in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

We adopt the following convention: i, j, m, n denote natural numbers, K denotes a field, and a denotes an element of K. Next we state several propositions: (1) Let A, B be matrices over K, n1 be an element of Nn, and m1 be an element of Nm. If rng n1 × rngm1 ⊆ the indices of A, then Segm(A + B,n1,m1) = Segm(A,n1,m1) + Segm(B,n1,m1). (2) For every without zero finite subset P of N such that P ⊆ ...

In this paper, a procedure is reported that discuss how linear algebra can be used in image compression. The basic idea is that each image can be represented as a matrix. We apply linear algebra (QR ‎factorization and wavelet ‎transformation ‎algorithm‏s) on this matrix and get a reduced matrix out such that the image corresponding to this reduced matrix requires much less storage space than th...

In this paper the earth’s magnetic field is simulated precisely while the intensity and direction of the field are verified with one of the standard references for selected points on the earth and the results are compared with some low-order models. In another simulation, the complete model is compared with a common approximate model. The magnetic field in orbital frame is described and to empl...

Abstract Linear transformations are widely used in data assimilation for covariance modeling, reducing dimensionality (such as averaging dense observations to form “superobs”), and managing sampling error ensemble assimilation. Here we describe a linear transformation that is optimal the sense that, transformed space, state variables have uncorrelated errors, diagonal gain matrix update step. W...