A comparative study of the thermal behaviour of phosphate washing sludge from Tunisia and Morocco

Journal of Thermal Analysis and Calorimetry - The aim of the present work is to characterize the phosphate sludge from two different countries: Morocco and Tunisia, and to study the difference...     

Estimate of the L-Fourier transform norm on nilpotent Lie groups

Let 1<p?2 and q be such that . It is well known that the norm of the L^p-Fourier transform of the additive group is , where . For a nilpotent Lie group G, we obtain the estimate , where m is the maximal dimension of the coadjoint orbits. Such a result was known only for some particular cases.     

A generalizaton of Hardy’s uncertainty principle on compact extensions of \mathbb R ^n

Let \(K\) be a compact subgroup of automorphisms of \(\mathbb R ^n\) . We prove in this paper a generalization of Hardy’s uncertainty principle on the semi-direct product \(K\ltimes \mathbb R ^n\) , and we solve the sharpness problem. As a consequence, a complete analogue of classical Hardy’s theorem is obtained. The representation theory and the Plancherel formula play an important role in the proofs.     

Identification of Potential SARS-CoV-2 Main Protease and Spike Protein Inhibitors from the Genus Aloe: An In Silico Study for Drug Development

Severe acute respiratory syndrome coronavirus (SARS-CoV-2) disease is a global rapidly spreading virus showing very high rates of complications and mortality. Till now, there is no effective specific treatment for the disease. Aloe is a rich source of isolated phytoconstituents that have an enormous range of biological activities. Since there are no available experimental techniques to examine these compounds for antiviral activity against SARS-CoV-2, we employed an in silico approach involving molecular docking, dynamics simulation, and binding free energy calculation using SARS-CoV-2 essential proteins as main protease and spike protein to identify lead compounds from Aloe that may help in novel drug discovery. Results retrieved from docking and molecular dynamics simulation suggested a number of promising inhibitors from Aloe. Root mean square deviation (RMSD) and root mean square fluctuation (RMSF) calculations indicated that compounds 132, 134, and 159 were the best scoring compounds against main protease, while compounds 115, 120, and 131 were the best scoring ones against spike glycoprotein. Compounds 120 and 131 were able to achieve significant stability and binding free energies during molecular dynamics simulation. In addition, the highest scoring compounds were investigated for their pharmacokinetic properties and drug-likeness. The Aloe compounds are promising active phytoconstituents for drug development for SARS-CoV-2.     

On the practical global uniform asymptotic stability of stochastic differential equations

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of stochastic differential equations (SDEs) by using Lyapunov functions when the origin is not necessarily an equilibrium point. The global uniform boundedness and the global practical uniform exponential stability of solutions of SDEs based on Lyapunov techniques are investigated. Furthermore, an example is given to illustrate the applicability of the main result.     

The L p -L q analog of Morgan’s theorem on exponential solvable Lie groups

In this paper, we define an analog of the L ^p -L ^q Morgan’s uncertainty principle for any exponential solvable Lie group G (p, q ∈ [1,+∞]). When G is nilpotent and has a noncompact center, the proof of such an analog is given for p, q ∈ [2,+∞], extending the earlier settings ([2], [4] and [5]). Such a result is only known for some particular restrictive cases so far. We also prove the result for general exponential Lie groups with nontrivial center.     

On the geometry of stable discontinuous subgroups acting on threadlike homogeneous spaces

Following the notion of stability introduced by T. Kobayashi and S. Nasrin in [14], we show in the context of a threadlike Lie group G that any non-Abelian discrete subgroup is stable. One consequence is that any resulting deformation space ?(Γ,G,H) is a Hausdorff space, where Γ acts on the threadlike homogeneous space G/H as a discontinuous subgroup. Whenever k = rank(Γ) > 3, this space is also shown to be endowed with a smooth manifold structure. But if k = 3, then ?(Γ,G,H) admits a smooth manifold structure as its open dense subset. These phenomena are strongly linked to the features of adjoint orbits of the basis group G on the parameter space ?(Γ,G,H) (which is semi-algebraic in this case) and specifically to their dimensions, as it will be seen throughout the paper. This also allows to provide a proof of the Local Rigidity Conjecture in this setup.     

On Hardy’s uncertainty principle for connected nilpotent Lie groups

In (Kaniuth and Kumar in Math. Proc. Camb. Phil. Soc. 131, 487–494, 2001) Hardy’s uncertainty principle for was generalized to connected and simply connected nilpotent Lie groups. In this paper, we extend it further to connected nilpotent Lie groups with non-compact centre. Concerning the converse, we show that Hardy’s theorem fails for a connected nilpotent Lie group G which admits a square integrable irreducible representation and that this condition is necessary if the simply connected covering group of G satisfies the flat orbit condition.