Time series are unstructured data; they are difficult to monitor, summarize and predict. Weather forecasts, stock market prices, medical data (ECG, EEG) are examples of non-stationary time series we wish to clean, classify and index. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). The popular piecewise...

In this paper, we propose a new approach to solve the unsteady gas equation. We apply the Modified Laplace decomposition method (MLDM) coupled with Pade ́ approximation to compute a series solution of unsteady flow of gas through a porous medium. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. The nonlinear terms can be easil...

The existence and uniqueness of the electron transport Wigner equation solution, determined by boundary conditions, is analyzed in terms of the Neumann series expansion of the integral form of the equation, obtained with the help of Newton’s trajectories. For understanding of the peculiarities of Wigner-quantum electron transport in semiconductor structures such mathematical issues can not be s...

Series solution of nonlinear dynamic system containing fractional derivative is obtained by the homotopy analysis method (HAM). The solution via HAM has auxiliary parameter h̄ which can control the convergent of the series to obey the exact or numerical solution. The model of viscoelastic behavior of a one-degree-of-freedom oscillator consisting of a discrete mass and a viscoelastic spring is co...

In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to  btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...

A method for calculating the relativistic path integral solution via sum over perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov-Bohm-Coulomb system is obtained by the method. Different from the earlier treatment based on the space-time transformation and infinite multiple-valued trasformation of Kustaanheimo-Stiefel in order to perform...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...