notes on a conservative nonlinear oscillator the amplitude frequency relationship is an important mathematical property for a nonlinear oscillator he s amplitude frequency formulation and the max min approach are used to handle the conservative nonlinear oscillator email protected email protected 2 x 0 for the amplitude frequency relationship the obtained result is compared with those in the open literature revealing the effectiveness of the used methods

variational iteration method some recent results and new interpretations this paper is an elementary introduction to the concepts of variational iteration method first the main concepts in variational iteration method such as general lagrange multiplier restricted variation correction functional are explained heuristically subsequently the solution procedure is systematically addressed in particular for nonlinear oscillators particular attention is paid throughout the paper to give an intuitive grasp for the method the main motivation is to put things together in a convenient form for later reference and systematic use

frequency analysis of strongly nonlinear generalized duffing oscillators using he s frequency amplitude formulation and he s energy balance method in this paper he s frequency amplitude formulation hfaf and he s energy balance method hebm are employed to solve the generalized duffing equation in the form of x x a 3x 3 a 5x 5 a 7x 7 a nx n 0 for any arbitrary power of n a frequency analysis is carried out and the relationship between the natural frequency and the initial amplitude is obtained in analytical form accuracy and validity of the proposed techniques are then verified by comparing the numerical results obtained based on the hfaf hebm and exact integration method numerical simulations are extended for even very strong nonlinearities and very good correlations are achieved between the numerical results

application of the modified frequency formulation to a nonlinear oscillator he s frequency formulation is used to obtain the relationship between the frequency and amplitude of a nonlinear oscillator the general approach is to choose two linear oscillators in this paper however one linear oscillator and the duffing oscillator are chosen as trial equations the solution procedure is of utter simplicity while the result is of high accuracy

new sufficient conditions for the stability of slowly varying linear systems the frozen time approach is used to state some new sufficient conditions for the stability of linear time varying systems an upper bound on the norm of the time derivative of system matrix which under different assumptions on frozen time system eigenvalues guarantees asymptotic stability or exponential stability of the system is established

on the almost sure spiraling of geodesics in negatively curved manifolds given a negatively curved geodesic metric space m we study the almost sure asymptotic penetration behavior of locally geodesic lines of m into small neighborhoods of points of closed geodesics and of other compact locally convex subsets of m we prove khintchine type and logarithm law type results for the spiraling of geodesic lines around these objets as a consequence in the tree setting we obtain diophantine approximation results of elements of non archimedian local fields by quadratic irrational ones 1

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

analysis of a nonlinear oscillator with discontinuity in this paper a nonlinear oscillator with discontinuity is analyzed using he s amplitude frequency formulation the natural frequency of the oscillator system can be obtained using concise and straightforward calculation steps good agreement between the results from the proposed and other classical approaches is reached

approximate periodic solutions for the helmholtz duffing equation approximate periodic solutions for the helmholtz duffing oscillator are obtained in this paper he s energy balance method hebm and he s frequency amplitude formulation hfaf are adopted as the solution methods oscillation natural frequencies are analytically analyzed error analysis is carried out and accuracy of the solution methods is evaluated

sufficient stability bounds for slowly varying direct form recursive linear filters and their applications in adaptive iir filters this article derives a sufficient time varying bound on the maximum variation of the coefficients of an exponentially stable time varying direct form homogeneous linear recursive filter the stability bound is less conservative than all previously derived bounds for time varying iir systems the bound is then applied to control the step size of output error adaptive iir filters to achieve bounded input bounded output bibo stability of the adaptive filter experimental results that demonstrate the good stability characteristics of the resulting algorithms are included this article also contains comparisons with other competing output error adaptive iir filters the results indicate that the stabilized method possesses better convergence behavior than other competing techniques

an ancient chinese mathematical algorithm and its application to nonlinear oscillators an ancient chinese mathematical method is briefly introduced and its application to nonlinear oscillators is elucidated where he s amplitude frequency formulation is outlined three examples are given to show the extremely simple solution procedure and remarkably accurate solutions

widths of subgroups we say that the width of an infinite subgroup h in g is n if there exists a collection of n essentially distinct conjugates of h such that the intersection of any two elements of the collection is infinite and n is maximal possible we define the width of a finite subgroup to be 0 we prove that a quasiconvex subgroup of a negatively curved group has finite width it follows that geometrically finite surfaces in closed hyperbolic 3 manifolds satisfy the k plane property for some k

splittings of knot groups let k be a knot of genus g if k is fibered then it is well known that the knot group pi k splits only over a free group of rank 2g we show that if k is not fibered then pi k splits over non free groups of arbitrarily large rank furthermore if k is not fibered then pi k splits over every free group of rank at least 2g however pi k cannot split over a group of rank less than 2g the last statement is proved using recent results of agol przytycki wise and wise

approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire in this paper the approximate solutions of the mathematical model of a mass attached to a stretched elastic wire are presented at the beginning of the study the equation of motion is derived in a detailed way he s max min approach he s frequency amplitude method and the parameter expansion method are implemented to solve the established model the numerical results are further compared with the approximate analytical solutions for both a small and large amplitude of oscillations and a very good agreement is observed the relative errors are computed to illustrate the strength of agreement between the numerical and approximate analytical results

he s frequency amplitude formulation for nonlinear oscillators with an irrational force in this paper he s frequency amplitude formulation is applied to determine the periodic solution for a nonlinear oscillator system with an irrational force comparison with the exact solution shows that the result obtained is of high accuracy

he s frequency formulation for nonlinear oscillators using a golden mean location he s frequency formulation derived on the basis of an ancient chinese mathematical method is an effective method for treating nonlinear oscillators there are different approaches for choosing location points in the formulation this paper suggests another location point an example is given and the accuracy is improved

intersections of analytically and geometrically finite subgroups of kleinian groups we consider the intersection of pairs of subgroups of a kleinian group of the second kind k whose limit sets intersect where one subgroup g is analytically finite and the other j is geometrically finite possibly infinite cyclic in the case that j is infinite cyclic generated by m we show that either some power of m lies in g or there is a doubly cusped parabolic element q of g with the same fixed point as m in the case that j is nonelementary we show that the intersection of the limit sets of g and j is equal to the limit set of the intersection g j union with a subset of the rank 2 parabolic fixed points of k hence in both cases the limit set of the intersection is essentially equal to the intersection of the limit sets the main facts used in the proof are results of beardon and pommerenke 4 and canary 6 which yield that the poincare metric on the ordinary set of an analytically finite kleinian group g is comparable to the euclidean distance to the limit set of g