An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays

AbstractThis paper deals with singularly perturbed boundary value problem for a linear second order delay differential equation. It is known that the classical numerical methods are not satisfactory when applied to solve singularly perturbed problems in delay differential equations. In this paper we present an exponentially fitted finite difference scheme to overcome the drawbacks of the corresponding classical counter parts. The stability of the scheme is investigated. The proposed scheme is analyzed for convergence. Several linear singularly perturbed delay differential equations have been solved and the numerical results are presented to support the theory

PHARMACEUTICAL AND ANALYTICAL STANDARDIZATION OF MAHA SHANKHA VATI

Khalveeya Rasa is the combinations of herbal, mineral and animal products, so that we can have the effects of all collectively in a single formula. It preserve the properties of freshly added Churna, Swarasa etc., with the help of Moorchita Parada i.e., Kajjali, Rasashindura & Hingula etc. Because of which Khalveeya Rasaushadhies occupies greater portion in therapeutics as compare to other Kalpana, Such as Vati, Gutika, Taila, Ghrita. In the present study three sample of “Maha Shankha Vati†have been prepared by adopting method describe in Ayurvedic Formulary of India (A.F.I.) Vol. 2 approved by government of India with some desire changes.AIMS: The aim of this study is to prepare three sample of “Maha Shankha Vati†for its Pharmacoanalytical standardization. And also prepare “Shankha Bhasmaâ€, “Hingullotha Parada†and processing of last three Sanskara of Parada. Analytical Standardization of self made Maha Shankha Vati & market sample of Maha Sankha Vati to compare analytically.RESULT: After evaluating organoleptic characters of the first three samples of self made Maha Shankha Vati revealed black colored substance in the form of Vati having Amla-Katu Rasa, Amla smell and smooth touch having pH 3.39. Similarly in case of market sample (fourth sample) shows black in colored in the form of Vati with Lavan-Katu in Rasa, Amla Smell and smooth touch having pH 4.37. Further the XRD pattern analysis of the combined sample of Maha Shankha Vati, reveals the presence of HgS, Caco3, NaCl. Same observation found in market sample.

A numerical scheme for singularly perturbed delay differential equations of convection-diffusion type on an adaptive grid

In this paper, an adaptive mesh strategy is presented for solving singularly perturbed delay differential equation of convection-diffusion type using second order central finite difference scheme. Layer adaptive meshes are generated via an entropy production operator. The details of the location and width of the layer is not required in the proposed method unlike the popular layer adaptive meshes mainly by Bakhvalov and Shishkin. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method

A novel mutation in STK11 gene is associated with Peutz-Jeghers Syndrome in Indian patients

BACKGROUND: Peutz-Jeghers syndrome (PJS) is a rare multi-organ cancer syndrome and understanding its genetic basis may help comprehend the molecular mechanism of familial cancer. A number of germ line mutations in the STK11 gene, encoding a serine threonine kinase have been reported in these patients. However, STK11 mutations do not explain all PJS cases. An earlier study reported absence of STK11 mutations in two Indian families and suggested another potential locus on 19q13.4 in one of them. METHODS: We sequenced the promoter and the coding region including the splice-site junctions of the STK11 gene in 16 affected members from ten well-characterized Indian PJS families with a positive family history. RESULTS: We did not observe any of the reported mutations in the STK11 gene in the index patients from these families. We identified a novel pathogenic mutation (c.790_793 delTTTG) in the STK11 gene in one index patient (10%) and three members of his family. The mutation resulted in a frame-shift leading to premature termination of the STK11 protein at 286(th )codon, disruption of kinase domain and complete loss of C-terminal regulatory domain. Based on these results, we could offer predictive genetic testing, prenatal diagnosis and genetic counselling to other members of the family. CONCLUSION: Ours is the first study reporting the presence of STK11 mutation in Indian PJS patients. It also suggests that reported mutations in the STK11 gene are not responsible for the disease and novel mutations also do not account for many Indian PJS patients. Large-scale genomic deletions in the STK11 gene or another locus may be associated with the PJS phenotype in India and are worth future investigation

TCF7L2 gene polymorphisms do not predict susceptibility to diabetes in tropical calcific pancreatitis but may interact with SPINK1 and CTSB mutations in predicting diabetes

<p>Abstract</p> <p>Background</p> <p>Tropical calcific pancreatitis (TCP) is a type of chronic pancreatitis unique to developing countries in tropical regions and one of its important features is invariable progression to diabetes, a condition called fibro-calculous pancreatic diabetes (FCPD), but the nature of diabetes in TCP is controversial. We analysed the recently reported type 2 diabetes (T2D) associated polymorphisms in the <it>TCF7L2 </it>gene using a case-control approach, under the hypothesis that <it>TCF7L2 </it>variants should show similar association if diabetes in FCPD is similar to T2D. We also investigated the interaction between the <it>TCF7L2 </it>variants and N34S <it>SPINK1 </it>and L26V <it>CTSB </it>mutations, since they are strong predictors of risk for TCP.</p> <p>Methods</p> <p>Two polymorphisms rs7903146 and rs12255372 in the <it>TCF7L2 </it>gene were analyzed by direct sequencing in 478 well-characterized TCP patients and 661 healthy controls of Dravidian and Indo-European ethnicities. Their association with TCP with diabetes (FCPD) and without diabetes was tested in both populations independently using chi-square test. Finally, a meta analysis was performed on all the cases and controls for assessing the overall significance irrespective of ethnicity. We dichotomized the whole cohort based on the presence or absence of N34S <it>SPINK1 </it>and L26V <it>CTSB </it>mutations and further subdivided them into TCP and FCPD patients and compared the distribution of <it>TCF7L2 </it>variants between them.</p> <p>Results</p> <p>The allelic and genotypic frequencies for both <it>TCF7L2 </it>polymorphisms, did not differ significantly between TCP patients and controls belonging to either of the ethnic groups or taken together. No statistically significant association of the SNPs was observed with TCP or FCPD or between carriers and non-carriers of N34S <it>SPINK1 </it>and L26V <it>CTSB </it>mutations. The minor allele frequency for rs7903146 was different between TCP and FCPD patients carrying the N34S <it>SPINK1 </it>variant but did not reach statistical significance (OR = 1.59, 95% CI = 0.93–2.70, P = 0.09), while, <it>TCF7L2</it><it/>variant showed a statistically significant association between TCP and FCPD patients carrying the 26V allele (OR = 1.69, 95% CI = 1.11–2.56, P = 0.013).</p> <p>Conclusion</p> <p>Type 2 diabetes associated <it>TCF7L2 </it>variants are not associated with diabetes in TCP. Since, <it>TCF7L2 </it>is a major susceptibility gene for T2D, it may be hypothesized that the diabetes in TCP patients may not be similar to T2D. Our data also suggests that co-existence of <it>TCF7L2 </it>variants and the <it>SPINK1 </it>and <it>CTSB </it>mutations, that predict susceptibility to exocrine damage, may interact to determine the onset of diabetes in TCP patients.</p

An exponentially fitted tridiagonal finite difference method for singularly perturbed differential-difference equations with small shift

This paper deals with the singularly perturbed boundary value problem for a linear second order differential-difference equation of convection-diffusion type. In the numerical treatment of such type of problems, first we use Taylor’s approximation to tackle the term containing the small shift. A fitting parameter has been introduced in a tridiagonal finite difference method and is obtained from the theory of singular perturbations. Thomas algorithm is used to solve the tridiagonal system. The method is analysed for convergence. Several numerical examples are solved to demonstrate the applicability of the method. Graphs are plotted for the solutions of these problems to illustrate the effect of small shift on the boundary layer solution

Estimation of shaft and base responses of a pile from pile load tests

This study aims to estimate the ultimate resistances and initial stiffnesses of shaft and base of a pile from initial pile load test results. The full-scale pile load test, describes the piles behaviour with a load-displacement curve but the main disadvantages are the time required, high costs. The nature of pile-soil interaction is three-dimensional and to complicate the problem further, response of soil is nonlinear. To avoid such problems, pile load tests are conducted on test piles instead of performing full-scale pile load test and load-displacement curve of test pile is used to estimate pile responses. Present study assumes non-linear hyperbolic responses for shaft and base of a pile. A set of equations are developed by Madhav and Vijay (2019) and solved iteratively using MATLAB for different load combinations. Results obtained are compared with those of Madhav and Vijay (2019). This method would help engineers to estimate the pile responses of actual site using the initial pile load test results. © 2022 Elsevier Ltd. All rights reserved

An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays

This paper deals with singularly perturbed boundary value problem for a linear second order delay differential equation. It is known that the classical numerical methods are not satisfactory when applied to solve singularly perturbed problems in delay differential equations. In this paper we present an exponentially fitted finite difference scheme to overcome the drawbacks of the corresponding classical counter parts. The stability of the scheme is investigated. The proposed scheme is analyzed for convergence. Several linear singularly perturbed delay differential equations have been solved and the numerical results are presented to support the theory