In the literature, a lot of numerical methods are available for solving both algebraic and transc... more In the literature, a lot of numerical methods are available for solving both algebraic and transcendental equations. The Newton-Raphson method is the most commonly used because of its simplicity and faster convergence. The intent of this paper is to fuzzify the generalized Newton Raphson type iterative scheme, known as He’s iteration for solving the nonlinear algebraic and transcendental equations arising in fuzzy environment. Several examples are taken for depicting the efficiency of new fuzzified He’s iterative scheme and its comparison table is given depicting the number of iterations required in Newton-Raphson, He’s Iteration and Fuzzified He’s iteration method. Key-Words: He’s iteration, nonlinear equations, Newton-Raphson method, Fuzzified iterative scheme.
We propose and prove a couple of formulas and infinite series involving the floor and the ceiling... more We propose and prove a couple of formulas and infinite series involving the floor and the ceiling functions. Formula relating to the difference of floor and ceiling functions is obtained using aforementioned formulas. Partial summations of floor and ceiling of qth roots of natural numbers are equated as simple formulas. Particular cases of the series are taken into consideration and it is proven that both the cases relate to the Riemann-Zeta function. Poles for the both series are mentioned and it is shown that even if both series individually fail to converge at the pole, their difference is convergent at the same. It is shown that our formulas reduce to the Gauss formula and the series reduce to the Riemann-Zeta for a particular value. Further some special cases and scope for future work are discussed.
In this paper, the solution for second order Cauchy Euler equation is derived using generalized t... more In this paper, the solution for second order Cauchy Euler equation is derived using generalized trapezoidal intuitionistic fuzzy number. Further as an application we study the problem for finding the radial displacement of a solid disk with given boundary condition in the form of generalized trapezoidal intuitionistic fuzzy number. The obtained solutions are drawn graphically for different radii using (α,β)-cuts. Key-Words: Fuzzy Sets; Cauchy-Euler differential equation; α,β–cuts; Trapezoidal Intuitionistic fuzzy number; Generalized Hukuhara Derivative, Solid Disk.
The present paper describes the method of finding the radial displacement of a solid disk which u... more The present paper describes the method of finding the radial displacement of a solid disk which uses the concept of a generalized trapezoidal intuitionistic fuzzy number. Key-Words: Cauchy-Euler fuzzy differential equations, Intuitionistic fuzzy number, Trapezoidal fuzzy number, Hukuhara Differentiability.
The global additive manufacturing industry has been rapidly increasing, owing to its unique layer... more The global additive manufacturing industry has been rapidly increasing, owing to its unique layer-by-layer production method. While additive manufacturing has superior capabilities compared to traditional subtractive manufacturing, limitations still exist, which significantly hinder the larger-scale implementations of additive manufacturing. Some challenging issues include unsatisfactory dimensional accuracy, surface quality, etc. In the literature, extensive research efforts have dedicated to detecting, predicting, and compensating process errors using various methodologies. In this work, a new approach is proposed for error compensation using multi-extrusion additive manufacturing process. Three demonstrative case studies are conducted, i.e., multicolor and/or multimaterial printing, geometric error compensation, and rough surface compensation. Experimental results have shown that the proposed approach is effective in utilizing the multi-nozzle capability in additive manufacturing...
Automation is seen in each and every sector of industry these days. Smart phones plays a major ro... more Automation is seen in each and every sector of industry these days. Smart phones plays a major role in promoting Automation. In metropolitan cities, the number of working parents are increasing day by day, which makes it difficult for the parents to work as well as take care of their babies. This paper presents a concept of Automated IOT based smart cradle which can be operated using an android application. Parents can monitor their baby 24/7 with the help of this system. Using multiple sensors and motors, this system will detect the temperature and humidity inside the cradle. It will swing the cradle automatically on sensing the cry of the baby and it will send an alert to parents on their android application if the baby is crying for a long period of time.
The Second World War, one of the most gruelling events in the history of mankind, also marks the ... more The Second World War, one of the most gruelling events in the history of mankind, also marks the emergence of one of modern-day’s most widely used scientific disciplines – Operations Research (OR). Rather than defining OR as a ‘part of mathematics’, a better characterization of the sequence of events would be that some mathematicians during World War II were coerced into mixed disciplinary units dominated by physicists and statisticians, and directed to participate in an assorted mix of activities which were clubbed together under the rubric of ‘Operations Research’. Some of these activities ranged from curating a solution for the neutron scattering problem in atomic bomb design to strategizing military attacks by means of choosing the best possible route to travel. Thus arose two major Operations Research techniques – Monte Carlo Simulation and Game Theory. More than 70 years later, managers face business problems that often seem as complicated as the design of an atomic bomb. Mode...
COVID-19 has been a public health challenge for the whole world. India implemented a multidimensi... more COVID-19 has been a public health challenge for the whole world. India implemented a multidimensional integrated management strategy encompassing several types of diagnostic approaches, contact, surveys, isolation, and treating of affected patients. Timely detection and isolation of cases and their contacts proved to be an effective aid to contain the epidemic. The recommended diagnostic method for SARS-CoV-2 is real-time reverse-transcription polymerase chain reaction (RT-PCR), which was introduced in January 2020. However, due to the large gap between the number of patients and the capacity of the laboratory to perform RT-PCR in a timely manner, its widespread use in public health containment strategies was limited. Alternative assays such as antigen detection tests based on rapid chromatographic immunoassay that can detect the presence of virus itself in respiratory samples was used.<sup>1-4</sup>
International Journal for Research in Applied Science and Engineering Technology
Vehicle positioning and classification is a vital technology in intelligent transportation and se... more Vehicle positioning and classification is a vital technology in intelligent transportation and self-driving cars. This paper describes the experimentation for the classification of vehicle images by artificial vision using Keras and TensorFlow to construct a deep neural network model, Python modules, as well as a machine learning algorithm. Image classification finds its suitability in applications ranging from medical diagnostics to autonomous vehicles. The existing architectures are computationally exhaustive, complex, and less accurate. The outcomes are used to assess the best camera location for filming, the vehicular traffic to determine the highway occupancy. An accurate, simple, and hardware-efficient architecture is required to be developed for image classification.
Abstract In this paper, a new two-step iterative scheme is developed by combining Newton-Raphson ... more Abstract In this paper, a new two-step iterative scheme is developed by combining Newton-Raphson (N-R) method and fixed point iterative scheme. It has been seen that using first N-R method and then Fixed Point iterative scheme, the number of iterations required to converge to the solutions shows a significant decrement. Here, we have also discussed the efficiency of the scheme using some examples. Graphs are also drawn for error against number of iterations.
This paper presents the effect of solar illumination on the differential potential generated on t... more This paper presents the effect of solar illumination on the differential potential generated on the surfaces of spacecraft body in space. Two geometrical cases are considered: 1) Cylindrical symmetry and 2) Tilted metallic plates forming an angle with the adjacent side. The capacitance required for estimation of the body potential is computed by Method of Moment. Nonuniform triangular meshing is used for both the geometrical structures. The differential potential generated on surfaces of a geometrical body due to photoelectric effect results in electrostatic discharge. In the case of the tilted plates, the differential potential at various tilt-angles is computed along with the capacitance computation. In the case of the cylindrical object, the estimation of potential at the day-night interface is shown. The variation in the potential for different incident angles of the solar photons and the changing (h/r) ratio is analyzed. The validity of the analysis is established with that obtained in open literature.
Iterative schemes are the important tool for solving nonlinear equations arising in many real lif... more Iterative schemes are the important tool for solving nonlinear equations arising in many real life problems. Our literature is rich with lots of iterative schemes, which are useful for solving nonlinear equations of one or more variables. Among them, Newton-Raphson method is the simplest and highly convergent with second order convergence. It is vastly used by researchers, applied mathematicians and engineers. Problems arising in our day to day life cannot be easily describe by crisp values, because in real life situations, always some uncertainty is involved and in those situations we receive some fuzzy values instead of crisp values. So it is immensely important to develop some iterative schemes, which can easily tackle this kind of fuzzy environment. The intent of this paper is to show advantage of using newly developed fuzzified He’s iterative method over N-R method and Kang method for solving nonlinear equations of one variable arising in the fuzzy environment. Some numerical e...
In the literature, a lot of numerical methods are available for solving both algebraic and transc... more In the literature, a lot of numerical methods are available for solving both algebraic and transcendental equations. The Newton-Raphson method is the most commonly used because of its simplicity and faster convergence. The intent of this paper is to fuzzify the generalized Newton Raphson type iterative scheme, known as He’s iteration for solving the nonlinear algebraic and transcendental equations arising in fuzzy environment. Several examples are taken for depicting the efficiency of new fuzzified He’s iterative scheme and its comparison table is given depicting the number of iterations required in Newton-Raphson, He’s Iteration and Fuzzified He’s iteration method. Key-Words: He’s iteration, nonlinear equations, Newton-Raphson method, Fuzzified iterative scheme.
We propose and prove a couple of formulas and infinite series involving the floor and the ceiling... more We propose and prove a couple of formulas and infinite series involving the floor and the ceiling functions. Formula relating to the difference of floor and ceiling functions is obtained using aforementioned formulas. Partial summations of floor and ceiling of qth roots of natural numbers are equated as simple formulas. Particular cases of the series are taken into consideration and it is proven that both the cases relate to the Riemann-Zeta function. Poles for the both series are mentioned and it is shown that even if both series individually fail to converge at the pole, their difference is convergent at the same. It is shown that our formulas reduce to the Gauss formula and the series reduce to the Riemann-Zeta for a particular value. Further some special cases and scope for future work are discussed.
In this paper, the solution for second order Cauchy Euler equation is derived using generalized t... more In this paper, the solution for second order Cauchy Euler equation is derived using generalized trapezoidal intuitionistic fuzzy number. Further as an application we study the problem for finding the radial displacement of a solid disk with given boundary condition in the form of generalized trapezoidal intuitionistic fuzzy number. The obtained solutions are drawn graphically for different radii using (α,β)-cuts. Key-Words: Fuzzy Sets; Cauchy-Euler differential equation; α,β–cuts; Trapezoidal Intuitionistic fuzzy number; Generalized Hukuhara Derivative, Solid Disk.
The present paper describes the method of finding the radial displacement of a solid disk which u... more The present paper describes the method of finding the radial displacement of a solid disk which uses the concept of a generalized trapezoidal intuitionistic fuzzy number. Key-Words: Cauchy-Euler fuzzy differential equations, Intuitionistic fuzzy number, Trapezoidal fuzzy number, Hukuhara Differentiability.
The global additive manufacturing industry has been rapidly increasing, owing to its unique layer... more The global additive manufacturing industry has been rapidly increasing, owing to its unique layer-by-layer production method. While additive manufacturing has superior capabilities compared to traditional subtractive manufacturing, limitations still exist, which significantly hinder the larger-scale implementations of additive manufacturing. Some challenging issues include unsatisfactory dimensional accuracy, surface quality, etc. In the literature, extensive research efforts have dedicated to detecting, predicting, and compensating process errors using various methodologies. In this work, a new approach is proposed for error compensation using multi-extrusion additive manufacturing process. Three demonstrative case studies are conducted, i.e., multicolor and/or multimaterial printing, geometric error compensation, and rough surface compensation. Experimental results have shown that the proposed approach is effective in utilizing the multi-nozzle capability in additive manufacturing...
Automation is seen in each and every sector of industry these days. Smart phones plays a major ro... more Automation is seen in each and every sector of industry these days. Smart phones plays a major role in promoting Automation. In metropolitan cities, the number of working parents are increasing day by day, which makes it difficult for the parents to work as well as take care of their babies. This paper presents a concept of Automated IOT based smart cradle which can be operated using an android application. Parents can monitor their baby 24/7 with the help of this system. Using multiple sensors and motors, this system will detect the temperature and humidity inside the cradle. It will swing the cradle automatically on sensing the cry of the baby and it will send an alert to parents on their android application if the baby is crying for a long period of time.
The Second World War, one of the most gruelling events in the history of mankind, also marks the ... more The Second World War, one of the most gruelling events in the history of mankind, also marks the emergence of one of modern-day’s most widely used scientific disciplines – Operations Research (OR). Rather than defining OR as a ‘part of mathematics’, a better characterization of the sequence of events would be that some mathematicians during World War II were coerced into mixed disciplinary units dominated by physicists and statisticians, and directed to participate in an assorted mix of activities which were clubbed together under the rubric of ‘Operations Research’. Some of these activities ranged from curating a solution for the neutron scattering problem in atomic bomb design to strategizing military attacks by means of choosing the best possible route to travel. Thus arose two major Operations Research techniques – Monte Carlo Simulation and Game Theory. More than 70 years later, managers face business problems that often seem as complicated as the design of an atomic bomb. Mode...
COVID-19 has been a public health challenge for the whole world. India implemented a multidimensi... more COVID-19 has been a public health challenge for the whole world. India implemented a multidimensional integrated management strategy encompassing several types of diagnostic approaches, contact, surveys, isolation, and treating of affected patients. Timely detection and isolation of cases and their contacts proved to be an effective aid to contain the epidemic. The recommended diagnostic method for SARS-CoV-2 is real-time reverse-transcription polymerase chain reaction (RT-PCR), which was introduced in January 2020. However, due to the large gap between the number of patients and the capacity of the laboratory to perform RT-PCR in a timely manner, its widespread use in public health containment strategies was limited. Alternative assays such as antigen detection tests based on rapid chromatographic immunoassay that can detect the presence of virus itself in respiratory samples was used.<sup>1-4</sup>
International Journal for Research in Applied Science and Engineering Technology
Vehicle positioning and classification is a vital technology in intelligent transportation and se... more Vehicle positioning and classification is a vital technology in intelligent transportation and self-driving cars. This paper describes the experimentation for the classification of vehicle images by artificial vision using Keras and TensorFlow to construct a deep neural network model, Python modules, as well as a machine learning algorithm. Image classification finds its suitability in applications ranging from medical diagnostics to autonomous vehicles. The existing architectures are computationally exhaustive, complex, and less accurate. The outcomes are used to assess the best camera location for filming, the vehicular traffic to determine the highway occupancy. An accurate, simple, and hardware-efficient architecture is required to be developed for image classification.
Abstract In this paper, a new two-step iterative scheme is developed by combining Newton-Raphson ... more Abstract In this paper, a new two-step iterative scheme is developed by combining Newton-Raphson (N-R) method and fixed point iterative scheme. It has been seen that using first N-R method and then Fixed Point iterative scheme, the number of iterations required to converge to the solutions shows a significant decrement. Here, we have also discussed the efficiency of the scheme using some examples. Graphs are also drawn for error against number of iterations.
This paper presents the effect of solar illumination on the differential potential generated on t... more This paper presents the effect of solar illumination on the differential potential generated on the surfaces of spacecraft body in space. Two geometrical cases are considered: 1) Cylindrical symmetry and 2) Tilted metallic plates forming an angle with the adjacent side. The capacitance required for estimation of the body potential is computed by Method of Moment. Nonuniform triangular meshing is used for both the geometrical structures. The differential potential generated on surfaces of a geometrical body due to photoelectric effect results in electrostatic discharge. In the case of the tilted plates, the differential potential at various tilt-angles is computed along with the capacitance computation. In the case of the cylindrical object, the estimation of potential at the day-night interface is shown. The variation in the potential for different incident angles of the solar photons and the changing (h/r) ratio is analyzed. The validity of the analysis is established with that obtained in open literature.
Iterative schemes are the important tool for solving nonlinear equations arising in many real lif... more Iterative schemes are the important tool for solving nonlinear equations arising in many real life problems. Our literature is rich with lots of iterative schemes, which are useful for solving nonlinear equations of one or more variables. Among them, Newton-Raphson method is the simplest and highly convergent with second order convergence. It is vastly used by researchers, applied mathematicians and engineers. Problems arising in our day to day life cannot be easily describe by crisp values, because in real life situations, always some uncertainty is involved and in those situations we receive some fuzzy values instead of crisp values. So it is immensely important to develop some iterative schemes, which can easily tackle this kind of fuzzy environment. The intent of this paper is to show advantage of using newly developed fuzzified He’s iterative method over N-R method and Kang method for solving nonlinear equations of one variable arising in the fuzzy environment. Some numerical e...
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