Liouville Numbers and Schanuel's Conjecture

In this paper, using an argument of P. Erdos, K. Alniacik and E. Saias, we extend earlier results on Liouville numbers, due to P. Erdos, G.J. Rieger, W. Schwarz, K. Alniacik, E. Saias, E.B. Burger. We also produce new results of algebraic independence related with Liouville numbers and Schanuel's Conjecture, in the framework of G delta-subsets.Comment: Archiv der Math., to appea

Liouville numbers, Liouville sets and Liouville fields

Following earlier work by E.Maillet 100 years ago, we introduce the definition of a Liouville set, which extends the definition of a Liouville number. We also define a Liouville field, which is a field generated by a Liouville set. Any Liouville number belongs to a Liouville set S having the power of continuum and such that the union of S with the rational number field is a Liouville field.Comment: Proceedings of the American Mathematical Society, to appea

Quadratic non-residues and non-primitive roots satisfying a coprimality condition

Let $q\geq 1$ be any integer and let $\epsilon \in [\frac{1}{11}, \frac{1}{2})$ be a given real number. In this short note, we prove that for all primes $p$ satisfying p\equiv 1\pmod{q}, \quad \log\log p > \frac{\log 6.83}{\frac{1}{2}-\epsilon} \mbox{ and } \frac{\phi(p-1)}{p-1} \leq \frac{1}{2} - \epsilon, there exists a quadratic non-residue $g$ which is not a primitive root modulo $p$ such that $gcd\left(g, \frac{p-1}{q}\right) = 1$.Comment: to appear in Bulletin of the Australian Mathematical Societ

ACUTE AND SUBACUTE TOXICITY OF SIDDHA FORMULATION DHATHU BHUSTI CHOORANAM

Dhathu busti chooranam (DBC) is a polyherbal formulation indicated in Siddha literature for the treatment of male infertility. The aim of this research was to evaluate the acute and sub-acute oral toxicity of the drug DBC. The acute toxicity test was conducted using albino rats of either sex. Water extract of DBC was administrated in a single dose of 2000 mg/kg via oral gavage and the animals were observed for any behavioral changes or mortality. In the sub-acute toxicity study, male albino rats received two doses of DBC (200, 400mg/kg) for 28 days via oral gavage and the rats were observed for toxicity symptoms. Following the 28-day treatment, the rats were sacrificed for hematological, biochemical and histopathology studies. In the acute toxicity study, DBC was found to be non-toxic at a dose of 2000 mg/kg b.w with no signs of mortality. In the sub-acute toxicity study, there was no significant variations in body weight, hematological and biochemical parameters found in the experimental groups at the dose of 200 and 400 mg/kg. The tested dose in experimental rats is significantly higher than the human therapeutic dosage. The acute and subacute toxicity study results show that DBC may be a safe drug without causing any serious side effects

Synthesis of H_xLi_1-xLaTiO₄ from quantitative solid-state reactions at room temperature

The layered perovskite HLaTiO4 reacts stoichiometrically with LiOH·H2O at room temperature to give targeted compositions in the series HxLi1-xLaTiO4. Remarkably, the Li+ and H+ ions are quantitatively exchanged in the solid state and this allows stoichiometric control of ion exchange for the first time in this important series of compounds

Evaluating spatial and frequency domain enhancement techniques on dental images to assist dental implant therapy

Dental imaging provides the patient's anatomical details for the dental implant based on the maxillofacial structure and the two-dimensional geometric projection, helping clinical experts decide whether the implant surgery is suitable for a particular patient. Dental images often suffer from problems associated with random noise and low contrast factors, which need effective preprocessing operations. However, each enhancement technique comes with some advantages and limitations. Therefore, choosing a suitable image enhancement method always a difficult task. In this paper, a universal framework is proposed that integrates the functionality of various enhancement mechanisms so that dentists can select a suitable method of their own choice to improve the quality of dental image for the implant procedure. The proposed framework evaluates the effectiveness of both frequency domain enhancement and spatial domain enhancement techniques on dental images. The selection of the best enhancement method further depends on the output image perceptibility responses, peak signal-to-noise ratio (PSNR), and sharpness. The proposed framework offers a flexible and scalable approach to the dental expert to perform enhancement of a dental image according to visual image features and different enhancement requirements

Performance of Activated Carbon Supported Cobalt Oxides and Iron Oxide Catalysts in Catalytic Cracking of Waste Cooking Oil

This work studied the catalyst activity of activated carbon (AC) supported Co, Fe and Co-Fe oxides in catalytic cracking of waste cooking oil. Reactions were carried out in a fixed bed reactor at 450 °C with WHSV 9 hr–1. Single metal Co/AC and Fe/AC catalysts with different metal loading (2.5–15 wt.%) and bimetal xCo-yFe/AC (x, y = 2.5 to 12.5 wt.%; x + y =15 wt.%) catalysts were investigated. Co/AC and Fe/AC catalysts both contributed to significant liquid yield with high selectivity towards C15 and C17 hydrocarbons. Fe/AC catalysts gave high C5 – C20 hydrocarbon yield whereas Co/AC attained more palmitic (C16) and oleic (C18) acid conversion. Synergistic effect in two metals Co-Fe/AC catalysts had further improved the liquid hydrocarbon yield (up to ~93 %) and fatty acid conversion (up to 94 %). The best catalyst, 10Co-5Fe/AC had been further tested under the effect of reaction temperature, feed flow rate (WHSV) and deactivation for its catalytic performance