On the dynamical symmetry points and the orientations of the principal axes of inertia of a rigid body

For an arbitrary rigid body, all dynamical symmetry points are found, and the directions of the axes of dynamical symmetry are determined for these points. We obtain conditions on the principal central moments of inertia under which the Lagrange and Kovalevskaya cases can be realized for the rigid body. We also analyze the set of orientations of the bases formed by the principal axes of inertia for various points of the rigid body.     

Composition and chemical variability of leaf oil of Myrtus communis from north-eastern Algeria

The chemical composition of 27 oil samples of Myrtus communis isolated from leaves collected in three locations in north-eastern Algeria was investigated by GC(RI) and 13C NMR spectroscopy. Yields ranged between 0.2-1.2% (w/w). The chemical composition of the oils was largely dominated by monoterpene hydrocarbons, with alpha-pinene (40.5-64.0%), 1,8-cineole (10.9-29.1%) and limonene (6.7-8.2%) being the major compounds. In all the samples, 3,3,5,5,8,8-hexamethyl-7-oxabicyclo[4.3.0]non-1(6)-ene-2,4-dione was identified (0.8-1.5%). The composition is similar to that reported for myrtle oils from Corsica, Sardinia and Tunisia, but differed from that of Moroccan and Spanish myrtle oils.     

A Nitrite Electrochemical Sensor Based on Boron‐Doped Diamond Planar Electrochemical Microcells Modified with a Monolacunary Silicotungstate Polyoxoanion

A new boron doped diamond microcells (BDD) was modified, for rapid, selective and highly sensitive determination of nitrite, using a coating film of polyoxometalates (POMs), formed by cyclic voltammetry on the molecular p‐phenylenediamine (PPD) functionalized BDD. The scanning electron microscopy (SEM) technique was used to examine the morphology of (PPD/SiW₁₁) modified (BDD) electrode. It was found that (SiW₁₁) layer was uniformly formed on the electrode surface. It was observed that (BDD/PPD/SiW₁₁) showed excellent electrocatalytic activities towards nitrite ion. Under the selected conditions, the anodic peak maximum at ?0.6 V was linear versus nitrite concentration in the 40 µM–4 mM range, and the detection limit obtained was 20 µM. The newly developed electrode has been successfully applied to the determination of nitrite content in real river water samples.     

Strong isochronism of polynomial reversible dynamical systems on the plane with homogeneous nonlinearities of degree 4

We find the maximum order and initial polar angle of strongly isochronous two-dimensional polynomial reversible systems with homogeneous nonlinearities of the fourth degree.     

Nanomaterials in mass spectrometry ionization and prospects for biological application

The rapid development of nanotechnology has revolutionized scientific developments in recent decades. Mass spectrometry (MS) measurements are no exception and have benefited greatly from integration of nanomaterials in every step of analysis. This brief review summarizes recent developments in the field with the focus on the use of nanomaterials as alternative media to facilitate analyte ionization in laser-desorption ionization–mass spectrometry (LDI–MS) and secondary ion mass spectrometry (SIMS). The biological applications of both techniques are also detailed. The use of nanomaterials in other aspects of MS analysis, for example in sample clean-up and indirect analyte quantification, is briefly discussed.     

Construction of a linear Pfaff system of Fuchsian type with algebraic manifold of singularities

We present a constructive proof of the existence of a two-dimensional completely integrable Fuchsian Pfaff system on CP ⁿ with four singular surfaces forming a pencil, with 2-step solvable monodromy group, and with fundamental solution matrix realizing a given homomorphism.     

On the Lévy–Khintchine representation of q-Bessel negative definite functions

We study q-Bessel negative definite functions and use their properties to give a proof of Lévy–Khintchine representation of q-infinitely divisible probability measures.     

Synthesis,molecular modeling,TD-DFT,antimicrobial, and in vitro therapeutic activity of new spherical nano-sized sulfonamide imine ligands and their zinc (II) and copper (II) complexes

A series of nanometer-sized spherical sulfonamide imine ligands HL ¹ -HL ⁵ and their copper and zinc complexes were synthesized and fully characterized based on elemental analyses, spectroscopic (UV/vis, FT-IR, NMR, EPR, SEM) studies, molar conductance and thermal analyses. Furthermore, computational studies of HL ¹ -HL ⁵ were carried out by the DFT/B3LYP method. TD-DFT, HOMO and LUMO energy values, chemical hardness, electronegativity, electrophilic index, softness, and other parameters were calculated. Screening against several pathogenic microorganisms indicated that HL ¹ exhibited high activity against the tested Gram-negative bacteria relative to other analogues and the inhibition activity is greater than the standard Gentamicin. Analogously, HL ² exhibited high potent activity against the tested Gram-positive bacteria. Copper complexes exhibited a higher potent activity than zinc analogues. Noteworthy, inhibition activity of [Cu ( L ³ )(OAc)] complex is higher than that of the standard Ampicillin. [Cu ( L ² )(OAc)] complex displayed a similar activity of the standard bactericides and fungicides in use. The complexes showed appreciated values of MIC against bacterial strains: B. subtilis (MIC = 0.4 μg / mL), E. coli and S. pneumonia (MIC = 1.95 μg / mL) and P. aeruginosa (MIC = 7.81 μg / mL). in vitro cytotoxic activities study proved that [Cu ( L ³ )(OAc)] complex exhibited appreciable activity versus (HEPG-2); IC₅₀ = 4.8 μg/ml, while [Cu( L ² )(OAc)] complex showed a high activity against (MCF-7); IC₅₀ = 6.2 μg/ml. These results could be considered as new findings of promising antitumor candidates for experimental chemotherapy.