Raghunathpur College

In 2002, the ground-breaking concept, known as Click Chemistry, was independently presented by Sharpless and Meldal. The reaction involves the advent of Cu(I)-catalyzed Huisgen type 1,3-dipolar cycloaddition known as copper-catalyzed azide-alkyne cycloaddition (CuAAC) to yield the 1,4-disubstituted 1,2,3 triazoles in a regioselective manner. Later on, several other metals such as Ni, Rh, Ir, Zn, Ag etc. are used, and non-metal pathways like the electrochemical method and thermal method have also been developed for the azide-alkyne cycloaddition (AAC). Click chemistry promotes chemical reactions that enable the connection of two species in a simple and selective way, with few or no by-products under mild conditions. The extensive applications of this reaction in several industries have made it a booming research area. Due to the triazole linkage's characteristics as a peptide mimic, this chemistry also facilitates bioconjugation and peptide ligation. Herein, we have summarized all the emerging methodologies developed during 2016-2025 with an enduring description. This review will be very useful to synthetic/medicinal chemists, researchers of materials science, and in the catalysis domains.

We study here relations between three inequality indices, namely the Gini (g), Pietra (p) and Kolkata (k) introduced in 1912, 1915 and 2014 respectively and all are derived from the Lorenz function L(x) introduced in 1905. The Kolkata index (which corresponds to a fixed point of the complementary Lorenz function L_c(x) ≡ 1-L(x)) gives the fraction of wealth k possessed by the richest 1-k fraction of people (k = 0.8 corresponds to Pareto's 80-20 law from 1896). We show rigorously that the Pietra or Robin Hood index p should equal to the excess wealth 2k-1 possessed by the richest 1-k people. Our numerical data analysis for US IRS Income data (1983-2022), Bollywood (India) movie income data (1999-2024) and the citation inequalities across the publications by forty Nobel Laureates (2020-2025) in Economics, Physics, Chemistry and Medicine clearly shows that p/(2k -1) is always greater than unity but the deviation is never more than five percent. Assuming some simple analytic form for the Lorenz function, we also derived the relations k = (1/2) + (3/8)g for small g values and p/g = 3/4. However, these relations generally deviate significantly for larger g or k values when compared with observations.

By emulating the complex hierarchical assemblies found in bio-derived materials, nanostructural synthetic designs expand material properties and enlarge their capability for versatile applications. Correspondingly, polymerization-induced self-assembly (PISA) emerges as a controllable, innovative pathway to realize such intricate nanostructures. The present study aims to design block copolymer nano/micro-objects spanning from typical micelles, worms, jellyfish, and vesicles to scarcely attainable large compound vesicles, spongosome-like complex structures, and inverted micelles through PISA formulation. To obtain these in situ self-assembled structures, a series of block copolymers was synthesized via reversible addition-fragmentation chain transfer (RAFT) dispersion polymerization of a pyroglutamate-pendant styrenic monomer (VBPGA) using poly(N,N-dimethylacrylamide) (PDMA) as a steric stabilizer in an alcohol/water binary solvent mixture at 65 °C. Various parameters, including solvophobic and solvophilic chain lengths, monomer solid content, cosolvent, stirring rate, and salt addition, were used as levers to achieve the morphological diversification. Differing from the traditional hydrophobicity or solvophobicity-driven self-assembly of block copolymers, the introduction of VBPGA as a unique core-forming precursor creates a fuzzy interface between hydrophilic and hydrophobic domains in PDMA-b-PVBPGA block copolymers through hydrogen bonding among amide groups and hydrophobic interactions, enabling the realization of an extended morphological window with fascinating inverse structures at a relatively shorter length of the PVBPGA segment.

The analysis of income and wealth inequality is often constrained by the lack of reliable data. In this work, we introduce a proxy-based approach in which sports performance data are used to mimic economic distributions. In particular, the total runs scored by a batter in a single T20 season are treated as an analogue of annual income, while the cumulative runs scored across all seasons are taken to represent individual wealth. Using run distributions from the Indian Premier League (IPL), we explore how inequality evolves and estimate its upper limits in the absence of policy intervention. Our findings indicate that inequality derived from seasonal runs closely resembles the highest levels of income inequality observed in real-world data. In addition, the distribution of cumulative runs evolves over time and gradually approaches a limiting value consistent with global patterns of wealth inequality, in line with the Pareto principle. Overall, this study shows that proxy systems can capture essential features of economic inequality and offer a useful way to understand its inherent limits.