Diameter of a direct power of a finite group

We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of Gⁿ with respect to each generating set is at most n(|G|?rank(G)); and the second one states that there exists a generating set 𝒜, of minimum size, for Gⁿ such that the diameter of Gⁿ with respect to 𝒜 is at most n(|G|?rank(G)). We will establish evidence for each of the above mentioned conjectures.     

MgO Nanoparticles as a Recyclable Heterogeneous Catalyst for the Synthesis of Polyhydroquinoline Derivatives under Solvent Free Conditions

Magnesium oxide nanopartticels in average size between 35–120 nm were prepared by sonochemistry method. Synthesis of polyhydroquinoline derivatives using MgO nanoparticles from the reaction of dimedone, benzaldehyde, ethyl acetoacetate and ammonium acetate under solvent‐free conditions is reported. Easy handling, reusability, thermal stability and non‐toxicity of the catalyst make the present protocol as an eco‐friendly and economically acceptable method for synthesis of these heterocycles.     

Phytochemical analysis and antimicrobial activities of methanolic extracts of leaf, stem and root from different varieties of Labisa pumila Benth

A local herb, Kacip Fatimah, is famous amongst Malay women for its uses in parturition; however, its phytochemical contents have not been fully documented. Therefore, a study was performed to evaluate the phenolics, flavonoids, and total saponin contents, and antibacterial and antifungal properties of the leaf, stem and root of three varieties of Labisia pumila Benth. Total saponins were found to be higher in the leaves of all three varieties, compared to the roots and stems. Leaves of var. pumila exhibited significantly higher total saponin content than var. alata and lanceolata, with values of 56.4, 43.6 and 42.3 mg diosgenin equivalent/g dry weight, respectively. HPLC analyses of phenolics and flavonoids in all three varieties revealed the presence of gallic acid, caffeic acid, rutin, and myricetin in all plant parts. Higher levels of flavonoids (rutin, quercitin, kaempferol) were observed in var. pumila compared with alata and lanceolata, whereas higher accumulation of phenolics (gallic acid, pyrogallol) was recorded in var. alata, followed by pumila and lanceolata. Antibacterial activities of leaf, stem and root extracts of all varieties determined against both Gram positive (Micrococcus luteus, Bacillus subtilis B145, Bacillus cereus B43, Staphylococcus aureus S1431) and Gram negative (Enterobacter aerogenes, Klebsiella pneumonia K36, Escherichia coli E256, Pseudomonas aeruginosa PI96) pathogens showed that crude methanolic extracts are active against these bacteria at low concentrations, albeit with lower antibacterial activity compared to kanamycin used as the control. Antifungal activity of methanolic extracts of all plant parts against Fusarium sp., Candida sp. and Mucor using the agar diffusion disc exhibited moderate to appreciable antifungal activities compared to streptomycin used as positive control.     

SBA-15-functionalized TEMPO confined ionic liquid: an efficient catalyst system for transition-metal-free aerobic oxidation of alcohols with improved selectivity

A novel SBA-15-functionalized TEMPO confined ionic liquid [BMIm]Br was found to be a highly efficient and recyclable catalyst system for the transition-metal-free aerobic oxidation of a wide range of structurally diverse alcohols. Thanks to the strong physical confinement of the ionic liquid inside the mesochannels of SBA-15-supported TEMPO, the resulting solid catalyst showed improved selectivity in the aerobic oxidation of allylic alcohols. The catalyst can be recovered and re-used for at least 11 reaction runs without significant loss of either activity or confined IL.     

An Efficient One‐Pot,Four‐Component Synthesis of {[(1H‐1,2,3‐Triazol‐4‐yl)methoxy]phenyl}‐1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione Derivatives

The 1‐{[(1H‐1,2,3‐Triazol‐4‐yl)methoxy]phenyl}‐1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione derivatives 5 were synthesized by a simple and efficient method, i.e., by the four‐component, one‐pot condensation reaction of phthalohydrazide 4 , a (propargyloxy)benzaldehyde 1 , an active methylene compound 3 (malononitrile or ethyl cyanoacetate), and an azide 2 in the presence of Cu(OAc)₂/sodium L ‐ascorbate as catalyst and 1‐methyl‐1H‐imidazolium trifluoroacetate ([Hmim](CF₃COO)) as an ionic‐liquid medium in good to excellent yields (Scheme 1).     

A novel lyotropic liquid crystal formed by triphilic star-polyphiles: hydrophilic/oleophilic/fluorophilic rods arranged in a 12.6.4. tiling

Triphilic star-polyphiles are short-chain oligomeric molecules with a radial arrangement of hydrophilic, hydrocarbon and fluorocarbon chains linked to a common centre. They form a number of liquid crystalline structures when mixed with water. In this contribution we focus on a hexagonal liquid crystalline mesophase found in star-polyphiles as compared to the corresponding double-chain surfactant to determine whether the hydrocarbon and fluorocarbon chains are in fact demixed in these star-polyphile systems, or whether both hydrocarbon and fluorocarbon chains are miscible, leading to a single hydrophobic domain, making the star-polyphile effectively amphiphilic. We report SANS contrast variation data that are compatible only with the presence of three distinct immiscible domains within this hexagonal mesophase, confirming that these star-polyphile liquid crystals are indeed hydrophilic/oleophilic/fluorophilic 3-phase systems. Quantitative comparison with scattering simulations shows that the experimental data are in very good agreement with an underlying 2D columnar (12.6.4) tiling. As in a conventional amphiphilic hexagonal mesophase, the hexagonally packed water channels (dodecagonal prismatic domains) are embedded in a hydrophobic matrix, but that matrix is split into oleophilic hexagonal prismatic domains and fluorophilic quadrangular prismatic domains.     

On the Properties of Convex Multilayered Cyclofusene

Cyclofusene is a corona-condensed benzenoid whose graph-theoretic representation consists of hexacycles each having exactly two non-adjacent shared edges. Multilayered cyclofusene is a fused hexacylic system which can be partitioned into successive layers of cyclofusene. In such systems, an edge shared by two consecutive hexacycles in the same layer is termed radial. We present upper bounds for the number of radial π-bonds in a convex k-layered cyclofusene.     

Analysis and design of a dye-doped polymer optical fiber amplifier

A rhodamine-B-doped polymer optical fiber amplifier (RBDPOFA) has been successfully fabricated and tested. In this paper, all parameters affecting the gain of the RBDPOFA are recognized. The time-dependent and time-independent rate equations are solved. By using Runge–Kutta and finite-element methods, different conditions are described and fluctuations of the fiber laser are analyzed. From the time-dependent rate equations, the gain and level-density variations with time can be predicted. These fiber amplifiers have unstable conditions. In experiments, the decay of dye dopants in the high pump power regime has been observed. For example, in a high pump power rhodamine-B is converted from the zwitterion isomer to the colorless lactone isomer [1]. Therefore, for complete coincidence of theoretical and experimental results, this effect must be included in the analysis, which is however beyond the scope of this paper and will be discussed in the near future. PACS 42.60.Da; 42.81.Wg; 31.15.Fx; 33.80.-b; 42.55.WdAn erratum to this article can be found at     

Electrochemical Characterization of In Situ Functionalized Gold Cysteamine Self‐Assembled Monolayer with 4‐Formylphenylboronic Acid for Detection of Dopamine

Functionalization of gold cysteamine (Au? CA) self‐assembled monolayer with 4‐formylphenylboronic acid (BA) via Schiff's base formation, through in situ method to fabricate Au‐CA‐BA electrode is presented and described. The fabricated electrode was used as a novel sensor for accumulation and determination of dopamine (DA). The accumulation of DA as a diol on the topside of Au‐CA‐BA as a Lewis acid, was performed via esterification (Au? CA? BA? DA), and followed for determination of DA. Functionalization, characterization, and determination steps were probed by electrochemical methods like cyclic voltammetry and electrochemical impedance spectroscopy. The data will be presented and discussed from which a new sensor for DA is introduced.     

Robust synchronization of a class of uncertain chaotic systems based on quadratic optimal theory and adaptive strategy

This paper presents a chaos synchronization method for a class of uncertain chaotic systems using the combination of an optimal control theory and an adaptive strategy. A quadratic optimal regulator and an adaptive control are used to represent the controller's structure. The asymptotic stability of the corresponding error dynamical system is guaranteed through Lyapunov stability analysis. The proposed controller is employed in two uncertain chaotic Lu systems, and their promising performances are illustrated.