Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Department of Mathematics

The aim of this paper is to establish the existence and uniqueness of the common solution for the system of nonlinear <a href="https://www.sciencedirect.com/topics/mathematics/fredholm-equation">Fredholm integral equations</a>, nonlinear <a href="https://www.sciencedirect.com/topics/mathematics/volterra-integral-equation">Volterra integral equations</a> and nonlinear <a href="https://www.sciencedirect.com/topics/mathematics/fractional-differential-equations">fractional differential equations</a> using the <a href="https://www.sciencedirect.com/topics/mathematics/common-fixed-point">common fixed point</a> results equipped with illustrative examples. Some common fixed point results satisfying the generalized contraction condition involving&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi is="true">w</mi></math>-distance and weak altering distance functions are proved. Then, an example is provided to support the usability of our result along with numerical experiments.

School of Advanced Sciences

Vellore Campus

Journal of Computational and Applied Mathematics

Common solution to a pair of nonlinear Fredholm and Volterra integral equations and nonlinear fractional differential equations

This study performed a land use and land cover (LULC) change analysis over Southern India for the period 1981–2006 from the normalized difference vegetation index (NDVI) images of AVHRR data and applied the “observation minus reanalysis” (OMR) method to investigate the impact of the LULC change on the temperature of the region. The LULC change analysis indicated that the areas under agriculture/fallow land were significantly increased while the areas under shrubs/small vegetation were decreased during the period 1981–2006. The areas under forest cover and barren land were also decreased but relatively low compared to the other LULC types. The OMR results showed that the LULC changes over urban areas contributed to warming with a temperature of 0.02 ◦C during this period, while that over non-urban areas showed a cooling effect with a temperature reduction of 0.29 ◦C and that over the whole Southern India (looked at an average) indicated a cooling effect with a temperature reduction of 0.063 ◦C. The comparative analysis between the two (LULC change analysis and OMR) results showed that the cooling over Southern India was mostly due to the expansion of agriculture/fallow land and the decline of shrubs/small vegetation. The study suggests that the OMR method reasonably demonstrates the effect of LULC changes on the temperature over Southern India.

Fulltext

ISPRS International Journal of Geo-Information

Application of “Observation Minus Reanalysis” Method towards LULC Change Impact over Southern India

During the past 30&nbsp;years (1990–2020), all extremely severe cyclonic storms (ESCS) that formed over the Bay of Bengal (BoB) region had undergone rapid intensifcation (RI) attributed due to climate change. A detailed evaluation is therefore necessary to forecast and ascertain the rapid changes in intensity especially the RI over BoB that has direct socio-conomic consequences in coastal regions. This study performed a detailed evaluation on the intensity and RI of ESCS over the BoB region using Weather Research and Forecasting (WRF) model. Observations were assimilated using conventional and satellite radiances to improve the initial conditions of four ESCSs (Mala, 2006; Sidr, 2007; Phailin, 2013 and Hudhud, 2014). Numerical experiments used a double-nested domain of 27 and 9&nbsp;km horizontal resolution with 73 vertical levels. The forecasted intensity, structure, and storm tracks were in good agreement with the available observations. Mean Absolute Error (MAE) of Maximum Surface Winds (MSW) were 5&nbsp;m&nbsp;s −1, 6&nbsp;m&nbsp;s −1, 5&nbsp;m&nbsp;s −1, and 5&nbsp;m&nbsp;s −1 from Day 1 to Day 4, respectively, with mean initial intensity error of about 4.5&nbsp;m&nbsp;s −1. Results indicate that RI of ESCS was well apprehended in WRF model showing significant differences in the forecast for different cases. In most of the cases, the RI was under-predicted. The overall performance of WRF model was reasonably good in forecasting RI, and the estimated statistics for Probability of Detection (POD) and False Alarm Rate (FAR) was about 68% and 21%, respectively, based on the four cases considered in this study. Forecasted reflectivity and vertical profiles of heating rate, divergence, hydrometeors, vertical winds, and temperature anomaly are also presented in this study. Mean track error of storms varied between 75 and 135&nbsp;km, at 24 to 96&nbsp;h, respectively, while the mean landfall time and positional errors were about 3&nbsp;h and 69&nbsp;km, respectively. This research has also highlighted the need for a re-evaluation of the WRF model’s performance in forecasting the track, structure, and intensity of ESCS over BOB during the RI.

Theoretical and Applied Climatology

Prediction of rapid intensification for land-falling extremely severe cyclonic storms in the Bay of Bengal

Assume that we have a fibration of smooth projective varieties X → S over a surface S such that X is of dimension four and that the geometric generic fiber has finite-dimensional motive and the first étale cohomology of the geometric generic fiber with respect to l coefficients is zero and the second étale cohomology is spanned by divisors. We prove that then A3(X), the group of codimension three algebraically trivial cycles modulo rational equivalence, is dominated by finitely many copies of A0(S); this means that there exist finitely many correspondences Γi on S × X such that ςi Γi is surjective from A2(S) to A3(X). © 2022 Walter de Gruyter GmbH, Berlin/Boston.

Advances in Geometry

Representability of Chow groups of codimension three cycles

In this paper, using the Mittag-Leffler-type Borel distribution, the authors introduce a new class of bi-Bazilevic functions defined in the open unit disc associated with Legendre polynomials, we find estimates for the general Taylor-Maclaurin coefficients of the functions in the subclass introduced, and the Fekete-Szego problem is solved. © 2022, International Scientific Research Publications All rights reserved.

World University root node

Journal of Mathematics and Computer Science

Bi-bazilevič functions based on the mittag-leffler-type borel distribution associated with legendre polynomials

In this article, we prove some new common fixed point results under the generalized contraction condition using w-distance and weak altering distance functions. Also, the validity of the results is demonstrated by an example along with numerical experiment for approximating the common fixed point. Later, as applications, the unique common solutions for the system of nonlinear Fredholm integral equations, nonlinear Volterra integral equations and nonlinear fractional differential equations of Caputo type are derived.

Mathematica Slovaca

Common fixed point results under w-distance with applications to nonlinear integral equations and nonlinear fractional Differential Equations

In this paper, we have studied the seventh-order time-fractional Sawada Kotera Ito equation via natural transform decomposition method (NTDM) with singular and nonsingular kernel derivatives. The fractional derivative considered in Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu-Caputo (ABC). We employed the natural transform with the Adomian decomposition process on time-fractional Sawada Kotera Ito equation to obtain the solution. To validate the method, we have considered a few examples and compared with the actual results. Numerical results are in accordance with the existing results.

Mathematical Methods in the Applied Sciences

Numerical solutions of time fractional Sawada Kotera Ito equation via natural transform decomposition method with singular and nonsingular kernel derivatives

The subsampling strategies in X-ray Computed Tomography (CT) gained importance due to their practical relevance. In this direction of research, also known as coded aperture X-ray computed tomography (CAXCT), both random and deterministic strategies were proposed in the literature. Of the techniques available, the ones based on Compressive Sensing (CS) recently gained more traction as CS based ideas eﬃciently exploit inherent duplication present in the system. The quality of the reconstructed CT images, nevertheless, depends on the sparse signal recovery properties (SRPs) of the sub-sampled Radon matrices. In the present work, we determine CAXCT deterministically in such a way that the corresponding sub-sampled Radon matrices remain close to the incoherent unit norm tight frames (IUNTFs) for better numerical behaviour. We show that this optimization, via Khatri-Rao product, leads to non-negative sparse approximation. While comparing and contrasting our method with its existing counterparts, we show that the proposed algorithm is computationally less involved. Finally, we demonstrate eﬃcacy of the proposed deterministic sub-sampling strategy in recovering CT images both in noiseless and noisy cases.&nbsp;

Measurement Science and Technology

Sparsity driven deterministic sampling strategy for coded aperture X-ray Computed Tomography

The frequency of extreme rainfall events in India has increased substantially during the recent decades, causing increased risk of inland flooding. This study investigated the impact and role of four different cumulus parameterization schemes (CPSs) in simulating heavy rainfall events (HRE) over Tamil Nadu State that occurred on 01 December 2015 with five different time step sizes (TSSs) using the Weather Research and Forecasting (WRF) model. Numerical simulations were carried out using a 3-km horizontal grid resolution with relevant forcing parameters from NCEP Global Forecasting System (GFS) datasets. The rainfall data were obtained from the Chennai Doppler Weather Radar station and two automated weather stations (AWS) located at the National Centre for Sustainable Coastal Management (NCSCM 13.01° N, 80.23° E) and Madhavaram AWS (13.2° N, 80.2° E), respectively. The results indicate that simulated HRE using the WRF model is more sensitive to the choice of CPS at different TSS. It is seen that with an increase in TSS, the Kain–Fritsch (KF) scheme over-predicts HRE, while the Grell–Freitas (GF) convection scheme provides reasonably better prediction at 20&nbsp;s TSS. The results clearly demonstrate that TSS is more sensitive to HRE forecasts in the WRF model, and the corresponding probability of detection (POD), critical success index (CSI) and bias varied from 0 to 81% as TSS increased from 6.67 to 20&nbsp;s. Also, this study clearly reveals that TSS is very sensitive to the model CPSs in HRE forecasting. Variations attributed to TSS and CPS are reflected not only in rainfall magnitude but also in terms of rainfall location pattern, and depend on changes in simulated distribution of hydrometers, rate of latent heat, vertical velocity and wind flow patterns. Statistical analysis was also carried out to verify model-computed HRE forecasts against the data from two automatic weather stations (AWS). This study indicates that the correlation coefficient (CC) was very good, while the root mean square error (RMSE) was smaller for simulations that used high TSS with simplified Arakawa–Schubert (SAS) and GF CPSs. Numerical simulations that employed KF with high TSS showed a higher intensity in the rainfall forecast.

Pure and Applied Geophysics

<a href="https://scholar.google.co.in/citations?view_op=view_citation&amp;hl=en&amp;user=xjTHnKgAAAAJ&amp;sortby=pubdate&amp;citation_for_view=xjTHnKgAAAAJ:QIV2ME_5wuYC">Impact of Time Step Size on Different Cumulus Parameterization Schemes in the Numerical Simulation of a Heavy Rainfall Event Over Tamil Nadu, India</a>