On the Variety of Shapes in Digital Trees

We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we be very explicit about the specification of the underlying measure-theoretic formulation. We show that (under appropriate normalization) for such a collection, any linear combination of the number of occurrences of each of the motifs in the data has a limiting normal distribution. In many instances, this can be interpreted in terms of the number of occurrences of individual motifs: They have a multivariate normal distribution. The methods of proof include combinatorics on words, integral transforms, and poissonization.     

The fractional natural decomposition method: theories and applications

In this paper, we propose a new method called the fractional natural decomposition method (FNDM). We give the proof of new theorems of the FNDM, and we extend the natural transform method to fractional derivatives. We apply the FNDM to construct analytical and approximate solutions of the nonlinear time‐fractional Harry Dym equation and the nonlinear time‐fractional Fisher's equation. The fractional derivatives are described in the Caputo sense. The effectiveness of the FNDM is numerically confirmed. Copyright © 2016 John Wiley & Sons, Ltd.     

TiO<Subscript>2</Subscript> nanoparticles doped with Celestine Blue as a label in a sandwich immunoassay for the hepatitis C virus core antigen using a screen printed electrode

The authors describe an electrochemical immunoassay for the core antigen of hepatitis C virus (HCV). The method is based on the use of a screen-printed carbon electrode (SPCE) that was modified with a Nafion@TiO₂ nanocomposite and loaded with secondary antibody (Ab2) to entrap Celestine Blue (CB). The material has architecture of the type CB/Ab2/Nafion@TiO₂. A nanocomposite consisting of graphene, ionic liquid and fullerene was deposited on the SPCE first, and rhodium nanoparticles (RhNPs) were then deposited on the surface of modified electrode in order to immobilize primary antibody (Ab1). The antigen and CB/Ab2/Nafion@TiO₂ were conjugated one by one to form a sandwich-type immunocomplex. The signal was obtained by differential pulse voltammetry whose intensity is related to the concentration of the antigen. The assay, if operated at a working voltage of typically 0.35 V (vs. Ag/AgCl) has a response that is linear in the 0.1 to 250 pg?mL^?1 HCV core antigen concentration range, and the limit of detection is as low as 25 fg?mL^?1. The assay was applied to the determination of the HCV core antigen in spiked human serum samples. In our perception, the method represents a promising platform for the detection of various antigens if appropriate antibodies are available.

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Graphical abstract An electrochemical immunoassay for the core antigen of Hepatitis C virus was studied. A nanocomposite consisting of graphene, ionic liquid and fullerene was deposited on the SPCE and rhodium nanoparticles were deposited on the surface of modified electrode in order to immobilize primary antibody. Nafion@TiO₂ was loaded with secondary antibody to entrap Celestine Blue.

     

Unusual product from the acid-catalyzed one-pot,multicomponent reaction of thiocarbohydrazide,aldehydes, and phenacyl bromides

A one-pot, three-component protocol for the synthesis of novel five-membered thiazole ring bonded to two hydrazone motifs is described. The acid-catalyzed reaction of one equivalent of thiocarbohydrazide, two equivalents of aromatic aldehydes, and one equivalent of phenacyl bromides afforded the five-membered thiazole ring. The reactions proceed with novel chemoselectivity. Similar reported protocols have always afforded 1,3,4-thiadiazines.     

Polymer-Enhanced Capillary Transient Isotachophoresis with Boronic Acid-Functionalized Squarylium Dyes for the Fluorescent Determination of Digoxin and Digoxigenin

Here is reported a new application of polymer-enhanced capillary transient isotachophoresis for the separation and quantification of the drug digoxin and its primary metabolite digoxigenin coupled with laser-induced fluorescence (LIF) detection facilitated by labeling with two boronic acid-functionalized squarylium dyes of different alkyl side chain lengths, SQ-BA1 and SQ-BA2. The conditions for drug–dye complex formation were optimized, as determined by absorbance and fluorescence spectra, according to solution pH and buffer composition. As digoxin has a digitoxose sugar moiety in its structure, it was shown to exhibit better enhancement in the fluorescence intensity of both dyes than digoxigenin, which lacks this moiety, presumably through the formation of a cyclic boronate ester complex. A comparison of analyte labeling in pre-column and on-column modes was conducted in subsequent capillary electrophoresis-LIF studies, with the latter labeling mode yielding superior sensitivity. However, to achieve the complete resolution of labeled digoxin and digoxigenin analytes, it was necessary to use the modified isotachophoresis method, with added borate ions that may differentially interact with the drug and its metabolite, hence affecting their mobilities. Limits of quantification of the method for the determination of digoxin with SQ-BA1 and SQ-BA2 were 2.61?×?10^?3 and 2.82?×?10^?3?M and limits of detection were 7.83?×?10^?4 and 8.47?×?10^?4?M while sensitivities were as great as 5.06?×?10⁹ and 2.89?×?10⁹?M^?1, respectively, indicating that the method is suitable for practical analysis.     

New nanobidentate Schiff base ligand of 2-aminophenol with 2-acetyl ferrocene with some lanthanide metal ions: synthesis,characterization and Hepatitis A,B, C and breast cancer docking studies

Three lanthanide complexes (La(III), Er(III), and Yb(III)) derived from ferrocene-based Schiff base ligand (HL) were synthesized from condensation of 2-aminophenol with 2-acetylferrocene. The ligand and metal complexes were characterized based on elemental analyses, IR, ¹H NMR, molar conductance, SEM and thermal analyses (TG, DTG). The molar conductance revealed that all the metal chelates were electrolytes having the general composition [M(L)(Cl)(H₂O)₃]Cl·4H₂O. HL and its complexes were screened for their antibacterial and antifungal activity by agar diffusion method. The results of these studies showed that the metal complexes are more effective antibacterial and antifungal agents as compared with the free ligand. The anticancer activity was screened against human breast cancer cell line (MCF-7). Results indicated that metal complexes showed an increased cytotoxicity in proliferation to cell lines as compared to free ligand. Molecular docking studies were performed to identify the binding orientation or conformation of a complex in the active site of the protein. HL and its complexes were docked with crystal structure of DDB1 of breast cancer, crystal structure of HCV, RNA-dependent RNA polymerase, receptors of HBV core protein, crystal structure of the Fab fragment of anti-HAV.     

A High Sensitive TNT Sensor Based on Electrochemically Reduced Graphene Oxide‐Poly(amidoamine) Modified Electrode

In this paper, the electrochemically reduced graphene oxide‐poly(amidoamine) hybrid (ErGO‐PAMAM) have been used for fabrication of TNT electrochemical sensor. The prepared modified electrode is characterized with X‐ray photoelectron spectroscopy (XPS), fourier transform infrared spectroscopy (FT‐IR), electrochemical impedance spectroscopy (EIS), energy‐dispersive X‐ray (EDX) spectroscopy, scanning electron microscopy (SEM) and atomic force microscope (AFM). Based on obtained results, it is can be seen that the ErGO‐PAMAM/GCE has high response to TNT than the other graphene based modified electrodes. The resulting electrochemical sensor exhibited good response to TNT with linear range from 0.05 to 1.2 ppm with a low detection limit of 0.0015 ppm.     

Thermal radiation effects on MHD flow of a micropolar fluid over a stretching surface with variable thermal conductivity

In this paper, the effects of variable thermal conductivity and radiation on the flow and heat transfer of an electrically conducting micropolar fluid over a continuously stretching surface with varying temperature in the presence of a magnetic field are considered. The surface temperature is assumed to vary as a power-law temperature. The governing conservation equations of mass, momentum, angular momentum and energy are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically. The numerical results show that the thermal boundary thickness increases as the thermal conductivity parameter S$S$ increases, while it decreases as the radiation parameter F$F$ increases. Also, it was found that the Nusselt number increases as F$F$ increases and decreases as S$S$ increases.     

Synthesis of tacrine derivatives under solventless conditions

Effects of microwave irradiation on the solid‐phase synthesis of tacrine and its derivatives have been evaluated. Preparation of tacrine analogues under conventional conditions suffers from poor synthetic efficiency and usually gives low yield. Reaction of substituted anthranilonitrile with cyclohexanone under microwave irradiation gave a good to excellent yield of the corresponding substituted 9‐amino‐1,2,3,4‐tetrahydroacridines.