Variational Approach to Medium Mass N=Z Nuclei

Author(s):  
A. Petrovici
Author(s):  
Shaya Shakerian

In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave–convex nonlinearities: [Formula: see text] where [Formula: see text] is a smooth bounded domain in [Formula: see text] containing [Formula: see text] in its interior, and [Formula: see text] with [Formula: see text] which may change sign in [Formula: see text]. We use the variational methods and the Nehari manifold decomposition to prove that this problem has at least two positive solutions for [Formula: see text] sufficiently small. The variational approach requires that [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text], the latter being the best fractional Hardy constant on [Formula: see text].


Marine Drugs ◽  
2021 ◽  
Vol 19 (7) ◽  
pp. 378
Author(s):  
Van-Tuyen Le ◽  
Samuel Bertrand ◽  
Thibaut Robiou du Pont ◽  
Fabrice Fleury ◽  
Nathalie Caroff ◽  
...  

Very little is known about chemical interactions between fungi and their mollusc host within marine environments. Here, we investigated the metabolome of a Penicillium restrictum MMS417 strain isolated from the blue mussel Mytilus edulis collected on the Loire estuary, France. Following the OSMAC approach with the use of 14 culture media, the effect of salinity and of a mussel-derived medium on the metabolic expression were analysed using HPLC-UV/DAD-HRMS/MS. An untargeted metabolomics study was performed using principal component analysis (PCA), orthogonal projection to latent structure discriminant analysis (O-PLSDA) and molecular networking (MN). It highlighted some compounds belonging to sterols, macrolides and pyran-2-ones, which were specifically induced in marine conditions. In particular, a high chemical diversity of pyran-2-ones was found to be related to the presence of mussel extract in the culture medium. Mass spectrometry (MS)- and UV-guided purification resulted in the isolation of five new natural fungal pyran-2-one derivatives—5,6-dihydro-6S-hydroxymethyl-4-methoxy-2H-pyran-2-one (1), (6S, 1’R, 2’S)-LL-P880β (3), 5,6-dihydro-4-methoxy-6S-(1’S, 2’S-dihydroxy pent-3’(E)-enyl)-2H-pyran-2-one (4), 4-methoxy-6-(1’R, 2’S-dihydroxy pent-3’(E)-enyl)-2H-pyran-2-one (6) and 4-methoxy-2H-pyran-2-one (7)—together with the known (6S, 1’S, 2’S)-LL-P880β (2), (1’R, 2’S)-LL-P880γ (5), 5,6-dihydro-4-methoxy-2H-pyran-2-one (8), (6S, 1’S, 2’R)-LL-P880β (9), (6S, 1’S)-pestalotin (10), 1’R-dehydropestalotin (11) and 6-pentyl-4-methoxy-2H-pyran-2-one (12) from the mussel-derived culture medium extract. The structures of 1-12 were determined by 1D- and 2D-MMR experiments as well as high-resolution tandem MS, ECD and DP4 calculations. Some of these compounds were evaluated for their cytotoxic, antibacterial, antileishmanial and in-silico PTP1B inhibitory activities. These results illustrate the utility in using host-derived media for the discovery of new natural products.


Author(s):  
Philipp Junker ◽  
Daniel Balzani

AbstractWe present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (2) the important constraints of bounded relative density and total structure volume are fulfilled analytically which simplifies the numerical implementation significantly; (3) it possesses a mathematical structure that allows for a variety of numerical procedures to solve the problem of topology optimization without distinct optimization routines. We present a detailed model derivation including the chosen numerical discretization and show the validity of the approach by simulating two boundary value problems with large deformations.


IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Mushtaq Ahmad Khan ◽  
Asmat Ullah ◽  
Sahib Khan ◽  
Murtaza Ali ◽  
Sheraz Khan ◽  
...  

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