Stability of the generalized quadratic and quartic type functional equation in non-Archimedean fuzzy normed spaces

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of non-Archimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-Archimedean absolute value of $2$ is less than $1$ cannot be omitted in our corollaries. The results improve and extend some recent results.     

Synthesis of brominated directly fused diporphyrins through gold(III)-mediated oxidation

Highly efficient synthesis of meso,meso-dibromo doubly and triply fused diporphyrins has been achieved through a powerful oxidative coupling mediated by AuCl3-AgOTf combination. In addition, palladium-catalyzed debromination of meso-bromoporphyrins has been developed. This debromination protocol enables employment of bromine as a protecting group for the reactive meso-position of porphyrins.     

Electric quadrupole moments of the D states of alkaline-earth-metal ions

The electric quadrupole moment for the 4d(2)D(5/2) state of (88)Sr(+); one of the most important candidates for an optical clock, has been calculated using the relativistic coupled-cluster theory. This is the first application of this theory to determine atomic electric quadrupole moments. The result of the calculation is presented and the important many-body contributions are highlighted. The calculated electric quadrupole moment is (2.94 +/- 0.07)ea(2)(0), where a(o) is the Bohr radius and the electronic charge while the measured value is (2.6 +/- 0.3) ea(2)(0). This is so far the most accurate determination of the electric quadrupole moment for the above mentioned state. We have also calculated the electric quadrupole moments for the metastable 4d(2)D(3/2) state of 88(Sr(+) and for the 3d(2)D(3/2.5/2) and 5d(2)D(3/2.5/2) states of (43)Ca(+) and (138)Ba(+), respectively.     

Gamma-induced modifications of polycarbonate polymer

Gamma-induced modifications in polycarbonate polymer have been studied in the dose range of 10¹–10⁶ Gy. Thin films of polycarbonate have been irradiated with different gamma doses from a Co⁶⁰ source. To monitor the modifications caused by gamma radiation, FT-IR, differential scanning calorimetry and X-ray diffraction studies have been performed. The studies have indicated that at the dose of 10⁶ Gy, phenolic group forms through scissioning of ester linkage. Though the effect of radiation is most significant at the highest dose, the process of modifications starts at 10³ Gy. Scissioning of the polymeric chain initiates a different morphological zone within the polymer matrix, and the polymer becomes more crystalline with increasing dose. Owing to chain scissioning, the mobility of the polymer increases, which in turn reduces the glass transition temperature of the polymer.     

Azoester-based H-shaped symmetrical mesogenic dimers containing – CH3/–OCH3 terminal substituent

Two extensive homologous series of H-shaped symmetrical dimers were synthesized and their thermotropic properties studied by differential scanning calorimetry and on a hot-stage of a polarizing microscope. These compounds consist of two mesogenic units of azoester interconnected through flexible spacers (n?=?4) resulting in the structure of ‘H-shaped’ dimeric compounds. The difference between the two series is in the structure of terminal substituents (–CH₃ for series I and –OCH₃ for series II) attached on the azoester mesogens at one terminus. All these compounds were found to be smectogenic. The effect of different terminal substituents on mesomorphism is discussed. The trans-azobenzene groups of the H-shaped dimeric compounds display a high-intensity π–π* transition at about 365?nm and a low-intensity π–π* transition at around 460?nm, therefore, photochromism can be achieved by the introduction of the azo linkage to the H-shaped dimeric compounds.     

Alkyne Versus Ynamide Reactivity: Regioselective Radical Cyclization of Yne‐Ynamides

Ynamides are typically more reactive than simple alkynes and olefins. However, a serendipitous observation revealed a rare case where the reactivity of simple alkynes exceeds that of ynamides. This led to the development of a unique sulfur‐radical‐triggered cyclization of yne‐tethered ynamides, which involves attack of the alkyne by a thiyl radical followed by cyclization with the ynamide. A wide range of novel 4‐thioaryl pyrroles that could tolerate common functional moieties and N‐protecting groups were expediently constructed by this strategy. The current method contrasts with the typical cyclization of yne‐ynamides, which involves the attack of the alkyne moiety by the ynamide core. Control experiments and DFT calculations supported the participation of the sulfur radical in the reaction and the regioselective cyclization. The synthetic potential of the substituted pyrroles is also discussed.     

Fabrication and evaluation of self-nanoemulsifying oil formulations (SNEOFs) of Efavirenz

The current work designed to fabricate and evaluate self-nanoemulsfying oil formulations (SNEOFs) of Efavirenz (Efz) a BCS class II drug with the objective of increasing its solubility as well as in vitro dissolution rate for improvisation of bioavailability. Preliminary screening of drug which includes solubility, emulsifying ability and ternary phase diagrams was carried out to fabricate SNEOFs. Various thermodynamic stability studies were exercised to find out the stable SNEOFs. Robustness to dilution, % transmittance and turbidity, droplet size analysis, TEM study, cloud point measurement, viscosity and refractive index were executed on the stable SNEOFs to characterize the delivery system. FTIR study was adopted for the compatibility of the additives with the drug. In vitro release profiles of SNEOFs compared with Efz, percent dissolution efficiency (DE) and dissolution half-life (t₅₀) were evaluated. A low percent DE (30.12%) and high t₅₀ was obtained for Efz whereas all SNEOFs showed a DE of greater than 78.48% and less than 9?min t₅₀. The optimized SNEOFs (F8) demonstrated a significant (p?<?0.05) increase in bioavailability over Efz. Thus the designed optimized delivery system could be instrumental in increasing aqueous solubility of Efz, improving its release performance and enhancement of oral absorption.     

Molecular conformation and structural correlations of liquid D-1-propanol through neutron diffraction

An analysis of neutron diffraction data of liquid deuterated 1-propanol at room temperature to extract its molecular conformation is presented. Being a big molecule with twelve atomic sites, the analysis is tricky and needs careful consideration. The resulting molecular parameters are compared with electron diffraction (gas phase), X-ray diffraction (liquid phase) and MD simulation results. Information about the hydrogen-bonded intermolecular structure in liquid is extracted and nature of the probable molecular association suggested.      

Solutions with concentration for conservation laws with discontinuous flux and its applications to numerical schemes for hyperbolic systems

Measure-valued weak solutions for conservation laws with discontinuous flux are proposed and explicit formulae have been derived. We propose convergent discontinuous flux-based numerical schemes for the class of hyperbolic systems that admit nonclassical -shocks, by extending the theory of discontinuous flux for nonlinear conservation laws to scalar transport equation with a discontinuous coefficient. The article also discusses the concentration phenomenon of solutions along the line of discontinuity, for scalar transport equations with a discontinuous coefficient. The existence of the solutions for transport equation is shown using the vanishing viscosity approach and the asymptotic behavior of the solutions is also established. The performance of the numerical schemes for both scalar conservation laws and systems to capture the -shocks effectively is displayed through various numerical experiments.