Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications

In this paper, we study certain interesting and useful properties of incomplete $\aleph$-functions. The incomplete $\aleph$-function is an extension of the $\aleph$-function. We find several useful classical integral transforms of these functions. Further, we examine the fractional calculus with the incomplete $\aleph$-functions and point out several special cases. Finally, we give the applications of incomplete $\aleph$-functions in detecting glucose supply in human blood.     

Ionic Assembly,Anion–π, Magnetic,and Electronic Attributes of Ambient Stable Naphthalenediimide Radical Ions

Organic spin-based molecular materials are considered to be attractive for the generation of functional materials with emergent optoelectronic, magnetic, or magneto-conductive properties. However, the major limitations to the utilization of organic spin-based systems are their high reactivity, instability, and propensity for dimerization. Herein, we report the synthesis, characterization, and magnetic and electronic studies of three ambient stable radical ions ( 1 a^.+ , 1 b^.+ , and 1 c^.+ ). The radical ions 1 b^.+ and 1 c^.+ with BPh₄⁻ and BF₄⁻ counter anions, respectively, were synthesized in excellent yields by means of anion metathesis of 1 a^.+ with Br⁻ as its counter anion. Notably, synthesis of 1 a^.+ was achieved in an ecofriendly, solvent-free protocol. The radical ions were characterized by means of single-crystal X-ray diffraction studies, which revealed the discrete nature of the radical ions and extensive hydrogen-bonding interactions within the radical ions and with the counter anions. Thus, radical ions can be organized to form infinite supramolecular arrays using weak noncovalent interactions. In addition, the Br⁻, BF₄⁻, and BPh₄⁻ anions formed diverse types of anion–π interactions with the naphthalene and imide rings of the radical ions. The radical ions were characterized by means of X-band electron paramagnetic resonance (EPR) spectroscopy in solution and in the solid state. Magnetic studies revealed their paramagnetic nature in the range of 10 to 300 K. The radical ions exhibited high resistivity approaching the gigaohm (GΩ) scale. In addition, the radical ions exhibited panchromism.     

Direct synthesis of Poly(Ԑ-Caprolactone)-block-poly (glycidyl methacrylate) copolymer and its usage as a potential nano micelles carrier for hydrophobic drugs

Ring-opening (ROP) and enzymatic copolymerization (ECP) are among the most widely used approaches for synthesizing copolymers of polycaprolactone (PCL). It involves multiple-step reactions and the utilization of enzymes that make the process a lot more complicated, time consuming, and expensive. Atom transfer radical polymerization (ATRP) has been adopted to synthesize a novel amphiphilic copolymer in our study. The study presents a method to eliminate the ROP/ECP multiple steps in monomer polymerization thus making the process simpler and smoother. The synthesis of cationic polymer micelles copolymer of PCL-PGMA (polycaprolactone grafted poly glycidyl methacrylate) was carried out using direct functionalization of hydroxy group in crude PCL to achieve a higher degree of functionalization, i.e., 12.8% for macroinitiator. FTIR and ¹H-NMR confirmed the successful synthesis of the copolymer with better control over the molecular weight with a PDI (1.84). DSC and XRD results showed the reduction of crystallinity by 86.81%, making copolymer more compatible for drug delivery application. The synthesized copolymer was further converted to nano-micelles drug carrier having an average size of 96.08 ± 21.22 nm. The drug encapsulation efficiency achieved was 60.0 ± 1.7%, and nano-micelles rendered a slow and controlled release of naproxen with long-term storage stability.     

Michael addition of ethyl anthranilate and phenyl monothioanthranilate to acetylenic esters: experimental and theoretical results

Structural Chemistry - The reaction of ethyl anthranilate with DMAD and with methyl propiolate in dichloromethane in the presence of ethylaluminium dichloride as catalyst at room temperature gives...     

MHD laminar wall jet over a curved surface in a variable normal magnetic field

The effects of a magnetic field on jets of an electrically conducting fluid flowing over a curved surface, in the presence of a variable normal magnetic field, are studied. It is noted that the convex surface curvature h and the magnetic interaction parameter m, in small perturbation similarity solution have qualitatively similar effects. They increase the mass flux, decrease the momentum flux, decrease the wall shear and cause an adverse pressure gradient in the flow field.     

Hydromagnetic laminar and turbulent free jet

The flow of a laminar and turbulent plane free jet of a viscous, incompressible, electrically conducting fluid in the presence of a transverse magnetic field is studied. Using the Prandtlvon Mises transformation, in both the cases, closed form solutions are obtained. A remarkable similarity with the nonmagnetic solutions is noticed. Critical values of the magnetic interaction parameter are determined when the dragging action of the initial momentum is exactly balanced by the retarding effect of the magnetic field resulting in the zero axial velocity field.On leave from V.V. (P.G.) College, Shamli-247776, INDIA.     

Synthesis of polyester from renewable feedstock: a comparison between microwave and conventional heating

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Effect of ion velocity on SHI-induced mixing in Ti/Bi system

Energetic ion beams are proving to be versatile tools for modification and depth profiling of materials. The energy and ion species are the deciding factor in the ion-beam-induced materials modification. Among the various parameters such as electronic energy loss, fluence and heat of mixing, velocity of the ions used for irradiation plays an important role in mixing at the interface. The present study is carried out to find the effect of the velocity of swift heavy ions on interface mixing of a Ti/Bi bilayer system. Ti/Bi/C was deposited on Si substrate at room temperature by an electron gun in a high-vacuum deposition system. Carbon layer is deposited on top to avoid oxidation of the samples. Eighty mega electron volts Au ions and 100?MeV Ag ions with same value of S_e for Ti are used for the irradiation of samples at the fluences 1?×?10¹³–1?×?10¹⁴ ions/cm². Different techniques like Rutherford backscattering spectroscopy, atomic force microscopy and grazing incidence X-ray diffraction were used to characterize the pristine and irradiated samples. The mixing effect is explained in the framework of the thermal spike model. It has been found that the mixing rate is higher for low-velocity Au ions in comparison to high-velocity Ag ions. The result could be explained as due to less energy deposition in thermal spike by high-velocity ions.