vibration of rotationally periodic structures abstract the purpose of this paper is to determine eigensolutions of a rotationally periodic structure p of period n in terms of those of the i th substructure s i of p let y i be the generalized displacement vector and f i be the generalized force vector at interface i i where substructures s i and s i 1 are connected transfer function formulation of s i implies that there exists a linear operator g mapping y t and f i at interface i i to y i 1 and f i 1 at interface i i 1 in addition the operator g depends on transfer functions and therefore eigensolutions of s i the periodicity of p then requires that gn be an identity map this results in n self adjoint fredholm integral equations the non trivial solutions of which predict eigensolutions of p as a consequence a periodic structure p with period n will have exactly n eigenvalues lying between two consecutive eigenvalues of the substructure s i if the interface i i contains only one degree of freedom finally three examples are illustrated the first example considers anti plane strain vibration of a linear elastic solid containing four slots of infinitesimal width the second example derives exact eigensolutions of a string mass periodic structure the third example illustrates how eigensolutions of an axisymmetric structure can be recovered under the formulation of rotationally periodic structures

excessive measures and the existence of right semigroups and processes given a resolvent u on a lusin space e f the paper gives necessary and sufficient conditions in terms of the excessive measures that ensure the existence of a right process resp a right continuous semigroup on e f with resolvent u furthermore a notion of nonbranch points with respect to un is introduced also in terms of the excessive measures and various characterizations are given they show in particular the equivalence of this definition with those introduced and discussed by engelbert and wittmann

general gauge and conditional gauge theorems general gauge and conditional gauge theorems are established for a large class of not necessarily symmetric strong markov processes including brownian motions with singular drifts and symmetric stable processes furthermore new classes of functions are introduced under which the general gauge and conditional gauge theorems hold these classes are larger than the classical kato class when the process is brownian motion in a bounded c 1 1 domain

low dimensional real lie algebras all real lie algebras of dimension up to 8 that admit a nontrivial levi decomposition are found

dynamic analysis of finite linear elastic solids containing small elastic imperfections theory with application to asymmetric circular plates abstract eigensolutions green s functions and steady state responses of three dimensional homogeneous isotropic finite linear elastic solids containing small linear elastic imperfections are presented in this paper the inhomogeneities are treated as perturbations to otherwise homogeneous solids the spectral eigensolutions of which are known the exact eigensolutions of the imperfect solid formulated through the betti reciprocal theorem satisfy a set of integral equations from which both analytic perturbation formulas and a numerical iteration scheme are developed special emphasis is given to analysis of perfect homogeneous elastic solids that are spectrally degenerate finally the vibration of circular plates with evenly spaced radial inclusions which cause splitting of some of the repeated vibration modes is analyzed both analytically and numerically for the eigensolutions

the equivalence of certain heat kernel and green function bounds abstract we show that certain upper and lower bounds on the green function and heat kernel of a second order elliptic operator in a bounded region are equivalent and imply a number of apparently stronger bounds we also show that these bounds are equivalent to the harnack inequality except for peculiar regions and are therefore almost always valid

solvable lie algebras of dimension six six dimensional solvable lie algebras over the field of real numbers that possess nilradicals of dimension four are classified into equivalence classes this completes mubarakzyanov s classification of the real six dimensional solvable lie algebras

vibration characteristics of systems with multiple blades abstract an interesting phenomenon can be observed when the state space dynamic substructural method is applied to the eigenproblem of bladed disk shaft systems whether or not the shaft is flexible each frequency of the single root fixed blade appears as a frequency of the whole structure with a multiplicity of at least n 3 wheren is the number of repetitive blades the presented result can be regarded as an extension of previous findings by the authors in the sense that the commonly interfaced repetitive substructures are allowed to be treated as a rigid body in modal analysis the defectiveness issue of the multiple eigenvalues arising from the repetitive substructures is also addressed examples of rotary wing models and a simplified turbine model are presented for validation together with attempting their physical explanations

dynamic stability of spinning viscoelastic cylinders at finite deformation the study of spinning axisymmetric cylinders undergoing finite deformation is a classic problem in several industrial settings the tire industry in particular we present a stability analysis of spinning elastic and viscoelastic cylinders using arpack to compute eigenvalues and eigenfunctions of finite element discretizations of the linearized evolution operator we show that the eigenmodes correspond to n peak standing or traveling waves for the linearized problem with an additional index describing the number of oscillations in the radial direction we find a second hierarchy of bifurcations to standing waves where these eigenvalues cross zero and confirm numerically the existence of finite amplitude standing waves for the nonlinear problem on one of the new branches in the viscoelastic case this analysis permits us to study the validity of two popular models of finite viscoelasticity we show that a commonly used finite deformation linear convolution model results in non physical energy growth and finite time blow up when the system is perturbed in a linearly unstable direction and followed nonlinearly in time on the other hand sidoroff style viscoelastic models are seen to be linearly and nonlinearly stable as is physically required 2014 elsevier ltd all rights reserved

potential theoretic nature of hardy s inequality for dirichlet forms we prove that the hardy inequality for dirichlet forms of symmetric markov processes recently proved by p j fitzsimmons can be established within the framework of our potential inequality this clearly emphasizes the role played by the maximum principle in the inequality

excessive measures and markov processes with random birth and death on utilise un processus markovien continu a droite stationnaire defini sur un intervalle de temps aleatoire comme outil naturel pour developper plusieurs aspects de la theorie des mesures excessives

vibration of rings on a general elastic foundation the free vibration eigensolutions of a thin ring on a general elastic foundation are obtained by perturbation and galerkin analyses natural frequencies and vibration modes are determined as closed form expressions for a ring having a circumferentially varying foundation of very general description the elastic foundation consists of two orthogonal distributed springs oriented at an arbitrary inclination angle the foundation stiffnesses vary circumferentially the simple eigensolution expressions explicitly show the parameter dependencies lead to natural frequency splitting rules for degenerate unperturbed eigenvalues at both first and second orders of perturbation and identify which nodal diameter fourier components contaminate a given n nodal diameter base mode of the free ring discrete spring supports are treated as a special case where the natural frequencies are determined by five parameters nondimensional spring stiffness stiffness angle support angle number of springs and location of the springs the predicted effects of these parameters on the natural frequencies are verified numerically as an application and as the motivating problem for the study the natural frequencies and vibration modes of a ring gear used in helicopter planetary gears with unequally spaced planets are investigated

gaugeability and conditional gaugeability new kato classes are introduced for general transient borel right processes for which gauge and conditional gauge theorems hold these new classes are the genuine extensions of the green tight measures in the classical brownian motion case however the main focus of this paper is on establishing various equivalent conditions and consequences of gaugeability and conditional gaugeability we show that gaugeability conditional gaugeability and the subcriticality for the associated schrodinger operators are equivalent for transient borel right processes with strong duals analytic characterizations of gaugeability and conditional gaugeability are given for general symmetric markov processes these analytic characterizations are very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases connections with the positivity of the spectral radii of the associated schrodinger operators are also established

riesz decompositions in markov process theory riesz decompositions of excessive measures and excessive functions are obtained by probabilistic methods without regularity assumptions the decomposition of excessive measures is given for borel right processes the results for excessive functions are formulated within the framework of weak duality these results extend and generalize the pioneering work of hunt in this area

estimates for solutions to equations of p laplace type in ahlfors regular nta domains this thesis consists of six scientific papers an introduction and a summary all six papers concern the boundary behavior of non negative solutions to partial differential equations paper i concerns solutions to certain p laplace type operators with variable coefficients suppose that u is a non negative solution that vanishes on a part of an ahlfors regular nta domain we prove among other things that the gradient du of u has non tangential limits almost everywhere on the boundary piece and that log du is a bmo function on the boundary furthermore for ahlfors regular nta domains that are uniformly n r0 approximable by lipschitz graph domains we prove a boundary harnack inequality provided that is small enough paper ii concerns solutions to a p laplace type operator with lower order terms in reifenberg flat domains we prove that the ratio of two non negative solutions vanishing on a part of the boundary is holder continuous provided that is small enough furthermore we solve the martin boundary problem provided is small enough in paper iii we prove that the boundary type riesz measure associated to an a capacitary function in a reifenberg flat domain with vanishing constant is asymptotically optimal doubling paper iv concerns the boundary behavior of solutions to certain parabolic equations of p laplace type in lipschitz cylinders among other things we prove an intrinsic carleson type estimate for the degenerate case and a weak intrinsic carleson type estimate in the singular supercritical case in paper v we are concerned with equations of p laplace type structured on hormander vector fields we prove that the boundary type riesz measure associated to a non negative solution that vanishes on a part of an x nta domain is doubling on paper vi concerns a one phase free boundary problem for linear elliptic equations of non divergence type assume that we know that the positivity set is an nta domain and that the free boundary is a graph furthermore assume that our solution is monotone in the graph direction and that the coefficients of the equation are constant in the graph direction we prove that the graph giving the free boundary is lipschitz continuous

a comparison of two classifications of solvable lie algebras the literature contains two different classifications of solvable lie algebras of dimensions up to and including 4 this paper is devoted to comparing the two classifications and translating each into the other in particular we exhibit an isomorphism between each solvable lie algebra of one classification and the corresponding algebra of the second the first classification is provided by de graaf and the second classification is from a recent book by snobl and winternitz

estimates for operator norms on weighted spaces and reverse jensen inequalities we examine the dependence on the a p norm of w of the operator norms of singular integrals maximal functions and other operators in l p w we also examine connections between some fairly general reverse jensen inequalities and the a p and rh p weight conditions

newton krylov method for computing the cyclic steady states of evolution problems in nonlinear mechanics this work is focused on the newton krylov technique for computing the steady cyclic states of evolution problems in non linear mechanics with space time periodicity conditions this kind of problems can be faced for instance in the modeling of a rolling tyre with a periodic tread pattern where the cyclic state satisfies rolling periodicity condition including shifts both in time and space the newton krylov method is a combination of a newton nonlinear solver with a krylov linear solver looking for the initial state which provides the space time periodic solution the convergence of the krylov iterations is proved to hold in presence of an adequate preconditioner after preconditioning the newton krylov method can be also considered as an observer controller method correcting the transient solution of the initial value problem after each period using information stored while computing the residual the krylov solver computation time becomes negligible with respect to the residual computation time the method has been analyzed and tested on academic applications and compared to the standard evolution fixed point method finally it has been implemented into the michelin industrial code applied to a full 3d rolling tyre model

the dirichlet problem in non smooth domains dirichlet problem for an elliptic operator 2s laj jaj with smooth coefficients aij in domains d in rm m 3 with non smooth boundaries the domains we treat are given locally in some cm coordinate system by the graph of a continuous function qs with vq5 e li for some p 1 p oo such domains are called li domains see section 1 for the precise definitions note that l domains are usually called lipschitz domains if d is an li domain and x e d we study the elliptic measure a7 associated with s and d at x thus for f a continuous function on ad the formula u x hf x f doh gives the perron wiener brelot generalized soluid

a criterion for the absolute continuity of the harmonic measure associated with an elliptic operator for some a o and for all x e q and 4 e r n we also assume a a for such operators the dirichlet problem is solvable in q if and only if it is solvable for the laplace operator according to a theorem of littman stampacchia and weinberger 1 this means that if q c r n is a sufficiently nice bounded region the unit ball b is an example and f is a given continuous function on the boundary of q then there exists a unique function u continuous on q so that l u 0 in q and u f on aq let us assume for convenience that the origin belongs to q then the mapping f c f aq u o is a positive linear functional so there exists a unique nonnegative measure w on aq such that for every f e aq

on multilinear square function and its applications to multilinear littlewood paley operators with non convolution type kernels abstract let m 2 n 1 and x r n define the multilinear square function t by t f x 0 r n m k t x y 1 y m j 1 m f j y j d y 1 d y m 2 d t t 1 2 where the kernel k satisfies a class of integral smooth conditions which is much weaker than the standard calderon zygmund kernel conditions in this paper we first established the l p 1 w 1 l p m w m l p estimate of t when each p i 1 and weak type l p 1 w 1 l p m w m l p estimate of t when there is a p i 1 where i 1 m i p p i and each w i is a nonnegative function on r n as applications of the above results we obtained the boundedness of multilinear littlewood paley operators with non convolution type kernels including multilinear g function marcinkiewicz integral and g function

homogenization of elliptic boundary value problems in lipschitz domains in this paper we study the lp boundary value problems for mathcal l u 0 in mathbb r d 1 where mathcal l rm div a nabla is a second order elliptic operator with real and symmetric coefficients assume that a is periodic in xd 1 and satisfies some minimal smoothness condition in the xd 1 variable we show that the lp neumann and regularity problems are uniquely solvable for 1 p 2 we also present a new proof of dahlberg s theorem on the lp dirichlet problem for 2 p dahlberg s original unpublished proof is given in the appendix as the periodic and smoothness conditions are imposed only on the xd 1 variable these results extend directly from mathbb r d 1 to regions above lipschitz graphs consequently by localization techniques we obtain uniform lp estimates for the dirichlet neumann and regularity problems on bounded lipschitz domains for a family of second order elliptic operators arising in the theory of homogenization the results on the neumann and regularity problems are new even for smooth domains

generalized solution of time dependent traveling load problem via moving finite element scheme abstract a finite element methodology is described which can handle the transient response of moving structures which are themselves subject to time dependent traveling load fields the generality of the approach is such that it can handle the overall transient response due to moving loads whose magnitude zone of application and trajectory are time dependent in addition to developing the overall transient solution methodology attention is also given to establishing the overall eigenvalue properties of the linear problem as well as developing a solution for the steady vibrating case to benchmark the overall procedure the results of several numerical experiments are included in the presentation

the dirichlet problem at the martin boundary of a fine domain abstract we adapt the perron wiener brelot method of solving the dirichlet problem at the martin boundary of a euclidean domain so as to cover also the dirichlet problem at the martin boundary of a fine domain u in r n n 2 i e a set u which is open and connected in the h cartan fine topology on r n the coarsest topology in which all superharmonic functions are continuous it is a complication that there is no harnack convergence theorem for so called finely harmonic functions we define resolutivity of a numerical function on the martin boundary u of u our main result theorem 4 14 implies the corresponding known result for the classical case we also obtain analogous results for the case where the upper and lower pwb classes are defined in terms of the minimal fine topology on the riesz martin space u u u instead of the natural topology the two corresponding concepts of resolutivity are compatible

capacity theory without duality the paper develops a theory of capacity for a borel right process without duality assumptions the basic tool in this approach is a stationary process ralative to an excessive measure ifp t t 0 denotes the semigroup of the process on the state spacee and ifm is an excessive measure one then there exists a processy y t t one with random birth and death and a finite measureq m such thaty is stationary underq m and markov with respect to p t for a setb ine the hitting resp last exit time ofy is denoted by b resp b andb is called transient resp cotransient ifq m b 0 resp q m b 0 the main theorem then states that for a both transient and contransient setb the distributions of b and b underq m are the same for suchb the capacity is denfined byc b q m b 0 1 and the cocapacity by hat c b q m b 0 1 and it is shown that these definitions in fact generalize previous definitions under duality assumptions without duality assumption there is no representation of the capacitary potential in terms of a capacitary measure but there exists a cocapacitary entrance law which generalizes the notion of a cocapacitary measure such that hat c b mathop sup limits t 0 1 the paper contains investigations of transience and cotransience a decomposition of the cocapacitrary entrance law some remarks on left versions and furthermore a generalization of spitzer s asymptotic formula

the solution of the kato problem for divergence form elliptic operators with gaussian heat kernel bounds which in turnhas applications to the perturbation theory for certain classes of hyperbolicequations see 16 we remark that 1 3 is equivalent to the oppositeinequality for the square root of the adjoint operator l in 13 14 kato conjectured that an abstract version of 1 3 might hold for regularly accretive operators see 14 18 for the details a counter example to this abstract conjecture was obtained by mcintosh 17 whothen reformulated the conjecture in the following form bearing in mind thatkato s interest in the problem had been motivated by the special case ofelliptic di erential operators conjecture 1 4 the estimate 1 3 holds for lde ned as in 1 2 for anyl

finely harmonic functions with finite dirichlet integral with respect to the green measure we consider finely harmonic functions h on a fine greenian domain v c rd with finite dirichlet integral wrt gm i e f ivh y 2 g x y dm y oo for x c v where m denotes the lebesgue measure g x y the green function we use brownian motion and stochastic calculus to prove that such functions h always have boundary values h along a a brownian paths this partially extends results by doob brelot and godefroid who considered ordinary harmonic functions with finite dirichlet integral wrt m and green lines instead of brownian paths as a consequence of theorem 1 we obtain several properties equivalent to one of these being that h is the harmonic extension to v of a random boundary function h of a certain type i e h x ex h for all x c v another application is that the polar sets are removable singularity sets for finely harmonic functions satisfying this is in contrast with the situation for finely harmonic functions with finite dirichlet integral wrt m

multilinear littlewood paley estimates with applications to partial differential equations abstract we obtain a collection of multilinear littlewood paley estimates which we then apply to two problems in partial differential equations the first problem is the estimation of the square root of an elliptic operator in divergence form and the second is the estimation of solutions to the cauchy problem for nondivergence form parabolic equations

conditional gauge theorem for non local feynman kac transforms feynman kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of markov processes general gauge and conditional gauge theorems are established for such transforms furthermore the l 2 infinitesimal generator of the schrodinger semigroup given by a non local feynman kac transform is determined in terms of its associated bilinear form

measurement and analysis of modulated doublet mode response in mock bladed disks the steady state response of spatially modulated doublet modes that occur in low count flexible bladed disks is investigated for the case in which the structure is driven by a harmonic travelling wave excitation source finite element simulation and modal testing of prototypical bladed disk structures demonstrate the presence of particular wavenumbers beyond the base number of nodal diameters which contaminate and distort the appearance of certain doublet modes the manner in which the natural frequency and wavenumber content of such modes shift and split as functions of the number of blades and their span angle is discussed in the light of a companion perturbation analysis for rotationally periodic structures resonance conditions are established and verified through simultaneous measurements made with a spin test stand using sensors that are placed in the rotating structure and stationary excitation frames of reference the travelling wave response components of a repeated frequency doublet mode are shown to propagate either in the same or opposite direction as the excitation source depending on whether certain algebraic relationships between the excitation order the base number of nodal diameters and the contamination wavenumbers are satisfied to the extent that such components can travel at different phase speeds and directions relative to one another the placement of sensors on the structure can be optimized to best measure the response amplitude conversely other placements can result in submaximal measurement of peak vibration amplitude over the structure

the dirichlet problem for higher order equations in composition form the present paper commences the study of higher order differential equations in composition form specifically we consider the equation lu divb adiva u 0 where a and b are elliptic matrices with complex valued bounded measurable coefficients and a is an accretive function elliptic operators of this type naturally arise for instance via a pull back of the bilaplacian 2 from a lipschitz domain to the upper half space more generally this form is preserved under a lipschitz change of variables contrary to the case of divergence form fourth order differential equations we establish well posedness of the dirichlet problem for the equation lu 0 with boundary data in l2 and with optimal estimates in terms of nontangential maximal functions and square functions

response of rotating rings to harmonic and periodic loading and comparison with the inverted problem abstract the harmonic and periodic forced vibrations of rotating rings are derived and investigated the modal expansion technique yields the forced solution which is characterized by four generalized co ordinates associated with each n circumferential wave number the inextensional assumption is presumed when flexural vibration is the only important component to reduce the order of the system the closed form solutions to the harmonic load cases once concentrated once distributed are demonstrated and interpreted the approach is then extended to periodic loads where fourier sine and cosine series is applied examples depict the numerical responses to all the cases being derived the solutions of a stationary ring subjected to traveling loads are also solved for comparison their difference is investigated and interpreted from various viewpoints

the in plane vibration of thin rings with in plane profile variations part ii application to nominally circular rings abstract geometric profile variations always exist in nominally circular rings due to limitations in the manufacturing processes such profile variations are known to lead to frequency splitting between pairs of modes which are degenerate in a perfect ring in this paper the effects of circumferential profile variations on the in plane vibration characteristics of such rings are studied using a numerical method the inner and outer ring surfaces are described in a very general way by fourier series and the rayleigh ritz method is used to obtain the natural frequencies and mode shapes results are presented for a number of example cases which include single and multiple harmonic variations in profile the relationship between the patterns of frequency splitting and the harmonic content of the ring profile is investigated and the most important causes of frequency splitting are identified

excitation of rotating circumferentially periodic structures abstract a circumferentially periodic structure consists of a finite number of identical substructures coupled together in identical ways to form a closed ring type structure the vibrational behaviour of such structures when rotating about the axis of structural symmetry is considered especially the forced response due to forces fixed in space it is known that for a circumferentially symmetric structure rotating about its axis of structural symmetry and excited by a force fixed in space resonance for the n nodal diameters mode is obtained when the corresponding natural frequency is n n where is the angular velocity of rotation the deformation at these resonances consists of waves travelling backwards in relation to the direction of the structure rotation this resonance condition also holds for a circumferentially periodic structure but then additional resonance possibilities exist given by n kn n where n is the number of sub structures and k 0 1 2 these results are known to hold true for a structure fixed in space and acted upon by a rotating force in this paper these results are shown to hold true also for a rotating structure acted upon by a force distribution fixed in space both backward and forward travelling waves can be excited in those cases when the rotating structure exhibits coriolis accelerations the natural frequencies for backward 1n and forward 2n rotating mode shapes are different this well known property has a pronounced effect on the forced response due to forces fixed in space in the absence of coriolis effects the magnification factor is essentially 1 n 2 2 where is the forcing frequency due to rotation but in the presence of coriolis effects the magnification factor has the characteristics 1 1n 2n

hardy s inequality for dirichlet forms abstract we prove an abstract form of hardy s l2 inequality in which the dirichlet integral is replaced by the dirichlet form of a general symmetric markov process a number of examples are provided

the response of a non uniformly tensioned circular string to a moving load abstract a non uniformly tensioned circular string on a damped elastic foundation is acted upon by a moving concentrated load this configuration can be viewed as a very simplified representation of a spinning rectangularly orthotropic disk acted upon by a spatially fixed force or of a stationary orthotropic disk subjected to a circumferentially moving load the natural frequencies and normal modes of vibration of the string on elastic foundation are determined for a range of values of the tension inhomogeneity the response of the string to a moving load is then determined the results indicate that there are many speeds below the critical speed of the uniformly tensioned string for which the forced response is large it is anticipated that the response of this simple model to a moving load can provide insight into the behavior of the mathematically more complicated rectangularly orthotropic circular disk

the theory of weights and the dirichlet problem for elliptic equations in this work we consider questions from the area of partial differential equations and the related questions from harmonic analysis specifically we will study the dirichlet problem for second order divergence form elliptic operators with bounded measurable coefficients roughly speaking we consider the following question suppose that we are given two operators lo and li and that we have good estimates for the dirichlet problem for lo good in this context could mean several different things for instance it might mean that there exists p 1 p oo so that the dirichlet problem is solvable in a suitable sense with lp data what are the optimal conditions on the difference between the coefficients of lo and l1 which guarantee that the dirichlet problem for li also has good estimates this question has been extensively studied recently cf f j k r f and d4 our work uses in a crucial way the results in r f the main results in d4 and r f are proved using an ingenious differential inequality for a family of harmonic measures introduced in d4 another of our goals in this article is to give new direct proofs of the results in d4 and r f without the use of this differential inequality theorems 2 4 2 5 and 2 18 these direct approaches have already had important applications k p2 an interesting class of examples for the theorems quoted above arises when one pulls back the laplacian via a quasiconformal mapping of the plane into itself specializing our theorem to this case suggests a new characterization of the class of am weights introduced in connection with several problems in harmonic analysis by muckenhoupt mul and coifman c fefferman co f we shall present in theorem 2 3 a criterion in terms of carleson measures which is very close to log w e bmo and is necessary and sufficient for w e ad

symmetry groups and translation invariant representations of markov processes the symmetry groups of the potential theory of a markov process xt are used to introduce new algebraic and topological structures on the state space and the process for example let g be the collection of bijections sp on e which preserve the collection of excessive functions assume there is a transitive subgroup h of the symmetry group g such that the only map 9 e h fixing a point e e e is the identity map on e there is a bijection p e h so that the algebraic structure of h can be carried to e making e into a group if there is a left quasi invariant measure on e then there is a topology on e making e into a locally compact second countable metric group there is also a time change r t of xt such that xt t is a translation invariant process on e and xt t is right continuous with left limits in the new topology

trace operator and the dirichlet problem for elliptic equations on arbitrary bounded open sets abstract we consider the dirichlet problem and the weak dirichlet problem on a general possibly nonregular bounded domain for elliptic linear equation with uniformly elliptic divergence form operator we investigate carefully the relationship between weak integral probabilistic soft and the perron wiener brelot solutions of the problem we also study the relationship between solutions of the dirichlet problem and weak dirichlet problem to this end we extend the usual notion of the trace operator and consider the dirichlet problem with martin boundary

the neumann problem for elliptic equations with non smooth coefficients in this paper we study the neumann and regularity problems for divergence form symmetric elliptic operators l div av where a aifix is a matrix of bounded measurable functions and ellipticity is the existence of a 0 such that 2 114 2 ais ir 21412 for all i r we assume that l is defined in the unit ball b but the methods of proof are sufficiently general to allow b to be a bounded starlike lipschitz domain the neumann problem lu 0 in b avun q f

an application of flows to time shift and time reversal in stochastic processes a simple proposition theorem 1 on flows allows the investigation of random time shift and time reversal in markov processes without assuming any regularity of paths theorem 5 is a generalization of nagasawa s time reversal theorem and theorem 4 generalizes a recent result of getoor and glover 1 flows 1 1 we consider a flow in a measurable space 2 y that is a family of transformations at t e r such that oat 0s t for all s t e r and t c oto e a e r x 4 for all a e f r is the borel a algebra in r we put oty x y otw for every function y and pot a p 0t71a a e y p pot dt for every measure p we denote by the collection of all sets a e y such that t1a a for all t e r a function y is measurable with respect to the a algebra wif and only if it is measurable and invariant under all transformations ot obviously p a 0 or oo for all a e sl nevertheless we prove theorem 1 if p is a finite over y it determines uniquely the values p a for all a e 1 2 as a tool we use stationary times a stationary time t is a measurable mapping from 2 to the extended real line oo oo such that ott t t for all t e r suppose that y coincides with its completion with respect to the class of all probability measures then the first hitting time of a set a e y ta inf t ot e a and the last exit time from a ta sup t ot co a are stationary times2 the measurability follows from 5 chapter 3 1 received by the editors march 13 1984 1980 mathematics subject classification primary 60g 601 1 supported in part by national science foundation grant mcs 8202286 2we put inf oo sup oo c1985 american mathematical society 0002 9947 85 1 00 25 per page

on the potential theory of symmetric markov processes on reprend des resultats de dynkin et on considere un processus de markov fort symetrique continu a droite on etudie la relation existant entre le cone de mesures positives d energie finie et la capacite

necessary and sufficient conditions for absolute continuity of elliptic harmonic measure our purpose in this paper is to give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding poisson kernel for the dirichlet problem exist this condition on the coefficients is global continuity together with the additional property that the modulus of continuity along some nontangential direction at each boundary point be bounded uniformly in these points and directions by a function 7 t satisfying the dini type condition

response of modulated doublet modes to travelling wave excitation the forced vibration of a rotationally periodic structure when subjected to travelling wave excitation is discussed with emphasis placed on the steady state response of doublet modes having either repeated or split frequencies such vibration modes have spatially modulated shapes defined by 1 the number of nodal diameters present in the limiting case of axisymmetry and 2 certain additional fourier harmonics which contaminate and distort their appearances the natural frequency and mode structure of a model periodic structure is discussed in the context of an otherwise axisymmetric disk having evenly spaced sector shaped line distributions of stiffness and inertia through perturbation analysis the contamination wavenumbers present in a doublet having repeated frequency are shown to comprise two subsets the members of which have sine and cosine coefficients of the same or of differing signs for each wavenumber in the mode shape s fourier expansion the structure of the wavenumber content is explored further with respect to the response of repeated and split doublets to a harmonic travelling wave excitation the individual fourier components comprising a modulated doublet can respond and propagate in the same direction as the excitation or opposite to it depending on the wavenumber of the excitation and the subset to which the contamination wavenumber belongs the response of the split frequency doublets and the circumstances under which travelling or standing wave responses or a blend of the two can occur in the structure s reference frame are also examined in the context of the model periodic structure the qualitative character of the response the forward or backward propagation direction of each mode s constituent wavenumber components and the phase speeds of those components are discussed in illustrative case studies

sub trans and supercritical variable magnitude travelling loads on cylindrical rings abstract the problem of time dependent variable magnitude travelling loads in a closed symmetric structure is considered this includes the circumferential propagation in viscoelastically supported cylindrical rings which can rotate about their axes the main emphasis of the work is to establish the effects of time dependent load variability on the response characteristics when travelling velocities are in the sub trans and supercritical speed ranges this will enable the doppler like interactions among the propagating bending and in plane waves at the various travelling load speed ranges to be evaluated as an example simulation the model is tuned to define the dynamic response characteristics of tires rolling on bumpy surfaces this enables the sub trans and the supercritical response characteristics to be evaluated

the in plane vibration of thin rings with in plane profile variations part i general background and theoretical formulation abstract this paper presents a methodology for the analysis of the free in plane vibration of thin rings with profile variations in the circumferential direction the methodology is suitable for any thin ring which is bounded by closed curves which are single valued functions of circumferential position the inner and outer profiles are expressed as fourier series thus allowing any profile to be approximated with any degree of accuracy an iterative numerical procedure for determining the true middle surface and the corresponding thickness at each cross section around the circumference is established a reduced plane stress form of novozhilov s thin shell theory is used to model the deformation mechanics of the ring the eigenvalue problem is then formulated using the rayleigh ritz method in conjunction with a harmonic series description of the displacements general expressions are presented for the corresponding mass and stiffness matrices a companion paper presents a comprehensive set of results which illustrates application of the theory

markov processes and nonsymmetric dirichlet forms without regularity we study right markov processes in weak duality satisfying the sector condition of silverstein dirichlet space techniques are employed but without the customary c0 regularity hypothesis nonetheless the potential theory of such processes is quite amenable in particular it is proved that semipolar sets are quasi polar this extends results of silverstein and lejan

divergence form operators in reifenberg flat domains we study the boundary regularity of solutions of elliptic operators in divergence form with c 0 coefficients or operators which are small perturbations of the laplacian in non smooth domains we show that as in the case of the laplacian there exists a close relationship between the regularity of the corresponding elliptic measure and the geometry of the domain

a simple theory for the analysis and correction of frequency splitting in slightly imperfect rings abstract the flexural radial vibration of circular rings with imperfections represented by small attached masses and springs is considered the concept of an equivalent imperfection mass is introduced this is used to quantify the frequency splitting which occurs in slightly imperfect axisymmetric bodies the concept is used to estimate the trimming mass which must be added to or removed from the ring and at which point in order to reduce or eliminate the frequency split in a given pair of modes the method can be applied to any axisymmetric body for which the mode shapes can be measured or computed

free and forced response of mistuned linear cyclic systems a singular perturbation approach abstract the effect of small deterministic parameter perturbations on the forced response of nearly periodic structures with cyclic symmetry is investigated the general methodology developed herein is applicable to any n degree of freedom strongly coupled cyclic system with two arbitrary and independent variations in system parameters that destroy the cyclic symmetry the specific system studied may be regarded as a simplified model of a strongly coupled bladed disk assembly singular perturbation methods along with modal expansion analysis are applied to gain a physical insight into the effects of parameter perturbations on the eigenvalues the eigenvectors as well as the forced response amplitudes the study shows that under appropriate conditions the splitting and veering of eigenvalues due to mistunings or small parameter variations increases the amplitude of vibration of some blades significantly compared to what would be predicted by an analysis of the perfectly tuned system furthermore modal bifurcations lead to uneven vibration amplitudes irrespective of the stiffness of the coupling springs the variations in blade amplitudes are also found to be strongly dependent on damping and the type of engine order excitation applied to the system for the same set of mistuning parameters

functional calculus of dirac operators and complex perturbations of neumann and dirichlet problems we prove that the neumann dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in l 2 for small complex l infty perturbations of a coefficient matrix which is either real symmetric of block form or constant all matrices are assumed to be independent of the transversal coordinate we solve the neumann dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order dirac type operator we establish quadratic estimates for this dirac operator which implies that the associated hardy projection operators are bounded and depend continuously on the coefficient matrix we also prove that certain transmission problems for k forms are well posed for small perturbations of block matrices

on the boundary values of sobolev wp1 functions abstract for each p n we use local oscillations to give intrinsic characterizations of the trace of the sobolev space w p 1 to the boundary of an arbitrary domain r n

drift transforms and green function estimates for discontinuous processes in this paper we consider girsanov transforms of pure jump type for discontinuous markov processes we show that under some quite natural conditions the green functions of the girsanov transformed process are comparable to those of the original process as an application of the general results the drift transform of symmetric stable processes is studied in detail in particular we show that the relativistic a stable process in a bounded c 1 1 smooth open set d can be obtained from symmetric a stable process in d through a combination of a pure jump girsanov transform and a feynman kac transform from this we deduce that the green functions for these two processes in d are comparable

differentiability of solutions to second order elliptic equations via dynamical systems for a second order elliptic equation in divergence form we investigate conditions on the coefficients which imply that all solutions are lipschitz continuous or differentiable at a given point we assume the coefficients have modulus of continuity satisfying the square dini condition and obtain additional conditions that examples show are sharp our results extend those of previous authors who assume the modulus of continuity satisfies the dini condition our method involves the study of asymptotic properties of solutions to a dynamical system that is derived from the coefficients of the elliptic equation

the l p dirichlet problem and nondivergence harmonic measure we consider the dirichlet problem lu 0 in d u g on d for two second order elliptic operators l k u n i j 1 a i j k x ij u x k 0 1 in a bounded lipschitz domain d r n the coefficients a i j k belong to the space of bounded mean oscillation bmo with a suitable small bmo modulus we assume that l 0 is regular in l p d d for some p 1 p that is nu lp c g lp for all continuous boundary data g here is the surface measure on d and nu is the nontangential maximal operator the aim of this paper is to establish sufficient conditions on the difference of the coefficients e i j x a i j 1 x a i j 0 x that will assure the perturbed operator l 1 to be regular in l q d d for some q 1 q

the dynamic analysis of a flat plate under a moving load by the finite element method summary the object of this paper is to analyse by the finite element method the dynamic responses of a flat plate subjected to various moving loads first of all the actual continuous flat plate was replaced by a discrete system composed of isoparametric rectangular plate elements and then the elementary and overall stiffness and mass matrices were determined and the natural frequencies and mode shapes of the flat plate were solved next the newmark direct integration method was used to find the dynamic responses of the flat plate the effects of eccentricity acceleration and initial velocity of the moving load and the effect of span length were the key points of study the dynamic behaviour of a multi span flat plate supported by the beam members of rigid plane frames and subjected to the action of a series of moving loads in identical or opposite directions were also investigated

dynamic time responses of a flexible spinning disk misaligned with the axis of rotation using the finite element method this study investigates the dynamic time responses of a flexible spinning disk of which axis of rotation is misaligned with the axis of symmetry the misalignment between the axes of symmetry and rotation is one of major vibration sources in optical disk drives such as cd rom cd r cd rw and dvd drives based upon the kirchhoff plate theory and the von karman strain theory three coupled equations of motion for the misaligned disk are obtained two of the equations are for the in plane motion while the other is for the out of plane motion after transforming these equations into two weak forms for the in plane and out of plane motions the weak forms are discretized by using newly defined annular sector finite elements applying the generalized time integration method to the discretized equations the time responses and the displacement distributions are computed and then the effects of misalignment on the responses and the distributions are analyzed the computation results show that the misalignment has an influence on the magnitudes of the in plane displacements it is also found that the misalignment results in the amplitude modulation or the beat phenomenon in the time responses of the out of plane displacement

homogeneous random measures and a weak order for the excessive measures of a markov process let x xt px be a right markov process and let m be an excessive measure for x associated with the pair x m is a stationary strong markov process yt qm with random times of birth and death with the same transition function as x and with m as one dimensional di stribution we use yt qm to study the cone of excessive measures for x a weak order is defined on this cone an excessive measure is weakly dominated by m if and only if there is a suitable homogeneous random measure tt such that yt q6 is obtained by birthing yt qm birth in t t dt occurring at rate s dt random measures such as s are studied through the use of palm measures we also develop aspects of the general theory of processes over yt qm including the moderate markov property of yt qm when the arrow of time is reversed applications to balayage and capacity are suggested

on the excursions of markov processes in classical duality on obtient des resultats comparables a ceux de getoor et sharpe 1982 sous des hypotheses de dualite classique