A NEW FIFTH-ORDER WEIGHTED RUNGE-KUTTA ALGORITHM BASED ON HERONIAN MEAN FOR INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

CHANDRU, M.,PONALAGUSAMY, R.,ALPHONSE, P.J.A. The Korean Society for Computational and Applied M 2017 Journal of applied mathematics & informatics Vol.35 No.1

A new fifth-order weighted Runge-Kutta algorithm based on heronian mean for solving initial value problem in ordinary differential equations is considered in this paper. Comparisons in terms of numerical accuracy and size of the stability region between new proposed Runge-Kutta(5,5) algorithm, Runge-Kutta (5,5) based on Harmonic Mean, Runge-Kutta(5,5) based on Contra Harmonic Mean and Runge-Kutta(5,5) based on Geometric Mean are carried out as well. The problems, methods and comparison criteria are specified very carefully. Numerical experiments show that the new algorithm performs better than other three methods in solving variety of initial value problems. The error analysis is discussed and stability polynomials and regions have also been presented.

A NEW FIFTH-ORDER WEIGHTED RUNGE-KUTTA ALGORITHM BASED ON HERONIAN MEAN FOR INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

M. Chandru,R. Ponalagusamy,P.J.A. ALPHONSE 한국전산응용수학회 2017 Journal of applied mathematics & informatics Vol.35 No.1

A new fth-order weighted Runge-Kutta algorithm based on heronian mean for solving initial value problem in ordinary dierential equations is considered in this paper. Comparisons in terms of numerical accuracy and size of the stability region between new proposed Runge- Kutta(5,5) algorithm, Runge-Kutta (5,5) based on Harmonic Mean, Runge- Kutta(5,5) based on Contra Harmonic Mean and Runge-Kutta(5,5) based on Geometric Mean are carried out as well. The problems, methods and comparison criteria are specied very carefully. Numerical experiments show that the new algorithm performs better than other three methods in solving variety of initial value problems. The error analysis is discussed and stability polynomials and regions have also been presented.

Experimental evaluation of machinability performance of CNT coated HSS tool during turning of titanium alloy

M. Chandru,V. Selladurai,C. Venkatesh 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.5

The present research deals with the deposition of carbon nanotubes (CNT) over the HSS tool, and to evaluate the machining performance of the coated tool with respect to the important machinability aspects like cutting tip temperature, cutting forces, surface roughness and tool wear and life. The plasma enhanced chemical vapour deposition (PECVD) technique was employed to deposit CNTs over the substrate. Microstructural investigations through SEM and Raman spectroscopy were carried out to acknowledge the dense deposition of CNTs. Scratch test was also performed to validate the bonding strength of the coated layer with the substrate. Machining experimental results under three different cutting conditions, concluded that the CNT coated tool is the right potential candidate for turning tougher materials. Drastic depletion in cutting tip temperature and cutting forces to the extent of 70 to 80 % was observed for coated tool due to the excellent mechanical and thermal properties of CNTs. However, there was no significant effect of coating to influence the surface roughness at a lower level of cutting conditions, but considerable improvement has been observed at elevated cutting condition. The tool wear and life analysis explored the steady improvement to a remarkable extent. Very specifically, under elevated machining conditions, tool life investigations concluded the fact that the CNT coated tool has a tool life of more than 60 minutes with negligible failure.

A Schwarz method for fourth-order singularly perturbed reaction-diffusion problem with discontinuous source term

M. Chandru,V Shanthi 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.5

A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter $\varepsilon$ multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

RADIO NUMBER OF kth POWER OF A PATH

P. DEVADAS RAO,B. SOORYANARAYANA,CHANDRU HEGDE 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.3

Let G be a connected graph. For any two vertices u and v, let d(u, v) denote the distance between u and v in G. The maximum distance between any pair of vertices is called the diameter of G and is denoted by diam(G). A radio labeling of a connected graph G is an assignment of distinct positive integers to the vertices of G, with v ∈ V (G) labeled by f(v), such that |f(u)-f(v)|+d(u, v) ≥ 1+diam(G) holds for all u, v ∈ V , u ≠ v. The radio number rn(f) of a radio labeling f of G is the maximum label assigned by f to a vertex of G. The radio number rn(G) of G is the minfrn(f)g over all radio labeling f of G. The kth power of a graph G, denoted by Gk, is the graph on the vertices of G with two vertices u and v are adjacent in Gk whenever d(u, v) ≤ k in G. In this paper, we completely determine the radio number of the graph Pk n for positive integers n, k with k ≥ 2.

Nephron-sparing management of upper tract urothelial carcinoma

Jason M. Farrow,Sean Q. Kern,Gustavo M. Gryzinski,Chandru P. Sundaram 대한비뇨의학회 2021 Investigative and Clinical Urology Vol.62 No.4

Urothelial carcinoma of the upper urinary tract is uncommon and presents unique challenges for diagnosis and management. Nephroureterectomy has been the preferred management option, but it is associated with significant morbidity. Nephron-sparing treatments are a valuable alternative and provide similar efficacy in select cases. A PubMed literature review was performed in English language publications using the following search terms: urothelial carcinoma, upper tract, nephron-sparing, intraluminal and systemic therapy. Contemporary papers published within the last 10 years were primarily included. Where encountered, systematic reviews and meta-analyses were given priority, as were randomized controlled trials for newer treatments. Core guidelines were referenced and citations reviewed for inclusion. A summary of epidemiological data, clinical diagnosis, staging, and treatments focusing on nephron-sparing approaches to upper tract urothelial carcinoma (UTUC) are outlined. Nephron-sparing management strategies are viable options to consider in patients with favorable features of UTUC. Adjunctive therapies are being investigated but the data remains mixed. Protocol variability and dosage differences limit statistical interpretation. New mechanisms to improve treatment dwell times in the upper tracts are being designed with promising preliminary results. Studies investigating systemic therapies are ongoing but implications for nephron-sparing management are uncertain. Nephron-sparing management is an acceptable treatment modality best suited for favorable disease. More work is needed to determine if intraluminal and/or systemic therapies can further optimize treatment outcomes beyond resection alone.

Allelic heterogeneity in <i>NCF2</i> associated with systemic lupus erythematosus (SLE) susceptibility across four ethnic populations

Kim-Howard, Xana,Sun, Celi,Molineros, Julio E.,Maiti, Amit K.,Chandru, Hema,Adler, Adam,Wiley, Graham B.,Kaufman, Kenneth M.,Kottyan, Leah,Guthridge, Joel M.,Rasmussen, Astrid,Kelly, Jennifer,Sá Oxford University Press 2014 Human Molecular Genetics Vol.23 No.6

<P>Recent reports have associated <I>NCF2</I>, encoding a core component of the multi-protein NADPH oxidase (NADPHO), with systemic lupus erythematosus (SLE) susceptibility in individuals of European ancestry. To identify ethnicity-specific and -robust variants within <I>NCF2</I>, we assessed 145 SNPs in and around the <I>NCF2</I> gene in 5325 cases and 21 866 controls of European-American (EA), African-American (AA), Hispanic (HS) and Korean (KR) ancestry. Subsequent imputation, conditional, haplotype and bioinformatic analyses identified seven potentially functional SLE-predisposing variants. Association with non-synonymous rs17849502, previously reported in EA, was detected in EA, HS and AA (<I>P</I><SUB>EA</SUB> = 1.01 × 10<SUP>−54</SUP>, <I>P</I><SUB>HS</SUB> = 3.68 × 10<SUP>−10</SUP>, <I>P</I><SUB>AA</SUB> = 0.03); synonymous rs17849501 was similarly significant. These SNPs were monomorphic in KR. Novel associations were detected with coding variants at rs35937854 in AA (<I>P</I><SUB>AA</SUB> = 1.49 × 10<SUP>−9</SUP>), and rs13306575 in HS and KR (<I>P</I><SUB>HS</SUB> = 7.04 × 10<SUP>−7</SUP>, <I>P</I><SUB>KR</SUB> = 3.30 × 10<SUP>−3</SUP>). In KR, a 3-SNP haplotype was significantly associated (<I>P</I> = 4.20 × 10<SUP>−7</SUP>), implying that SLE predisposing variants were tagged. Significant SNP–SNP interaction (<I>P</I> = 0.02) was detected between rs13306575 and rs17849502 in HS, and a dramatically increased risk (OR = 6.55) with a risk allele at each locus. Molecular modeling predicts that these non-synonymous mutations could disrupt NADPHO complex assembly. The risk allele of rs17849501, located in a conserved transcriptional regulatory region, increased reporter gene activity, suggesting <I>in vivo</I> enhancer function. Our results not only establish allelic heterogeneity within <I>NCF2</I> associated with SLE, but also emphasize the utility of multi-ethnic cohorts to identify predisposing variants explaining additional phenotypic variance (‘missing heritability’) of complex diseases like SLE.</P>