The Tate-Shafarevich group for elliptic curves with complex multiplication II

Let E be an elliptic curve over Q with complex multiplication. The aim of the present paper is to strengthen the theoretical and numerical results of \cite{CZS}. For each prime p, let t_{E/Q, p} denote the Z_p-corank of the p-primary subgroup of the Tate-Shafarevich group of E/Q. For each \epsilon 0, we prove that t_{E/Q, p} is bounded above by (1/2+\epsilon)p for all sufficiently large good ordinary primes p. We also do numerical calculations on one such E of rank 3, and 5 such E of rank 2, showing in all cases that t_{E/Q, p} = 0 for all good ordinary primes p < 30,000. In fact, we show that, with the possible exception of one good ordinary prime in this range for just one of the curves of rank 2, the p-primary subgroup of the Tate-Shafarevich group of the curve is zero (always supposing p is a good ordinary prime).Comment: 24 page

Lexical Similarities and Differences in the Mathematics, Science and English Language Textbooks

The teaching of Science and Math in English in Malaysia is an area of great concern to educators and students alike. This study looks, in particular, at the common word classes among keywords identified in the Science, Math and English language Form One textbooks used in Malaysia and the differences in language use identified in the Science and Math textbooks

The GL_2 main conjecture for elliptic curves without complex multiplication

The main conjectures of Iwasawa theory provide the only general method known at present for studying the mysterious relationship between purely arithmetic problems and the special values of complex L-functions, typified by the conjecture of Birch and Swinnerton-Dyer and its generalizations. Our goal in the present paper is to develop algebraic techniques which enable us to formulate a precise version of such a main conjecture for motives over a large class of p-adic Lie extensions of number fields. The paper ends by formulating and briefly discussing the main conjecture for an elliptic curve E over the rationals Q over the field generated by the coordinates of its p-power division points, where p is a prime greater than 3 of good ordinary reduction for E.Comment: 39 page

C7: Comparison of Four Dental Pulp-Capping Agents by Cone-Beam Computed Tomography and Histological Techniques—A Split-Mouth Design Ex Vivo Study

Dental pulp-capping is done to preserve vital teeth when the pulp is exposed due to caries, trauma or instrumentation. Various materials are used as pulp-capping agents. The introduction of newer materials requires scientific studies to assess their clinical efficacy. The study was designed as a split-mouth randomized analysis of four pulp-capping agents (calcium hydroxide, mineral trioxide aggregate (MTA), Biodentine and EndoSequence root repair material (ERRM)). Based on selection criteria, 15 orthodontic patients requiring the extraction of four premolars (60 teeth total) were included in the study. After pulp-capping, the teeth were extracted after 8 weeks. We analyzed the extracted teeth using cone-beam computed tomography (CBCT) and histological sections to determine the quality of the dentinal bridge and the pulpal response. Ordinal scores were given based on the completeness of the dentinal bridge, the type of bridge and the degree of pulpal inflammation. Results were analyzed using a Kruskal–Wallis test (p \u3c 0.05) with post hoc Conover values being used when applicable. All four pulp-capping materials elicited dentinal bridge formation (60/60). MTA had the highest scores (10/15) in dentinal bridge formation followed by ERRM (8/15). Both materials showed more samples with complete dentinal bridges (9/15 each) and a favorable pulpal response (15/15). Teeth capped with calcium hydroxide showed more cases of incomplete bridge formation (9/15) and pulpal inflammation. These differences in dentinal bridge formation and pulpal inflammation were statistically significant (p 0.001 and p 0.00005, respectively), with post hoc tests revealing no significant differences between MTA and ERRM (p 0.49 and p 0.71, respectively). MTA and ERRM performed better than the other pulp-capping materials but did not differ significantly from each other. The individual preference for a pulp-capping material may be based on clinical efficacy and handling characteristics

The main conjecture

In his important papers [16], [17], Wiles proved in most cases the so-called main conjecture for the cyclotomic Zp-extension of any totally real base field F, for all odd primes p, and for all abelian characters of Gal(Q¯ /F) (we say most cases because his work only establishes the main conjecture up to µ-invariants for those abelian characters whose order is divisible by p). It would be technically too difficult for us in these introductory lectures to attempt to explain his proof in this generality. Instead, we have chosen the much more modest path of giving a sketch of his proof in the very special case that F = Q, and for all abelian characters of Q of p-power conductor. In fact, our account of Wiles’ proof in this case has been directly inspired by a series of lectures on this theme, which we attended, given by Chris Skinner in an instructional conference held at the Centre of Mathematical Sciences, Zhejiang University, Hangzhou, China, in August 2004

B1: Determination of reliability and practicality of saliva as a genetic source by analyzing DNA yield in forensic investigation : A systematic review”

Background Genetic analysis has become the mainstay of forensic identification protocols. Oral fluids including saliva are invariably present in crime and disaster scenarios; their availability probably exceeding that of conventional sources like blood. Due to the intrinsic nature of fluids, the substrates may be degraded due to time delay and environmental exposure. Therefore, a review of the reliability and practicality of saliva in forensic analysis is warranted. Objectives This review is designed and planned to present and critically analyze the most relevant clinical trials on the application of saliva in forensic settings in order to assess the reliability of saliva for DNA analysis. Data sources and eligibility criteria Thorough literature search was performed via Pubmed/Medline database, the Cochrane Trial register and Clinical Trial registry of India. Only the clinical trials that specifically mentioned the use of saliva for DNA analysis were eligible and included. Eight trials were included for the analysis. Study appraisal Customized data collection were generated and compiled by two independent evaluators. Risk assessment and qualitative synthesis was performed. Results and conclusions Using qualitative thematic synthesis, it was observed that saliva, especially whole saliva, collected in specific kits under stabilization, was a sufficient source of DNA, especially for PCR and genotyping methods, irrespective of environmental conditions and time delay. The observations indicate that saliva is a reliable and practical source of DNA for forensic settings

Level and Witt groups of real enriques surfaces

The Witt group of a real Enriques surface having real points is computed purely in terms of the topology of the real part. For a real Enriques surface without real points the level of the function field is shown to be 2, and the Witt group is computed in this case as well

A study on the efficacy and adverse effects of methotrexate in psoriasis patients in a tertiary care centre

Background: Psoriasis is a common, chronic and recurrent inflammatory disease of the skin. Methotrexate has been used in patient with psoriasis, a folic acid antagonist interfering with purine pathway and the mechanism of action in psoriasis is immune modulation and anti-inflammation. So, this study aims at monitoring the efficacy and adverse effects of methotrexate in south Indian patients with psoriasis attending a tertiary care hospital.Methods: It is a prospective, observational study conducted for a period of one year in subjects of either sex having psoriasis. Methotrexate was initiated in a single weekly oral dose of 5mg to 25mg. The efficacy was evaluated using psoriasis Area and Severity Index (PASI) score in all patients before starting methotrexate therapy and the end of first month, third month and sixth month of therapy. Adverse reaction was monitored.Results: All 40 psoriasis patients after treatment with methotrexate therapy showed improved  skin lesions by falling PASI scoring at the end of first, third and sixth month of treatment. None of the patients in our study had pulmonary toxicity, life threatening adverse effects which required hospitalization.Conclusions: Use of methotrexate in the treatment of psoriasis in this study was found to be safe and highly efficacious and caused minimal adverse effects and it was well tolerated

Optimization and Performance Evaluation of Single Axis Arduino Solar Tracker

The use of clean energy (Solar, Wind etc) in other words, renewable energy is becoming more important for lowering global warming as the world becomes hotter as a result of global warming . The aim of this paper is to consume the maximum solar energy through solar panel. A Solar Tracker is a device onto which solar panels are built-in which tracks the motion of the sun ensuring that maximum amount of sunlight strikes the panels all over the day. Power output from a solar cell will be high when it is facing the sun. The components used for its construction are servo motor, Arduino Mega (microcontroller) and LDR. Light Dependent Resistors (LDRs) are used for sunlight detection. The active sensors continuously monitor the sunlight and alternate the panel towards the direction of the sun. Four light dependent resistors (LDR) have been used to trace the synchronization of sunlight by detecting brightness level of sunlight. For rotation, two standard servo motors are been used. The effectiveness of output power will increase when compared with the traditional model(Fixed solar panel)