Extended Abstract. Forecasting is one of the most important purposes of time series analysis. For many years, classical methods were used for this aim. But these methods do not give good performance results for real time series due to non-linearity and non-stationarity of these data sets. On one hand, most of real world time series data display a time-varying second order structure. On th...

Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on differential manifolds. These algebras have been extensively studied in recent years, both from algebraic operadic points of view and through numerous applications in numerical analysis, control theory, stochastic differential equations and renormalization. Butcher series are formal power series founded on pre-Lie alg...

an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

differential transform method has been applied to solve many functional equations so far. in this article, we have used this method to solve wave-like equations. differential transform method is capable of reducing the size of computational work. exact solutions can also be achieved by the known forms of the series solutions. some examples are prepared to show theefficiency and simplicity of th...

An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo-and photo-acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centers of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our a...

An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermoand photo-acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centres of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our ap...