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

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

To evaluate the efficacy of diagnostic modalities used in chronic pancreatitis: prospective hospital based observational study

INTRODUCTION: Chronic pancreatitis is a continuous or recurrent inflammatory disease of the pancreas characterized by progressive and irreversible morphological changes. It typically causes pain and permanent impairment of pancreatic function. Late in the course of the disease a progressive loss of endocrine and exocrine functions occur. AIM OF THE STUDY: To study the efficacy of imaging modalities like USG, CT, MRCP, and EUS in a case of chronic pancreatitis. MATERIALS AND METHODS: Study Design: Prospective and observational analysis of patients with chronic pancreatitis admitted in PSG Hospital, Coimbatore, during the period Jan 2011 - June 2012. Study Population: Study will be conducted in 30 patients with chronic pancreatitis admitted in PSG Hospital in general surgery and medical gastroenterology departments. Ethical approval: The study protocol was approved by the Institute Human Ethics Committee (IHEC) prior to the start of the study. Inclusion Criteria: All chronic pancreatitis patient admitted in our hospital will be included in the study. Exclusion Criteria: 1. Patient’s with previous history of surgery for chronic pancreatitis. 2. Chronic pancreatitis in children. 3. Malignancy. 4. Patient who do not consent. CONCLUSION: In this prospective observational study conducted in 30 patients with chronic pancreatitis at PSG Hospital, Coimbatore, the following conclusions were made. • Most of the patients in their 3rd decade of life. • Male preponderance was observed in the ratio 2.7:1 • Most common etiological factor was alcohol followed by idiopathic. • Pain abdomen and epigastric tenderness is the common presentation in our study. • In our study MRCP was the commonly done imaging modality in diagnosing Chronic Pancreatitis as the morphologic changes in the glandular tissue, ductal anatomy, degree and level of pancreatic duct obstruction are well made out in comparison to CT. In our small study group it has been seen that MRCP scores over CT in diagnosis of CP having specificity of 100%. • Though CT is less specific than MRCP in diagnosing CP, still it is a valuable radiological tool in diagnosing CP in centers where MRCP is not available. • Efficacy of EUS can not be concluded in our study as it was done in only two patients. • Medical management is the first line treatment in CP. • Out of 30 patients, 5 (16.7%) underwent surgery. Four out of five patients underwent modified Puestow’s as this is the commonly performed surgery for chronic pancreatitis, one underwent head coring (Frey’s Procedure). • Post operatively pain relief was 65% in our study. • None of the patient had pancreatic leak