Frame properties of systems arising via iterated actions of operators

Motivated by recent progress in dynamical sampling we prove that every frame which is norm-bounded below can be represented as a finite union of sequences ${\{{(T_j)}^n{\phi }_j\}}_{n=0}^{\infty },j=1,\dots ,J$ for some bounded operators $T_j$ and elements ${\phi }_j$ in the underlying Hilbert space. The result is optimal, in the sense that it turns out to be problematic to replace the collection of generators ${\phi }_1,\dots ,{\phi }_J$ by a singleton: indeed, for linearly independent frames we prove that we can represent the frame in terms of just one system ${\{T^n\phi \}}_{n=0}^{\infty }$, but unfortunately this representation often forces the operator T to be unbounded. Several examples illustrate the connection of the results to typical frames like Gabor frames and wavelet frames, as well as generic constructions in arbitrary separable Hilbert spaces.     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

Effect of quality control on the proliferation of the extract from Taraxacum mongolicum Hand.‐Mazz. in Lactobacillus plantarum

In recent years, the fingerprint of high‐performance liquid chromatography has been extensively applied in the identification and quality control of traditional Chinese medicine. It can be a potential protocol for assessing the authenticity, stability and consistency of traditional Chinese medicine and guaranteeing the expected biological activity. In this paper, a method using high‐performance liquid chromatography to identify and control the quality of the extract of Taraxacum mongolicum Hand.‐Mazz. (TME) was established. With this method, the correlation coefficients of the similarity of 10 batches were ≥0.994. The TME displayed a steady proliferative effect in Lactobacillus plantarum. In brief, this study successfully built a reliable, simple and efficient method to control and confirm the quality and the stability of biological activity of the TME.     

A-posteriori KAM theory with optimal estimates for partially integrable systems

In this paper we present a-posteriori KAM results for existence of d-dimensional isotropic invariant tori for n-DOF Hamiltonian systems with additional $n?d$ independent first integrals in involution. We carry out a covariant formulation that does not require the use of action-angle variables nor symplectic reduction techniques. The main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates, which may cause difficulties and underperformance when quantifying the hypotheses of the KAM theorem in such reduced coordinates. The results include ordinary and (generalized) iso-energetic KAM theorems. The approach is suitable to perform numerical computations and computer assisted proofs.     

Intermolecular interactions between natural humic substances and tricyclic antidepressants

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Trimetallic NiCoM catalysts (M = Mn,Fe, Cu) for methane conversion into synthesis gas

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Biosynthesis of gold nanoparticles using Allium noeanum Reut. ex Regel leaves aqueous extract; characterization and analysis of their cytotoxicity,antioxidant, and antibacterial properties

Gold nanoparticles have unique and excellent medical and nonmedical properties and application compared with other metallic nanoparticles. Recently, they have been used for the prevention, control, and treatment of bacterial and fungal diseases. In the recent study, fresh and clean leaves of Allium noeanum Reut. ex Regel leaves have been used for the synthesis of gold nanoparticles. Also, we evaluated the cytotoxicity, antioxidant, and antibacterial properties of HAuCl₄, A. noeanum, and the synthesized nanoparticles (Au NPs). These nanoparticles were analyzed by FT‐IR, UV, XRD, EDS, FE‐SEM, and TEM tests. FTIR results offered antioxidant compounds in the plant were the sources of reducing power, reducing gold ions to Au NPs. In TEM images revealed an average diameter of 10‐30 nm. At the beginning of biological experiments, DPPH free radical scavenging test was carried out to examine the antioxidant property. Also, in the bacterial part of this study, the concentration of HAuCl₄, A. noeanum, and AuNPs with minimum dilution and no turbidity was considered MIC. To determine MBC, 60 μL of MIC and three preceding chambers were cultured on Muller Hinton Agar. The minimum concentration with no bacterial growth was considered MBC. Au NPs revealed excellent antioxidant potential against DPPH, non‐toxicity property against human umbilical vein endothelial cells, and antibacterial activities against Streptococcus pneumonia, Bacillus subtilis, Staphylococcus aureus, Staphylococcus saprophyticus, Salmonella typhimurium, Pseudomonas aeruginosa, Shigella flexneri, and Escherichia coli O157:H7. These findings show that the inclusion of A. noeanum extract improves the solubility of Au NPs, which led to a notable enhancement in the antioxidant and antibacterial effects.