On the study of pH effects in the microwave enhanced rapid synthesis of nano-ZnO

The rapid synthesis of ZnO nanostructures by microwave treatment of aqueous solutions of different pH values is reported for the first time. Microwave in various wattages was used as the source of heating or energy feeding the aqueous precursors. The pH of the zinc metal source was altered by a suitable amount of mineralisers. The considered pH values are 8, 10, 12 and 13.5. Microwave dielectric heating is dependent on the ability of the material to absorb microwave. This is responsible for molecular friction and dielectric loss, which as a result produce internal heating of the dielectric medium, in this case the solution. In typical microwave assisted synthesis, the total exposure to the microwave treatment was near about 25 to 35 minutes. The ZnO nanostructures obtained were studied by XRD, SEM and TEM characterisations. From the XRD pattern and the full width half maximum of the dominant reflections, microstructural parameters of the nanostructures are calculated and compared for the different pH values. Flower petal like flakes and hexagonal nanorods are formed for the lower and higher pH solutions, respectively. From the SEM images, the size distributions for the pH 12 and 13.5 cases are compared by drawing a histogram.     

Electrical characterization of LiCo3/5Fe2/5VO4 ceramics

LiCo_3/5Fe_2/5VO₄ has been synthesized by solution-based chemical method. X-ray diffraction study at room temperature reveals an orthorhombic phase of the compound. Electrical properties are studied using complex impedance spectroscopy (CIS) technique in a range of frequency and temperature. The complex impedance plots identify the grain interior, grain boundary and electrode–material interface contributions to electrical response in the material. Temperature dependence of a.c. and d.c. conductivity indicates that electrical conduction in the material is a thermally activated process. The value of activation energy computed from the Arrhenius plot of σ_dc with 10³/T is ～(0.356 ± 0.012) eV (25–275 °C). Frequency dependence of a.c. conductivity at different temperatures is found to obey Jonscher's universal law.     

Synthesis and characterization of LiCo3/5Mn2/5VO4 ceramics

Dielectric and a.c. conductivity properties of LiCo_3/5Mn_2/5VO₄ ceramic are investigated. This compound is prepared by solution-based chemical method and the formation is checked by X-ray diffraction (XRD) study. XRD analysis at room temperature shows an orthorhombic phase. Frequency dependence of dielectric constant (?_r) at different temperatures shows a dispersive behavior at low frequencies. Temperature dependence of ?_r at different frequencies indicates the transition temperature (T_c) = 235 °C, 245 °C, 257 °C and 265 °C with (?_r)_max. ～3689, 1373, 750 and 386 for 10, 50, 100 and 200 kHz respectively. A.c. conductivity analysis indicates that electrical conduction in the material is a thermally activated process.     

Simultaneous densitometric determination of shikonin,acetylshikonin, and β‐acetoxyisovaleryl‐shikonin in ultrasonic‐assisted extracts of four Arnebia species using reversed‐phase thin layer chromatography

A simple, precise, and rapid high‐performance thin‐layer chromatographic (HPTLC) method for the simultaneous quantification of pharmacologically important naphthoquinone shikonin ( 1 ) together with its derivatives acetylshikonin ( 2 ), and β‐acetoxyisovalerylshikonin ( 3 ) in four species of genus Arnebia (A. euchroma, A. guttata, A. benthamii, and A. hispidissima) from the Indian subcontinent has been developed. In addition, the effect of solvents with varying polarity (hexane, chloroform, ethyl acetate, and methanol) for the extraction of these compounds was studied. HPTLC was performed on precoated RP‐18 F_254S TLC plates. For achieving good separation, mobile phase consisting of ACN/methanol/5% formic acid in water (40:02:08 v/v/v) was used. The densitometric determination of shikonin derivatives was carried out at 520 nm in reflection/absorption mode. The method was validated in terms of linearity, accuracy, precision, robustness, and specificity. The calibration curves were linear in the range of 100–600 ng for shikonin and acetylshikonin, and 100–1800 ng for β‐acetoxyisovalerylshikonin. Lower LOD obtained for compounds 1 – 3 were 18, 15, and 12 ng, respectively, while the LOQ obtained were 60, 45, and 40 ng, respectively.     

Sequential stir bar extraction,thermal desorption and retention time locked GC–MS for determination of pesticides in water

A method based on sequential stir bar sorptive extraction followed by automated thermal desorption–GC–MS for the determination of pesticides in underground and superficial water samples has been developed. Retention time locked GC–MS and deconvolution Automated Mass Spectral Deconvolution and Identification System software allows the use of pesticide databases for identification and quantification in routine applications. Quantitation limits and repetitivity using full scan mass spectrometric determination guarantee the applicability of the method, which enables considerable savings to be made in total analysis time, with data processing times of around 2 min/sample.     

Corrigendum to “Note on zeros of the derivative of the Selberg zeta-function”

We correct constants in asymptotic formulas of our paper “Note on zeros of the derivative of the Selberg zeta-function”, Arch. Math. 91 (2008), 238–246. The online version of the original article can be found under doi:.     

Effective equidistribution of eigenvalues of Hecke operators

In 1997, Serre proved an equidistribution theorem for eigenvalues of Hecke operators on the space S(N,k) of cusp forms of weight k and level N. In this paper, we derive an effective version of Serre's theorem. As a consequence, we estimate, for a given d and prime p coprime to N, the number of eigenvalues of the pth Hecke operator Tp acting on S(N,k) of degree less than or equal to d. This allows us to determine an effectively computable constant Bd such that if J₀(N) is isogenous to a product of Q-simple abelian varieties of dimensions less than or equal to d, then N?Bd. We also study the effective equidistribution of eigenvalues of Frobenius acting on a family of curves over a fixed finite field as well as the eigenvalue distribution of adjacency matrices of families of regular graphs. These results are derived from a general “all-purpose” equidistribution theorem.     

Linear independence of digamma function and a variant of a conjecture of Rohrlich

Let ψ(x) denote the digamma function. We study the linear independence of ψ(x) at rational arguments over algebraic number fields. We also formulate a variant of a conjecture of Rohrlich concerning linear independence of the log gamma function at rational arguments and report on some progress. We relate these conjectures to non-vanishing of certain L-series.     

General proximal point algorithm involving η-maximal accretiveness framework in Banach spaces

First, based on η-maximal accretiveness, a generalization to Rockafellar’s theorem (1976) in the context of approximating a solution to a general inclusion problem involving a multivalued η-maximal accretive mapping using the proximal point algorithm in a q-uniformly smooth Banach space setting is considered. Then an application to a minimization problem of a functional is examined. The general framework for η-maximal accretiveness generalizes the general theory of multivalued maximal monotone mappings.      

Unusual sulfanylation through ring transformation of arene-tethered 2H-pyran-2-ones by in situ built Michael adduct

A novel synthesis of highly functionalized alkylsulfanylmethyl arenes 8a-m through the ring transformation of 6-aryl-4-methyl/ethylsulfanyl-2H-pyran-2-one-3-carbonitriles 1a-j, by reaction with methyl vinyl ketone 2, is delineated and illustrated. To ascertain the course of reaction, 3-arylsulfanylmethyl-2-methyl-6-methylsulfanyl-4-phenylbenzonitriles 8k-m were also prepared from the reaction of 1 with 4-arylsulfanyl-butan-2-ones 7c,d.