Quantum Birkhoff-Gustavson normal form in some completely resonant cases

The goal of this paper is to present an explicit computation of the Birkhoff-Gustavson normal form in the 1:1, 1:2 and 1:3 resonances, by using the concept of Weyl quantization, especially when it is about the first terms. We use in particular the Weyl symbolic calculus and the abstract theorem of the quantum Birkhoff-Gustavson normal form in infinite dimension.     

On local existence and blowup of solutions for a time‐space fractional diffusion equation with exponential nonlinearity

In this paper, we are concerned with local existence and blowup of a unique solution to a time‐space fractional evolution equation with a time nonlocal nonlinearity of exponential growth. At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, the blowup result of the solution in finite time is established by the test function method with a judicious choice of the test function.     

Determination of the Phenolic Profile by Liquid Chromatography,Evaluation of Antioxidant Activity and Toxicity of Moroccan Erica multiflora,Erica scoparia,and Calluna vulgaris (Ericaceae)

This study aimed to investigate the phenolic profile and selected biological activities of the leaf and aerial extracts of three Ericaceae species, namely Erica multiflora, Erica scoparia, and Calluna vulgaris, collected from three different places in the north of Morocco. The phenolic composition of all extracts was determined by LC coupled with photodiode array and mass spectrometry detection. Among the investigated extracts, that of E. scoparia aerial parts was the richest one, with a total amount of polyphenols of 9528.93 mg/kg. Up to 59 phenolic compounds were detected: 52 were positively identified and 49 quantified—11 in C. vulgaris, 14 in E. multiflora, and 24 in E. scoparia. In terms of chemical classes, nine were phenolic acids and 43 were flavonoids, and among them, the majority belonged to the class of flavonols. The antioxidant activity of all extracts was investigated by three different in vitro methods, namely DPPH, reducing power, and Fe²⁺ chelating assays; E. scoparia aerial part extract was the most active, with an IC₅₀ of 0.142 ± 0.014 mg/mL (DPPH test) and 1.898 ± 0.056 ASE/mL (reducing power assay). Further, all extracts were non-toxic against Artemia salina, thus indicating their potential safety. The findings attained in this work for such Moroccan Ericaceae species, never investigated so far, bring novelty to the field and show them to be valuable sources of phenolic compounds with interesting primary antioxidant properties.     

On mean distance and girth

We bound the mean distance in a connected graph which is not a tree in terms of its order n and its girth g. On one hand, we show that the mean distance is at most if g is even and at most if g is odd. On the other hand, we prove that the mean distance is at least unless G is an odd cycle. This resolves two conjectures of AutoGraphiX.     

Production and Characterization of a Novel Exopolysaccharide from Ramlibacter tataouinensis

The current study examines the desiccation-resistant Ramlibacter tataouinensis TTB310^T as a model organism for the production of novel exopolysaccharides and their structural features. This bacterium is able to produce dividing forms of cysts which synthesize cell-bound exopolysaccharide. Initial experiments were conducted on the enrichment of cyst biomass for exopolysaccharide production under batch-fed conditions in a pilot-scale bioreactor, with lactate as the source of carbon and energy. The optimized medium produced significant quantities of exopolysaccharide in a single growth phase, since the production of exopolysaccharide took place during the division of the cysts. The exopolysaccharide layer was extracted from the cysts using a modified trichloroacetic acid method. The biochemical characterization of purified exopolysaccharide was performed by gas chromatography, ultrahigh-resolution mass spectrometry, nuclear magnetic resonance, and Fourier-transform infrared spectrometry. The repeating unit of exopolysaccharide was a decasaccharide consisting of ribose, glucose, rhamnose, galactose, mannose, and glucuronic acid with the ratio 3:2:2:1:1:1, and additional substituents such as acetyl, succinyl, and methyl moieties were also observed as a part of the exopolysaccharide structure. This study contributes to a fundamental understanding of the novel structural features of exopolysaccharide from a dividing form of cysts, and, further, results can be used to study its rheological properties for various industrial applications.     

On pseudo 2-factors

We show that a graph with minimum degree δ, independence number α≥δ and without isolated vertices, possesses a partition by vertex-disjoint cycles and at most α−δ+1 edges or vertices.     

Resonances of diatomic molecules in the born-oppenheimer approximation

We study the spectral properties of general diatomic molecules near a scattering level. We prove that in the Born-Oppenheimer approximation, this study can be reduced to the one of a a matrix of semiclassical pseudodifferential operators. More precisely, we provide a link between the resonances of the molecule which are close enough to the real axis, and the discrete spectrum of this matrix (the principal symbol of which being made explicit via the electronic levels of the molecule).     

Left and right generalized Drazin invertible operators

In this paper, we define and study the left and the right generalized Drazin inverse of bounded operators in a Banach space. We show that the left (resp. the right) generalized Drazin inverse is a sum of a left invertible (resp. a right invertible) operator and a quasi-nilpotent one. In particular, we define the left and the right generalized Drazin spectra of a bounded operator and also show that these sets are compact in the complex plane and invariant under additive commuting quasi-nilpotent perturbations. Furthermore, we prove that a bounded operator is left generalized Drazin invertible if and only if its adjoint is right generalized Drazin invertible. An equivalent definition of the pseudo-Fredholm operators in terms of the left generalized Drazin invertible operators is also given. Our obtained results are used to investigate some relationships between the left and right generalized Drazin spectra and other spectra founded in Fredholm theory.