In this paper, we propose a simple modification over Chun’s method for constructing iterative met... more In this paper, we propose a simple modification over Chun’s method for constructing iterative methods with at least cubic convergence [5]. Using iteration formulas of order two, we now obtain several new interesting families of cubically or quartically convergent iterative methods. The fourth-order family of Ostrowski’s method is the main finding of the present work. Per iteration, this family of Ostrowski’s method requires two evaluations of the function and one evaluation of its first-order derivative. Therefore, the efficiency index of this Ostrowski’s family is E=43≈1.587, which is better than those of most third-order iterative methods E=33≈1.442 and Newton’s method E=2≈1.414. The performance of Ostrowski’s family is compared with its closest competitors, namely Ostrowski’s method, Jarratt’s method and King’s family in a series of numerical experiments.
The solution of the boundary value problems for singularly perturbed differential equations, i.e.... more The solution of the boundary value problems for singularly perturbed differential equations, i.e., where the highest order derivative is multiplied by a small parameter, exhibits layer behavior. The classical numerical schemes to solve such types of the boundary value problems do not give satisfactory result when the perturbation parameter is sufficiently small. To resolve this difficulty, there are mainly two approaches, namely, fitted operator and fitted mesh. Both the scheme are uniformly convergent, i.e., their convergence is independent of the small perturbation parameter.It is justified to adopt the two approach rather than the classical numerical schemes to solve the boundary value problems for singularly perturbed differential equations. Now if we compare the two approaches, one thing is common that both the approaches give the parameter-uniform schemes which is the primary requirement in construction of the numerical scheme to solve such type of problem. Secondly, one desire a higher order numerical scheme to approximate the solution of a problem. As far as order of convergence is concerned, the numerical scheme based on fitted operator approach is better than the numerical scheme constructed using fitted mesh approach.The researchers who adopted the fitted mesh rather than fitted operator approach to solve a singularly perturbed problem faced the question due to the loss of order of convergence, most of them justified it by quoting the simplicity of the method and there are some non-linear problems for which a parameter uniform scheme cannot be constructed based on fitted operator approach while for the same problem, a parameter uniform scheme is constructed based on fitted mesh method. Now question remains unanswered in the case of linear problem. In this article, we replied to this question by giving an example of linear problem for which one cannot construct a parameter uniform scheme based on fitted operator approach while for the same problem a parameter uniform numerical scheme based fitted mesh approach has been constructed [M.K. Kadalbajoo, K.K. Sharma, ε uniform fitted mesh method for singularly perturbed differential difference equations with mixed type of shifts with layer behavior, Int. J. Comput. Math. 81 (2004) 49–62]. A theoretical reason behind the inability in construction of a parameter uniform scheme using fitted operator approach is revealed. In support of the predicted theory, a number of numerical experiments are carried out.
Journal of Optimization Theory and Applications, 2002
In this paper, we use a numerical method to solve boundary-value problems for a singularly-pertur... more In this paper, we use a numerical method to solve boundary-value problems for a singularly-perturbed differential-difference equation of mixed type, i.e., containing both terms having a negative shift and terms having a positive shift. Similar boundary-value problems are associated with expected first exit time problems of the membrane potential in models for the neuron. The stability and convergence analysis of the method is given. The effect of a small shift on the boundary-layer solution is shown via numerical experiments. The numerical results for several test examples demonstrate the efficiency of the method.
ABSTRACT In this paper, we study the influence of Dzyaloshinskii-Moriya (DM) interaction on quant... more ABSTRACT In this paper, we study the influence of Dzyaloshinskii-Moriya (DM) interaction on quantum correlations in two-qubit Werner states and maximally entangled mixed states (MEMS). We consider our system as a closed system of a qubit pair and one auxiliary qubit, which interact with any one of the qubit of the pair through DM interaction. We show that DM interaction, taken along any direction (x or y or z), does not affect two-qubit Werner states. On the other hand, the MEMS are affected by x and z components of DM interaction and remain unaffected by the y component. Further, we find that the state (i.e., probability amplitude) of auxiliary qubit does not affect the quantum correlations in both the states, and only DM interaction strength influences the quantum correlations. So one can avoid the intention to prepare the specific state of auxiliary qubit to manipulate the quantum correlations in both the states. We mention here that avoiding the preparation of state can contribute to cost reduction in quantum information processing. We also observe the phenomenon of entanglement sudden death in the present study.
Purpose -The purpose of this paper is to propose a numerical method to solve time dependent Burge... more Purpose -The purpose of this paper is to propose a numerical method to solve time dependent Burgers' equation with appropriate initial and boundary conditions. Design/methodology/approach -The presence of the nonlinearity in the problem leads to severe difficulties in the solution approximation. In construction of the numerical scheme, quasilinearization is used to tackle the nonlinearity of the problem which is followed by semi discretization for spatial direction using differential quadrature method (DQM). Semi discretization of the problem leads to a system of first order initial value problems which are followed by fully discretization using RK4 scheme. The method is analyzed for stability and convergence. Findings -The method is illustrated and compared with existing methods via numerical experiments and it is found that the proposed method gives better accuracy and is quite easy to implement. Originality/value -The new scheme is developed by using some numerical schemes. The scheme is analyzed for stability and convergence. In support of predicted theory some test examples are solved using the presented method.
Journal of community hospital internal medicine perspectives, 2014
Objectives: There is wide variability in the discussion of code status by residents among hospita... more Objectives: There is wide variability in the discussion of code status by residents among hospitalized patients. The primary objective of this study was to determine the effect of a scripted code status explanation on patient understanding of choices pertaining to code status and end-of-life care.
In this work, an effective and economic way of transition metal doping in tin oxide nanoparticles... more In this work, an effective and economic way of transition metal doping in tin oxide nanoparticles is presented. The x-ray diffraction (XRD) measurements confirmed that the SnO 2 nanoparticles are of single phase with rutile structure. Transmission electron microscopy (TEM) micrographs show that nanoparticles exhibit spherical shape with size of ~ 4 nm. To check the incorporation of cobalt and its chemical bonding with oxygen, systematic FTIR measurements were performed. The stretching-vibration mode (A 2u ) of Sn-O and deformation-vibration mode (E u ) of O-Sn-O were found to be broadened and shifted towards the higher wave numbers in case of cobalt doped samples. The Co-O/O-Co-O modes of the stable phase of cobalt oxide (Co 2 O 3 ) were not detected in any doped samples. The results indicate that cobalt is present in the tin oxide lattice and do not form any metallic clusters or its oxide phases.
The paper deals with the analysis of a non-stationary parabolic partial differential equation wit... more The paper deals with the analysis of a non-stationary parabolic partial differential equation with a time delay. The highest order derivative term is affected by the small parameter. This is precisely the case when the magnitude of the convective term becomes much larger compare to that of diffusion term. The solution of problem exhibits steep gradients in the narrow intervals of space and short interval of times. In these cases a dissipative loss turned out to be more complex. Even for the one spatial dimension and one temporal variable, not all difference scheme can capture these steep variation. Although the analysis is restricted to the model in one space dimension, the technique and comparison principles developed should prove useful in assessing the merits of numerical solution of other nonlinear model equations too.
The results of the distorted-wave theory for electron-impact excitation of atoms are applied to t... more The results of the distorted-wave theory for electron-impact excitation of atoms are applied to the excitation of the 6s6p1P1 state of mercury. The spin polarization and the differential cross section are given for unpolarized incident electron beams with energies between 25 and 180 eV. The distorted-wave results are compared with experimental data, and good agreement is found for both the
ABSTRACT Zinc sulpho selenide has been proposed as a novel buffer layer, alternative to CdS for s... more ABSTRACT Zinc sulpho selenide has been proposed as a novel buffer layer, alternative to CdS for solar cell applications. In this paper Zn-Se-S composite thin layers have been synthesized on ultra clean glass substrate by screen-printing method followed by sintering process. Zinc sulphide, zinc selenide and zinc chloride have been used as the basic source material. To deposit good quality films, optimum conditions have been determined. X-ray diffraction analysis exhibited polycrystalline nature of layers with strong preferential orientation of grains along (200) direction. These layers have the wurtzite crystal structure. The optical band gap (Eg) of the films has been studied by using reflection spectra in wavelength range 325–600 nm. The optical band gap of Zn-Se-S composite thin layer has been found to be in between individual band-gaps of ZnS and ZnSe. The DC electrical conductivity of the layers has been measured in vacuum by a two probe technique and was found to be of the order of 10−6 ohm−1cm−1. These properties make these layers suitable for application as a buffer layer in solar cells.
International Journal of Computer Applications, 2012
This paper presents an approach to model content based metasearch engine which search all the con... more This paper presents an approach to model content based metasearch engine which search all the content related images present in the dataset. Searching through the keywords in an image database require a lot of Meta data (keywords about the image) to be stored for each image in a separate database. This does not lead to an effective search mechanism. This mechanism basically works for the relevant output for the input query image. The process based on the image extraction by the implemented functions like "edge histogram", "image feature extraction i.e. sharpness, smoothness, color etc.
In this paper, we propose a simple modification over Chun’s method for constructing iterative met... more In this paper, we propose a simple modification over Chun’s method for constructing iterative methods with at least cubic convergence [5]. Using iteration formulas of order two, we now obtain several new interesting families of cubically or quartically convergent iterative methods. The fourth-order family of Ostrowski’s method is the main finding of the present work. Per iteration, this family of Ostrowski’s method requires two evaluations of the function and one evaluation of its first-order derivative. Therefore, the efficiency index of this Ostrowski’s family is E=43≈1.587, which is better than those of most third-order iterative methods E=33≈1.442 and Newton’s method E=2≈1.414. The performance of Ostrowski’s family is compared with its closest competitors, namely Ostrowski’s method, Jarratt’s method and King’s family in a series of numerical experiments.
The solution of the boundary value problems for singularly perturbed differential equations, i.e.... more The solution of the boundary value problems for singularly perturbed differential equations, i.e., where the highest order derivative is multiplied by a small parameter, exhibits layer behavior. The classical numerical schemes to solve such types of the boundary value problems do not give satisfactory result when the perturbation parameter is sufficiently small. To resolve this difficulty, there are mainly two approaches, namely, fitted operator and fitted mesh. Both the scheme are uniformly convergent, i.e., their convergence is independent of the small perturbation parameter.It is justified to adopt the two approach rather than the classical numerical schemes to solve the boundary value problems for singularly perturbed differential equations. Now if we compare the two approaches, one thing is common that both the approaches give the parameter-uniform schemes which is the primary requirement in construction of the numerical scheme to solve such type of problem. Secondly, one desire a higher order numerical scheme to approximate the solution of a problem. As far as order of convergence is concerned, the numerical scheme based on fitted operator approach is better than the numerical scheme constructed using fitted mesh approach.The researchers who adopted the fitted mesh rather than fitted operator approach to solve a singularly perturbed problem faced the question due to the loss of order of convergence, most of them justified it by quoting the simplicity of the method and there are some non-linear problems for which a parameter uniform scheme cannot be constructed based on fitted operator approach while for the same problem, a parameter uniform scheme is constructed based on fitted mesh method. Now question remains unanswered in the case of linear problem. In this article, we replied to this question by giving an example of linear problem for which one cannot construct a parameter uniform scheme based on fitted operator approach while for the same problem a parameter uniform numerical scheme based fitted mesh approach has been constructed [M.K. Kadalbajoo, K.K. Sharma, ε uniform fitted mesh method for singularly perturbed differential difference equations with mixed type of shifts with layer behavior, Int. J. Comput. Math. 81 (2004) 49–62]. A theoretical reason behind the inability in construction of a parameter uniform scheme using fitted operator approach is revealed. In support of the predicted theory, a number of numerical experiments are carried out.
Journal of Optimization Theory and Applications, 2002
In this paper, we use a numerical method to solve boundary-value problems for a singularly-pertur... more In this paper, we use a numerical method to solve boundary-value problems for a singularly-perturbed differential-difference equation of mixed type, i.e., containing both terms having a negative shift and terms having a positive shift. Similar boundary-value problems are associated with expected first exit time problems of the membrane potential in models for the neuron. The stability and convergence analysis of the method is given. The effect of a small shift on the boundary-layer solution is shown via numerical experiments. The numerical results for several test examples demonstrate the efficiency of the method.
ABSTRACT In this paper, we study the influence of Dzyaloshinskii-Moriya (DM) interaction on quant... more ABSTRACT In this paper, we study the influence of Dzyaloshinskii-Moriya (DM) interaction on quantum correlations in two-qubit Werner states and maximally entangled mixed states (MEMS). We consider our system as a closed system of a qubit pair and one auxiliary qubit, which interact with any one of the qubit of the pair through DM interaction. We show that DM interaction, taken along any direction (x or y or z), does not affect two-qubit Werner states. On the other hand, the MEMS are affected by x and z components of DM interaction and remain unaffected by the y component. Further, we find that the state (i.e., probability amplitude) of auxiliary qubit does not affect the quantum correlations in both the states, and only DM interaction strength influences the quantum correlations. So one can avoid the intention to prepare the specific state of auxiliary qubit to manipulate the quantum correlations in both the states. We mention here that avoiding the preparation of state can contribute to cost reduction in quantum information processing. We also observe the phenomenon of entanglement sudden death in the present study.
Purpose -The purpose of this paper is to propose a numerical method to solve time dependent Burge... more Purpose -The purpose of this paper is to propose a numerical method to solve time dependent Burgers' equation with appropriate initial and boundary conditions. Design/methodology/approach -The presence of the nonlinearity in the problem leads to severe difficulties in the solution approximation. In construction of the numerical scheme, quasilinearization is used to tackle the nonlinearity of the problem which is followed by semi discretization for spatial direction using differential quadrature method (DQM). Semi discretization of the problem leads to a system of first order initial value problems which are followed by fully discretization using RK4 scheme. The method is analyzed for stability and convergence. Findings -The method is illustrated and compared with existing methods via numerical experiments and it is found that the proposed method gives better accuracy and is quite easy to implement. Originality/value -The new scheme is developed by using some numerical schemes. The scheme is analyzed for stability and convergence. In support of predicted theory some test examples are solved using the presented method.
Journal of community hospital internal medicine perspectives, 2014
Objectives: There is wide variability in the discussion of code status by residents among hospita... more Objectives: There is wide variability in the discussion of code status by residents among hospitalized patients. The primary objective of this study was to determine the effect of a scripted code status explanation on patient understanding of choices pertaining to code status and end-of-life care.
In this work, an effective and economic way of transition metal doping in tin oxide nanoparticles... more In this work, an effective and economic way of transition metal doping in tin oxide nanoparticles is presented. The x-ray diffraction (XRD) measurements confirmed that the SnO 2 nanoparticles are of single phase with rutile structure. Transmission electron microscopy (TEM) micrographs show that nanoparticles exhibit spherical shape with size of ~ 4 nm. To check the incorporation of cobalt and its chemical bonding with oxygen, systematic FTIR measurements were performed. The stretching-vibration mode (A 2u ) of Sn-O and deformation-vibration mode (E u ) of O-Sn-O were found to be broadened and shifted towards the higher wave numbers in case of cobalt doped samples. The Co-O/O-Co-O modes of the stable phase of cobalt oxide (Co 2 O 3 ) were not detected in any doped samples. The results indicate that cobalt is present in the tin oxide lattice and do not form any metallic clusters or its oxide phases.
The paper deals with the analysis of a non-stationary parabolic partial differential equation wit... more The paper deals with the analysis of a non-stationary parabolic partial differential equation with a time delay. The highest order derivative term is affected by the small parameter. This is precisely the case when the magnitude of the convective term becomes much larger compare to that of diffusion term. The solution of problem exhibits steep gradients in the narrow intervals of space and short interval of times. In these cases a dissipative loss turned out to be more complex. Even for the one spatial dimension and one temporal variable, not all difference scheme can capture these steep variation. Although the analysis is restricted to the model in one space dimension, the technique and comparison principles developed should prove useful in assessing the merits of numerical solution of other nonlinear model equations too.
The results of the distorted-wave theory for electron-impact excitation of atoms are applied to t... more The results of the distorted-wave theory for electron-impact excitation of atoms are applied to the excitation of the 6s6p1P1 state of mercury. The spin polarization and the differential cross section are given for unpolarized incident electron beams with energies between 25 and 180 eV. The distorted-wave results are compared with experimental data, and good agreement is found for both the
ABSTRACT Zinc sulpho selenide has been proposed as a novel buffer layer, alternative to CdS for s... more ABSTRACT Zinc sulpho selenide has been proposed as a novel buffer layer, alternative to CdS for solar cell applications. In this paper Zn-Se-S composite thin layers have been synthesized on ultra clean glass substrate by screen-printing method followed by sintering process. Zinc sulphide, zinc selenide and zinc chloride have been used as the basic source material. To deposit good quality films, optimum conditions have been determined. X-ray diffraction analysis exhibited polycrystalline nature of layers with strong preferential orientation of grains along (200) direction. These layers have the wurtzite crystal structure. The optical band gap (Eg) of the films has been studied by using reflection spectra in wavelength range 325–600 nm. The optical band gap of Zn-Se-S composite thin layer has been found to be in between individual band-gaps of ZnS and ZnSe. The DC electrical conductivity of the layers has been measured in vacuum by a two probe technique and was found to be of the order of 10−6 ohm−1cm−1. These properties make these layers suitable for application as a buffer layer in solar cells.
International Journal of Computer Applications, 2012
This paper presents an approach to model content based metasearch engine which search all the con... more This paper presents an approach to model content based metasearch engine which search all the content related images present in the dataset. Searching through the keywords in an image database require a lot of Meta data (keywords about the image) to be stored for each image in a separate database. This does not lead to an effective search mechanism. This mechanism basically works for the relevant output for the input query image. The process based on the image extraction by the implemented functions like "edge histogram", "image feature extraction i.e. sharpness, smoothness, color etc.
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