Browsing by Author "Arvind K. Singh"

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A Delay Mathematical Model for the Control of Unemployment
(2013) A.K. Misra; Arvind K. Singh
In this paper, we have proposed and analyzed a nonlinear mathematical model for control of unemployment in the developing countries by incorporating time delay in creating new vacancies. In the modeling process, three dynamic variables have been considered, namely, (i) number of unemployed persons, (ii) number of employed persons, and (iii) number of newly created vacancies. The model is studied using stability theory of differential equations. It is found that the model has only one equilibrium, which is stable in absence of delay. It is further shown that this stable equilibrium becomes unstable as delay crosses some critical value. This critical value of delay has been obtained analytically. Further, direction of Hopf bifurcation and stability of the bifurcating periodic solutions are studied by applying the normal form theory and the center manifold theorem. Numerical simulation of the model has been carried out to illustrate the analytical results. © 2013 Foundation for Scientific Research and Technological Innovation.
A derivative free globally convergent method and its deformations
(Springer Science and Business Media Deutschland GmbH, 2021) Manoj Kumar Singh; Arvind K. Singh
The motive of the present work is to introduce and investigate the quadratically convergent Newton’s like method for solving the non-linear equations. We have studied some new properties of a Newton’s like method with examples and obtained a derivative-free globally convergent Newton’s like method using forward difference operator and bisection method. Finally, we have used various numerical test functions along with their fractal patterns to show the utility of the proposed method. These patterns support the numerical results and explain the compactness regarding the convergence, divergence and stability of the methods to different roots. © 2021, The Author(s).
A mathematical model for unemployment
(2011) A.K. Misra; Arvind K. Singh
In this paper we have proposed and analyzed a non-linear mathematical model for unemployment by considering three variables, namely the numbers of unemployed, temporarily employed and regularly employed persons. The model is studied using the stability theory of differential equations. It is found that the model has only one equilibrium, which is non-linearly stable under certain conditions. Numerical simulation of the model has been carried out to confirm the analytical results. © 2010 Published by Elsevier Ltd. All rights reserved.
An optimal 8th order Newton’s-type method with basin of attraction
(Springer Nature, 2022) Manoj Kumar Singh; Ioannis K. Argyros; Arvind K. Singh
The goal of the present work is to obtain an eighth order optimal Newton like method to solve non-linear algebraic equations. We also examine the dynamics of the proposed method. It is an optimal eighth order consistent with Kung–Traub conjecture with efficiency index 1.682. We have tested the proposed method using several numerical examples and also discussed the basin of attraction related to some numerical examples. © 2021, The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada.
Apoptosis in mammalian oocytes: A review
(Springer New York LLC, 2015) Meenakshi Tiwari; Shilpa Prasad; Anima Tripathi; Ashutosh N. Pandey; Irfan Ali; Arvind K. Singh; Tulsidas G. Shrivastav; Shail K. Chaube
Apoptosis causes elimination of more than 99 % of germ cells from cohort of ovary through follicular atresia. Less than 1 % of germ cells, which are culminated in oocytes further undergo apoptosis during last phases of oogenesis and depletes ovarian reserve in most of the mammalian species including human. There are several players that induce apoptosis directly or indirectly in oocytes at various stages of meiotic cell cycle. Premature removal of encircling granulosa cells from immature oocytes, reduced levels of adenosine 3′,5′-cyclic monophosphate and guanosine 3′,5′-cyclic monophosphate, increased levels of calcium (Ca2+) and oxidants, sustained reduced level of maturation promoting factor, depletion of survival factors, nutrients and cell cycle proteins, reduced meiotic competency, increased levels of proapoptotic as well as apoptotic factors lead to oocyte apoptosis. The BH3-only proteins also act as key regulators of apoptosis in oocyte within the ovary. Both intrinsic (mitochondria-mediated) as well as extrinsic (cell surface death receptor-mediated) pathways are involved in oocyte apoptosis. BID, a BH3-only protein act as a bridge between both apoptotic pathways and its cleavage activates cell death machinery of both the pathways inside the follicular microenvironment. Oocyte apoptosis leads to the depletion of ovarian reserve that directly affects reproductive outcome of various mammals including human. In this review article, we highlight some of the important players and describe the pathways involved during oocyte apoptosis in mammals. © 2015 Springer Science+Business Media.
Bioaccumulation of selenium in halotolerant microalga Dunaliella salina and its impact on photosynthesis, reactive oxygen species, antioxidative enzymes, and neutral lipids
(Elsevier Ltd, 2023) Prabhakar Singh; Sakshi Singh; Priyanka Maurya; Abhishek Mohanta; Hardik Dubey; Sk. Riyazat Khadim; Ankit K. Singh; Adarsh K. Pandey; Arvind K. Singh; Ravi K. Asthana
Selenium (Se) is an essential element for living systems, however, toxic at higher levels. In the present study, Dunaliella salina cells were exposed to different Se concentrations for their growth (EC50 195 mg L−1) as well as Se accumulation. The cells exposed to 50 mg L−1 Se showed photoautotrophic growth parallel to control and accumulated 65 μg Se g−1 DW. A decrease in photosynthetic quantum yield, chlorophyll content, and the increase in intracellular reactive oxygen species, proline content, and lipid peroxidation accompanied by higher neutral lipid accumulation, were recorded at higher Se level. The enzymes superoxide dismutase and catalase played a pivotal role in antioxidative defense. Heterogeneity in accumulated carotenoids at varying concentrations of selenium was prevalent. The cells exposed to 200 mg L−1 Se resulted in the disorganization of organelles. Thus, the Se enriched biomass obtained at 50 mg L−1 may be explored for bio-fortification of food and feed. © 2023 Elsevier Ltd
Modeling the Role of Skill Development to Control Unemployment
(Springer, 2022) A.K. Misra; Arvind K. Singh; Pushkar Kumar Singh
In this paper, a nonlinear mathematical model to study the effect of skill development on the control of unemployment is proposed and analyzed. In the modeling process, three different classes; namely unemployed, self/temporary employed and regular employed are considered. It is also assumed that some academic institutions develop skills among the youths to get the employment; however the avenues to develop skills among the unemployed persons increases as the number of unemployed persons increases. It is further assumed that the rate of movement from unemployed class to self/temporary employed class increases as the avenues for skill development increases. The model is analyzed using stability theory of differential equations. It is found that the proposed model exhibits only one equilibrium, which is globally stable under certain conditions. Numerical simulation of the model has been carried out to confirm the analytical results. © 2017, Foundation for Scientific Research and Technological Innovation.
Newton-like Normal S-iteration under Weak Conditions
(MDPI, 2023) Manoj K. Singh; Ioannis K. Argyros; Arvind K. Singh
In the present paper, we introduced a quadratically convergent Newton-like normal S-iteration method free from the second derivative for the solution of nonlinear equations permitting (Formula presented.) at some points in the neighborhood of the root. Our proposed method works well when the Newton method fails and performs even better than some higher-order converging methods. Numerical results verified that the Newton-like normal S-iteration method converges faster than Fang et al.’s method. We studied different aspects of the normal S-iteration method regarding the faster convergence to the root. Lastly, the dynamic results support the numerical results and explain the convergence, divergence, and stability of the proposed method. © 2023 by the authors.
On a Newton-Type method under weak conditions with dynamics
(World Scientific, 2021) Manoj Kumar Singh; Arvind K. Singh
In this paper, we present new cubically convergent Newton-Type iterative methods with dynamics for solving nonlinear algebraic equations under weak conditions. The proposed methods are free from second-order derivative and work well when f′(x) = 0. Numerical results show that the proposed method performs better when Newton's method fails or diverges and competes well with same order existing method. Fractal patterns of different methods also support the numerical results and explain the compactness regarding the convergence, divergence, and stability of the methods to different roots. © 2021 World Scientific Publishing Company.
On the convergence of a fourth-order method for a class of singular boundary value problems
(2009) R.K. Pandey; Arvind K. Singh
In the present paper we extend the fourth order method developed by Chawla et al. [M.M. Chawla, R. Subramanian, H.L. Sathi, A fourth order method for a singular two-point boundary value problem, BIT 28 (1988) 88-97] to a class of singular boundary value problems (p (x) y′)′ = p (x) f (x, y), 0 < x ≤ 1y′ (0) = 0, α y (1) + β y′ (1) = γ where p (x) = xb0 q (x), b0 ≥ 0 is a non-negative function. The order of accuracy of the method is established under quite general conditions on f (x, y) and is also verified by one example. The oxygen diffusion problem in a spherical cell and a nonlinear heat conduction model of a human head are presented as illustrative examples. For these examples, the results are in good agreement with existing ones. © 2008 Elsevier B.V. All rights reserved.
On the synthesis, characterisation and hydrogenation behaviour of V-Ti-Fe alloy
(1995) Arvind K. Singh; Ajay K. Singh; O.N. Srivastava
A hydrogen storage vanadium-based solid solution alloy V0.85Ti0.10Fe0.05 has been synthesised through a new route involving solid state diffusion. For the diffusion, a specific temperature-time profile has been determined, this corresponds to 30 °C (30 °C min-1) → 700 °C (12 h); 1.5 °C min-1 → 900 °C (36 h); 2.5 °C min-1 → 30 °C. The structural characterisation of the alloy has been carried out through XRD and electron diffraction techniques, the compositional analysis has been done by applying the EDAX technique. These investigations reveal the alloy lattice to be b.c.c. type solid solution with a = 3.042 A ̊, which is in accordance with the lattice parameter a = 3.046 A ̊ determined from Vegard's law and average compositions correspond to the envisaged stoichiometry. The formation of the alloy has also been checked through hydrogenation-dehydrogenation behaviour. © 1995.
The optimal order newton’s like methods with dynamics
(MDPI AG, 2021) Manoj Kumar Singh; Arvind K. Singh
In this paper, we have obtained three optimal order Newton’s like methods of order four, eight, and sixteen for solving nonlinear algebraic equations. The convergence analysis of all the optimal order methods is discussed separately. We have discussed the corresponding conjugacy maps for quadratic polynomials and also obtained the extraneous fixed points. We have considered several test functions to examine the convergence order and to explain the dynamics of our proposed methods. Theoretical results, numerical results, and fractal patterns are in support of the efficiency of the optimal order methods. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Variant of Newton’s Method Using Simpson’s 3/8th Rule
(Springer, 2020) Manoj Kumar Singh; Arvind K. Singh
The main objective of this work is to present a new closed type third order variant of Newton’s method for solving system of nonlinear equations, which not only accelerates the Newton’s method but also removes its certain limitations. For this purpose we applied Simpson’s three eighth rule instead of trapezoid and rectangle in approximating the integral and thereby reducing the error. Numerical results show that the method is superior to the same order existing methods and well compete with some higher order methods. © 2020, Springer Nature India Private Limited.