interpolation of unequal intervals
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This document discusses interpolation methods for unequal intervals, specifically Lagrange's interpolation formula. It provides an example of using Lagrange's formula to compute an interpolated value f(9.2) given data points with unequal x-values of 9, 9.5, and 11 and their corresponding f-values. The interpolation is calculated and the result is 2.2191. Lagrange's formula is applicable to problems with equal or unequal intervals between data points and is preferable for unequal intervals. It involves multiplying and dividing polynomials based on the given x-values and f-values.
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Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
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Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
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Comparative analysis between traditional aquaponics and reconstructed aquapon...
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Embedded machine learning-based road conditions and driving behavior monitoring
Car accident rates have increased in recent years, resulting in losses in human lives, properties, and other financial costs. An embedded machine learning-based system is developed to address this critical issue. The system can monitor road conditions, detect driving patterns, and identify aggressive driving behaviors. The system is based on neural networks trained on a comprehensive dataset of driving events, driving styles, and road conditions. The system effectively detects potential risks and helps mitigate the frequency and impact of accidents. The primary goal is to ensure the safety of drivers and vehicles. Collecting data involved gathering information on three key road events: normal street and normal drive, speed bumps, circular yellow speed bumps, and three aggressive driving actions: sudden start, sudden stop, and sudden entry. The gathered data is processed and analyzed using a machine learning system designed for limited power and memory devices. The developed system resulted in 91.9% accuracy, 93.6% precision, and 92% recall. The achieved inference time on an Arduino Nano 33 BLE Sense with a 32-bit CPU running at 64 MHz is 34 ms and requires 2.6 kB peak RAM and 139.9 kB program flash memory, making it suitable for resource-constrained embedded systems.
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interpolation of unequal intervals
- 1. Gandhinagar Institute of Technology Numerical & Statistical Methods For Information Technology (2140706) Active Learning Assignment “Topic : Interpolation for unequal intervals and Lagrange's interpolation” Name: Vaani Pathak (170120107131) Branch : CE Div : B3
- 2. Interpolation with unequal intervals • If the values of x are unequally spaced then interpolation formulae for equally spaced points cannot be used. It is therefore, desirable to develop interpolation formulae for unequally spaced values of x. • There are two such formulae for unequally spaced values of x. i. Lagrange's interpolation formula. ii. Newton’s interpolation formula with divided difference.
- 3. Lagrange • Lagrange’s formula is applicable to problems where the independent variable occurs at equal and unequal intervals, but preferably this formula is applied in a situation where there are unequal intervals for the given independent series.
- 4. Lagrange's interpolation formula f(x) = (x-x1 ) (x-x2 )…. (x-xn) y0 + (x- x0) (x-x2)….(x- xn) y1 (x0 - x1 ) (x0 - x2)….(x0 - xn) (x1 – x0)(x1 – x2)….(x1 - xn) + (x- x0) (x- x1)….(x- xn-1) yn (xn – x0) (xn – x1)….(xn – xn-1)
- 5. Example : Compute f(9.2) by using Lagrange's interpolation method from the following data : • Solution : By Lagrange's interpolation formula, f(x) = (x - x1) (x - x2) f(x0) + (x- x0) (x- x2) f(x1) + (x0- x1)(x0 – x2) (x1- x0)(x1 – x2) (x – x0) (x – x1) f(x2) (x2 – x0) (x2- x1) x 9 9.5 11 f(x) 2.1972 2.2513 2.3973
- 6. f(9.2) = (9.2 – 9.5) (9.2 - 11) (2.1972) + (9 - 9.5) (9 - 11) (9.2 – 9) (9.2-11) (2.2513) + (9.5 – 9) (9.5 – 11) (9.2 – 9) (9.2 - 9.5) (2.3979) (11 – 9) (11 - 9.5) = 1.1865 + 1.0806 + 0.048 =2.2191
- 7. Thank you