Bounds for the generalized Marcum function of the second kind

The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use...     

Rapid identification of trimethyl and triethyl amines using sulphonic acidic ionic liquids: A time-of-flight secondary ion mass spectrometry study of fragmentation reactions

The time-of-flight secondary ion mass spectrometry (TOF-SIMS) has emerged as a powerful tool for the unswerving detection of biomolecules, in particular, proteins and peptides. To date, there is very little information available on the direct determination of trimethyl/triethyl amines using TOF-SIMS. One major hurdle in this regard is an ultrahigh vacuum system, usually needed in TOF-SIMS, which hampers its usability to trimethyl/triethyl amines owing to their high evaporation rate. We designed an efficient and sensitive protocol for rapid identification and sensitive determination of tertiaryalkyl amines using TOF-SIMS. The amines were derivatized by reaction with 1,4-butane sultone and sulphuric acid sequentially to afford the corresponding sulphonic acidic ionic liquids (ILs). The TOF-SIMS analysis of these task-specific ILs (TSILs) was carried out in both positive and negative polarity. The positive ion mass spectra of TSILs showed sharp fragmented peaks for tertiaryalkyl amines at typical level and up to 10 ppm. The possible mechanism for different fragmentation pathways in positive polarity was discussed.     

Common fixed point theorems under a new continuity condition

The aim of the present paper is to generalize the notion of reciprocal continuity and obtain common fixed point theorems in diverse settings as an application of the new notion. The new notion unifies the approaches of three well known notions- reciprocal continuity, subsequential continuity and conditional commutativity. Our results generalize and extend several fixed point theorems. We also demonstrate that the new notion is a necessary condition for the existence of common fixed points.     

A Hydrosilylation Approach to Silicon‐Bridged Functional Dipyrromethanes: Introducing Silicon to A New Arena

Two silylene‐spaced ((E)‐vinylsilyl)anthracene‐dipyrromethane dyads have been designed and synthesized by RhCl(PPh₃)₃‐catalyzed hydrosilylation reactions of 5‐methyl‐5′‐(ethynylaryl)dipyrromethanes with (9‐Anthryl)‐dimethylsilane. The complexation studies of dyads toward different anions have also been performed, which reveal that dyads exhibit a highly selective response towards fluoride anion attributable to both hydrogen‐bonding and pentacoordination phenomena. This dual‐mode fluoride recognition event is unprecedented and may pave the way for future developments in the areas of porphyrinoids, organosilicon, polymer, and supramolecular chemistry.     

Synthesis and anion binding of 2-arylazo-meso-octamethylcalix[4]pyrroles

2-Arylazo-5,5,10,10,15,15,20,20-octamethylcalix[4]pyrroles (azo-OMCPs) have been synthesised by the reaction of calix[4]pyrrole with aryldiazonium chloride in 15–45% yields. The solution-state binding studies of the synthesised hosts were investigated by absorption spectroscopy and ¹H NMR in DMSO and CDCl₃, respectively. These receptors, appended with electron-donating and electron-withdrawing groups, displayed enhanced affinity and selectivity for fluoride anion. Well-defined colour change in the visible region of the spectrum was observed upon addition of fluoride ion in DMSO solution of azo-OMCPs. Detailed NMR studies in CDCl₃ revealed that azo-OMCPs with nitro and chloro groups have higher binding affinity for fluoride ion.

     

Room temperature thermoelectric performance of Methyl Ammonium Lead Iodide Perovskite and their MWCNT-PANI composites

The excellent properties of Methyl Ammonium Lead Iodide (MAPI) have already created an extensive research interest in photovoltaic applications. However, their utility in thermoelectric application is still not realized thoroughly by researchers. By continuing this interest, we have explored the formation of low dimensional CH₃NH₃PbI₃ (MAPI) perovskite in presence of Polyaniline (PANI) and Multi-Walled Carbon Nanotubes (MWCNT) and its thermoelectric performance. For this purpose, a two stage, in-situ synthesis method was developed to prepare various composites such as MAPI-PANI, MWCNT-MAPI and MWCNT-PANI-MAPI. The as-formed MWCNT-PANI-MAPI composite revealed p-type conductivity with enhanced ZT (up to ~20,000 times) and power factor (3000 times) at room temperature as compared to pristine MAPI sample. Finally, we have demonstrated a proto-type thermoelectric power generator (TE device) fabricated using the best performing composite sample and measured its power output and efficiency at varied δT.     

Optical nonlinearity of organic dyes as studied by Z-scan and transient grating techniques

The excited state absorption cross-section of 5,5′-dichloro-11-diphenyl-amino-3,3′-diethyl-10, 12-ethylinethiatricarbocyanine perchlorate (IR140) have been measured by using a single beam transmission technique. Z-scan experiments have been used to find out a few nonlinear parameters. The excited state relaxation times have also been measured by using laser induced transient grating (LITG) technique.     

Revisiting Quaternion Dual Electrodynamics

Dual electrodynamics and corresponding Maxwell’s equations (in the presence of monopole only) are revisited from dual symmetry and accordingly the quaternionic reformulation of field equations and equation of motion is developed in simple, compact and consistent manner.     

Generalized Split-Octonion Electrodynamics

Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell’s equations in presence of electric and magnetic charges (dyons). We have thus written the generalized potential, generalized field, and generalized current of dyons in terms of split octonions and accordingly the split octonion forms of generalized Dirac Maxwell’s equations are obtained in compact and consistent manner. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.