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 $\mathbb{H}^d.$     

Synthesis and evaluation of new phosphonated δ-lactam and glutarimide derivatives as angiotensin converting enzyme inhibitors

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.     

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.     

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.     

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.     

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.     

Chemical Composition,Antioxidant, and Antimicrobial Activities of Leaves of Ajuga Iva

The main objective of this research was to study the biological characteristics in terms of antioxidant and antimicrobial activities of Ajuga iva and determine the best analytical and extraction methods applicable to this specie and studied compounds. A short screening of its nutritional value in terms of chemical composition is also included. A. iva leaves were analyzed for crude protein (CP), cell wall [neutral detergent fiber (NDF), acid detergent fiber (ADF), and acid detergent lignin (ADL)], minerals, fatty acids, essential oils, and phenolic compounds. Mature aerial parts of A. iva were randomly collected during the Spring season from Mograne-Zaghouan, Tunisia. Leaves of A. iva contained 13.4 ± 0.4% CP, 26.3 ± 0.35% NDF, 20.2 ± 0.42% ADF, and 5.13 ± 0.21% ADL. Mineral content (13.0 ± 0.45%) was mainly composed of potassium (4.5% g DM) and magnesium (4.25% DM). Leaves of A. iva had linolenic (26.29 ± 0.760%) and linoleic (37.66 ± 2.35%) acids as the main components of the acid profile. Thymol was found to be the most dominant (23.43%) essential oil, followed by 4-vinylguaiacol (14.27%) and linalool (13.66%). HPLC-PDA-ESI-MS/MS analysis pointed out the presence of phytoecdysteroids. Phenolic acids and flavonoids, such as glycosylated derivatives of naringenin, eriodyctiol, and apigenin, were detected in the methanol extract of A. iva leaves. Our results underline the importance of choosing proper extraction methods and solvents to extract and characterize the described compounds profile of A. iva leaves. Results also show A. iva leaves as a potential source of functional ingredients with beneficial health-promoting properties. Overall, leaves of A. iva have low biological activities (antioxidant and antimicrobial activities) with a chemical composition suitable as a feed for ruminants in rangeland pasture. It also has low-grade antibacterial or medicinal characteristics when fed to ruminants.     

Decay estimates for the critical semilinear wave equation

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.