Regular homeomorphisms of connected 3-manifolds

We establish some equivalent conditions to the Hilbert–Smith conjecture on connected n-manifolds M. For n = 3; we show that regularly almost periodic homeomorphisms of M are periodic; this result extends Theorem 5.34 of Gottschalk and Hedlund (Topological Dynamics. American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, 1956). For the special case of \({M = \mathbb{R}^3}\) , we extend the result of Brechner (Pac J Math 59(2):367–374, 1975) saying that “almost periodic homeomorphisms of the plane are periodic” to \({\mathbb{R}^3}\) , and we show that any compact abelian group of homeomorphisms of \({\mathbb{R}^3}\) is either finite or topologically equivalent to a subgroup of the orthogonal group O(3).     

Bio-based Poly(hydroxy urethane)s: Synthesis and Pre/Post-Functionalization

New and emerging demand for polyurethane (PU) continues to rise over the years. The harmful isocyanate binding agents and their integrated PU products are at the height of environmental concerns, in particular PU (macro and micro) pollution and their degradation problems. Non-isocyanate poly(hydroxy urethane)s (NIPUs) are sustainable and green alternatives to conventional PUs. Since the introduction of NIPU in 1957, the market value of NIPU and its hybridized materials has increased exponentially in 2019 and is expected to continue to rise in the coming years. The secondary hydroxyl groups of these NIPU′s urethane moiety have revolutionized them by allowing for adequate pre/post functionalization. This minireview highlights different strategies and advances in pre/post-functionalization used in biobased NIPU. We have performed a comprehensive evaluation of the development of new ideas in this field to achieve more efficient synthetic biobased hybridized NIPU processes through selective and kinetic understanding.     

Selective Structural Derivatization of Flavonoid Acetamides Significantly Impacts Their Bioavailability and Antioxidant Properties

Flavonoids show abundant favorable physicochemical and drug related properties, leading to substantial biological applications which are limited by undesirable properties such as poor solubility, high polarity, low bioavailability, and enzymatic degradations. Chemical modification with bioisosteres can be used to address some of these challenges. We report the synthesis and characterization of partial flavonoid acetamide derivatives from quercetin, apigenin and luteolin and the evaluation of their structure-activity relationships based on antioxidant, bioavailability, drug likeness, and toxicity properties. The sequential synthesis was achieved with 76.67–87.23% yield; the structures of the compounds were confirmed using ¹H & ¹³C NMR characterizations. The purity of each compound was determined by HPLC while the molecular weights were determined by mass spectrometry. The % bioavailability was determined using the dialysis tubing procedure and the values were in the range 15.97–38.12%. The antioxidant activity was determined by the 2,2-diphenyl-1-picrylhydrazyl (DPPH) assay and expressed as the IC₅₀ values which were in the range 31.52–198.41 µM. The drug likeness and the toxicity properties of compounds 4, 5, 7, 11 and 15 were predicted using computational tools and showed satisfactory results. A structure-activity relationship evaluation reveals that hydroxyl and methylene groups attached on the 2-phenylchromen-4-one structure of the flavonoid play a colossal role in the overall antioxidant and bioavailability properties. The improved bioavailability and excellent drug relevance and toxicity properties present flavonoid acetamide derivatives as prospective drug candidates for further evaluations.     

Hybrid solar cells using nanorod zinc oxide electrodes and perylene monoimide–monoanhydride dyes

Hybrid solar cells have been fabricated using perylene monoimide–monoanhydride dyes with nanorod zinc oxide electrodes as electron transporting layers. We have investigated the influence of the spacer alkyl chain length of perylene monoimide–monoanhydride (PMIMA) dyes on the device performance in hybrid solar cells using nanorod zinc oxide electrodes. Nanorod zinc oxide electrodes with 50–150 nm of diameter were synthesized in the presence of PEG400 by using microwave heating method. We observed that the dyes with longer and brunched alkyl chains exhibit higher efficiencies in hybrid solar cells. We report the highest efficiency obtained with zinc oxide nanorods under standard conditions for perylene monoimide–monoanhydride derivative with PMIMA_1 that performs 400 mV open circuit voltage, 2.81 mA/cm² short-circuit current and 0.59% overall conversion efficiency.     

Synthesis,vibrational and UV–visible studies of sodium cadmium orthophosphate

In this paper, NaCdPO₄ orthophosphate was prepared by solid-state reaction technique at high temperature. Structural, vibrational and optical properties have been investigated. X-ray powder diffraction analysis revealed that the titled compound crystallizes in the orthorhombic system with Pmnb space group. Vibrational study by means of Raman and FTIR spectroscopies confirms the existence of the (PO₄)^3? functional group. Optical properties were recorded at room temperature using UV–visible spectroscopy in the spectral range (200–800) nm. The UV–Vis absorption bands are attributed to the charge transfer from the oxygen ligands to the central phosphate atom inside the PO₄ ^3? groups. The optical absorbance was measured also to determinate the optical band gap using Kubelka–Munk function. The dispersion parameters (E₀ and E_d) of this compound were estimated using the Wemple Di-Domenico model.     

Necessary optimality conditions for a semivectorial bilevel optimization problem using the kth-objective weighted-constraint approach

Positivity - In this paper, we have pointed out that the proof of Theorem 11 in the recent paper (Lafhim in Positivity, 2019. https://doi.org/10.1007/s11117-019-00685-1 ) is erroneous. Using...     

Extremal Problems on Components and Loops in Graphs

The authors recently defined a new graph invariant denoted by Ω(G) only in terms of a given degree sequence which is also related to the Euler characteristic. It has many important combinatorial applications in graph theory and gives direct information compared to the better known Euler characteristic on the realizability, connectedness, cyclicness, components, chords, loops etc. Many similar classification problems can be solved by means of Ω. All graphs G so that Ω(G) ≤-4 are shown to be disconnected, and if Ω(G) ≥-2, then the graph is potentially connected. It is also shown that if the realization is a connected graph and Ω(G) =-2, then certainly the graph should be a tree.Similarly, it is shown that if the realization is a connected graph G and Ω(G) ≥ 0, then certainly the graph should be cyclic. Also, when Ω(G) ≤-4, the components of the disconnected graph could not all be cyclic and if all the components of G are cyclic, then Ω(G) ≥ 0. In this paper, we study an extremal problem regarding graphs. We find the maximum number of loops for three possible classes of graphs.We also state a result giving the maximum number of components amongst all possible realizations of a given degree sequence.     

Analysis of five HMG-CoA reductase inhibitors-- atorvastatin, lovastatin, pravastatin, rosuvastatin and simvastatin: pharmacological, pharmacokinetic and analytical overview and development of a new method for use in pharmaceutical formulations analysis and in vitro metabolism studies

A specific, accurate, precise and reproducible high-performance liquid chromatographic (HPLC) method was developed and validated for the simultaneous quantitation of five 3-hydroxy-3-methyglutaryl coenzyme A (HMG-CoA) reductase inhibitors, viz. atorvastatin, lovastatin, pravastatin, rosuvastatin and simvastatin, in pharmaceutical formulations and extended the application to in vitro metabolism studies of these statins. Ternary gradient elution at a flow rate of 1 mL/min was employed on an Intertisl ODS 3V column (4.6 x 250 mm, 5 microm) at ambient temperature. The mobile phase consisted of 0.01 m ammonium acetate (pH 5.0), acetonitrile and methanol. Theophylline was used as an internal standard (IS). The HMG-CoA reductase inhibitors and their metabolites were monitored at a wavelength of 237 nm. Drugs were found to be 89.6-105.6% of their label's claim in the pharmaceutical formulations. For in vitro metabolism studies the reaction mixtures were extracted with simple liquid-liquid extraction using ethyl acetate. Baseline separation of statins and their metabolites along with IS free from endogenous interferences was achieved. Nominal retention times of IS, atorvastatin, lovastatin, pravastatin, rosuvastatin and simvastatin were 7.5, 17.2, 21.6, 28.5, 33.5 and 35.5 min, respectively. The proposed method is simple, selective and could be applicable for routine analysis of HMG-CoA reductase inhibitors in pharmaceutical preparations as well as in vitro metabolism studies.