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L^p estimates for the wave equation associated to the Grushin operator
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2014 We prove that the solution of the wave equation as- sociated to the Grushin operator $ G = -Δ+|x|^2 \partial_t^2 $ is bounded on $ L^p(R^{n+1})(1 < p < \infty)$, when $|1/p- 1/2 | < 1/n+2$ .
Jotsaroop, Kaur, Thangavelu, Sundaram
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Turbocharging synaptic transmission
FEBS Letters, Volume 597, Issue 18, Page 2233-2249, September 2023., 2023 State1, a vesicle is captured by the six Upright Munc13s and pSNAREpins are formed by the outer VAMP2. State 2, diacylglycerol binding rearranges Munc13s to lateral closed conformation. State 3, the vesicle proceeds to a readily releasable pool. All pSNAREpins concomitantly exert high pressure for a longer time to ‘turbocharge’ the neurotransmitter ...
James E. Rothman +3 more
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The Chemical Record, Volume 23, Issue 9, September 2023., 2023 In recent years, the rise of both organofluorine chemistry and photochemistry have intersected to bring about a myriad of visible light‐mediated protocols. The development of new reagents and advances in photo‐mediated processes have synergistically provided mild, effective, and reliable fluorine‐related transformations.
Daniel Lin +4 more
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Journal of Inequalities and Applications, 2020 We examine the weighted Grushin system involving advection terms given by { Δ G u − a ⋅ ∇ G u = ( 1 + ∥ z ∥ 2 ( α + 1 ) ) γ 2 ( α + 1 ) v − p in R n , Δ G v − a ⋅ ∇ G v = ( 1 + ∥ z ∥ 2 ( α + 1 ) ) γ 2 ( α + 1 ) u − q in R n , $$ \textstyle\begin{cases}
Belgacem Rahal
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The Chemical Record, Volume 23, Issue 9, September 2023., 2023 The propensity of Ag to undergo 1e− redox events makes Ag an unlikely catalyst in cross‐coupling. However, isolable organo‐AgIII species bearing macrocycles or perfluorinated ligands were recently found active in C−C and C‐heteroatom bond formation. Main advances in aryl‐F and aryl‐CF3 couplings proceeding via AgI/AgIII redox sequences, and comparison ...
Luca Demonti +2 more
wiley +1 more source
Chemistry – A European Journal, Volume 29, Issue 41, July 20, 2023., 2023 A combination of gas‐phase fragmentation experiments and quantum chemical calculations affords detailed insight into the reactivity of high‐valent trifluoromethylated cuprate complexes. Depending on the nature of the organyl group R, these key intermediates of synthetically valuable trifluoromethylation reactions lose two radicals or undergo concerted ...
Bastian Zimmer +2 more
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Radical Deoxyfunctionalisation Strategies**
European Journal of Organic Chemistry, Volume 2022, Issue 26, July 14, 2022., 2022 With the development of milder technologies to access open‐shell species, radical deoxyfunctionalisation reactions have emerged as a powerful strategy to build C−C and C‐heteroatom bonds from readily available alcohols. This Review highlights the exciting advancements made in this field during the last decade using photochemistry, electrochemistry or ...
Khadijah Anwar +3 more
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Stable weak solutions to weighted Kirchhoff equations of Lane–Emden type
Advances in Difference Equations, 2021 This paper is concerned with the Liouville type theorem for stable weak solutions to the following weighted Kirchhoff equations: − M ( ∫ R N ξ ( z ) | ∇ G u | 2 d z ) div G ( ξ ( z ) ∇ G u ) = η ( z ) | u | p − 1 u , z = ( x , y ) ∈ R N = R N 1 × R N 2 ,
Yunfeng Wei, Hongwei Yang, Hongwang Yu
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On the Grushin operator and hyperbolic symmetry [PDF]
Proceedings of the American Mathematical Society, 2000 Complexity of geometric symmetry for differential operators with mixed homogeniety is examined here. Sharp Sobolev estimates are calculated for the Grushin operator in low dimensions using hyperbolic symmetry and conformal geometry.
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On some operator-valued Fourier pseudo-multipliers associated to Grushin operators [PDF]
, 2023 This is a continuation of our work [BBGG23, BBGG22] where we have initiated the study of sparse domination and quantitative weighted estimates for Grushin pseudo-multipliers.
Basak, Riju +3 more
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