A new regularisation for time-fractional backward heat conduction problem

It is well-known that the backward heat conduction problem of recovering the temperature $u(\cdot, t)$ at a time $t\geq 0$ from the knowledge of the temperature at a later time, namely $g:= u(\cdot, \tau)$ for $\tau>t$, is ill-posed, in the sense that small error in $g$ can lead to large deviation in $u(\cdot, t)$. However, in the case of a time fractional backward heat conduction problem (TFBHCP), the above problem is well-posed for $t>0$ and ill-posed for $t=0$. We use this observation to obtain stable approximate solutions for the TFBHCP for $t=0$, and derive error estimates under suitable source conditions. We shall also provide some numerical examples to illustrate the approximation properties of the regularized solutions

A source identification problem in a bi-parabolic equation: convergence rates and some optimal results

This paper is concerned with identification of a spatial source function from final time observation in a bi-parabolic equation, where the full source function is assumed to be a product of time dependent and a space dependent function. Due to the ill-posedness of the problem, recently some authors have employed different regularization method and analysed the convergence rates. But, to the best of our knowledge, the quasi-reversibility method is not explored yet, and thus we study that in this paper. As an important implication, the H{\"o}lder rates for the apriori and aposteriori error estimates obtained in this paper improve upon the rates obtained in earlier works. Also, in some cases we show that the rates obtained are of optimal order. Further, this work seems to be the first one that has broaden the applicability of the problem by allowing the time dependent component of the source function to change sign. To the best of our knowledge, the earlier known work assumed the fixed sign of the time dependent component by assuming some bounded below condition.Comment: Comments are welcome. Typos and some mistakes with sign in the PDE are rectified. Section 4 and 5 are majorly revise

Spatial distribution of diatoms in surface sediments from the Indian sector of Southern Ocean

A multidisciplinary scientific expedition to the Southern Ocean (Pilot Expedition to the Southern Ocean - PESO) onboard ORV Sagar Kanya during the austral summer of 2004 collected various physical, chemical, biological and geological data/samples. From the sediment cores collected during the expedition, six representative core-top samples were studied along a latitudinal transect from 28° to 56° south to ascertain the modern variation in distribution of siliceous microfossils called diatoms. This is the first Indian attempt to understand the latitudinal variation in the distribution of diatom species in Southern Ocean, its relationship with the changing nutrient availability and/or supply, and its utility in palaeoceanographic reconstruction. In all, 24 diatom species were identified. The diatom population seems to be dominated by seven species namely Fragilariopsis kerguelensis, Fragilariopsis separanda, Thalassionema nitzschioides, Thalassiothrix spp., Thalassiosira lentiginosa, Eucampia antarctica and Azpeitia tabularis. Of these, F. kerguelensis and T. lentiginosa dominate the diatom community in the Southern Ocean sediments. The spatial distribution of most of the diatoms in surface sediments seems to be controlled by physicochemical parameters like sea surface temperature, salinity, silicate, nitrate and phosphate concentrations

Anemia in relation to body mass index among female students of North Kerala: a pilot study

Background: Anemia among women causes many serious health problems and is pervasive in developing country. Many research studies have documented that malnutrition affects body growth and development, especially during the crucial period of adolescence. The association between anemia and body mass index (BMI) is a measure of nutrition and health status of adults. Aim was to study the association between anemia and BMI among female students.Methods: An observational study was conducted among first year medical and dental female students (n=109) aged 18-20years. Hemoglobin (Hb) levels (g/dL) by Sahli’s hemoglobinometer and BMI (kg/m2) were estimated. Anemia was defined as Hb content <12g/dL. Subjects were classified by BMI categories as underweight (BMI <18.5kg/m2), normal weight (BMI:18.5-24.99kg/m2), overweight (BMI ≥25kg/m2) and obesity (BMI ≥30kg/m2) according to WHO. Then the relation between anemia and BMI were statistically analyzed.Results: Overall, 48.62% female students were anemic. Of which 43.4% were underweight, 22.6% normal weight and 34.5% were above normal weight (over weight and obese). Mean value of hemoglobin was significantly decreased in underweight and overweight compared to normal weight (p<0.001). Anemia was significantly associated with BMI (χ2 =46.48, p=0.000).Conclusions: The study concludes the occurrence of anemia in both undernourished and over-nourished individuals which were significantly associated. Further studies are needed with larger sample size to document the factors that may be associated with anemia in females

Dune associated calcretes, rhizoliths and paleosols from the Western continental shelf of India

The calcareous deposits on the western continental shelf of India, off Bhatkal (water depths 50 to 58 m) occur as crusts, sheets, cylinders and reddish brown mudstones. The outer layers of the crusts are micrite-dominated and beneath this layer detrital/carbonate sands with thin heavy mineral laminations are found. Textural studies indicate that the detrital sands are derived from dunes. Drusy calcite and neomorphic calcite cements are associated with the sands. Sheet deposits contain coarse calcareous component-dominated layer within micrite layers and abundant micrite cements. These are similar to dune associated calcretes. Cylinders are rhizoliths and show different stages of root calcification. Circular bodies, about 0.15 mm to 0.70 mm diameter, interpreted as vascular cylinders of the root tissues are typical. Radial fibrous calcite and spar calcite with inclusions indicate neomorphic cements. Reddish brown mudstones contain calcified root-hair sheaths, micrite glaebules and reworked pollen suggesting that these are indurated soils. X-ray diffraction studies indicate the presence of ferroan calcite, quartz, pyriie and dolomite in rhizoliths and ferroan calcite, goethite and quartz in mudstones. Mudstones and some rhizoliths are Fe-rich and some other rhizoliths are Fe-poor but enriched with Mg and Mn. The particulate matter in the calcareous deposits were initially at the proximity of the coast and cemented by metastable calcites during the ultimate Pleistocene intcrglacial sea-level stands on the shelf. Pedogenic cementation processes overprinted and developed them into eolianites and paleosols during the subsequent Late Pleistocene sea-level regression. The compositional differences of these deposits were apparently controlled by type of sediments and associated sedimentary environments