Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

Metabolomics techniques applied in the investigation of phenolic acids from the agro-industrial by-product of Carapa guianensis Aubl

Processing of Carapa guianensis seeds to obtain oil on an industrial scale generates a significant amount of by-product, approximately 66% w/w, which is called cake and is a potential source of biomolecules, including simple phenolic structures. For this reason, studies were carried out on the chemical profiles of hydrolyzed extract from this agro-industrial by-product through High Performance Thin-Layer Chromatography (HPTLC) and Gas Chromatography coupled to Mass Spectrometry (GC–MS). These techniques were used to detect metabolic classes and/or groups, and to identify, for the first time, thirteen simple phenolic acids in this by-product. The sample antioxidant capacity was determined by methods of 2,2-diphenyl-1-picrylhydrazyl (DPPH)and 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt (ABTS⁺) radicals direct sequestration. The hydrolyzed fraction showed a total of 63.47% in the relative abundance of the total of compounds, standing out: p-hydroxybenzoic acid (39.19%) and protocatechuic acid (3,4-dihydroxybenzoic acid) (5.62%), both from hydroxybenzoic acids and 3-(3,4-dihydroxyphenyl)lactic acid, (7.76%) hydroxycinnamic acids derivatives. In these results, the fraction rich in simple phenolic acids was obtained, attributing the prominent behavior of this matrix antioxidant activity, expressed by (IC₅₀: of 16.42 µg/mL and 6.52 µg/mL for DPPH and ABTS⁺ radicals, respectively). The research demonstrated an alternative to applicability that involves sustainability from agro-industrial. These techniques were used to detect metabolic classes and/or groups, and to identify, for the first time, thirteen simple phenolic acids in this by-product, generating a process capable of converting biomass into a bioproduct, consisting of bioactive compounds, in addition to adding value to the industrial chain.     

A generalized super AKNS hierarchy associated with orthosymplectic Lie superalgebra OSP(2,2) and its super bi-Hamiltonian structures

For the orthosymplectic Lie superalgebra $\text{◂⋅▸}OSP(2,2)$, we choose a set of basis matrices. A linear combination of those basis matrices presents a spatial spectral matrix. The compatible condition of the spatial part and the corresponding temporal parts of the spectral problem leads to a generalized super AKNS (GSAKNS) hierarchy. By making use of the supertrace identity, the obtained GSAKNS hierarchy can be written as the super bi-Hamiltonian structures.     

A simple,rapid and sensitive method based on modified multiwalled carbon nanotube for preconcentration and determination of lead ions in aqueous media in natural pHs

In this study, multiwalled carbon nanotube (MWCNT) was modified by the pyridine group using a silane agent and characterized by infrared spectroscopy (IR), thermal analysis (TG/DTA), and elemental analysis (CHN) and scanning electron microscopy (SEM). The application of this sorbent was investigated in determination of lead ions in aqueous samples, using flame atomic absorption spectrometry (FAAS). Through this study, different parameters such as pH and sample flow rate on adsorption process and eluent concentration, volume and flow rate were optimized. The limit of detection (LOD), the relative standard deviation and the recovery of the method were 2 ng mL^?1, 1.3% and 99.7%, respectively. Two standard reference materials (NIST 1571 and NIST 1572) were used to verify accuracy of this method. Finally, the sorbent was successfully applied for extraction and determination of low levels of Pb(II) ions in aqueous samples.     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Synthesis and antimycobacterial activity of purine conjugates with (S)-lysine and (S)-ornithine

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Rigidity and flexibility of virtual polytopes

All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.     

On universal subsets of Banach spaces

We prove that to most of the known hypercyclic operators A on separable Banach spaces there exist compact (compact convex, compact connected) subsets K of E such that each compact (compact convex, compact connected) subset of E can be approximated with respect to Hausdorff's distance by for suitable . Received July 8, 1997, in final form October 17, 1997