Results 121 to 130 of about 393,013 (283)
Spectral Asymptotics for Fractional Laplacians [PDF]
, 2019 In this article we consider fractional Laplacians which seem to be of interest to probability theory. This is a rather new class of operators for us but our methods works (with a twist, as usual). Our main goal is to derive a two-term asymptotics as one-term asymptotics is easily obtained by R.~Seeley's method.
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Perspectives of Earth and Space Scientists, Volume 6, Issue 1, December 2025.Abstract Although the concept of thermodynamic entropy due to Clausius dates back to the early 1850s, the mathematical theory of informational entropy was not developed until the pioneering work of Shannon in 1948, the development of principle of maximum entropy (POME) and theorem of concentration by Jaynes in 1957, principle of minimum cross entropy ...
Vijay P. Singh
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Resolvent kernel for the Kohn Laplacian on Heisenberg groups
Electronic Journal of Differential Equations, 2002 We present a formula that relates the Kohn Laplacian on Heisenberg groups and the magnetic Laplacian. Then we obtain the resolvent kernel for the Kohn Laplacian and find its spectral density.
Neur Eddine Askour, Zouhair Mouayn
doaj
Fractional centered difference scheme for high-dimensional integral fractional Laplacian
Journal of Computational Physics, 2021 Zhaopeng Hao, Zhongqiang Zhang, R. Du
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What Is the Fractional Laplacian?
, 2018 The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature as to which definition of the fractional Laplacian in bounded domains is most appropriate for ...
Lischke, Anna +10 more
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A Level Set Topology Optimization Theory Based on Hamilton's Principle
International Journal for Numerical Methods in Engineering, Volume 126, Issue 17, 15 September 2025.ABSTRACT In this article, we propose a unified variational framework for deriving the evolution equation of the level set function in topology optimization, departing from conventional Hamilton–Jacobi‐based formulations. The key idea is the introduction of an auxiliary domain, geometrically identical to the physical design domain, occupied by ...
Jan Oellerich, Takayuki Yamada
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Journal of Applied Clinical Medical Physics, Volume 26, Issue 9, September 2025.Abstract Background In external beam radiation therapy (EBRT) for prostate cancer, both MRI and CT are typically used—CT provides electron density for dose calculation and visualization of bony anatomy and fiducial markers, while MRI offers superior soft tissue contrast.
Jie Deng +13 more
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C(sp2)─H Bond Activation with a Heterometallic Nickel–Aluminium Complex
Angewandte Chemie, Volume 137, Issue 36, September 1, 2025.Despite the prevalence of Ni/Al catalysts for pyridine C─H functionalization, mechanistic details of such systems remain scarce. Herein, we present the discovery of PCy3‐catalyzed bond‐breaking and making processes that occur in the coordination sphere of a novel Ni─Al heterometallic complex.
Joseph A. Zurakowski +3 more
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Inverse problems for the fractional-Laplacian with lower order non-local perturbations
Transactions of the American Mathematical Society, 2021 Sombuddha Bhattacharyya +2 more
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Hopf's lemmas for parabolic fractional Laplacians and parabolic fractional $p$-Laplacians
, 2020 In this paper, we first establish Hopf's lemmas for parabolic fractional equations and parabolic fractional $p$-equations. Then we derive an asymptotic Hopf's lemma for antisymmetric solutions to parabolic fractional equations. We believe that these Hopf's lemmas will become powerful tools in obtaining qualitative properties of solutions for nonlocal ...
Wang, Pengyan, Chen, Wenxiong
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