two component kp hierarchy and the classical boussinesq equation it has been shown that solutions to the kp equation and other equations in the kp hierarchy take a wronskian form the authors extend these ideas to two component wronskians and the hirota equations 1986 which they satisfy by a reduction procedure they show how dependence on some of the variables can be removed and look in detail at the classical boussinesq equation and its modifications and show how these equations fit into the two component kp hierarchy

nonlinear stability of cylindrical shells subjected to axial flow theory and experiments abstract this paper is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow in particular it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid the theoretical model employs the donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure the clamped beam eigenfunctions are used to describe the axial variations of the shell deformation automatically satisfying the boundary conditions and the circumferential continuity condition exactly the fluid is assumed to be incompressible and inviscid and the fluid structure interaction is described by linear potential flow theory the partial differential equation of motion is discretized using the galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo arclength continuation and collocation techniques and the gear backward differentiation formula a theoretical model for shells with simply supported ends is presented as well experiments are also described for i elastomer shells subjected to annular external air flow and ii aluminium and plastic shells with internal water flow the experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour finally theory and experiments are compared showing good qualitative and reasonable quantitative agreement

prime ends for domains in metric spaces in this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions we compare our prime ends to those of caratheodory and nakki modulus ends and

on solutions of constrained kp equations we derive solutions of general wronskian form for the vector constrained kp hierarchies as one explicit example we discuss rational solutions in order to introduce our method we give a direct elementary proof of the existence of wronskian solutions for the l modified kp hierarchies l 0 1

a hydroelastic investigation of circular cylindrical shells containing flowing fluid with different end conditions abstract this paper presents the effects of different end conditions on the response behavior of thin circular cylindrical shell structures fully in contact with flowing fluid the investigated end conditions are as follows simply supported clamped clamped clamped simply supported and clamped free cantilever shell ends additionally the dynamic responses of a tapered cylindrical shell conveying flowing fluid and simply supported at its ends were investigated the method employed in this study is a hybrid method a boundary integral equation method for the calculation of the fluid structure interaction effects and a finite element method for the structural analysis in this study the mathematical model presented before b ugurlu a ergin a hydroelasticity method for vibrating structures containing and or submerged in flowing fluid journal of sound and vibration 290 2006 572 596 is extended by applying the direct boundary integral equation method and by using a higher order panel method linear distribution it should also be said that the method used in this study could be applied to any shape of cylindrical structure in contact with internal and or external flowing fluid in contrast to the studies found in the literature in the analysis of the linear fluid structure system it is assumed that the fluid is ideal i e inviscid incompressible and its motion is irrotational it is assumed that the flexible structure vibrates in its in vacuo modes when it is in contact with flowing fluid and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure the in vacuo dynamic properties of the dry structure are obtained by using a standard finite element software in the wet part of the analysis the wetted surface is idealized by using appropriate boundary elements referred to as hydrodynamic panels the fluid structure interaction forces are calculated in terms of the generalized added mass coefficients generalized coriolis fluid force coefficients and generalized centrifugal fluid force coefficients to demonstrate the applicability of the method and assess the influences of the flowing fluid and end support conditions on the dynamic response behavior of the shell structures the non dimensional eigenfrequencies and associated eigenmodes are presented as a function of the non dimensional axial flow velocity and they compare well with the analytical solutions found in the literature

metric differentiation monotonicity and maps to l1 this is one of a series of papers on lipschitz maps from metric spaces to l1 here we present the details of results which were announced in cheeger and kleiner ann math 2006 to appear arxiv math mg 0611954 sect 1 8 a new approach to the infinitesimal structure of lipschitz maps into l1 and as a first application an alternative proof of the main theorem of cheeger and kleiner ann math 2006 to appear arxiv math mg 0611954 that the heisenberg group does not admit a bi lipschitz embedding in l1 the proof uses the metric differentiation theorem of pauls commun anal geom 9 5 951 982 2001 and the cut metric description in cheeger and kleiner ann math 2006 to appear arxiv math mg 0611954 to reduce the nonembedding argument to a classification of monotone subsets of the heisenberg group a quantitative version of this classification argument is used in our forthcoming joint paper with assaf naor cheeger et al in arxiv 0910 2026 2009

a characterization of supersymmetric polynomials soit t m n l ensemble des polynomes supersymetriques dans f x 1 x m y 1 y n pour r 1 on definit m n r x 1 r x 2 r x m r y 1 r y r y n r soit s m n la sous algebre de t m n generee par 1 et m n r r 1 on demontre que s m n t m n

factorisation of energy dependent schrodinger operators miura maps and modified systems we consider the energy dependent schrodinger operator mathbb l sum limits i 0 n lambda i varepsilon i partial 2 u i which we have previously shown to be associated with multi hamiltonian structures 2 in this paper we use an unusual form of the lax approach to derive by asingle construction the time evolutions of the eigenfunctions of mathbb l the associated hamiltonian operators and the hamiltonian functionals we then generalise the well known factorisation of standard lax operators to the case of energy dependent operators the simple product of linear factors is replaced by a dependent quadratic form we thus generalise the resulting construction of miura maps and modified equations we show that for some of our systems there exists a sequence ofn such modifications therth modification possessing n r 1 hamiltonian structures

dynamic analysis of conical shells conveying fluid abstract a formulation based on the semi analytical finite element method is proposed for elastic conical shells conveying fluids the structural equations are based on the shell element proposed by ramasamy and ganesan finite element analysis of fluid filled isotropic cylindrical shells with constrained viscoelastic damping computers structures 70 1998 363 376 while the fluid model is based on velocity potential formulation used by jayaraj et al a semi analytical coupled finite element formulation for composite shells conveying fluids journal of sound and vibration 258 2 2002 287 307 dynamic pressure acting on the walls is derived from bernoulli s equation by imposing the requirement that the normal component of velocity of the solid and fluid are equal leads to fluid structure coupling the computer code developed has been validated using results available in the literature for cylindrical shells conveying fluid the study has been carried out for conical shells of different cone angles and for boundary condition like clamped clamped simply supported and clamped free in general instability occurs at a critical fluid velocity corresponding to the shell circumferential mode with the lowest natural frequency critical fluid velocities are lower than that of equivalent cylindrical shells this result holds good for all boundary conditions

a semi analytical coupled finite element formulation for composite shells conveying fluids abstract a coupled formulation based on the semi analytical finite element technique is developed for composite shells conveying fluid the structural finite element formulation is from ramasamy and ganesan 1998 computers and structures70 363 376 while the fluid part is modelled by the characteristic wave equation the fluid part is modelled using a velocity potential formulation and the dynamic pressure acting on the walls is derived from bernoulli s equation impermeability and dynamic condition are imposed on the fluid structure interface the finite element equations for the composite shell conveying fluid are validated using available results in the literature a detailed parametric study is carried out for various boundary conditions as well as for different length to radius and radius to thickness ratios

the poincare inequality is an open ended condition let p 1 and let x d be a complete metric measure space with borel and doubling that admits a 1 p poincare inequality then there exists e 0 such that x d admits a 1 q poincare inequality for every q p e quantitatively

non linear dynamics and stability of circular cylindrical shells containing flowing fluid part i stability abstract the study presented is an investigation of the non linear dynamics and stability of simply supported circular cylindrical shells containing inviscid incompressible fluid flow non linearities due to large amplitude shell motion are considered by using the non linear donnell s shallow shell theory with account taken of the effect of viscous structural damping linear potential flow theory is applied to describe the fluid structure interaction the system is discretiszd by galerkin s method and is investigated by using a model involving seven degrees of freedom allowing for travelling wave response of the shell and shell axisymmetric contraction two different boundary conditions are applied to the fluid flow beyond the shell corresponding to i infinite baffles rigid extensions of the shell and ii connection with a flexible wall of infinite extent in the longitudinal direction permitting solution by separation of variables they give two different kinds of dynamical behaviour of the system as a consequence of the fact that axisymmetric contraction responsible for the softening non linear dynamical behaviour of shells is not allowed if the fluid flow beyond the shell is constrained by rigid baffles results show that the system loses stability by divergence

schur s q functions and the bkp hierarchy in this letter we define q shift operators q lambda of hirota derivatives that leads to a simple technique of constructing the hierarchy of bkp soliton equations using schur s q functions

a study on the dynamic stability of a cylindrical shell conveying a pulsatile flow of hot fluid abstract the flow of hot fluid having a harmonic component superposed on the mean flow velocity is considered flowing through an insulated cylindrical shell the cylindrical shell will be subjected to thermal load due to the flow of hot fluid the semi analytical finite element forms the basis for modelling the structural continuum under the influence of temperature and the flowing fluid the fluid flowing through the cylindrical shell is incompressible and linear potential flow theory is used to formulate the fluid domain bernoulli s principle and impermeability conditions of the fluid are the basis for a coupled fluid structure interaction analysis model reduction technique in conjunction with the fourth order runge kutta method using gill s coefficient is adopted to compute the state transition matrix which provides the stability information of the periodic system the results of the theoretical studies are presented related to instability regions due to a pulsatile flow of hot fluid through a cylindrical shell hot fluid at various magnitude of constant temperature limited by the critical thermal buckling temperature is considered in the study the effect of fluid temperature and excitation parameter on the behavior of dynamic instability of the system is examined

compression bounds for lipschitz maps from the heisenberg group to l 1 we prove a quantitative bi lipschitz non embedding theorem for the heisenberg group with its carnot caratheodory metric and apply it to give a lower bound on the integrality gap of the goemans linial semidefinite relaxation of the sparsest cut problem

finite element analysis of the vibratory characteristics of cylindrical shells conveying fluid a finite element formulation is developed to predict the vibration of cylindrical shells conveying fluid the method is based on the three dimensional theory of elasticity and the linearised eulerian equations the hydrodynamic pressure is derived from the condition for dynamic coupling of the fluid structure and the eulerian equation the influence of initial stresses within the shell due to fluid pressure is taken into account predicted natural frequencies for fluid shell systems in the radius to thickness ratio range of r h 38 96 1624 are compared with published experimental results to validate the model and are also compared with results obtained using other finite element models based on the classical shell theory and potential flow theory to demonstrate advantages and disadvantages in terms of accuracy the effect of variation in flow velocities and hydrostatic pressures on the dynamic behaviour of fluid conveying shells is examined and the influence of supported conditions on the free vibration is also discussed

self improving properties of john nirenberg and poincare inequalities on spaces of homogeneous type abstract we give a condition which ensures that if one inequality of sobolev poincare type is valid then other stronger inequalities of a similar type also hold including weighted versions our main result includes many previously known results as special cases we carry out the analysis in the context of spaces of homogeneous type but the main result is new even in the usual euclidean setting

wronskian determinants the kp hierarchy and supersymmetric polynomials by using the wronskian representation of the solutions of the bilinear kp hierarchy a connection between hirota derivatives and supersymmetric polynomials is brought to light this correspondence is used in order to give an alternative construction of the hierarchy

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

a hydroelasticity method for vibrating structures containing and or submerged in flowing fluid this paper presents a method for investigating the dynamics of elastic structures containing and or submerged in flowing fluid the method presented is based on a boundary integral equation method in conjunction with the method of images in order to impose appropriate boundary condition on the fluid s free surface the method of analysis can be applied to any shape of cylindrical structure partially in contact with flowing fluid in the analysis of the linear fluid structure system it is assumed that the fluid is ideal i e inviscid incompressible and its motion is irrotational it is assumed that the flexible structure vibrates in its in vacuo eigenmodes when it is in contact with flowing fluid and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure the in vacuo dynamic properties of the dry structure are obtained by using a standard finite element software in the wet part of the analysis the wetted surface is idealized by using appropriate boundary elements referred to as hydrodynamic panels the fluid structure interaction effects are calculated in terms of the generalized added mass coefficients generalized coriolis fluid force coefficients and generalized centrifugal fluid force coefficients in order to demonstrate the applicability of the proposed method a circular cylindrical shell simply supported at both ends was adopted for the calculations the cylindrical shell was considered separately with rigid and flexible extensions at its ends to assess the influence of flowing fluid on the dynamic behavior of the shell structure the non dimensional eigenfrequencies and associated eigenmodes are presented as a function of the non dimensional fluid velocity the predictions compare well with available analytical calculations found in the literature

modulus and the poincare inequality on metric measure spaces the purpose of this paper is to develop the understanding of modulus and the poincare inequality as defined on metric measure spaces various definitions for modulus and capacity are shown to coincide for general collections of metric measure spaces consequently modulus is shown to be upper semi continuous with respect to the limit of a sequence of curve families contained in a converging sequence of metric measure spaces moreover several competing definitions for the poincare inequality are shown to coincide if the underlying measure is doubling one such characterization considers only continuous functions and their continuous upper gradients and extends work of heinonen and koskela applications include showing that the p poincare inequality with a doubling measure for p 1 persists through to the limit of a sequence of converging pointed metric measure spaces this extends results of cheeger a further application is the construction of new doubling measures in euclidean space which admit a 1 poincare inequality

differentiating maps into l1 and the geometry of bv functions this is one of a series of papers examining the interplay between differentiation theory for lipschitz maps x v and bi lipschitz nonembeddability where x is a metric measure space and v is a banach space here we consider the case v l 1 where differentiability fails we establish another kind of differentiability for certain x including n and h the heisenberg group with its carnot caratheodory metric it follows that does not bi lipschitz embed into l 1 as conjectured by j lee and a naor when combined with their work this provides a natural counterexample to the goemans linial conjecture in theoretical computer science the first such counterexample was found by khot vishnoi kv05 a key ingredient in the proof of our main theorem is a new connection between lipschitz maps to l 1 and functions of bounded variation which permits us to exploit results on the structure of bv functions on the heisenberg group fssc01

hall littlewood symmetric functions and the bkp equation the connection between solutions of the bkp equation and hall littlewood symmetric functions is utilised in a unified approach to soliton and polynomial solutions this is analogous to the wronskian formulation of the solution of the kp equation as a by product two novel expressions for certain hall littlewood functions in terms of pfaffians are derived

from local to global in quasiconformal structures abstract we exhibit a large class of metric spaces whose infinitesimal quasiconformal structure is strong enough to capture the global quasiconformal structure a sufficient condition for this to happen is described in terms of a poincare type inequality

lp self improvement of generalized poincare inequalities in spaces of homogeneous type abstract in this paper we study self improving properties in the scale of lebesgue spaces of generalized poincare inequalities in spaces of homogeneous type in contrast with the classical situation the oscillations involve approximation of the identities or semigroups whose kernels decay fast enough and the resulting estimates take into account their lack of localization the techniques used do not involve any classical poincare or sobolev poincare inequalities and therefore they can be used in general settings where these estimates do not hold or are unknown we apply our results to the case of riemannian manifolds with doubling volume form and assuming gaussian upper bounds for the heat kernel of the semigroup e t with being the laplace beltrami operator we obtain generalized poincare inequalities with oscillations that involve the semigroup e t and with right hand sides containing either or 1 2

the perron method for varvec p harmonic functions in unbounded sets in mathbf r n and metric spaces the perron method for solving the dirichlet problem for p harmonic functions is extended to unbounded open sets in the setting of a complete metric space with a doubling measure supporting a p poincare inequality 1 p infty the upper and lower p harmonic perron solutions are studied for open sets which are assumed to be p parabolic if unbounded it is shown that continuous functions and quasicontinuous dirichlet functions are resolutive i e that their upper and lower perron solutions coincide that the perron solution agrees with the p harmonic extension and that perron solutions are invariant under perturbation of the function on a set of capacity zero

bilinearization of the non local boussinesq equation a single field bilinear system generating the so called non local boussinesq equation is constructed from the bilinearization procedure it can be seen that the associated hierarchy of soliton systems which we construct shares part of the solution set of a hierarchy related to the kadomtsev petviashvili equation a bilinear representation of the recursion operator for the kaup hierarchy is essential in the construction and a systematic way of obtaining such a representation from just two soliton considerations is presented

symmetric functions and the kp and bkp hierarchies we study the kp hierarchy through its relationship with s functions using results from the classical theory of symmetric functions the plucker equations for the hierarchy are derived from the tau function bilinear identity and are given in terms of composite s functions their connection to the hirota bilinear form of the hierarchy is clarified a novel combinatorial proof is given of the fact that schur polynomials solve the kp hierarchy we show how the analysis can be carried through for the bkp hierarchy in a completely parallel fashion with the s functions replaced by schur q functions

soliton solutions of the korteweg de vries and the kadomtsev petviashvili equations the wronskian technique the well known soliton solutions of the kadomtsev petviashvili equations are written in terms of determinants of wronskian form by using this compact representation together with the hirota bilinear form of the equations it is demonstrated by elementary algebraic methods that the n soliton solution satisfies the evolution equation and the n and n 1 soliton solutions satisfy the associated backlund transformation the relation of these results to the eigensolutions of the inverse scattering method and to the more usual representation of the n soliton solution is also given

quasiconformal maps in metric spaces with controlled geometry this paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry the principal message is that such a theory is both relevant and viable the first main issue is the problem of definition which we next describe quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount this requirement makes sense in every metric space given a homeomorphism f from a metric space x to a metric space y then for x x and r 0 set

a differentiable structure for metric measure spaces abstract the main result of this paper is the provision of conditions under which a metric measure space admits a differentiable structure this differentiable structure gives rise to a finite dimensional l cotangent bundle over the given metric measure space and then to a sobolev space h 1 p over the given metric measure space the latter which is reflexive for p 1 this extends results of cheeger geom funct anal 9 1999 3 428 to a wider collection of metric measure spaces

self improving properties for abstract poincare type inequalities we study self improving properties in the scale of lebesgue spaces of generalized poincar e inequalities in the euclidean space we present an abstract setting where oscillations are given by certain operators e g approximations of the identity semigroups or mean value operators that have o diagonal decay in some range our results provide a unied theory that is applicable to the classical poincar e inequalities and furthermore it includes oscillations dened in terms of semigroups associated with second order elliptic operators as those in the kato conjecture in this latter situation we obtain a direct proof of the john nirenberg inequality for the associated bmo and lipschitz spaces of hmay hmm

multi soliton and pfaffian solutions of a 2 1 dimensional nonlinear evolution equation via the jaulent miodek hierarchy abstract under investigation in this paper is a 2 1 dimensional nonlinear evolution equation generated by the jaulent miodek hierarchy via the hirota bilinear method multi soliton solutions of such equation are obtained soliton propagation and interactions are analyzed and both the elastic and inelastic interactions are seen with some parameters selected furthermore it is proved that the equation possesses the n soliton solutions expressed in terms of gramm type pfaffian and can be written in the form of a pfaffian identity

fluid structure interaction analysis by the finite element method a variational approach we have developed a finite element method for analysing non linear and linear fluid structure interaction problems by working directly from a variational indicator based on hamilton s principle we restrict our analyses to inviscid irrotational and isentropic fluid flows the variational indicator includes the fluid potential energy due to gravity which is often ignored this and the fact that we consider our domain to be variable provide us with the capability to model free surfaces we demonstrate the effectiveness of both linear and non linear finite element formulations in analysing a variety of fluid structure interaction problems

non linear dynamics and stability of circular cylindrical shells containing flowing fluid part ii large amplitude vibrations without flow abstract the non linear response of empty and fluid filled circular cylindrical shells to harmonic excitations is investigated both modal and point excitations have been considered the model is suitable to study simply supported shells with and without axial constraints donnell s non linear shallow shell theory is used the boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied the radial deflection of the shell is expanded by using a basis of seven linear modes the effect of internal quiescent incompressible and inviscid fluid is investigated the equations of motion obtained in part i of this study are studied by using a code based on the collocation method the validation of the present model is obtained by comparison with other authoritative results the effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated clarifying questions open for a long time the results show the occurrence of travelling wave response in the proximity of the resonance frequency the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half wave and limit cycle responses modes with two longitudinal half waves are also investigated

natural vibrations and stability of shells of revolution interacting with an internal fluid flow abstract a finite element algorithm is proposed to investigate the dynamic behavior of elastic shells of revolution containing a quiescent or a flowing inviscid fluid in the framework of linear theory the fluid behavior is described using the perturbed velocity potential the shell behavior is treated in the framework of the classical shell theory and variational principle of virtual displacements incorporating a linearized bernoulli equation for calculation of hydrodynamic pressure acting on the shell the problem reduces to evaluation and analysis of the eigenvalues in the connected system of equations obtained by coupling the equations for velocity perturbations with the equations for shell displacements for cylindrical shells the results of numerical simulations are compared with recently published experimental analytical and numerical data the paper also reports the results of studying the dynamic behavior of shells under various boundary conditions for the perturbed velocity potential the investigation made for conical shells has shown that under certain conditions an increase in the cone angle can change a divergent type of instability to a flutter type