Ultrasound irradiation in heterocycle synthesis: An overview

The synthesis of heterocyclic compounds has been a hot topic for several decades. Synthetic organic chemists are always in search of new methodologies which are greener for the synthesis of heterocyclic compounds. The ultrasound-assisted reactions have contributed much to this field. This review focuses on the impact of sonochemistry in the synthesis of heterocyclic compounds and covers the literature from 2009 to 2020.     

A supersingular coincidence

The Ramanujan Journal - The 15 primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 are called the supersingular primes: they occur in several contexts in number theory and also,...     

Measurement of gamma radiation from rocks used as building material in Tiruchirappalli district,Tamil Nadu,India

Tiruchirappalli district is naturally endowed with rich building material resources which are also used in neighboring districts. Hence, measurements of activity concentrations and absorbed dose rate of primordial radionuclides (²³⁸U, ²³²Th and ⁴⁰K) in the rock samples collected from 14 sedimentary rocks and 9 igneous rocks were carried out employing gamma ray spectrometry. In sedimentary rocks the geometric mean activity concentrations of ²³⁸U, ²³²Th and ⁴⁰K were found to be 7.4, 29.5 and 233.6 Bq kg^?1, respectively. On the other hand in igneous rocks geometric mean activity concentrations of ²³⁸U, ²³²Th and ⁴⁰K were distinctly higher and found to be 13.1, 105.7 and 888.8 Bq kg^?1, respectively. The mean radium equivalent activity (Ra_eq) recorded in both sedimentary (20.8 Bq kg^?1) and igneous rocks (245.4 Bq kg^?1) were well within the limit prescribed for dwellings (370 Bq kg^?1) except Vilathupatti (689.3 Bq kg^?1) and Narthamalai (371.6 Bq kg^?1). The mean absorbed dose rate from igneous rock (115 nGy h^?1) exceeded the prescribed limit of 55 nGy h^?1. The mean indoor annual effective dose from the sedimentary rock (0.056 mSv y^?1) and igneous rock (0.580 mSv y^?1) did not exceed the prescribed limit (1 mSv y^?1) except the igneous rock from Vilathupatti (1.51 mSv y^?1). The study concludes that sedimentary and igneous rocks analyzed were radiologically safe when used as building materials except igneous rock from Vilathupatti and Narthamalai.     

On continuous maps between Grassmann manifolds

LetG _n,k denote the Grassmann manifold ofk-planes in ?ⁿ. We show that for any continuous mapf: G _n,k→G_n,l the induced map inZ/2-cohomology is either zero in positive dimensions or has image in the subring generated by w₁(γ_{n, k}), provided 1≤l<k≤[n/2] andn≥k+2l-1. Our main application is to obtain negative results on the existence of equivariant maps between oriented Grassmann manifolds. We also obtain positive results in many cases on the existence of equivariant maps between oriented Grassmann manifolds.     

Evidence for synchronous cleavage of N-H and C-C bonds: bis(2,2￠-bipyridyl)copper(II) permanganate oxidation of cobalt(III) bound and unbound α-amino acids

Summary Oxidation of pentaamminecobalt(III) complexes of α-aminoacids by bis(2,2¢-bipyridyl) copper(II) permanganate in 50% HOAc-50% H₂O (v/v) aqueous acetic acid medium. This oxidation as a diagnostic tool to find out the fraction proceeding by synchronous cleavages of N-H and C-C bonds.     

Molecular Diffusion Measurement in Lipid Bilayers over Wide Concentration Ranges: A Comparative Study

Molecular diffusion in biological membranes is a determining factor in cell signaling and cell function. In the past few decades, three main fluorescence spectroscopy techniques have emerged that are capable of measuring molecular diffusion in artificial and biological membranes at very different concentration ranges and spatial resolutions. The widely used methods of fluorescence recovery after photobleaching (FRAP) and single‐particle tracking (SPT) can determine absolute diffusion coefficients at high (>100 μm^?2) and very low surface concentrations (single‐molecule level), respectively. Fluorescence correlation spectroscopy (FCS), on the other hand, is well‐suited for the intermediate concentration range of about 0.1–100 μm^?2. However, FCS in general requires calibration with a standard dye of known diffusion coefficient, and yields only relative measurements with respect to the calibration. A variant of FCS, z‐scan FCS, is calibration‐free for membrane measurements, but requires several experiments at different well‐controlled focusing positions. A recently established FCS method, electron‐multiplying charge‐coupled‐device‐based total internal reflection FCS (TIR‐FCS), referred to here as imaging TIR‐FCS (ITIR–FCS), is also independent of calibration standards, but to our knowledge no direct comparison between these different methods has been made. Herein, we seek to establish a comparison between FRAP, SPT, FCS, and ITIR–FCS by measuring the lateral diffusion coefficients in two model systems, namely, supported lipid bilayers and giant unilamellar vesicles.