In this paper we provide some important and significant observations on invo-regular rings appeared in Ann. Univ. Mariae Curie-Sklodowska Sect. A Mathematica (2018). In addition we exhibit that strongly invo-regular rings, invo-regular rings and quasi invo-regular rings all coincide with the well known and well characterized tripotent rings and all these rings further coincide with the well known unit regular rings.

In this note we consolidate and give a brief description of several recently published results in ring theory having disproof. These results have been published during 2016 to 2021 in the so called non-predatory reputed mathematical journals indexed in the well known database like Scopus. We have considered results on rings in which each element is a sum of two idempotents appeared in Canad. Math. Bull. (2016), weakly tripotent rings appeared in Bull. Korean Math. Soc. (2018) and Rendiconti Sem. Mat. Univ. Pol. Torino (2021), involution t-clean rings appeared in Eur. J. Pure Appl. Math (2022) and strongly 2-nil clean rings with units of order two appeared in Eur. J. Pure Appl. Math (2023).

In this article some important observations have been reported on recent works related to weakly tripotent rings and locally invo-regular rings. Our findings give additional results as well as correct some recent results on weakly tripotent rings and locally invo-regular rings appeared in Rendiconti Sem. Mat. Univ. Pol. Torino (2021) and Azerbaijan Journal of Mathematics (2021) respectively. In addition we exhibit that if the Jacobson radical J(A) of a ring is strongly involution t-clean then the characteristic of J(A) need not be four. This finding improves an important result appeared in Eur. J. Pure Appl. Math (2022).

Several mathematicians and physicists are working all over the globe to get a unified theory. However, most of them are discarding Einstein’s view at the very first step of their theories. This article provides a brief description about this. Also, on the basis of Koga’s theory we point out two reasons which might have caused Einstein’s failure to get a unified theory.

In this note we introduce the notion of polynions and discuss their mathematical relevance. We note that the well-known mathematical structures like quaternions, octonions and sedenions etc. are special cases of polynions.

Pre-monsoon dust aerosols over Indian regions are closely linked to the monsoon dynamics and Indian summer monsoon rainfall. Past observational studies have shown a decline in dust loading over the Indian landmass potentially caused by changing rainfall patterns over the desert regions. Such changes are expected to have far reaching impact on regional energy balance and monsoon rainfall. Using a regional climate-chemistry model, RegCM4.5 with an updated land module, we have simulated the long-term (2001-2015) changes in dust over the arid and semi-arid dust source regions of the North-Western part of the sub-continent. It is found that the area-averaged dust aerosol optical depth (AOD) over the arid and semi-arid desert regions has declined by 17% since the start of this millennium. The rainfall over these regions exhibits a positive trend of 0.1 mm day^-1year^-1 and a net increase of > 50%. The wet deposition is found to be dominant and ~5 fold larger in magnitude over dry deposition and exhibits total changes of ~ 79 % and 48% in the trends in atmospheric dust. As a response, significant change in the surface (11%), top of the atmosphere radiative forcing (7%), and widespread atmospheric cooling are observed in short wave domain of radiation spectrum, over the Northern part of the Indian landmass. Such quantification and long term change studies are necessary for understanding the regional climate change and the water cycle.