What do the Engel laws and positive laws have in common?

The work is inspired by a question of R. Burns: What do the Engel laws and positive laws have in common that forces finitely generated, locally graded groups satisfying them to be nilpotent-by-finite? The answer is that these laws have the same so-called Engel construction.     

Synthesis and temperature dependence of physical properties of four pyridinium-based ionic liquids: Influence of the size of the cation

In this paper, the ionic liquids 1,2-diethylpyridinium ethylsulfate, EEpyESO₄; 1-methylpyridinium methylsulfate, MpyMSO₄; 1,3-dimethylpyridinium methylsulfate, MMpyMSO₄; and 2-ethyl-1-methylpyridinium methylsulfate, EMpyMSO₄; were synthesized in our laboratory, and their experimental densities, speeds of sound, dynamic viscosities, and refractive indices were studied as a function of temperature at atmospheric pressure. Thermal expansion coefficient, molar volume, and molar refraction of these ionic liquids were calculated from the experimental density and refractive index values.     

Evaluation of antioxidant capacity and synergistic associations of quinonemethide triterpenes and phenolic substances from Maytenus ilicifolia (Celastraceae)

This work describes the isolation of the secondary metabolites identified as the quinonemethides maytenin (1) and pristimerin (2) from Maytenus ilicifolia extracts obtained from root barks of adult plants and roots of seedlings and their quantification by high performance liquid chromatography coupled to a diode array detector. The electrochemical profiles obtained from cyclic voltammetry and a coulometric detector coupled to high-performance liquid chromatography contributed to the evaluation of their antioxidant capacity. The antioxidant properties of individual components and the crude extracts of the root barks of Maytenus ilicifolia were compared and the possible synergistic associations of quinonemethide triterpenes and phenolic substances were investigated by using rutin as a model phenolic compound.     

Thermal characterization of the solid state and raw material fluconazole by thermal analysis and pyrolysis coupled to GC/MS

This article had studied the thermal characterization of the raw material and different fluconazole crystals, obtained through recrystallization with different solvents using thermoanalytical techniques (TG, DTA, DSC-50, DSC Photovisual, DSC-60) and Pyr-GC/MS. The results confirmed that the fluconazole volatilizes without decomposition until 250 °C. Pyr-GC/MS showed hexachlorobenzene like impurities in fluconazole raw material.     

Electron microscope observations of phase separation near spinodal boundary in a sodium borosilicate glass

Time evolution of volume fraction of the minor phase is studied in an alumina-doped sodium borosilicate glass inside the immiscible region. It is shown that such a study permits a distinction between the two mechanisms of phase separation; namely spinodal decomposition and nucleation and growth. For spinodal decomposition, the volume fraction decreases initially, whereas for nucleation and growth, it increases with heat-treatment time.     

KCl effect on the solubility of five different amino acids in water

Using the analytical gravimetric method the solubility of glycine and dl-alanine in aqueous systems of KCl at 323.15 K, and of l-isoleucine, l-threonine and l-serine in the same system, at 298.15 and 323.15 K, were measured for salt concentrations ranging up to 2.0 molal.     

An accurate relativistic universal Gaussian basis set for hydrogen through Nobelium without variational prolapse and to be used with both uniform sphere and Gaussian nucleus models

An accurate relativistic universal Gaussian basis set (RUGBS) from H through No without variational prolapse has been developed by employing the Generator Coordinate Dirac-Fock (GCDF) method. The behavior of our RUGBS was tested with two nuclear models: (1) the finite nucleus of uniform proton-charge distribution, and (2) the finite nucleus with a Gaussian proton-charge distribution. The largest error between our Dirac-Fock-Coulomb total energy values and those calculated numerically is 8.8 mHartree for the No atom.     

Group Laws [x,y −1] ≡ u(x,y) and Varietal Properties

Let F = ?x, y? be a free group. It is known that the commutator [x, y ^?1] cannot be expressed in terms of basic commutators, in particular in terms of Engel commutators. We show that the laws imposing such an expression define specific varietal properties. For a property 𝒫 we consider a subset U(𝒫) ? F such that every law of the form [x, y ^?1] ≡ u, u ∈ U(𝒫) provides the varietal property 𝒫. For example, we show that each subnormal subgroup is normal in every group of a variety 𝔙 if and only if 𝔙 satisfies a law of the form [x, y ^?1] ≡ u, where u ∈ [F′, ?x?].     

Fucoxanthin Holds Potential to Become a Drug Adjuvant in Breast Cancer Treatment: Evidence from 2D and 3D Cell Cultures

Fucoxanthin (Fx) is a carotenoid derived from marine organisms that exhibits anticancer activities. However, its role as a potential drug adjuvant in breast cancer (BC) treatment is still poorly explored. Firstly, this study investigated the cytotoxic effects of Fx alone and combined with doxorubicin (Dox) and cisplatin (Cis) on a panel of 2D-cultured BC cell lines (MCF7, SKBR3 and MDA-MB-231) and one non-tumoral cell line (MCF12A). Fucoxanthin induced cytotoxicity against all the cell lines and potentiated Dox cytotoxic effects towards the SKBR3 and MDA-MB-231 cells. The combination triggering the highest cytotoxicity (Fx 10 µM + Dox 1 µM in MDA-MB-231) additionally showed significant induction of cell death and genotoxic effects, relative to control. In sequence, the same combination was tested on 3D cultures using a multi-endpoint approach involving bioactivity assays and microscopy techniques. Similar to 2D cultures, the combination of Fx and Dox showed higher cytotoxic effects on 3D cultures compared to the isolated compounds. Furthermore, this combination increased the number of apoptotic cells, decreased cell proliferation, and caused structural and ultrastructural damages on the 3D models. Overall, our findings suggest Fx has potential to become an adjuvant for Dox chemotherapy regimens in BC treatment.