Rank of quantized universal enveloping algebras and modular functions

We compute an intrinsic rank invariant for quasitriangular Hopf algebras in the case of general quantum groupsU _q (g). As a function ofq the rank has remarkable number theoretic properties connected with modular covariance and Galois theory. A number of examples are treated in detail, including rank (U _q (su(3))) and rank (U _q (e ₈)). We briefly indicate a physical interpretation as relating Chern-Simons theory with the theory of a quantum particle confined to an alcove ofg.     

Three New Acrylic Acid Derivatives from Achillea mellifolium as Potential Inhibitors of Urease from Jack Bean and α-Glucosidase from Saccharomyces cerevisiae

(1) Background: Achillea mellifolium belongs to a highly reputed family of medicinal plants, with plant extract being used as medicine in indigenous system. However, limited data is available regarding the exploitation of the medicinal potential of isolated pure compounds from this family; (2) Methods: A whole plant extract was partitioned into fractions and on the basis of biological activity, an ethyl acetate fraction was selected for isolation of pure compounds. Isolated compounds were characterized using different spectroscopic techniques. The compounds isolated from this study were tested for their medicinal potential using in-vitro enzyme assay, coupled with in-silico studies; (3) Results: Three new acrylic acid derivatives (1–3) have been isolated from the ethyl acetate fraction of Achillea mellifolium. The characterization of these compounds (1–3) was carried out using UV/Vis, FT-IR, 1D and 2D-NMR spectroscopy (¹H-NMR, ¹³C-NMR, HMBC, NOESY) and mass spectrometry. These acrylic acid derivatives were further evaluated for their enzyme inhibition potential against urease from jack bean and α glucosidase from Saccharomyces cerevisiae, using both in-silico and in-vitro approaches. In-vitro studies showed that compound 3 has the highest inhibition against urease enzyme (IC₅₀ =10.46 ± 0.03 μΜ), followed by compound 1 and compound 2 with percent inhibition and IC₅₀ value of 16.87 ± 0.02 c and 13.71 ± 0.07 μΜ, respectively, compared to the standard (thiourea-IC₅₀ = 21.5 ± 0.01 μΜ). The investigated IC₅₀ value of compound 3 against the urease enzyme is two times lower compared to thiourea, suggesting that this compound is twice as active compared to the standard drug. On the other hand, all three compounds (1–3) revealed mild inhibition potential against α-glucosidase. In-silico molecular docking studies, in combination with MD simulations and free energy, calculations were also performed to rationalize their time evolved mode of interaction inside the active pocket. Binding energies were computed using a MMPBSA approach, and the role of individual residues to overall binding of the inhibitors inside the active pockets were also computed; (4) Conclusions: Together, these studies confirm the inhibitory potential of isolated acrylic acid derivatives against both urease and α-glucosidase enzymes; however, their inhibition potential is better for urease enzyme even when compared to the standard.     

X-ray investigation of the crystallization of chalcogenide glasses of the type (As2Se3)1−x:(Tl2Se)x

Amorphous and crystalline states of As₂Se₃, (As₂Se₃)₃ : Tl₂Se and As₂Se₃ : Tl₂Se have been studied using X-ray diffraction techniques. Structural changes arise during the process of annealing in the temperature range between their softening and melting points are reported and their rates investigated. The crystallization temperatures were found to be 105 ± 5 °C, 135 ± 5 °C and 180 ± 5 °C respectively. The unit cell parameters are identified for each of the three resulting crystalline phases, that for As₂Se₃ : Tl₂Se being orthorhombic while the other two are monoclinic.     

Switching adaptive controllers to control fractional‐order complex systems with unknown structure and input nonlinearities

This article investigates the chaos control problem for the fractional‐order chaotic systems containing unknown structure and input nonlinearities. Two types of nonlinearity in the control input are considered. In the first case, a general continuous nonlinearity input is supposed in the controller, and in the second case, the unknown dead‐zone input is included. In each case, a proper switching adaptive controller is introduced to stabilize the fractional‐order chaotic system in the presence of unknown parameters and uncertainties. The control methods are designed based on the boundedness property of the chaotic system's states, where, in the proposed methods the nonlinear/linear dynamic terms of the fractional‐order chaotic systems are assumed to be fully unknown. The analytical results of the mentioned techniques are proved by the stability analysis theorem of fractional‐order systems and the adaptive control method. In addition, as an application of the proposed methods, single input adaptive controllers are adopted for control of a class of three‐dimensional nonlinear fractional‐order chaotic systems. And finally, some numerical examples illustrate the correctness of the analytical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 211–223, 2015     

Nephroprotective Effects of Alhagi camelorum against Cisplatin-Induced Nephrotoxicity in Albino Wistar Rats

Alhagi camelorum (AC) is an old plant with a significant therapeutic value throughout Africa, Asia, and Latin America. The overuse of cisplatin (Cis > 50 mg/m²) is associated with observed nephrotoxicity, ototoxicity, gastrotoxicity, myelosuppression, and allergic reactions. Remedial measures are needed for the protection of nephrotoxicity against cisplatin. Thus, we investigated the nephroprotective effects of AC plant extract to prevent cisplatin-induced nephrotoxicity in albino Wistar rats. The presence of polyphenols, phenolic compounds, tannins, and saponins was revealed during phytochemical investigation, and a significantly intense antioxidant activity was recorded. There were no toxicological symptoms in the treated rats, and no anatomical, physiological, or histological abnormalities were found compared to the control rats. The results of correcting cisplatin-induced nephrotoxicity revealed that the extract has a significant ability to treat kidney damage, with most parameters returning to normal after only three weeks of therapy. It is concluded that co-administration of cisplatin with AC extract showed exceptional nephroprotective effects at a dose of 600 mg/kg for Cis-induced nephrotoxicity.     

The Effect of the Protein Synthesis Entropy Reduction on the Cell Size Regulation and Division Size of Unicellular Organisms

The underlying mechanism determining the size of a particular cell is one of the fundamental unknowns in cell biology. Here, using a new approach that could be used for most of unicellular species, we show that the protein synthesis and cell size are interconnected biophysically and that protein synthesis may be the chief mechanism in establishing size limitations of unicellular organisms. This result is obtained based on the free energy balance equation of protein synthesis and the second law of thermodynamics. Our calculations show that protein synthesis involves a considerable amount of entropy reduction due to polymerization of amino acids depending on the cytoplasmic volume of the cell. The amount of entropy reduction will increase with cell growth and eventually makes the free energy variations of the protein synthesis positive (that is, forbidden thermodynamically). Within the limits of the second law of thermodynamics we propose a framework to estimate the optimal cell size at division.     

Ferroptosis: A New Road towards Cancer Management

Ferroptosis is a recently described programmed cell death mechanism that is characterized by the buildup of iron (Fe)-dependent lipid peroxides in cells and is morphologically, biochemically, and genetically distinct from other forms of cell death, having emerged to play an important role in cancer biology. Ferroptosis has significant importance during cancer treatment because of the combination of factors, including suppression of the glutathione peroxidase 4 (Gpx4), cysteine deficiency, and arachidonoyl (AA) peroxidation, which cause cells to undergo ferroptosis. However, the physiological significance of ferroptosis throughout development is still not fully understood. This current review is focused on the factors and molecular mechanisms with the diagrammatic illustrations of ferroptosis that have a role in the initiation and sensitivity of ferroptosis in various malignancies. This knowledge will open a new road for research in oncology and cancer management.