Prime Producing Quadratic Polynomials and Class Number One or Two

Let d≡ 5 mod 8 be a positive square-free integer and let h(d) be the class number of the real quadratic field ℚ(√d). Let p be a divisor of d = pq and let . Assume that is prime or equal to 1 for all integers x with 0≤x<W. Under the assumption that the Riemann hypothesis is true, we prove that if , then h(d) < 2. Furthermore we show that h(d)< 2 implies d < 4245. In the case when there exists at least one split prime less than W, we prove the following results without any assumptions on the Riemann hypothesis. If then h< 2 or h = 4. If , then h≤ 2, h = 4 or h = 2^t−2, where t is the number of primes dividing d. In the case when h = 2^t−2 we have , where φ = 2 or 4. 2000 Mathematics Subject Classification: Primary–11R29     

Thermal and energy management prospects of γ-AlOOH hybrid nanofluids for the application of sustainable heat exchanger systems

Journal of Thermal Analysis and Calorimetry - This study focuses on double-tube heat exchanger (DTHE) to numerically examine their thermal performance by considering two types of hybrid nanofluids:...     

Multi-targeted molecular docking,drug-likeness and ADMET studies of derivatives of few quinoline- and acridine-based FDA-approved drugs for anti-breast cancer activity

Structural Chemistry - Quinoline- and acridine-based drugs are widely used as anti-breast cancer agents. These drugs act through various mechanisms of action; for example, neratinib acts on...     

The isomeric compounds nimbolide and isonimbolide

Nimbolide [systematic name: (4α,5α,6α,7α,15β,17α)‐7,15:21,23‐diepoxy‐6‐hydroxy‐4,8‐dimethyl‐1‐oxo‐18,24‐dinor‐11,12‐secochola‐2,13,20,22‐tetraene‐4,11‐dicarboxylic acid γ‐lactone methyl ester], C₂₇H₃₀O₇, was isolated from the leaves of Azadirachta indica, and its isomer, isonimbolide [systematic name: (4α,5α,6α,7α,15α)‐7,15:21,23‐diepoxy‐6‐hydroxy‐4,8‐dimethyl‐1‐oxo‐18,24‐dinor‐11,12‐secochola‐2,16,20,22‐tetra­ene‐4,11‐dicarboxylic acid γ‐lactone methyl ester], was prepared from a novel rearrangement reaction of nimbolide, using boron trifluoride etherate and tetra­butyl­ammonium bromide. The reaction conditions are probably responsible for the ether cleavage, double‐bond rearrangement and reformation of the ether linkage. As a result, there are conformational changes in two cyclo­pentane rings and the side‐chain –CH₂COOMe group. In isonimbolide, an (24) hydrogen‐bond motif is observed.     

Influence of pH in La-doped SnO2 nanoparticles towards sensor applications

The present investigation has been carried out to optimize the pH level of lanthanum (La)-doped tin dioxide (SnO₂) nanoparticles towards the potential application in gas sensor. The La-doped SnO₂ nanoparticles were synthesized by sol-gel method in different pH values varying from acidic to base nature. The synthesized nanoparticles were characterized by X-ray diffraction (XRD), ultraviolet (UV), photoluminescence (PL), and scanning electron microscopy (SEM) techniques. The XRD, UV, and PL analyses show the pH influences on the crystallite size of La-doped SnO₂ nanoparticles. The SEM images show the formation of porous structure at pH 11. Also, the electrical conductivity of 1 mol% La-doped SnO₂ at pH 3 and pH 11 were measured by impedance analyzer. In addition, we have fabricated and demonstrated device performance of synthesized La-doped SnO₂ nanoparticles for gas-sensing application. Real-time current response and long-time response to the gas sensing were also studied for the fabricated device.

     

Synthesis and characterization of immobilized activated carbon doped TiO2 thin films

Immobilized activated carbon doped TiO₂ thin films were prepared by sol–gel dip coating method by using Titanium IV isopropoxide as a precursor. Aim of our work is to synthesize and investigate the structural, surface morphology and optical properties of the synthesized thin film. X-ray diffraction pattern reveals that the crystallinity of the film increases with increase in temperature. Also, the structural parameters such as particle size, microstrain and dislocation density have been calculated. The formation of nanosphere of diameter ranging from 300 nm to 500 nm has been confirmed by Scanning electron microscope. Photocatalytic active large optical band gap at 3.75 eV was found by using UV–visible sspectrum.     

Development and validation of an LC-MS/MS-ESI method for the determination of lorglumide, a CCK-1 antagonist in mouse plasma: application to a pharmacokinetic study

A highly sensitive, rapid assay method was developed and validated for the estimation of lorglumide in mouse plasma using liquid chromatography coupled to tandem mass spectrometry with electrospray ionization in positive‐ion mode. The assay procedure involves extraction of lorglumide and phenacetin (internal standard, IS) from mouse plasma with simple protein precipitation. Chromatographic separation was achieved using an isocratic mobile (0.2% formic acid solution–acetonitrile, 20:80, v/v) at a flow‐rate of 0.5 mL/min on an Atlantis dC₁₈ column maintained at 40 °C with a total run time of 4.0 min. The MS/MS ion transitions monitored were 459.2 → 158.4 for lorglumide and 180.1 → 110.1 for IS. Method validation was performed as per FDA guidelines and the results met the acceptance criteria. The lower limit of quantitation achieved was 0.42 ng/mL and the linearity range extended from 0.42 to 500 ng/mL. The intra‐ and inter‐day precisions were in the ranges of 1.47–10.9 and 3.56–7.53, respectively. Copyright © 2011 John Wiley & Sons, Ltd.     

EXISTENCE OF LIMIT CYCLES FOR A CUBIC KOLMOGOROV SYSTEM WITH A PARABOLIC SOLUTION WHICH DOES NOT CONTACT AND INTERSECT THE COORDINATE AXES

This paper is concerned with a cubic Kolmogorov system with a parabolicsolution which does not contact and intersect the coordinates. The conclusionis that such a system may possess limit cycles.     

Effect of substrates on the structural,morphological, and optical properties of sprayed CdO thin films using nebulizer

CdO thin films were deposited on glass, quartz, FTO, silicon wafers of p-type and n-type at 200?°C of substrate temperature employing spray pyrolysis technique using nebulizer. As deposited cadmium oxide thin films were analyzed to find crystallite size, morphology of the substrate, elemental composition and band gap using X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDAX) and UV–Vis spectrophotometer. Nature of the thin film was found to be polycrystalline with face centered cubic structure with (111) preferential orientation and evaluated structural parameters show significant effect of used substrates. Spherical sized grains were observed on the surface of the thin films using SEM. The EDAX analysis confirmed that cadmium and oxygen were present in the sample. Direct allowed transition with band gap values lying in the range 2.34–2.44?eV for all the films deposited on various substrates. Among, these thin film coated on FTO substrate was found to have high crystallinity with a narrow band gap, which may be more suitable for opto-electronic applications.

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The absorption co-efficient spectra and inset of transmittance spectra with wavelength of CdO thin films at different substrates (Glass, Quartz and FTO).