Efficient generation, unimodular element in a geometric subring of a polynomial ring

Let $R$ be a commutative Noetherian ring of dimension $d$. First, we define the "geometric subring" $A$ of a polynomial ring $R[T]$ of dimension $d+1$ (the definition of geometric subring is more general, see (1.2)). Then we prove that every locally complete intersection ideal of height $d+1$ is a complete intersection ideal. Thus improving the general bound of Mohan Kumar \cite{NMK78} for an arbitrary ring of dimension $d+1$. Afterward, we deduce that every finitely generated projective $A$-module of rank $d+1$ splits off a free summand of rank one. This improves the general bound of Serre \cite{Serre58} for an arbitrary ring. Finally, applications are given to a set-theoretic generation of an ideal in the geometric ring $A$ and its polynomial extension $A[X]$.Comment: 12 page

Facile and Green Synthesis of Novel Fluorescent Carbon Quantum Dots and Their Silver Heterostructure: An In Vitro Anticancer Activity and Imaging on Colorectal Carcinoma

Carbon dots (CQDs) have been widely investigated as prime candidates for developing a tumor theranostic platform due to their tunable fluorescence emission and excitation, high water solubility, good photostability, and biocompatibility. Among the CQDs, natural CQDs are an emerging class of nanomaterials in the carbon family. Herein, highly fluorescent carbon quantum dots (CQDs) were synthesized from orange juice using a one-step hydrothermal method and characterized by different techniques. After that, CQD/Ag heterostructures were synthesized by the reduction of silver salt, in particular silver nitrate (AgNO3) solution using sodium borohydride (NaBH4) in different ratios. The photostability and characterization of CQD/Ag heterostructures were investigated. At last, a comparative cellular toxicity measure-ment was done to select the superior CQD/Ag heterostructure in the human colorectal carcinoma (HCT 116) cell line along with the imaging property. The detailed cell death signaling was also observed in the HCT 116 cell line via the ROS-dependent mitochondrial-mediated pathway, where Akt (RAC-alpha serine/threonine-protein kinase) played a important role

Abstracts of National Conference on Research and Developments in Material Processing, Modelling and Characterization 2020

This book presents the abstracts of the papers presented to the Online National Conference on Research and Developments in Material Processing, Modelling and Characterization 2020 (RDMPMC-2020) held on 26th and 27th August 2020 organized by the Department of Metallurgical and Materials Science in Association with the Department of Production and Industrial Engineering, National Institute of Technology Jamshedpur, Jharkhand, India. Conference Title: National Conference on Research and Developments in Material Processing, Modelling and Characterization 2020Conference Acronym: RDMPMC-2020Conference Date: 26–27 August 2020Conference Location: Online (Virtual Mode)Conference Organizer: Department of Metallurgical and Materials Engineering, National Institute of Technology JamshedpurCo-organizer: Department of Production and Industrial Engineering, National Institute of Technology Jamshedpur, Jharkhand, IndiaConference Sponsor: TEQIP-