Integrability of det▽u and Evolutionary Wente''s Problem Associated to Heat Operator

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det▽u for u ∈ H1(R2,R2) is used.     

Spectral and voltammetric studies on titanium substituted Keggin-type heteropolyanions

Bonding and redox properties of mono- and dititanium substituted 12-heteropolytungsto-phosphates and their complexes with bivalent Mn, Co, Ni and Cu are studied by UV-Vis, ESR and cyclicvoltammetric techniques. The heteropoly blue analogue [Ti^IIITi^IVW₁₀PO₄₀]⁸⁻ is unstable and its presence in solution is proved by optical and ESR spectroscopy. ESR results reveal that the odd electron is trapped on the titanium atom at 77 K. The optical electronegativity of Ti(III) in this heteropoly blue is estimated to be 2.4 from the intervalence charge transfer (IVCT) bands. X-ray powder diffraction results show that the complexes K₅M^II[Ti₂W₁₀PO₄₀].xH₂O(M^II = Cu or Mn) are isomorphous with K₇[Ti₂W₁₀PO₄₀].6H₂O. Electronic spectroscopy indicates very high symmetry around the bivalent metal ion M in the K₅M^II[Ti₂W₁₀PO₄₀].xH₂O complexes. This high symmetry is confirmed in K₅Cu[Ti₂W₁₀PO₄₀] by the observation of dynamic Jahn-Teller (JT) distortion at 300 K and static JT distortion at 77 K.     

Turing determinacy and the continuum hypothesis

From the hypothesis that all Turing closed games are determined we prove: (1) the Continuum Hypothesis and (2) every subset of ₁ is constructible from a real.     

Pinacol-Pinacolone Rearrangement of 1, 2-Di-(p-methoxyphenyl)-ethane-1, 2-diol and Bis-(4-methoxyphenyl)-acetaldehyde in Acid Media

1, 2-Di-(p-methoxyphenyl)-ethane-1, 2-diol gave in acid media bis-(4-methoxy-phenyl)-acetaldehyde, 4-4′-dimethoxy-deoxybenzoin, and 1, 2-di-(p-methoxyphenyl)-ethylene oxide; their respective yields being influenced by at least 3 factors: (i) the acid, (ii) its concentration, and (iii) the reaction period. Bis-(4-methoxyphenyl)-acetaldehyde rearranged to the deoxybenzoin in boiling sulfuric (50%) or phosphoric (75%) acids (w/w), and to two isomeric 1, 2-diacetoxy-1, 2-di-(p-methoxyphenyl) ethanes when it was heated with acetic anhydride. The mechanisms of these reactions are discussed.     

Unsteady incompressible flow of magnetized aluminium oxide and titanium oxide nanoparticles with blood base fluid

In this investigation, a mixed convective nanoparticles fluid flow over an inclined plate is deliberated. The effects of slip boundary wall and magnetic field are also considered. The dimensionless governing system for the considered problem is attained by implementing recent definitions of fractional derivatives (FD). The generalized solution is obtained through the Laplace Transformation Scheme (LTS) for the momentum and thermal expressions. To improve the novelty and to demonstrate some more physical perception of the stated research work, some remarkable special cases of velocity distribution through CF and AB-fractional derivative concept are addressed, whose daily life implication is well known in the existing literature. Moreover, to evaluate the physical interest of the stated problem, the outcomes of the obtained system graphical illustrations are made by utilizing MATHEMATICA. As a result, we concluded that the aluminium oxide $A{l}_2{O}_3$ nanoparticles show more decaying behavior as compared to titanium oxide $Ti{O}_2$ nanoparticles for temperature and velocity profile. Furthermore, both fields i.e., momentum and thermal distributions are increased with the help of rising estimations parameter. Current results report novel applications in enhancement of heat transfer, thermal engineering, chemical processes, engineering and electronics devices, solar systems, extrusion processes, fission reactions etc.     

Hall effects and entropy generation applications for peristaltic flow of modified hybrid nanofluid with electroosmosis phenomenon

The electroosmotic peristaltic flow of modified hybrid nanofluid in presence of entropy generation has been presented in this thermal model. The Hall impact and thermal radiation with help of nonlinear relations has also been used to modify the analysis. The assumed flow is considered due to a non-uniform trapped channel. The properties of modified hybrid nanofluid model are focused with interaction of three distinct types of nanoparticles namely copper ($Cu)$, silver ($Ag$) and aluminum oxide ($A{l}_2{O}_3).$ The mathematical modeling and significances of entropy generation and Bejan number are identified. With certain flow assumptions, the governing equations are attained for optimized peristaltic electroosmotic problem. Widely used assumptions of long wave length and low Reynolds number reduced the governing equations in ordinary differential equations. The ND solver is flowed for the solution process. The physical significant of results is observed by assigning the numerical values to parameters.     

Microscale Thermophoresis and Molecular Modelling to Explore the Chelating Drug Transportation in the Milk to Infant

The microscale thermophoresis (MST) technique was utilized to investigate lactoferrin–drug interaction with the iron chelator, deferiprone, using label-free system. MST depends on the intrinsic fluorescence of one interacting partner. The results indicated a significant interaction between lactoferrin and deferiprone. The estimated binding constant for the lactoferrin–deferiprone interaction was 8.9 × 10⁻⁶ ± 1.6, SD, which is to be reported for the first time. Such significant binding between lactoferrin and deferiprone may indicate the potentiation of the drug secretion into a lactating mother’s milk. The technique showed a fast and simple approach to study protein–drug interaction while avoiding complicated labeling procedures. Moreover, the binding behavior of deferiprone within the binding sites of lactoferrin was investigated through molecular docking which reflected that deferiprone mediates strong hydrogen bonding with ARG121 and ASP297 in pocket 1 and forms H-bond and ionic interaction with ASN640 and ASP395, respectively, in pocket 2 of lactoferrin. Meanwhile, iron ions provide ionic interaction with deferiprone in both of the pockets. The molecular dynamic simulation further confirmed that the binding of deferiprone with lactoferrin brings conformational changes in lactoferrin that is more energetically stable. It also confirmed that deferiprone causes positive correlation motion in the interacting residues of both pockets, with strong negative correlation motion in the loop regions, and thus changes the dynamics of lactoferrin. The MM-GBSA based binding free energy calculation revealed that deferiprone exhibits ∆G TOTAL of −63,163 kcal/mol in pocket 1 and −63,073 kcal/mol in pocket 2 with complex receptor–ligand difference in pocket 1 and pocket 2 of −117.38 kcal/mol and −111.54 kcal/mol, respectively, which in turn suggests that deferiprone binds more strongly in the pocket 1. The free energy landscape of the lactoferrin–deferiprone complex also showed that this complex remains in a high energy state that confirms the strong binding of deferiprone with the lactoferrin. The current research concluded that iron-chelating drugs (deferiprone) can be transported from the mother to the infant in the milk because of the strong attachment with the lactoferrin active pockets.