Results 41 to 50 of about 474,728 (134)
The restriction theorem for the Grushin operators
, 2014 We study the Grushin operators acting on $\mathbb{R}^{d_1}_x \times \mathbb{R}^{d_2}_t$ and defined by the formula \begin{equation*} L=-\overset{d_1}{\underset{j=1}{\sum}}\partial_{x_j}^2-\left(\overset{d_1}{\underset{j=1}{\sum}}|x_j|^2\right)\overset{d_2}{\underset{k=1}{\sum}}\partial_{t_k}^2.
Liu, Heping, Song, Manli
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A Hardy inequality for the Grushin type operators [PDF]
Mathematical Inequalities & Applications, 2012 Summary: We prove a Hardy inequality related to Carnot-Carathéodory distance for the Grushin type operators like \(\Delta_x + |x|^2\partial^2_t\). The procedure is based on a representation formula for such operators.
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On the Dynamics of Nonautonomous Parabolic Systems Involving the Grushin Operators
International Journal of Mathematics and Mathematical Sciences, 2011 We study the long‐time behavior of solutions to nonautonomous semilinear parabolic systems involving the Grushin operators in bounded domains. We prove the existence of a pullback 𝒟‐attractor in (L2(Ω)) m for the corresponding process in the general case.
Anh Cung The, Toi Vu Manh
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Nonvariational and singular double phase problems for the Baouendi-Grushin operator
, 2021 In this paper we introduce a new double phase Baouendi-Grushin type operator with variable coefficients. We give basic properties of the corresponding functions space and prove a compactness result.
Rǎdulescu, Vicenţiu +5 more
core +1 more source
Synthesis and Reactivity of Ruthenium(BINAP)(PPh3)
Angewandte Chemie, Volume 136, Issue 14, April 2, 2024.The synthesis of a Ru(0)(BINAP)(PPh3) complex (BINAP:2,2′‐bis(diphenylphosphino)‐1,1′‐binaphthyl) is reported. It behaves as a “masked” 16‐electron Ru(0) complex: while being quite stable, it is capable to substitute PPh3 with alkenes/dienes, and activate C−H, N−H or inert N−Et bonds.
Yifei Zhou +3 more
wiley +2 more sources
Cu‐Catalyzed Tetrafluoroethylation of Aryl Iodides Using “Safe Supply” Tetrafluoroethylene
ChemCatChem, Volume 18, Issue 6, 27 March 2026.Reaction of [CuH(PPh3)]6 with PMePh2 and readily obtained 1:1 CO2: tetrafluoroethylene affords Cu complex 1 that ffects the CuCl(NHC)‐catalysed tetrafluoroethylation of aryl iodides. ABSTRACT The success of Cu‐mediated, late‐stage fluoroalkylation, originally developed for CF3 transfer, has expanded to additional RF groups including C2F5, CF2H, OCF3 ...
Nicholas O. Andrella +4 more
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Unprecedented Formation of a Formally Cu(III) Trifluoromethyl Hydroxide Tetramer
Chemistry – A European Journal, Volume 32, Issue 5, 2 February 2026.Novel high‐valent Cu(III) trifluoromethyl hydroxide scaffold with an unprecedented heterocubane structure was synthesized. Its neutralization reactions with acids afford a broad variety of Cu(III) complexes with two trifluoromethyl groups. Synthetic relevance of this compound for C─CF3 bond formation was demonstrated.
Vladimir Motornov, Niklas Limberg
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Synthetic Strategies to Access Fluorinated Azoles
European Journal of Organic Chemistry, Volume 28, Issue 47, December 15, 2025.This review highlights recent synthetic strategies for introducing fluorine groups (mono‐, di‐, and trifluoromethylation) into 11 major azole classes, identifying research gaps to inform future innovations in materials science, medicinal chemistry, and biomedical research.
Mohammed K. Abd El‐Gaber +4 more
wiley +1 more source
The Journal of Physiology, Volume 603, Issue 20, Page 6107-6134, October 15, 2025.Abstract figure legend The independent assembly of the protein tethers synaptotagmin (Syt1/2), Munc13 and the SNAREs (upper) affects the stochastic movement of a synaptic vesicle (SV) with respect to the plasma membrane (lower). SV and proteins are not drawn to scale.
Manon M. M. Berns +3 more
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Riesz Transforms Associated with the Grushin Operator with Drift
Potential AnalysisWe consider the Grushin operator with drift which is symmetric with respect to a measure having exponential growth. For the corresponding Riesz transforms, we study strong-type $(p, p)$, $1 < p < \infty$, and weak-type $(1, 1)$ boundedness.
Garg, Nishta, Garg, Rahul
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