asymptotic formula for the number of integer vectors v in a ball of radius t, with value Q(v) in a shrinking interval of size t^{−λ}, that is valid for almost all indefinite quadratic forms in n variables for any λ 

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5. Impacts of urban decline on local climatology: A comparison of growing and shrinking cities in the post-industrial Rust Belt

   https://doi.org/10.3389/fclim.2023.1010849  

   Hwang, Kyotaek; Eklund, Alex; Valdez, Cecily; Papuga, Shirley A. (January 2023, Frontiers in Climate)

   Cities such as Detroit, MI in the post-industrial Rust Belt region of the United States, have been experiencing a decline in both population and economy since the 1970's. These “shrinking cities” are characterized by aging infrastructure and increasing vacant areas, potentially resulting in more green space. While in growing cities research has demonstrated an “urban heat island” effect resulting from increased temperatures with increased urbanization, little is known about how this may be different if a city shrinks due to urban decline. We hypothesize that the changes associated with shrinking cities will have a measurable impact on their local climatology that is different than in areas experiencing increased urbanization. Here we present our analysis of historical temperature and precipitation records (1900–2020) from weather stations positioned in multiple shrinking cities from within the Rust Belt region of the United States and in growing cities within and outside of this region. Our results suggest that while temperatures are increasing overall, these increases are lower in shrinking cities than those cities that are continuing to experience urban growth. Our analysis also suggests there are differences in precipitation trends between shrinking and growing cities. We also highlight recent climate data in Detroit, MI in the context of these longer-term changes in climatology to support urban planning and management decisions that may influence or be influenced by these trends. 

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