unique continuation for sublinear elliptic equations based on carleman estimates abstract in this article we deal with different forms of the unique continuation property for second order elliptic equations with nonlinear potentials of sublinear growth under suitable regularity assumptions we prove the weak and the strong unique continuation property moreover we also discuss the unique continuation property from measurable sets which shows that nodal domains to these equations must have vanishing lebesgue measure our methods rely on suitable carleman estimates for which we include the sublinear potential into the main part of the operator

capturing complexity classes by fragments of second order logic abstract we investigate the expressive power of certain fragments of second order logic on finite structures the fragments are second order horn logic second order krom logic as well as a symmetric and a deterministic version of the latter it is shown that all these logics collapse to their existential fragments in the presence of successor relation they provide characterizations of polynomial time deterministic and nondeterministic logspace and of the complement of symmetric logspace without successor relation these logics still can express certain problems that are complete in the corresponding complexity classes but on the other hand they are strictly weaker than previously known logics for these classes and fail to express some very simple properties

representing ontologies using description logics description graphs and rules description logics dls are a family of state of the art knowledge representation languages and their expressive power has been carefully crafted to provide useful knowledge modeling primitives while allowing for practically effective decision procedures for the basic reasoning problems recent experience with dls however has shown that their expressivity is often insufficient to accurately describe structured objects objects whose parts are interconnected in arbitrary rather than tree like ways dl knowledge bases describing structured objects are therefore usually underconstrained which precludes the entailment of certain consequences and causes performance problems during reasoning to address this problem we propose an extension of dl languages with description graphs a knowledge modeling construct that can accurately describe objects with parts connected in arbitrary ways furthermore to enable modeling the conditional aspects of structured objects we also extend dls with rules we present an in depth study of the computational properties of such a formalism in particular we first identify the sources of undecidability of the general unrestricted formalism based on that analysis we then investigate several restrictions of the general formalism that make reasoning decidable we present practical evidence that such a logic can be used to model nontrivial structured objects finally we present a practical decision procedure for our formalism as well as tight complexity bounds

the poor bending response of the four node plane stress quadrilateral many plane stress finite elements which can exactly represent rigid body and constant strain modes are too stiff in their response to the simple flexural action of a beam this problem has received considerable interest this paper explores a new interpretation of the problem and shows that the poor bending response of the original 4 node plane stress quadrilateral can be quantitatively predicted by an error model

exponential decay of eigenfunctions in many body type scattering with second order perturbations abstract we show the exponential decay of eigenfunctions of second order geometric many body type hamiltonians at non threshold energies moreover in the case of first order and small second order perturbations we show that there are no eigenfunctions with positive energy

undecidability of subsumption in nikl abstract subsumption determining whether one concept is more general than another is known to be np hard for all reasonably expressive terminological logics but up to now the decidability of subsumption for terminological logics used in current knowledge representation systems such as nikl remained unknown this paper shows that subsumption in the terminological logic of nikl is undecidable and thus that there are no complete algorithms for subsumption or classification in nikl

carleman inequalities for the dirac and laplace operators and unique continuation on demontre les meilleures inegalites de type carleman possibles dans le cas de l operateur de dirac on obtient la propriete de prolongement unique pour d v ou v l loc r n 3n 2 2 n 3

an assessment of four noded plate finite elements based on a generalized third order theory plate finite elements based on the generalized third order theory of reddy and the first order shear deformation theory are analysed and compared on the basis of thick and thin plate modelling behaviour distortion sensitivity overall accuracy reliability and efficiency in particular several four noded reddy type elements and the nine noded lagrangian and heterosis mindlin type plate elements are analysed to assess their behaviour in bending vibration and stability of isotropic and laminated composite plates a four noded reddy type element is identified which is free of all spurious stiffness and zero energy modes computationally efficient and suitable for use in any general purpose finite element program

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

counting modulo quantifiers on finite structures we give a combinatorial method for proving elementary equivalence in first order logic fo with counting modulo n quantifiers dn inexpressibility results for fo dn with built in linear order are also considered for instance the class of linear orders of length divisible by n 1 cannot be expressed in fo dn using this result we prove that comparing cardinalities or connectivity of ordered graphs are not definable in fo dn we also show that the height of complete n ary trees cannot be expressed in fo dn with linear order interpreting the predicate y nx as a complete n ary tree we show that the predicate y px cannot be defined in fo dn with linear order whenever p has a prime factor that does not divide n this solves the problem raised by niwi ski and stolboushkin lics 93 we also discuss a connection between our results and the well known open problem in circuit complexity theory whether acc nc1

expressiveness of concept expressions in first order description logics we introduce a method for characterizing the expressive power of concept expressions in first order description logics the method is essentially model theoretic in nature in that it gives preservation results uniquely identifying a wide range of description logics as fragments of first order logic the languages studied in the paper all belong to the well known email protected email protected and plane1d 49c hierarchies

equivariant e theory for groupoids acting on c algebras we define equivariant asymptotic morphisms between c0 x algebras and construct the category of homotopy classes of such morphisms based on this category we construct the category of homotopy classes of asymptotic morphisms which are equivariant with respect to an action of a groupoid we then define and study the corresponding equivariant e theory

analysis of locking and stress oscillations in a general curved beam element the exactly integrated general quadratic curved beam element has both membrane and shear locking and significant quadratic oscillations in the axial force and cubic oscillations in the shear force the functional re constitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations the orthogonally correct field consistent interpolations are determined for the optimal form of the element and it is shown that the popular two point gaussian integrated13 version of the element is non orthogonal and has a cubic13 oscillation in the shear force that curiously vanishes at the barlow points

the curved beam deep arch finite ring element revisited an attempt is made to understand the errors arising in curved finite elements which undergo both flexural and membrane deformation it is shown that with elements of finite size i e a practical level of discretization at which reasonably accurate results can be expected there can be errors of a special nature that arise because the membrane strain fields are not consistently interpolated with terms from the two independent field functions that characterize such a problem these lead to errors described here as of the second kind and a physical phenomenon called membrane locking it seems possible to determine optimal integration rules that will allow the extensional deformation of a curved beam deep arch finite ring element to be modelled by independently chosen low order polynomial functions and which will recover the inextensional case in the penalty limit of extreme thinness without spurious locking constraints what is emphasized is that the choice of shape functions or subsequent operations to determine the discretized functionals must consistently model the physical requirements the problem imposes on the field variables

bounded linear logic a modular approach to polynomial time computability typing is a way of describing the interactive behavior of algorithms usual typing systems are mainly concerned with input output specifications e g given terms f a b and a a the computation of f a by normalization yields a result of type b however one can dream of more refined typings that would not only ensure ethereal termination but would for instance yield feasible resource bounds it seems that time complexity does not lend itself naturally to modular manipulation we seek something more primitive

uniqueness properties of solutions of schrodinger equations under suitable assumptions on the potentials v and a we prove that if u c 0 1 h1 is a solution of the linear schrodinger equation i t x u vu a xu on rd 0 1 and if u 0 in x r 0 1 for some r 0 then u 0 in rd 0 1 as a consequence we obtain uniqueness properties of solutions of nonlinear schrodinger equations of the form i t x u g x t u u xu xu on rd 0 1 where g is a suitable nonlinear term the main ingredient in our proof is a carleman inequality of the form e x1 v lx2lt2 e x1 xv bx 2lt2 c e x1 i t x v bx1 2lt2 for any v c r h1 with v t 0 for t 0 1 in this inequality bx 2 and bx1 2 are banach spaces of functions on rd and e x1 is a suitable weight

on the relative expressiveness of description logics and predicate logics abstract it is natural to view concept and role definitions in description logics as expressing monadic and dyadic predicates in predicate calculus we show that the descriptions built using the constructors usually considered in the dl literature are characterized exactly as the predicates definable by formulas in tl3 the subset of first order predicate calculus with monadic and dyadic predicates which allows only three variable symbols in order to handle number bounds we allow numeric quantifiers and for transitive closure of roles we use infinitary disjunction using previous results in the literature concerning languages with limited numbers of variables we get as corollaries the existence of formulas of fopc which cannot be expressed as descriptions we also show that by omitting role composition descriptions express exactly the formulas in tl2 which is known to be decidable

on bisimulations for description logics we study bisimulations for useful description logics the simplest among the considered logics is alc reg a variant of pdl the others extend that logic with the features inverse roles nominals qualified number restrictions the universal role and or the concept constructor for expressing the local reflexivity of a role they also allow role axioms our contributions are as follows we propose to treat named individuals as initial states and give an appropriate bisimulation condition for that we also give bisimulation conditions for the universal role and the concept constructor r self we prove that all of the bisimulation conditions for the features can be combined together to guarantee invariance of concepts and the hennessy milner property for the whole class of studied description logics we address and give results on invariance or preservation of aboxes rboxes and knowledge bases in description logics independently from lutz et al 26 27 we also give results on invariance of tboxes we introduce a new notion called qs interpretation which is needed for dealing with minimizing interpretations in description logics with qualified number restrictions and or the concept constructor r self we formulate and prove results on minimality of quotient interpretations w r t the largest auto bisimulations we adapt hopcroft s automaton minimization algorithm to give an efficient algorithm for computing the partition corresponding to the largest auto bisimulation of a finite interpretation in any description logic of the considered family using the invariance results we compare the expressiveness of the considered description logics w r t concepts tboxes and aboxes our results about separating the expressiveness of description logics are naturally extended to the case when instead of alc reg we have any sublogic of alc reg that extends alc

carleman inequalities and the heat operator we prove a strong unique continuation theorem for functions u vanishing to infinite order in the space time variables at 0 0 and verifying the inequality 4u tu v x t u on rn 0 t when t1 n 2r 1 s v x t lt locl r x n 2r 1 s 1 n 2 r

strong unique continuation for the lame system with less regular coefficients we study the strong unique continuation property sucp for the lame system in the plane the main contribution of our work is to prove that the sucp holds when lame coefficients mu lambda in w 2 s omega times l infty omega for some s 4 3 in other words we establish the sucp for the lame system in the plane when lambda is bounded and mu belongs to certain holder classes

an epistemic operator for description logics abstract description logics also called terminological logics or concept languages are fragments of first order logic that provide a formal account of the basic features of frame based systems however there are aspects of frame based systems such as nonmonotonic reasoning and procedural rules that cannot be characterized in a standard first order framework such features are needed for real applications and a clear understanding of the logic underlying them is necessary for principled implementations we show how description logics enriched with an epistemic operator can formalize such aspects the logic obtained is a fragment of a first order nonmonotonic modal logic we show that the epistemic operator formalizes procedural rules as provided in many knowledge representation systems and enables sophisticated query formulation including various forms of closed world reasoning we provide an effective procedure for answering epistemic queries posed to a knowledge base expressed in a description logic and extend this procedure in order to deal with rules we also address the computational complexity of reasoning with the epistemic operator identifying cases in which an appropriate use of the epistemic operator can help in decreasing the complexity of reasoning

strong unique continuation results for differential inequalities the main result of this paper is a strong uniqueness theorem for differential inequalities of the form u x v x u x w x u x wherevandware radial functions inln 2loc andlnloc respectively and is a connected open subset of rn other results involving other spaces of potentialsvandware proved our method relies on sharp carleman estimates

oscillatory integrals and unique continuation for second order elliptic differential equations a well known counterexample see 11 indicates that the condition v e lpn2 is in the best possible nature this counterexample however has to do loc with unique continuation from a point rather than from open sets as in theorem 1 1 we hope to treat unique continuation from a point in a subsequent paper results of this type for constant coefficient operators were obtained by sawyer 14 for low dimensions and jerison and kenig 11 for general n there was a lot of previous work and we refer the reader to 11 14 for further references also jerison and kenig proved the stronger result that there is unique continuation from a point for constant coefficient operators for variable coefficient operators our results improve one of h6rmander 8 which says that there is unique continuation from open sets for solutions to 1 1

riemannian manifolds with maximal eigenfunction growth on any compact riemannian manifold m g of dimension n the l sp 2 normalized eigenfunctions phi sb lambda satisfy lvert rvert phi sb lambda lvert rvert sb infty leq c lambda sp n 1 2 where delta phi sb lambda lambda sp 2 phi sb lambda the bound is sharp in the class of all m g since it is obtained by zonal spherical harmonics on the standard n sphere s sp n but of course it is not sharp for many riemannian manifolds for example for flat tori mathbb r sp n gamma we say that s sp n but not mathbb r sp n gamma is a riemannian manifold with maximal eigenfunction growth the problem that motivates this paper is to determine the m g with maximal eigenfunction growth our main result is that such an m g must have a point x where the set mathscr l sb x of geodesic loops at x has positive measure in s sp ast sb xm we show that if m g is real analytic this puts topological restrictions on m for example only m s sp 2 or m mathbb r p sp 2 topologically in dimension 2 can possess a real analytic metric of maximal eigenfunction growth we further show that generic metrics on any m fail to have maximal eigenfunction growth in addition we construct an example of m g for which mathscr l sb x has positive measure for an open set of x but which does not have maximal eigenfunction growth thus it disproves a naive converse to the main result

the expressiveness of a family of finite set languages abstract in this paper we characterize exactly the complexity of a set based database language called srl which presents a unified framework for queries and updates by imposing simple syntactic restrictions on it we are able to express exactly the classes p and logspace we also discuss the role of ordering in database query languages and show that the hom operator of machiavelli language in ohori et al 1989 does not capture all the order independent properties

an additional stiffness parameter measure of error of the second kind in the finite element method conventional error analyses norms in the finite element method are based on the percentage error or its equivalent in some computed value as compared to the theoretically predicted value in problems where two or more field variables are coupled it is possible that if the field interpolation functions do not consistently reproduce limiting situations of physical behaviour there may be very large errors which are exaggerated enormously when some structural parameters become indefinitely large in a penalty limiting sense the percentage error norms therefore saturate quickly to a value approaching 100 per cent and do not sensibly reflect the relationship between error and the structural parameter even on a logarithmic plot errors due to these spurious constraints have recently been recognized as belonging to a special class described as errors of the second kind a new error norm called the additional stiffening parameter helps to recognize the manner in which errors of the second kind can be blown out of propprtion by a large variation in some structural parameter recent investigations in some multi field problems are summarized here to demonstrate the usefulness of this concept

a partial answer to a conjecture of b simon concerning unique continuation in his survey paper on schrijdinger semigroups s b simon formulated the following conjecture see s p 5193 let ve kfp the local kato class of potentials then the time independent schrddinger operator h d v has the unique continuation property ucp by this it is meant that given any connected open subset 52 c r the only solution u of hu 0 in 52 that can vanish in an open subset 52 c sz is u 0 a measurable function v on r is said to belong to the kato class k if

concerning the lp norm of spectral clusters for second order elliptic operators on compact manifolds in this paper we study the lp l2 mapping properties of a spectral projection operator for riemannian manifolds this operator is a generalization of the harmonic projection operator for spherical harmonics on s see c d sogge duke math j 53 1986 43 65 among other things we generalize the l2 restriction theorems of c fefferman e m stein and p tomas bull amer math sot 81 1975 477478 for the fourier transform in r to the setting of riemannian manifolds we obtain these results for the spectral projection operator as a corollary of a certain sobolev inequality involving d r2 for large r this sobolev inequality generalizes certain results for r of c kenig a ruiz and the author duke math j 55 1987 329 347 the main tools in the proof of the sobolev inequalities for riemannian manifolds are the hadamard parametrix cf l hbrmander acta mad 88 1968 341 370 and the analysis of linear partial differential equations vol iii springer verlag new york 1985 and oscillatory integral theorems of l carleson and p sjolin studia math 44 19x 287 299 and stein arm math stud 112 1986 307 357 0 1988 academic pnss iw

infinitary logic and inductive definability over finite structures the extensions of first order logic with a least fixed point operator fo lfp and with a partial fixed point operator fo pfp are known to capture the complexity classes p and pspace respectively in the presence of an ordering relation over finite structures recently abiteboul and vianu in proceedings of the 23rd acm symposium on the theory of computing 1991 investigated the relationship of these two logics in the absence of an ordering using a machine model of generic computation in particular they showed that the two languages have equivalent expressive power if and only if p pspace these languages can also be seen as fragments of an infinitary logic where each formula has a bounded number of variables l see for instance kolaitis and vardi in proceedings of the 5th ieee symposium on logic in computer science pp 156 167 1990 we investigate this logic on finite structures and provide a normal form for it we also present a treatment of abiteboul and vianu s results from this point of view in particular we show that we can write a formula of fo lfp that defines an ordering of the lk types uniformly over all finite structures one consequence of this is a generalization of the equivalence of fo lfp and p from ordered structures to classes of structures where every element is definable we also settle a conjecture mentioned by abiteboul and vianu by showing that fo lfp is properly contained in the polynomial time computable fragment of l raising the question of whether the latter fragment is a recursively enumerable class

an analysis of fixed point queries on binary trees lindell s an analysis of fixed point queries on binary trees theoretical computer science 85 1991 75 95 the presence of ordering appears to play an essential role in the logical expressibility of polynomialtime queries on finite structures by examining the expressibility and complexity of inductive queries on the class of complete unordered binary trees we are able to show that the ability to calculate cardinality is strictly less powerful than the assumption of order

a strong unique continuation theorem for parabolic equations the unique continuation is best understood for second order elliptic operators the classical paper by carleman 7 established the strong unique continuation theorem for second order elliptic operators which need not have analytic coefficients this was remarkable since it indicates that even a non analytic solution of an elliptic equation can behave somewhat in an analytic manner the powerful technique he used the so called carleman weighted inequality has played a central role in later developments in 1950 s aronszajn 4 and cordes 11 generalized his result to higher dimensions in recent years this classical subject caught new attention from a great number of people much efforts have been made to relax the smoothness hypotheses on the coefficients see 6 17 43 1 22 a seminal paper by jerison and kenig 26 has shown the unique continuation property for operators of the form c x with c l 2 loc where n 3 is the space dimension further improvements have been carried out in considering other classes of coefficients fefferman phong class and kato class 42 8 12 29 in extending the result to operators with first derivative terms and variable leading coefficients 46 47 51 52 and etc see 25 15 16 28 5 27 and the references therein for second order linear parabolic operators with time independent coefficients the strong unique continuation property along with detailed estimates on the hausdorff measures of nodal sets was reduced in 32 33 to the previously established elliptic counterparts the reduction from time independent parabolic

uniqueness of self similar shrinkers with asymptotically conical ends in this paper we show the uniqueness of smooth embedded selfshrinkers asymptotic to generalized cylinders of infinite order also we construct non rotationally symmetric self shrinking ends asymptotic to generalized cylinders with rate as fast as any given polynomial

unique continuation and absence of positive eigenvalues for schrodinger operators on considere l operateur de laplace sur r n et une fonction v x sur un sous ensemble connexe ouvert de r n on montre que si n 3 une propriete de prolongement unique est vraie pour v l loc n 2 r n dans l espace de sobolev h loc 2 q r n avec q 2n n 2

l p eigenfunction bounds for the hermite operator author s koch herbert tataru daniel abstract we obtain l p eigenfunction bounds for the harmonic oscillator in r n and for other related operators improving earlier results of thangavelu and karadzhov we also construct suitable counterexamples which show that our estimates are sharp

equivalence and normal forms for the restricted and bounded fixpoint in the nested algebra the nested model is an extension of the traditional flat relational model in which relations can also have relation valued entries its default query language the nested algebra is rather weak unfortunately since it is only a conservative extension of the traditional flat relational algebra and thus can express only a small fraction of the polynomial time queries therefore it was proposed to extend the nested algebra with a fixpoint construct but the resulting language turned out to be too powerful many inherently exponential queries could also be expressed two polynomial time restrictions of the fixpoint closure of the nested algebra were proposed the restricted fixpoint closure by gyssens and van gucht and the bounded fixpoint closure by suciu here we prove two results first we show that both restrictions are equivalent in expressive power the proof technique relies on known encodings of nested relations into flat ones and on a novel technique called type substitution by which we reduce the equivalence of the two restrictions to its obvious counterpart in the flat relational model second we prove that both the bounded fixpoint queries and the restricted fixpoint queries admit normal forms in which the fixpoint occurs exactly once the proof technique relies on a novel encoding method of nested relations into flat ones

combining deduction and model checking into tableaux and algorithms for converse pdl this paper presents a prefixed tableaux calculus for propositional dynamic logic with converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for calculus we prove the correctness and completeness of the calculus and illustrate its features we also discuss the transformation of the tableaux method naively nexptime into an exptime algorithm

on spectral stability of the nonlinear dirac equation abstract we study the point spectrum of the nonlinear dirac equation in any spatial dimension linearized at one of the solitary wave solutions we prove that in any dimension the linearized equation has no embedded eigenvalues in the part of the essential spectrum beyond the embedded thresholds we then prove that the birth of point eigenvalues with nonzero real part the ones which lead to linear instability from the essential spectrum is only possible from the embedded eigenvalues or thresholds and therefore can not take place beyond the embedded thresholds we also prove that in the nonrelativistic limit m the point eigenvalues can only accumulate to 0 and 2 m i

on the strong unique continuation principle for inequalities of maxwell type our goal of this paper is to prove carleman type inequalities for solutions a of maxwell type inequalities curl a div a cre 1 a assuming ij ec 0 1 in a neighborhood of 0 such inequalities also arise by nonlinear maxwell equations with lipschitz nonlinearity f a provided that a is locally bounded our investigation was inspired by the study of the corresponding problem for the elliptic dirac system

explanation and elimination of shear locking and membrane locking with field consistence approach abstract in this paper in the context of beam elements shear locking and membrane locking are explained and cured in a unified way with a field consistence approach in the view of field consistence approach when transverse displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are adopted shear locking will occur similarly when in plane displacements are coupled with section rotations in euler lagrangian equations and low order interpolations are used membrane locking will happen the beam elements derived by field consistence approach are not only free of shear locking and membrane locking but also highly efficient compared with their isoparametric counterparts although theoretically the internal forces generalized strains in mixed variational principles can vary independently they are neither independent to each other nor independent of displacement fields from the point of view of the field consistence approach

a simple plate shell triangle a simple shear flexible triangular plate shell element with three five displacement degrees of freedom at the three corner nodes only is identified it does not lock or have zero energy mechanisms the specific geometrical configurations in which this is possible are derived through field consistency patch tests

circumscribing datalog expressive power and complexity abstract in this paper we study a generalization of datalog the language of function free definite clauses it is known that standard datalog semantics i e least herbrand model semantics can be obtained by regarding programs as theories to be circumscribed with all predicates to be minimized the extension proposed here called datalog circ consists in considering the general form of circumscription where some predicates are minimized some predicates are fixed and some vary we study the complexity and the expressive power of the language thus obtained we show that this language and actually its non recursive fragment is capable of expressing all the queries in db co np and as such is much more powerful than standard datalog whose expressive power is limited to a strict subset of ptime queries both data and combined complexities of answering datalog circ queries are studied data complexity is proved to be co np complete combined complexity is shown to be in general hard for co ne and complete for co ne in the case of herbrand bases containing k distinct constant symbols where k is bounded

subsumption computed algebraically abstract this paper deals with terminological representation languages for kl one type knowledge representation systems such languages are based on the two primitive syntactic types called concepts and roles which are usually represented model theoretically as sets and binary relations respectively rather than following the model theoretic route we show that the semantics can be naturally accomodated in the context of an equational algebra of relations interacting with sets equational logic is then a natural vehicle for computing subsumptions both of concepts and of roles we thus propose the algebraic rather than model theoretic computation of subsumption

a comparison between algebraic query languages for flat and nested databases abstract recently much attention has been paid to query languages for nested relations in the present paper we consider the nested algebra and the powerset algebra and compare them both mutually as well as to the traditional flat algebra we show that either nest or difference can be removed as a primitive operator in the powerset algebra while the redundancy of the nest operator might have been expected the same cannot be said of the difference basically this result shows that the presence of one nonmonotonic operator suffices in the powerset algebra as an interesting consequence of this result the nested algebra without the difference remains complete in the sense of bancilhon and paredaens finally we show there are both similarities and fundamental differences between the expressiveness of query languages for nested relations and that of their counterparts for flat relations

hardy carleman type inequalities for dirac operators general hardy carleman type inequalities for dirac operators are proved new inequalities are derived involving particular traditionally used weight functions in particular a version of the agmon inequality and treve type inequalities is established the case of a dirac particle in a potential magnetic field is also considered the methods used are direct and based on quadratic form techniques

quantitative unique continuation for schrodinger operators abstract we investigate the quantitative unique continuation properties of solutions to second order elliptic equations with singular lower order terms the main theorem presents a quantification of the strong unique continuation property for v that is for any non trivial u that solves u v u 0 in some open connected subset of r n we estimate the vanishing order of solutions in terms of the l t norm of v our results apply to all t n 2 and n 3 with these maximal order of vanishing estimates we employ a scaling argument to produce quantitative unique continuation at infinity estimates for global solutions to u v u 0 to handle v l t for every t n 2 we prove a novel l p l q carleman estimate by interpolating a known l p l 2 estimate with a new endpoint carleman estimate this new carleman estimate may also be used to establish improved order of vanishing estimates for equations with a first order term those of the form u w u v u 0

attributive concept descriptions with complements abstract we investigate the consequences of adding unions and complements to attributive concept descriptions employed in terminological knowledge representation languages it is shown that deciding coherence and subsumption of such descriptions are pspace complete problems that can be decided with linear space

foundations of instance level updates in expressive description logics in description logic dl aboxes are used for describing the state of affairs in an application domain we consider the problem of updating aboxes when the state changes assuming that update information is described at an atomic level i e in terms of possibly negated abox assertions that involve only atomic concepts and roles we analyze such basic abox updates in several standard dls in particular addressing questions of expressibility and succinctness can updated aboxes always be expressed in the dl in which the original abox was formulated and if so what is the size of the updated abox it turns out that dls have to include nominals and the constructor of hybrid logic for updated aboxes to be expressible and that this still holds when updated aboxes are approximated moreover the size of updated aboxes is exponential in the role depth of the original abox and the size of the update we also show that this situation improves when updated aboxes are allowed to contain additional auxiliary symbols then dls only need to include nominals for updated aboxes to exist and the size of updated aboxes is polynomial in the size of both the original abox and the update

field consistency and violent stress oscillations in the finite element method the fact that finite element models can give rise to13 violent stress oscillations has been known for some time it is also well known that in many problems there are optimal locations where stresses can be correctly sampled in spite of the presence of these violent stress fluctuations however it is less well known that these oscillations arise in a specific class of problems where there are multiple strain fields arising from one or more field variables and where one or more of these strain fields must be constrained in particular physical13 limits in this paper we show that unless the interpolations for these constrained strain fields are x2018 field consistentx2019 violent oscillations would set in these oscillations represent spurious self equilibrating stress fields generating spurious energy terms that lead to x2018 lockingx2019

linear time and the power of one first order universal quantifier the aim of this paper is to give two new logical characterizations of nlin nondeterministic linear time improving significantly a previous characterization of e grandjean 1994 siam j comput 23 573 597 and f olive 1998 comput complexity 7 54 97 it is known that nlin coincides with the class of problems definable by formulas of the prenex form f1 fk where the fi are unary function symbols and is first order prenex with only one universal quantifier we show that the characterization remains true in the two following cases a unary functions are replaced by a single binary relation whose outdegree is bounded by some fixed constant h b when only ordered structures are considered unary functions are restricted to be bijective

dirac operators schrodinger type operators in cn and huygens principle abstract a detailed study of the holomorphic continuations of primitives of iterates of the dirac operator d in c n is given this analysis is used to study holomorphic continuations of solutions to shrodinger type equations also analytic and continuous extensions of solutions to homogeneous dirac equations are studied and it is shown that for each cell of harmonicity considered here there exist solutions to each iterate of the dirac operator which may not be extended beyond any point of the closure of the cell

carleman inequalities and unique continuation for higher order elliptic differential operators in this thesis we study the weak unique continuation property for higher order elliptic differential operators with real coefficients via carleman inequalities we get several carleman inequalities with sharp gaps for operators in a reasonable class which lead eventually to the weak unique continuation property for differential inequalities with optimal conditions on potentials we also get some carleman inequalities for general operators with simple or double characteristics the gaps here are not as good as in the first case but we may prove the gaps in these inequalities are sharp in general actually we will provide counterexamples to prove such gaps are sharp in carleman inequalities for operators in some subclasses of simple or double characteristics class in particular we prove that there is no carleman inequality with positive gap for the highest order term for any operator whose symbol has double characteristics

machine independent characterizations and complete problems for deterministic linear time this article presents two algebraic characterizations and two related complete problems for the complexity class dlin that was introduced in e grandjean ann math artif intell 16 1996 pp 183 236 dlin is essentially the class of all functions that can be computed in linear time on a random access machine which uses only numbers of linear value during its computations the algebraic characterizations are in terms of recursion schemes that define unary functions one of these schemes defines several functions simultaneously while the other one defines only one function from the algebraic characterizations we derive two complete problems for dlin under new very strict and machine independent affine reductions

the complexity of concept languages abstract a basic feature of terminological knowledge representation systems is to represent knowledge by means of taxonomies here called terminologies and to provide a specialized reasoning engine to do inferences on these structures the taxonomy is built through a representation language called a concept language or description logic which is given a well defined set theoretic semantics the efficiency of reasoning has often been advocated as a primary motivation for the use of such systems the main contributions of the paper are 1 a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages 2 algorithms for these inferences that comply with the worst case complexity of the reasoning task they perform

consistency aspects of out of plane bending torsion and shear in a quadratic curved beam element curved beams in civil engineering applications call for out of plane bending and torsion under the action of out of plane transverse shear loads the design of a quadratic displacement type curved beam element capable of representing shear deformation as in the timoshenko beam theory will call for special attention to be paid to the manner in which the shear strain is to be represented field inconsistent representations of the out of plane transverse shear strain will result in a loss gf efficiency and introduce spuriou oscillations in the bending moment torsional moment and shear force the optimal field consistent assumed strain interpolation for the shear is derived here and it is demonstrated that it has very high accuracy and is free from spurious force and moment oscillations

making fuzzy description logic more general a version of fuzzy description logic based on the basic continuous t norm based fuzzy predicate logic bl is presented problems of satisfiability validity and subsumption of concepts are discussed and reduced to problems of fuzzy propositional logic known to be decidable for any continuous t norm for lukasiewicz t norm some stronger results are obtained

relational queries computable in polynomial time we characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe we also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation this proves that the fixed point query hierarchy suggested by chandra and harel collapses at the first fixed point level it is also a general result showing that in finite model theory one application of fixed point suffices

the kl one family abstract the knowledge representation system kl one has been one of the most influential and imitated knowledge representation systems in the artificial intelligence community begun at bolt beranek and newman in 1978 kl one pioneered the development of taxonomic representations that can automatically classify and assimilate new concepts based on a criterion of terminological subsumption this theme generated considerab interest in both the formal community and a large community of potential users the kl one community has since expanded to include many systems at many institutions and in many different countries this paper introduces the kl one family and discusses some of the main themes explored by kl one and its successors we give an overview of current research describe some of the systems that have been developed and outline some future research directions

two theses of knowledge representation language restrictions taxonomic classification and the utility of representation services abstract levesque and brachman argue that in order to provide timely and correct responses in the most critical applications general purpose knowledge representation systems should restrict their languages by omitting constructs which require nonpolynomial worst case response times for sound and complete classification they also separate terminological and assertional knowledge and restrict classification to purely terminological information we demonstrate that restricting the terminological language and classifier in these ways limits these general purpose facilities so severely that they are no longer generally applicable we argue that logical soundness completeness and worst case complexity are inadequate measures for evaluating the utility of representation services and that this evaluation should employ the broader notions of utility and rationality found in decision theory we suggest that general purpose representation services should provide fully expressive languages classification over relevant contingent information approximate forms of classification involving defaults and rational management of inference tools

a restriction theorem for the heisenberg group since the discovery by e m stein see fefferman 5 that the fourier transform of an lp function on r has a well defined restriction to the unit sphere s which is square integrable on sn 1 if p is close enough to 1 various new restriction theorems have been proved see e g 10 22 27 29 the importance of such theorems in harmonic analysis see e g 5 6 24 28 as well as in the theory of partial differential equations 18 19 25 has become evident it has turned out 29 that the crucial step in proving the stein tomas restriction theorem is the following let a denote the surface measure of s n 1 and let k denote the fourier transform of a then the operator af f k is bounded from lp to lp if p is sufficiently close to 1 9 can be interpreted in terms of the laplacian a on rn let a fox dex be the spectral decomposition of a then formally 9 const f106 1 x dex where 6 denotes dirac s point measure therefore it is natural to study analogues for 9 where a is replaced by a more general positive differential operator l in the case of second order elliptic operators on compact manifolds this has been done by sogge 25

reduced integration and the shear flexible beam element the timoshenko beam element is studied in an investigation of shear locking in the development of c 0 continuous elements using shear flexible or penalty function type formulations a penalty type argument is used to degenerate thick elements to thin elements and the various approximations of the shear related energy terms act as different types of constraints depending on the formulation two types of constraints may emerge which are classified as true or spurious formulations that ensure only true constraints in the extreme penalty limit cases display superior performance in the thick element situation the argument is extended to a shallow curved timoshenko beam and another mechanism inplane locking arises if all energy terms corresponding to the membrane energy are exactly integrated