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1.
Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group 下载免费PDF全文
Hajer Bahouri & Isabelle Gallagher 《数学研究通讯:英文版》2023,39(1):1-35
It was proved by Bahouri et al. [9] that the Schrödinger equation on
the Heisenberg group $\mathbb{H}^d,$ involving the sublaplacian, is an example of a totally
non-dispersive evolution equation: for this reason global dispersive estimates
cannot hold. This paper aims at establishing local dispersive estimates on $\mathbb{H}^d$ for the linear Schrödinger equation, by a refined study of the Schrödinger kernel $S_t$ on $\mathbb{H}^d.$ The sharpness of these estimates is discussed through several
examples. Our approach, based on the explicit formula of the heat kernel on $\mathbb{H}^d$ derived by Gaveau [19], is achieved by combining complex analysis and
Fourier-Heisenberg tools. As a by-product of our results we establish local Strichartz estimates and prove that the kernel $S_t$ concentrates on quantized horizontal hyperplanes of $\mathbb{H}^d.$ 相似文献
2.
In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings. 相似文献
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Hajer Bahouri Clotilde Fermanian-Kammerer Isabelle Gallagher 《Comptes Rendus Mathematique》2012,350(7-8):393-397
We construct a Littlewood–Paley decomposition associated to a Rockland operator on graded Lie groups, which allows us to deduce refined Gagliardo–Nirenberg, Sobolev and Hardy inequalities. 相似文献
5.
Abderrahmen Abdelli Oumayma Bejaoui Hajer Bougatef Sarra Ouni Assaâd Sila Hedi M'rabet Xavier Moreau Mohamed Lotfi Efrit Damien Prim 《Journal of heterocyclic chemistry》2023,60(1):96-105
An efficient synthesis of new γ,δ-insaturated δ-lactam and glutarimide derivatives bearing a phosphonomethyl group from a common allylphosphonate precursor is described. Our approach is based on a two-step procedure involving the preparation of phosphonated-1,5-ketoester and −1,5-diester followed by an amidation–heterocyclization sequence. The first step proceeds via Michael's addition of ethyl acetoacetate and diethyl malonate on an allylphosphonate starting material. The second step consists of a base-promoted intramolecular amidation-cyclization sequence with primary amines, which accounts for the construction of δ-lactams and glutarimide skeletons. We performed the evaluation of angiotensin I-converting enzyme (ACE) inhibition using an in vitro enzyme assay on six new compounds. Five compounds showed potent ACE inhibitory activity, with IC50 values ranging from 0.02 to 0.27 mg/ml. Compared with Captopril, used as a reference drug, two new glutarimide derivatives exhibited higher efficiency ACE inhibition activity. 相似文献
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In this paper, a model predictive control (MPC) scheme based on Hammerstein model is carried on. The use of such nonlinear models complicates the implementation of the MPC in terms of computational time and burden since a nonlinear and so a nonconvex optimization problem will result. The Nelder Mead (NM) algorithm, as a free derivative method, is used to solve the resulting optimization problem. NM algorithm proves its efficiency in terms of computation time and global optimum seeking that can be successfully exploited especially with fast dynamic systems. A comparative study between the NM algorithm and the gradient-based method (GBM) based on computation time is established. The efficiency of the NM algorithm is illustrated with SISO and MIMO examples compared to GBM algorithm. 相似文献
8.
Marwa Moumni Mohamed Bechir Allagui Kaies Mezrioui Hajer Ben Amara Gianfranco Romanazzi 《Molecules (Basel, Switzerland)》2021,26(8)
Essential oils are gaining interest as environmentally friendly alternatives to synthetic fungicides for management of seedborne pathogens. Here, seven essential oils were initially tested in vivo for disinfection of squash seeds (Cucurbita maxima) naturally contaminated by Stagonosporopsis cucurbitacearum, Alternaria alternata, Fusarium fujikuro, Fusarium solani, Paramyrothecium roridum, Albifimbria verrucaria, Curvularia spicifera, and Rhizopus stolonifer. The seeds were treated with essential oils from Cymbopogon citratus, Lavandula dentata, Lavandula hybrida, Melaleuca alternifolia, Laurus nobilis, and Origanum majorana (#1 and #2). Incidence of S. cucurbitacearum was reduced, representing a range between 67.0% in L. nobilis to 84.4% in O. majorana #2. Treatments at 0.5 mg/mL essential oils did not affect seed germination, although radicles were shorter than controls, except with C. citratus and O. majorana #1 essential oils. Four days after seeding, seedling emergence was 20%, 30%, and 10% for control seeds and seeds treated with C. citratus essential oil (0.5 mg/mL) and fungicides (25 g/L difenoconazole plus 25 g/L fludioxonil). S. cucurbitacearum incidence was reduced by ~40% for plantlets from seeds treated with C. citratus essential oil. These data show the effectiveness of this essential oil to control the transmission of S. cucurbitacearum from seeds to plantlets, and thus define their potential use for seed decontamination in integrated pest management and organic agriculture. 相似文献
9.
Hajer Bahouri Jalal Shatah 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》1998,15(6):783
In this paper we prove that finite energy solutions (with added regularity) to the critical wave equation □u + u5 = 0 on
3 decay to zero in time. The proof is based on a global space-time estimate and dilation identity. 相似文献
10.
Libraries of steroid derivatives with two levels of molecular diversity were prepared to optimize the antiproliferative activity
on leukemia HL-60 cells by first varying the amino acid (AA) at R1 (libraries A, B, C, and D: with 45, 45, 20, and 20 members, respectively) and, subsequently, the capping group at R2 (library E: 168 members). The screening of these aminosteroids revealed interesting structure–activity relationships. In
library A, the compounds bearing a tetrahydroisoquinolone residue as the first element of diversity showed potent cytotoxicity,
principally when isovaleric or cyclohexyl acetic acid was used as a capping group (>40% of cell growth inhibition at 1 μM).
In library B, the phenylalanine (Phe) derivatives bearing a cyano group induced a higher growth inhibition than the other
Phe derivatives. The screening of library C indicated the increase of hydrophobicity of proline (Pro) seems to preserve the
cytotoxic effect achieved by the lead compound. However, the synthesis of structural Pro variants (library D) clearly shows
weaker activities when compared to L-Pro building blocks. Finally, by incorporating some of the most active AA of libraries A–D in library E, we observed that
the amide coupling functionality gave stronger cytotoxic activity compared to the corresponding sulfonamides or benzylamines.
Six of the most active amide derivatives (E-37P, E-41P, E-42P, E-46P, E-48F, and E-12T) were selected and IC50 determined on HL-60 cells as well as on normal human lymphocytes. Among this series of new anticancer agents, good to high
selectivity indices (SI = IC50 (lymphocytes)/IC50 (HL-60 cells) = 5 - 55) were obtained. 相似文献