a control theory for cartesian flexible robot arms in this article we first use a fourth order partial differential equation with boundary conditions to model a flexible robot arm on a moving base with a payload at the tip end through the state space formulation we show that such a system is both controllable and observable in an infinite dimensional hilbert space we also show that the system is stabilizable via a feedback control

einstein maxwell solitons the application of the inverse scattering method to the einstein maxwell equations for stationary axisymmetric exterior fields leads the authors to an explicit formula for the ernst and electromagnetic potentials of new exact solutions generated from an arbitrary seed solution

burrows wheeler transform and palindromic richness the investigation of the extremal case of the burrows wheeler transform leads to study the words w over an ordered alphabet a a 1 a 2 a k with a 1

on the mathematical model for linear elastic systems with analytic damping in the present paper we investigate linear elastic systems with damping ddot y b dot y ay 0 in hilbert spaces where a is a positive definite unbounded linear operator and b is a closed linear operator related in various ways to a alpha frac 1 2 leqq alpha leqq 1 we discuss the spectral property of these systems and obtain some fundamental results for the holomorphic property and the exponential stability of the semigroups associated with these systems

a new general algebraic method and its applications to the 2 1 dimensional broer kaup kupershmidt equations abstract using a computerized symbolic computation technique a new method named the repeated general algebraic method rgam is established in this study in order to find exact solutions of nonlinear partial differential equations nlpdes the new method is validated based on the 2 1 dimensional broer kaup kupershmidt bkk equations by using the rgam in various conditions a number of exact solutions of nlpdes have been obtained showing potential importance in future physical applications also it is anticipated that the rgam can be applied to other nonlinear evolution equations in mathematical physics to produce some interesting outcomes

new exact solutions for mch and mdp equations by auxiliary equation method abstract with the aid of symbolic computation auxiliary equation method is introduced to investigate modified forms of camassa holm and degasperis procesi equations a series of new exact traveling wave solutions including smooth solitary wave solution peakons singular solution periodic wave solution jacobi elliptic solution are obtained in general form these new exact solutions will enrich previous results and help us further understand the physical structures of these two nonlinear equations

two new wronskian conditions for the 3 1 dimensional jimbo miwa equation abstract in this paper we obtain two kinds of sufficient conditions consisting of systems of linear partial differential equations which guarantee that the corresponding wroskian determinant solves the 3 1 dimensional jimbo miwa equation in the hirota bilinear form our results suggest that more general conditions could be derived by further study

balance properties of multi dimensional words a word u is called 1 balanced if for any two factors v and w of u of equal length we have 1 v i w i1 for each letter i where v i denotes the number of occurrences of i in the factor v the aim of this paper is to extend the notion of balance to multi dimensional words we first characterize all 1 balanced words on zn in particular we prove they are fully periodic for n 1 we then give a quantitative measure of non balancedness for some words on z2 with irrational density including two dimensional sturmian words

orientation and stabilization of a flexible beam attached to a rigid body planar motion the author considers a flexible structure modeled as a rigid body which rotates in inertial space a light flexible beam is clamped to the rigid body at one end and free one is clamped at the other it is assumed that the flexible beam performs only planar motion the equations of motion are obtained by using free body diagrams two control problems are posed namely the orientation and stabilization of the system it is shown that suitable boundary controls applied to the free end of the beam and suitable control torques applied to the rigid body solve the problems posed above the proofs are obtained by using the energy of the system as a lyapunov functional

exact solutions to the two dimensional korteweg de vries burgers equation two methods are described for obtaining exact travelling monotone shock wave solutions to the two dimensional korteweg de vries burgers equation they are compared with two methods that have been reported recently by other authors

exact travelling wave solutions of nonlinear evolution equation of surface waves in a convecting fluid exact travelling wave solutions in terms of the weierstrass p function of the equation eta t a0 eta x a1 eta eta x a2 eta xxx b0 eta xx b 1 eta eta x x b2 eta xxxx 0 are obtained these solutions may describe particularly both the evolution of a bounded conoidal wave and kink shaped waves

standard sturmiam morphisms abstract we give a characterization of morphisms which preserve finite and infinite standard sturmian words the class of such morphisms coincides with the monoid d e of the endomorphisms of a where a a b generated by the two elementary morphisms e which interchanges the letter a with b and d which is the fibonacci morphism defined as d a ab d b a some new properties of these morphisms are shown in particular we prove the following result let x n n 0 be the sequence of sets inductively defined as x 0 e x 1 a x n 1 ax n for n 1 where e denotes the empty word and is the operator of left palindrome closure associating to each word w the shortest word having w as suffix for all n 0 one has x n 1 e g d x n a where denotes the identity map from this we derive a new characterization of the set per of all words w having two periods p and q which are coprimes and such that w p q 2 indeed one has that per aa xcup n 0 e l od x n a

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

quasiperiodic waves and asymptotic behavior for bogoyavlenskii s breaking soliton equation in 2 1 dimensions based on a multidimensional riemann theta function the hirota bilinear method is extended to explicitly construct multiperiodic quasiperiodic wave solutions for the 2 1 dimensional bogoyavlenskii breaking soliton equation among these periodic waves the one periodic waves are well known cnoidal waves their surface pattern is one dimensional and often they are used as one dimensional models of periodic waves in shallow water the two periodic biperiodic waves are a direct generalization of one periodic waves their surface pattern is two dimensional that is they have two independent spatial periods in two independent horizontal directions the two periodic waves may be considered to represent periodic waves in shallow water without the assumption of one dimensionality a limiting procedure is presented to analyze asymptotic behavior of the one and two periodic waves in details the exact relations between the periodic wave solutions and the well known soliton solutions are established it is rigorously shown that the periodic wave solutions tend to the soliton solutions under a small amplitude limit

soliton structure of the drinfel d sokolov wilson equation an integrable equation due to drinfel d and sokolov sov math dokl 23 457 1981 and wilson phys lett a 89 332 1982 dsw is studied in detail it is shown how this system can be obtained as a six reduction of the kadomtsev petviashvili hierarchy this equation presents a novel type of solutions called static solitons they are static solutions that interact with moving solitons without deformations examples of such solutions are given together with a general procedure for their construction finally the painleve analysis of the dsw equation is performed directly on the bilinear form which constitutes a new application of the singularity analysis method

darboux transformation and soliton like solutions for the gerdjikov ivanov equation an explicit n fold darboux transformation with multiparameters for a kind of coupled derivative nonlinear schrodinger equation is constructed with the help of a gauge transformation of a spectral problem as a reduction a darboux transformation of the gerdjikov ivanov equation is obtained furthermore the explicit soliton like solutions of the gerdjikov ivanov equation are given by applying its darboux transformation

new exact solitary wave and multiple soliton solutions of quantum zakharov kuznetsov equation abstract by employing auxiliary equation method and hirota bilinear method the quantum zakharov kuznetsov equation which arises in quantum magnetoplasma is investigated with the aid of symbolic computation both solitary wave solutions and multiple soliton solutions are obtained these new exact solutions will extend previous results and help us explain the properties of multidimensional nonlinear ion acoustic waves in dense magnetoplasma

sturmian words structure combinatorics and their arithmetics abstract we prove some new results concerning the structure the combinatorics and the arithmetics of the set per of all the words w having two periods p and q p q which are coprimes and such that w p q 2 a basic theorem relating per with the set of finite standard sturmian words was proved in de luca and mignosi 1994 the main result of this paper is the following simple inductive definition of per the empty word belongs to per if w is an already constructed word of per then also aw and bw belong to per where denotes the operator of palindrome left closure i e it associates to each word u the smallest palindrome word u having u as a suffix we show that by this result one can construct in a simple way all finite and infinite standard sturmian words we prove also that up to the automorphism which interchanges the letter a with the letter b any element of per can be codified by the irreducible fraction p q this allows us to construct for any n 0 a natural bijection that we call farey correspondence of the set of the farey series of order n 1 and the set of special elements of length n of the set st of all finite sturmian words finally we introduce the concepts of farey tree and farey monoid this latter is obtained by defining a suitable product operation on the developments in continued fractions of the set of all irreducible fractions p q

are all the equations of the kadomtsev petviashvili hierarchy integrable the kadomtsev petviashvili kp hierarchy is an infinite set of nonlinear partial differential equations in which the number of independent variables increases indefinitely as one proceeds down the hierarchy since these equations were obtained as part of a group theoretical approach to soliton equations it would appear that the kp hierarchy provides integrable scalar equations with an arbitrary number of independent variables it is shown by investigating a specific equation in 3 1 dimensions that the higher equations in the kp hierarchy are only integrable in a conditional sense the equation under study taken in isolation does not pass certain well known and reliable integrability tests thus applying painleve analysis we find that solutions exist allowing movable critical points furthermore solitary wave solutions are shown to exist that do not behave like solitons in multiple collisions on the other hand if the dependence of a solution on the first 2 1 variables is restricted by the fact that it should also satisfy the kp equation itself then the integrability conditions in the other dimensions are satisfied conditional integrability thus means that linear techniques will provide only those solutions of equations in the hierarchy that simultaneously satisfy lower equations in the same hierarchy

a feedback control and a simulation of a torsional elastic robot arm a feedback control is designed for a torsional elastic robot arm to be exponentially stable and to arrive at any designated position an eigenvalue problem is discussed and a finite dimensional approximation theorem is proposed and proved based on the numerical analysis and the approximation theorem we can simulate the system and show that the bending vibration the torsional vibration the rigid turning angle and the bending moment of the robot arm can be controlled in a short period of time

new exact solutions for a generalized variable coefficient kdv equation new exact solutions for a generalized variable coefficient kdv equation were obtained using the generalized expansion method r sabry m a zahran e g fan phys lett a 326 2004 93 the obtained solutions include solitary wave solutions besides jacobi and weierstrass doubly periodic wave solutions

darboux transformation and solutions for an equation in 2 1 dimensions painleve analysis and the singular manifold method are the tools used in this paper to perform a complete study of an equation in 2 1 dimensions this procedure has allowed us to obtain the lax pair darboux transformation and functions in such a way that a plethora of different solutions with solitonic behavior can be constructed iteratively

new similarity reductions and painleve analysis for the symmetric regularised long wave and modified benjamin bona mahoney equations the author discusses similarity reductions and painleve analysis for the symmetric regularised long wave and modified benjamin bona mahoney equations 1972 both of which arise in several physical applications including shallow water waves both equations are thought to non integrable i e not solvable by inverse scattering since numerical studies show that the interaction of solitary waves in inelastic in particular we determine some new similarity reductions of the symmetric regularised long wave equation these new similarity reductions are not obtainable using the classical lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method which involves no group theoretical techniques it is shown that every similarity reduction of both the symmetric regularised long wave and modified benjamin bona mahoney equations obtained using the classical lie group method reduces the associated partial differential equation to an ordinary differential equation of painleve type whereas the new similarity solution of the symmetric regularised long wave equation reduces it to an ordinary differential equation which is not of painleve type it is also shown that neither the symmetric regularised long wave equation nor the modified benjamin bona mahoney equation possesses the painleve property for partial differential equations as defined by weiss et al 1983

traveling wave solutions for nonlinear equations using symbolic computation abstract in this paper a direct and unified algorithm for constructing multiple travelling wave solutions of nonlinear partial differential equations pdes is presented and implemented in a computer algebraic system the key idea of this method is to take full advantage of a riccati equation involving a parameter and use its solutions to replace the tanh function in the tanh method it is quite interesting that the sign of the parameter can be used to exactly judge the number and types of such travelling wave solutions in this way we can successfully recover the previously known solitary wave solutions that had been found by the tanh method and other more sophisticated methods more importantly for some equations with no extra effect we also find other new and more general solutions at the same time by introducing appropriate transformations our method is further extended to the nonlinear pdes whose balancing numbers may be any nonzero real numbers the efficiency of the method can be demonstrated on a large variety of nonlinear pdes such as those considered in this paper burgers huxley equation coupled korteweg de vries equation caudrey dodd gibbon kawada equation active dissipative dispersive media equation generalized fisher equation and nonlinear heat conduction equation

an algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations an algebraic method is devised to uniformly construct a series of exact solutions for general integrable and nonintegrable nonlinear evolution equations compared with most existing tanh methods the jacobi function expansion method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters the solutions obtained in this paper include a polynomial solutions b exponential solutions c rational solutions d triangular periodic wave solutions e hyperbolic and solitary wave solutions and f jacobi and weierstrass doubly periodic wave solutions the efficiency of the method can be demonstrated on a large variety of nonlinear equations such as those considered in this paper new 2 1 dimensional calogero kdv equation 3 1 dimensional jimbo miwa equation symmetric regular long wave equation drinfel d sokolov wilson equation 2 1 dimensional generalized dispersive long wave equation double sine gordon equation calogero degasperis fokas equation and coupled schrodinger boussinesq equation in addition the links among our proposed method the tanh method the extended method and the jacobi function expansion method are also clarified generally

response to comment on penetrability of a one dimensional coulomb potential by roger g newton for original paper see ibid vol 26 p 2445 1993 by expressing in matrix form the one dimensional hamiltonians where the potentials are proportional to mod x mod 1 and x 1 i show that we are dealing with two very different problems thus in my viewpoint the criticism of r g newton of the paper mentioned in the title which is based on results relating to mod x mod 1 does not apply to a potential of the form x 1

mathematics of dispersive water waves a commuting hierarchy of dispersive water wave equations makes a three hamiltonian system which belongs to a general class of nonstandard integrable systems whose theory is developed the modified water wave hierarchy is a bi hamiltonian system its modification bifurcates the water wave hierarchy and the hierarchies of the korteweg de vries and the modified korteweg de vries equations as well as the classical miura map are given new representations through various specializations of nonstandard systems

episturmian words and some constructions of de luca and rauzy abstract in this paper we study infinite episturmian words which are a natural generalization of sturmian words to an arbitrary alphabet a characteristic property is they are closed under reversal and have at most one right special factor of each length they are first obtained by a construction due to de luca which utilizes the palindrome closure they can also be obtained by the way of extended rauzy rules

the generalized bifurcation method for deriving exact solutions of nonlinear space time fractional partial differential equations abstract in this paper we develop a generalized bifurcation method to study exact solutions of nonlinear space time fractional partial differential equations pdes which is based on the bifurcation theory of dynamical systems we present the procedure of the method and illustrate it with application to the space time fractional drinfel d sokolov wilson equation we identify all bifurcation conditions and derive the phase portraits of the system from which we obtain different new exact solutions and more interestingly we find the so called m w shaped solitary wave solutions the results demonstrate the efficiency of the method in deriving exact solutions of space time fractional pdes

direct strain feedback control of flexible robot arms new theoretical and experimental results this paper addresses control problems for flexible robot arms by using direct strain feedback the purpose is to make clear why direct strain feedback can damp out vibration of flexible arms satisfactorily we concentrate on one link flexible robot arms whose dynamic models can be represented by linear partial differential equations with appropriate boundary conditions which have been well examined in a number of papers a key contribution of this paper is the introduction of the concept of strict a dependent operators which allows us to prove rigorously the closed loop stability of direct strain feedback and the existence and uniqueness of nonstandard second order abstract differential equations in hilbert spaces several control experiments are performed verifying the main theoretical points of this paper demonstrating satisfactory control results of direct strain feedback and leading to potential application of this simple control method for flexible robot control

many new kinds exact solutions to 2 1 dimensional burgers equation and klein gordon equation used a new method with symbolic computation abstract in this paper we obtained many new exact solutions including 2 soliton solutions complexiton solutions which possess various combination of trigonometric periodic hyperbolic function jacobi elliptic function and rational function solutions periodic solutions and rational solutions to 2 1 dimensional burgers equations and cubic klein gordon equation by introducing two sub equations with different variables we should point out that this method could be extended in many aspect if we introduce n sub equations with different variables for solving nonlinear partial differential equations we could get n soliton solutions to nonlinear partial differential equations

a simple approach for reducing the order of equations with higher order nonlinearity abstract in this paper we introduce a simple approach to reduce the order of equations with higher order nonlinearity we choose the generalized forms of the kdv equation the camassa holm equation and the zakharov kuznetsov equation to illustrate the validity and advantages of the approach then the explicit solutions with different physical structures of the reduced equations can be discussed further the approach used here can be applied to some other nonlinear equations with higher order nonlinearity and is also suitable for some higher dimensional models

exact travelling wave solutions of the discrete sine gordon equation obtained via the exp function method abstract in this paper we generalize the exp function method which was used to find new exact travelling wave solutions of nonlinear partial differential equations npdes or coupled nonlinear partial differential equations to nonlinear differential difference equations nddes as an illustration two series of exact travelling wave solutions of the discrete sine gordon equation are obtained by means of the exp function method as some special examples these new exact travelling wave solutions can degenerate into the kink type solitary wave solutions reported in the open literature

reduction technique for matrix nonlinear evolution equations solvable by the spectral transform the main purpose of this paper is to describe a technique of reduction whereby from the class of evolution equations for matrices of order n solvable via the spectral transform associated to the matrix linear schrodinger eigenvalue problem one derives subclasses of nonlinear evolution equations involving less than n2 fields to illustrate the method from the equations for matrices of order 2 two subclasses of equations for 2 fields rather than 4 are obtained the first class coincides or rather includes that solvable via the spectral transform associated to the generalized zakharov shabat spectral problem further reduction to nonlinear evolution equations for a single field reproduces a number of well known equations but also yields a novel one highly nonlinear the second class also yields highly nonlinear equations some examples are given including another novel evolution equation for a single field

analysis and control of a two link and three joint elastic robot arm a robot system composed of two link arm and three joint is considered in this paper an evolution equation corresponding to the robot system formulated by partial differential equations with initial and boundary conditions is established in an appropriate hilbert space the spectral properties of the main operator of the evolution equation is first discussed and then its semigroup generation is presented based on the resulting spectral properties of finally an asymptotical behavior of the robot system under a designed feedback control is shown in terms of semigroup approach

new exact solutions for the classical drinfel d sokolov wilson equation in this paper we investigate the classical drinfel d sokolov wilson equation dswe u t pvv t 0 v t ruv x su xv qv x x x 0 where p q r s are some nonzero parameters some explicit expressions of solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems these solutions contain solitary wave solutions blow up solutions periodic solutions periodic blow up solutions and kink shaped solutions some previous results are extended

an extended method and its application to whitham broer kaup equation and two dimensional perturbed kdv equation abstract an extended method is proposed for constructing new forms of exact travelling wave solutions to nonlinear evolution equations by making a more general transformation for illustration we apply the extended method to whitham broer kaup equation and two dimensional perturbed kdv equation and successfully cover the previously known travelling wave solutions found by chen s method chaos solitons and fractals 22 2004 675 int j mod phys c 4 2004 595 moreover some new forms of solutions are obtained

exact solutions of the drinfel d sokolov wilson equation using the exp function method abstract the generalized solitary solutions of the classical drinfel d sokolov wilson equation dswe are obtained using the exp function method then some of these solutions are easily converted into kink shaped solutions and blow up solutions by a simple transformation

palindromes in circular words there is a very short and beautiful proof that the number of distinct non empty palindromes in a word of length n is at most n in this paper we show with a very complicated proof that the number of distinct non empty palindromes with length at most n in a circular word of length n is less than 5n 3 for n divisible by 3 we present circular words of length n containing 5n 3 2 distinct palindromes so the bound is almost sharp the paper finishes with some open problems

palindromes and sturmian words abstract an infinite word x over the alphabet a is sturmian if and only if g x n n 1 for any integer n where g x n is the number of distinct words of length n occurring in x a palindrome is a word that can be read indistinctly from left to right or from right to left we prove that x is sturmian if and only if h x n 1 n mod 2 for any integer n where h x n is the number of palindromes of length n occurring in x an infinite word x over the alphabet a is generated by a morphism f if there exists a letter c a such that lim n f n c x we prove the existence of a morphism that generates the palindromes of any infinite sturmian word generated by a morphism

control and stability of a torsional elastic robot arm a mathematical model for a long elastic torsional robot beam is determined the above system can be expressed as an evolution equation on a hilbert space furthermore the system is shown to be stable and controllable and we design a controller for the system

elliptic solutions of the quintic complex one dimensional ginzburg landau equation the conte musette method has been modified for the search of only elliptic solutions to systems of differential equations a key idea of this a prior restriction is to simplify calculations by means of the use of a few laurent series solutions instead of one and the use of the residue theorem the application of this approach to the quintic complex one dimensional ginzburg landau equation cgle5 allows us to find elliptic solutions in the wave form restrictions on coefficients which are necessary conditions for the existence of elliptic solutions for the cgle5 have been found as well we demonstrate that to find elliptic solutions the analysis of a system of differential equations is preferable to the analysis of the equivalent single differential equation

palindromic richness for languages invariant under more symmetries for a given finite group g consisting of morphisms and antimorphisms of a free monoid a we study infinite words with language closed under the group g we focus on the notion of g richness which describes words rich in generalized palindromic factors i e in factors w satisfying q w w for some antimorphism email protected g we give several equivalent descriptions which are generalizations of known characterizations of rich words in the terms of classical palindromes and show two examples of g rich words

new solitonic solutions to a 3 1 dimensional jimbo miwa equation abstract performing computerized symbolic computation we are able to present new analytic solutions of a 3 1 dimensional jimbo miwa equation which does not pass any of the conventional integrability tests applying the generalized tanh method we have found such exact solutions as both the nontraveling solitonic and traveling solitary waves

symbolic computation and a uniform direct ansatze method for constructing travelling wave solutions of nonlinear evolution equations on the basis of the computer symbolic system maple and the tanh method the riccati equation method as well as all kinds of improved versions of these methods we present a further uniform direct ansatze method for constructing travelling wave solutions of nonlinear evolution equations compared with the existing methods the presented method can be used to construct more new general solutions and we give some examples to illustrate the key step of our method

proof of the brlek reutenauer conjecture brlek and reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2d u email protected n 0 t u n in which d u denotes the defect of u and t u n denotes c u n 1 c u n 2 p u n 1 p u n where c u and p u are the factor and palindromic complexity of u respectively this conjecture was verified for periodic words by brlek and reutenauer themselves using their results for periodic words we have recently proved the conjecture for uniformly recurrent words in the present article we prove the conjecture in its general version by a new method without exploiting the result for periodic words