Commutators and Anti-Commutators of Idempotents in Rings

We show that a ring $\,R\,$ has two idempotents $\,e,e'\,$ with an invertible commutator $\,ee'-e'e\,$ if and only if $\,R \cong {\mathbb M}_2(S)\,$ for a ring $\,S\,$ in which $\,1\,$ is a sum of two units. In this case, the "anti-commutator" $\,ee'+e'e\,$ is automatically invertible, so we study also the broader class of rings having such an invertible anti-commutator. Simple artinian rings $\,R\,$ (along with other related classes of matrix rings) with one of the above properties are completely determined. In this study, we also arrive at various new criteria for {\it general\} $\,2\times 2\,$ matrix rings. For instance, $R\,$ is such a matrix ring if and only if it has an invertible commutator $\,er-re\,$ where $\,e^2=e$.Comment: 21 page

Interpreting iron studies

No abstract available

Performance Improvement of Constant Current Controller Based T-type DVR Multilevel Inverter for Solar PV Integrated with Grid

The performance improvement of the T-type DVR Multilevel Inverter for Solar PV Integrated with Grid based Constant Current Controller is defined in this paper. The T-type DVR Multilevel Inverter has decreased the number of switches here. The Controller used for the DVR based T-type MLI is Constant Current Controller which is in cooperated to the solar PV Power Generator with integration to the Grid. A 3 Phase PLL is used in Constant Current Controller for utility grid phase angle tracking and this mechanism will react fast enough to the load changes or different states of Grid connection. This result is supplying constant voltage without any phase jump to the load. Results are discussed for load currents for supplying 2mw load and even a load about 30Mw, 2MVAR. By using Matlab/Simulink, the overall framework is planned and modeled

Socio-Economic Prospects and Major Constraints of Vannamei Shrimp Farming in Kerala

Shrimp farming plays a pivotal role in the socio-economic development of the coastal population of India by way of contributing to foreign exchange earnings and livelihood options. In the current study, the culture technique and stocking density are taken into account for investigating the influence of these factors on the production performance and economic feasibility of vannamei shrimp farming in Kerala. Along with the major constraints faced by the Kerala vannamei farmers also undergoing investigation. In recent years, vannamei shrimp farming has been getting excellent responses from shrimp farmers around Kerala due to the attractive and profitable rewards of shrimp farming. Kodungalloor from Thrissur District is a key area in Vannamei shrimp farming in Kerala, more than 60 shrimp farmers are doing Vannamei shrimp farming very enthusiastically and efficiently. But Kerala State still depends on other States to cater to the processing industry which is a highly labour-intensive sector providing the major avocation to thousands of families. Continuous unfavourable weather conditions and delay in the farm registration process led to non-adoption of vannamei shrimp farming in Kerala. Though the State Government support the vannamei shrimp farmers by notifying shrimp farming as an essential activity, our study showed that additional efforts and supports are required to implement solid plans at the ground level

INTEGRATING PROBLEM-BASED LEARNING SESSIONS WITH DIDACTIC LECTURES IN ANATOMY: A CROSS-SECTIONAL STUDY.

Background:  Anatomy is a very essential science. Knowledge of anatomy is significantly associated in situations with nearly every characteristic of medical modules. Therefore, it is required to be educated and mastered competently by medical students. Aim: The chief objective of this research is to note and examine the outcome of teaching methods for example problem-based learning and seminars when integrated with educational lectures by first-year UG students. Materials and Methods:  This is a cross-sectional study carried out at Andhra Medical College, Visakhapatnam, Andhra Pradesh, India in which 150 students from the first year were included. They were divided into 2 categories, 75 students in each category. Categories 1 and 2 are again subdivided into three categories. Both of the categories undergo seminar and problem-based learning in four chosen topics in the anatomy of the abdomen. An autonomous assessment was done to acknowledge the desired methods. Results:  In topic 1 the average difference between the case-based learning and lecture in both categories is 4 ± 1.18 and 3.4 ± 1.4 respectively. In topic 2, the average difference between the case-based learning and lecture in both categories is 3.9 ± 1.7 and 1.8 ± 1.3 respectively. Conclusion:  In this study, it was evaluated that problem-based learning is more efficacious in relating to critical thinking. However, problem-based learning and seminars both are required with didactic lectures. Recommendation:  Problem-based learning and tuition classes along with conventional lecture sessions are very effective in helping students understand anatomy in a better manner