Refined inequalities on graded Lie groups

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.     

Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group

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 $\mathbb{H}^d.$     

Fixed point results on a metric space endowed with a finite number of graphs and applications

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.     

Nonlinear model predictive control based on Nelder Mead optimization method

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.     

Libraries of 2β-(N-substituted piperazino)-5α-androstane-3α, 17β-diols: chemical synthesis and cytotoxic effects on human leukemia HL-60 cells and on normal lymphocytes

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.     

Asymmetric synthesis of the oxygenated polycyclic system of (+)-harringtonolide

A straightforward asymmetric synthesis of the cage oxygenated structure of (+)-harringtonolide has been accomplished for the first time. The key steps involved (i) a templated stereoselective IMDA reaction to build a highly functionalized cyclohexene ring D, (ii) functionalization of the cycloadduct, (iii) ring-closing metathesis providing the five-membered ring C, and finally (iv) a challenging one-step cascade cyclization of an epoxy-alcohol toward the target structure, whose mechanism was investigated.     

Evaluation of Seven Essential Oils as Seed Treatments against Seedborne Fungal Pathogens of Cucurbita maxima

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.