Bounded starlike functions of complex order

LetF(b, M) (b ≠ 0 complex,M>1/2) denote the class of functionsf(z) =z + Σ _n=2 ^∞ a _n z ⁿ analytic in U={z:|z|<1} which satisfy for fixedM, f(z)/z ≠ 0 inU and \(\left| {\frac{{b - 1 + \left[ {zf'{{\left( z \right)} \mathord{\left/ {\vphantom {{\left( z \right)} {f\left( z \right)}}} \right. \kern-0em} {f\left( z \right)}}} \right]}}{b} - M} \right|< M, z \in U\) . In this note we obtain various representations for functions inF(b, M). We maximize |a₃=μa ₂ ² | over the classF(b, M). Also sharp coefficient bounds are established for functions inF(b, M). We also obtain the sharp radius of starlikeness of the classF(b, M).     

Novel quantum description of time-dependent molecular interactions obeying a generalized non-central potential

Nonlinear Dynamics - Quantum features of time-dependent molecular interactions are investigated by introducing a time-varying Hamiltonian that involves a generalized non-central potential....     

Probing new physics scale with high-energy neutrinos

Motivated by the new physics beyond the Standard Model through the scale at which neutrino mass has origin, we investigate its possible manifestation at low energy within the corresponding propagation of the energetic neutrino. Then, we consider the SN1987A and base on the recorded neutrino data to explore the scale range of the new physics.     

Electrochemical insights into the mechanisms of proton reduction by [Fe2(CO)6{micro-SCH2N(R)CH2S}] complexes related to the [2Fe](H) subsite of [FeFe]hydrogenase

Electrochemical investigations on a structural analogue of the [2Fe](H) subsite of [FeFe]H(2)ases, namely, [Fe(2)(CO)(6){micro-SCH(2)N(CH(2)CH(2)- OCH(3))CH(2)S}] (1), were conducted in MeCN/NBu(4)PF(6) in the presence of HBF(4)/Et(2)O or HOTs. Two different catalytic proton reduction processes operate, depending on the strength and the concentration of the acid used. The first process, which takes place around -1.2 V for both HBF(4)/Et(2)O and HOTs, is limited by the slow release of H(2) from the product of the {2 H(+)/2 e} pathway, 1-2H. The second catalytic process, which occurs at higher acid concentrations, takes place at different potentials depending on the acid present. We propose that this second mechanism is initiated by protonation of 1-2H when HBF(4)/Et(2)O is used, whereas the reduction of 1-2H is the initial step in the presence of the weaker acid HOTs. The potential of the second process, which occurs around -1.4 V (reduction potential of 1-3H(+)) or around -1.6 V (the reduction potential of 1-2H) is thus dependent on the strength of the available proton source.     

Cleavage of Diethyl Chromonyl α-Aminophosponate with Nitrogen and Carbon Nucleophiles: A Synthetic Approach and Biological Evaluations of a Series of Novel Azoles,Azines, and Azepines Containing α-Aminophosphonate and Phosphonate Groups

A convenient synthetic approach leading to a series of novel substituted azoles, azines, and azepines linked to the α-aminophosphonate moiety was achieved. The methodology depends on ring opening and ring closure (RORC) of the chromone ring of diethyl chromonyl α-aminophosphonate 1 via its reaction with nitrogen nucleophiles such as primary amines and 1,2-, 1,3-, and 1,4-bi-nucleophiles in ethanolic sodium ethoxide. Also, treatment of compound 1 with some acyclic and cyclic active methylene compounds under the same reaction conditions afforded interesting novel isolated and fused pyridine systems bearing phosphonate groups at the α-position. The screening of antimicrobial activity for the synthesized compounds indicates that connection of pyrazole, oxazepine, and benzodiazepine rings with α-aminophosphonate moiety exhibited good antimicrobial effects. Also, evaluation of their antioxidant properties shows that the compounds having 1,5-benzoxazepinyl and 1,5-benzodiazepinyl units in combination with α-aminophosphonic diester moiety are the most powerful antioxidant agents.     

Assessment of Lewis-Acidic Surface Sites Using Tetrahydrofuran as a Suitable and Smart Probe Molecule

Measuring the Lewis-acidic surface sites in catalysis is problematic when the material‘s surface area is very low (S_BET ≤1 m² ⋅ g⁻¹). For the first time, a quantitative assessment of total acidic surface sites of very small surface area catalysts (MoO₃ as pure and mixed with 5–30 % CdO (wt/wt), as well as CdO for comparison) was performed using a smart new probe molecule, tetrahydrofuran (THF). The results were nearly identical compared to using another commonly used probe molecule, pyridine. This audition is based on the limited values of the surface area of these samples that likely require a relatively moderate basic molecule as THF with pK_b=16.08, rather than strong basic molecules such as NH₃ (pK_b=4.75) or pyridine (pK_b=8.77). We propose mechanisms for the interaction of vapour phase molecules of THF with the Lewis-cationic Mo and Cd atoms of these catalysts. Besides, dehydration of isopropyl alcohol was used as a probe reaction to investigate the catalytic activity of these catalysts to further support our findings in the case of THF in a temperature range of 175–300 °C. A good agreement between the obtained data of sample MoO₃-10 % CdO, which is characterised by the highest surface area value, the population of Lewis-acidic sites and % selectivity of propylene at all the applied reaction temperatures was found.     

Caracte´risation ete´tude structurale du bichromate mixte AgKCr2O7

The crystal structure of AgKCr₂O₇ has been determined by single crystal X-ray diffraction. The structure is orthorhombic, space groupPnam, with cell constantsa = 15.175(7),b = 7.414(4), andc = 6.014(2)A? forZ = 4. The structure was refined to a finalR of 0.072 for 934 reflections. The configuration of the dichromate ion, pseudo-C_2v, is similar to that found in most other dichromate structures. The potassium ion is surrounded by eight oxygen atoms and the silver ion has a square planar coordination.     

Photoelectrochemical behavior of coupled SnO2|CdSe nanocrystalline semiconductor films

A photoelectrochemical cell with a coupled SnO₂|CdSe nanocrystalline semiconductor electrode has been prepared by sequential deposition of SnO₂ and CdSe films onto an optically transparent electrode (OTE), and its photoelectrochemical behavior has been studied. The results show that the coupling of CdSe with SnO₂ leads to an improvement in the performance of OTE|SnO₂|CdSe over OTE|CdSe cells in terms of increased incident photon-to-current conversion efficiency, increased stability and smaller reversal of current. The favorable positioning of the energy bands of SnO₂ and CdSe is responsible for the above observations. Various photoelectrochemical parameters of the OTE|SnO₂|CdSe cell obtained for an incident light power of 0.31 mW cm⁻² at 470nm, are as follows: I_sc ≈ 25–30 μA cm⁻², V_oc ≈ 0.5–0.6 V, ƒƒ = 0.47 and a power conversion efficiency of about 2.25%.     

Characterization of polyoxometalate/polymer photo-composites: A toolbox for the photodegradation of organic pollutants

Different inorganic/organic photocomposites based on polyoxometalate (POM) nanoparticles have been developed for photocatalytic applications. Currently, polyoxometalate nanoparticles have been successfully in-situ embedded into an acrylate polymer network by photopolymerization upon mild visible light irradiation at 405 nm. The proposed POM/polymer photocomposites have been characterized using complementary techniques for a better understanding of their photocatalytic activity. Interestingly, the obtained photocomposites exhibit high rigidity, excellent thermal stability, a non-negligible porosity and new functionalities such as light reactivity and redox properties. Moreover, developed composites showed efficient catalytic activity for the color removal of aqueous solutions of erythrosine and rose Bengal under Light Emitting Diodes LED@375 nm irradiation reaching 80 and 90% as a final color removal, respectively.     

Biochemical Properties of Tyrosinase from Aspergillus terreus and Penicillium copticola; Undecanoic Acid from Aspergillus flavus,an Endophyte of Moringa oleifera,Is a Novel Potent Tyrosinase Inhibitor

Tyrosinase is a copper-containing monooxygenase catalyzing the O-hydroxylation of tyrosine to 3,4-dihydroxyphenylalanine then to dopaquinone that is profoundly involved in melanin synthesis in eukaryotes. Overactivation of tyrosinase is correlated with hyperpigmentation that is metabolically correlated with severe pathological disorders, so, inhibition of this enzyme is the most effective approach in controlling the overproduction of melanin and its hazardous effects. Thus, searching for a powerful, selective inhibitor of human tyrosinase to limit the hyper-synthesis of melanin is a challenge. Unlike the difficulty of overexpression of human tyrosinase, using fungal tyrosinase as a model enzyme to the human one to evaluate the mechanistics of enzyme inhibition in response to various compounds is the most feasible strategy. Thus, the purification of highly catalytic-efficient fungal tyrosinase, exploring a novel inhibitor, and evaluating the mechanistics of enzyme inhibition are the main objectives of this work. Aspergillus terreus and Penicillium copticola were reported as the most potential tyrosinase producers. The biochemical properties suggest that this enzyme displays a higher structural and catalytic proximity to human tyrosinase. Upon nutritional bioprocessing by Plackett–Burman design, the yield of tyrosinase was increased by about 7.5-folds, compared to the control. The purified tyrosinase was strongly inhibited by kojic acid and A. flavus DCM extracts with IC₅₀ values of 15.1 and 12.6 µg/mL, respectively. From the spectroscopic analysis, the main anti-tyrosinase compounds of A. flavus extract was resolved, and verified as undecanoic acid. Further studies are ongoing to unravel the in vivo effect and cytotoxicity of this compound in fungi and human, that could be a novel drug to various diseases associated with hyperpigmentation by melanin.