In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

We describe the isomorphism classes of infinite-dimensional graded Lie algebras of maximal class over fields of odd characteristic.

We survey a number of applications of the wavelet transform in time series prediction. The Haar à trous wavelet transform is proposed as a means of handling time series data when future data is unknown. Results are exemplified on financial futures and S&P500 data. Nonlinear and linear multiresolution autoregression models are studied. Experimentally, we show that multiresolution approaches can ...

In this paper, we present the advantages of Maximum overlapping Discrete Wavelet Transform (MODWT) in improving the forecasting accuracy financial time series data. Amman stock market (ASE) in Jordan was selected as a tool to show the ability of MODWT in forecasting financial time series, using Banking sector. Experimentally, this article suggests a novel technique for forecasting the banking d...

Providing an appropriate definition of a horizontal subbundle of a Lie algebroid will lead to construction of a better framework on Lie algebriods. In this paper, we give a new and natural definition of a horizontal subbundle using the prolongation of a Lie algebroid and then we show that any linear connection on a Lie algebroid generates a horizontal subbundle and vice versa. The same correspo...

the s-transform has widely been used in the analysis of non-stationary time series. a simple method to obtain depth estimates of gravity field sources is introduced in this study. we have developed a new method based on the spectral characteristics of downward continuation to estimate depth of structures. this calculation procedure is based on replacement of the fourier transform with the s-tra...

The statistical properties of speckles in paraxial optical systems depend on the system parameters. In particular, the speckle orientation and the lateral dependence (x and y) of the longitudinal speckle size can vary significantly. For example, the off-axis longitudinal correlation length remains equal to the on-axis size for speckles in a Fourier transform system, while it decreases dramatica...

in this paper, a useful classification of all lie subalgebras of a given lie algebraup to an inner automorphism is presented. this method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. after main results, we have applied this procedure for classifying the lie subalgebras of some examples of lie al...

In this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the Hunter-Saxton equation. The main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. It is a semi analytical-numerical method t...