USED CAR PRICE PREDICTION

Cars have become a necessity in this modern world. Every middle class family needs a vehicle or a mode of transport in order to move from one place to another. Not everyone is able to afford a new vehicle as they are costly and there’s an added cost of taxes and various other expenses by both the provider/company of the car as well as the government. Moreover, not every customer is sure of spending a sum of their wealth on a certain car. The product might not meet their needs. The solution to this problem of having a car despite not being able to afford one is met by buying and selling second hand cars. It has become its own market now. There are already numerous companies and websites and app based services that serve as a mediator or a platform for the dealing of second hand or used cars and other vehicles. Establishment of such places is easy but there is another problem that still remains- How to price the used car appropriately at a price comfortable for both the seller and the buyer? Luckily, the Used Car Price Prediction systems exist and can be developed. Users might think that it’s easy to determine the price of a used car, and whether there is even a need to have such a system. In truth, there are a lot of factors that are important in determining the price of a second hand vehicle. The quality of a vehicle deteriorates with age1 of course but that is not all. Every single vehicle is different even when it is manufactured and sold as a new product and even more so when the same vehicle is used over time. Different people may use their vehicles more or less depending on their everyday activity, making kilometers driven as one of the important factors for the price prediction. It is obvious that a vehicle which is driven for 2000 kilometers in 1 year would be priced less than a vehicle which has been driven for only 500 kilometers in 2 years. This is just one of the factors that determine the price of a used car. In our Car Price Prediction System, we have used the Year of Manufacturing (used to determine the age of the vehicle by subtracting this from the date of selling), the original maximum retail price of the vehicle (the price at which the vehicle was sold at from the manufacturing company/garage), the fuel type of the vehicle (Petrol, Diesel, CNG, Electric ; This affects the pricing severely as different fuel type engines have different prime performance periods and different rates of deterioration), Seller Type (Individual or Dealership), Transmission (Manual or Automatic), Number of past owners of the vehicle. Using all these factors2, we are going to determine which model is best to determine a price for the used vehicle. For the Car Price Prediction System, Regression models3are used since these models give the results as a continuous curve instead of a categorized value as a result. Due to this, we can use the continuous curve to determine an accurate price for each and every scenario which won’t be possible if the results obtained were in the form of a range. The final model of the system will implement the best suited algorithm and have a UI (User Interface) which make it possible for a user to be able to enter the values of these deciding factors and the system will predict the price for them. Keywords: Car price prediction, machine learning, regression analysis, linear regression, correlation analysis

Double Resonance: Forcing Equivalence

This chapter assesses the choice of cohomology and Aubry-Mather type at the double resonance. It begins by choosing cohomology classes for the (unperturbed) slow mechanical system. As in the case of single-resonance, the strategy is to choose a continuous curve in the cohomology space and prove forcing equivalence up to a residual perturbation. To do this, one needs to use the duality between homology and cohomology. The chapter then proves Aubry-Mather type for the perturbed slow mechanical system and reverts to the original coordinates. As the system has been perturbed, one needs to modify the choice of cohomology classes to connect the single and double resonances. Finally, the chapter proves Theorem 2.2, proving the main theorem.

Realization of Arbitrary Configuration of Limit Cycles of Piecewise Linear Systems

In this paper, we consider the realization of configuration of limit cycles of piecewise linear systems on the plane. We show that any configuration of finite number of Jordan curves can be realized by a discontinuous piecewise linear system with two zones separated by a continuous curve.

A Mathematical Approach with Fractional Calculus for the Modelling of Children’s Physical Development

From birth to now, it is getting more and more important to keep track of the children development, because knowing and determining the factors related to the physical development of the children would provide better and reliable results for children care. In this study, we developed a mathematical approach to have the ability of analysing and examining factors such as weight, height, and body mass index with respect to the age. We used 7 groups for weight, height, and body mass index in Percentage Chart of Turkey. We developed a continuous curve which is valid for any time interval by using discrete weight, height, and body mass index data of 0–18 years old children and the least squares method. By doing so, it became possible to find the percentage and location of the children in Percentage Chart. We advanced a new mathematical model with the help of fractional calculus theory. The results are quite successful and better compared to linear and Polynomial Model analysis. The method provides the opportunity to predict expected values of the children for the future by using previous data obtained in the development of the children.

Approximation Algorithms for Barrier Sweep Coverage

Time-varying coverage, namely sweep coverage is a recent development in the area of wireless sensor networks, where a few mobile sensors sweep or monitor a comparatively large number of locations periodically. In this article, we study barrier sweep coverage with mobile sensors where the barrier is considered as a finite length continuous curve on a plane. The coverage at every point on the curve is time-variant. We propose an optimal solution for sweep coverage of a finite length continuous curve. Usually, energy source of a mobile sensor is a battery with limited power, so energy restricted sweep coverage is a challenging problem for long running applications. We propose an energy-restricted sweep coverage problem where every mobile sensor must visit an energy source frequently to recharge or replace its battery. We propose a [Formula: see text]-approximation algorithm for this problem. The proposed algorithm for multiple curves achieves the best possible approximation factor 2 for a special case. We propose a 5-approximation algorithm for the general problem. As an application of the barrier sweep coverage problem for a set of line segments, we formulate a data gathering problem. In this problem a set of mobile sensors is arbitrarily monitoring the line segments one for each. A set of data mules periodically collects the monitoring data from the set of mobile sensors. We prove that finding the minimum number of data mules to collect data periodically from every mobile sensor is NP-hard and propose a 3-approximation algorithm to solve it.

Conservative Chaos in a Class of Nonconservative Systems: Theoretical Analysis and Numerical Demonstrations

This paper proposes a class of nonlinear systems and presents one example system to illustrate its interesting dynamics, including quasiperiodic motion and chaos. It is found that the example system is a subsystem of a non-Hamiltonian system, which has a continuous curve of equilibria with time-reversal symmetry. In this study, the dynamical evolution of the example system with three different kinds of external excitations are fully investigated by using general chaotic analysis methods such as Poincaré sections, phase portraits, Lyapunov exponents and bifurcation diagrams. Both theoretical analysis and numerical simulations show that the example system is nonconservative but has conservative chaotic flows, which are numerically verified by the sum of its Lyapunov exponents. It is also found that the example system has time-reversal symmetry.

Analysis of Two-Dimensional Kinetic Shape Systems

A Kinetic Shape has a physical and continuous curve with a changing radius that is exactly defined by its kinetic behavior. A Kinetic Shape curve is defined by specifying the force applied to the Kinetic Shape and the force with which the Kinetic Shape subsequently reacts at ground contact. This concept allows for predictable, position-dependent, and purely mechanical force redirection which make it broadly applicable. Kinetic Shapes have been previously used in several applications to predict the redirection of forces applied to the shape into ground reaction forces. Here, we analyze various ways 2D Kinetic Shapes interact and show how different mechanical force-based computational operations can be performed using these interconnected Kinetic Shapes, which we call Kinetic Shape Systems.

Large-amplitude solitary water waves with discontinuous vorticity

Consider a two-dimensional body of water with constant density which lies below a vacuum. The ocean bed is assumed to be impenetrable, while the boundary which separates the uid and the vacuum is assumed to be a free boundary. Under the assumption that the vorticity is only bounded and measurable, we prove that for any upstream velocity field, there exists a continuous curve of large-amplitude solitary wave solutions. This is achieved via a local and global bifurcation construction of weak solutions to the elliptic equations which constitute the steady water wave problem. We also show that such solutions possess a number of qualitative features; most significantly that each solitary wave is a symmetric, monotone wave of elevation.