the freiheitssatz of magnus for one-relator groups is one of the cornerstones of combinatorial group theory. in this short note which is mostly expository we discuss the relationship between the freiheitssatz and corre-sponding results in free power series rings over fields. these are related to results of schneerson not readily available in english. this relationship uses a faithful representa...

in this paper, optimum location of power system stabilizers in order to damp inter-area oscillations has been investigated by using modal series method. nonlinear effects grow in dynamical behaviors of heavily loaded stressed power systems significantly. hence linear based methods and techniques no longer present clear and exact response of the systems. in this article by defining new nonlinear...

Harmonics have become an important issue in modern power systems. The widespread penetration of non-linear loads to emerging power systems has turned power quality analysis into an important operation issue under both steady state and transient conditions. This paper employs an Extended Harmonic Domain (EHD) based framework for dynamic analysis of long term analysis over voltages during the tra...

This paper deals with the construction of random power series solution of second order linear differential equations of Hermite containing uncertainty through its coefficients and initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random power series solution is mean square convergent. We provide conditions in order to obtain random polynomial soluti...

in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...

in the present study, vibration of cylindrical laminates with different layers and angles were studied. in order to actuate and polarize in radial direction, a piezoelectric layer was located at outer surface of composite shell. laminates were assumed long enough so that plane strain state analysis in 2d can be used properly. in order to satisfy the boundary conditions, variables in terms of fo...

This paper presents the effect of centrifugal load in functionally graded (FG) hollow sphere subjected to uniform magnetic field. Analytical solution for stresses and perturbation of the magnetic field vector are determined using the direct method and the power series method. The material stiffness, the magnetic permeability and the density vary continuously across the thickness direction accor...

Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...