nonlocal symmetries and formulae for generation of solutions for a class of diffusion convection equations abstract new formulae of nonlocal nonlinear superposition and generation of solutions are proposed for nonlinear diffusion convection equations which are linearizable or are invariant with respect to a generalized hodograph transformation or connected by this transformation we study in what particular ways additional lie symmetries of diffusion convection equations induce nonlocal symmetries of equations obtained from the initial ones by nonlocal transformations the formulae derived are used for the construction of exact solutions

control of unstable steady states by extended time delayed feedback time delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states we present an application of extended time delay autosynchronization introduced by socolar et al phys rev e 50 3245 1994 to an unstable focus this system represents a generic model of an unstable steady state which can be found for instance in hopf bifurcation in addition to the original controller design we investigate effects of control loop latency and a bandpass filter on the domain of control furthermore we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase we present an analysis of the domain of control and support our results by numerical calculations

vessiot structure for manifolds of hyperbolic type darboux integrability and symmetry it is well known that if a scalar second order hyperbolic partial differential equation in two independent variables is darboux integrable then its local cauchy problem may be solved by ordinary differential equations in addition such an equation has infinitely many non trivial conservation laws moreover darboux integrable equations have properties in common with infinite dimensional completely integrable systems in this paper we employ a geometric object intrinsically associated with any hyperbolic partial differential equation its hyperbolic structure to study the darboux integrability of the class e of semilinear second order hyperbolic partial differential equations in one dependent and two independent variables it is shown that the problem of classifying the darboux integrable equations in e contains as a subproblem that of classifying the manifolds of p q hyperbolic type of rank 4 and dimension 2k 3 k 2 p 2 q 2 in turn it is shown that the problem of classifying these manifolds in the two lowest cases p q 2 2 2 3 contains as a subproblem the classification problem for lie groups this generalizes classical results of e vessiot the main result is that if an equation in e is 2 2 or 2 3 darboux integrable on the k jets k 2 then its intrinsic hyperbolic structure admits a lie group of symmetries of dimension 2k 1 or 2k 2 respectively it follows that part of the moduli space for the darboux integrable equations in e is determined by isomorphism classes of lie groups the lie group in question is the group of automorphisms of the characteristic systems of the given equation which leaves invariant the foliation induced by the characteristic or riemann invariants of the equation the tangential characteristic symmetries the isomorphism class of the tangential characteristic symmetries is a contact invariant of the corresponding darboux integrable partial differential equation

symmetries of pde systems and correspondences between jet spaces abstract let m be a manifold a pde system r j m 1 m can be prolonged to another one r t m jimenez et al 2005 10 in analogy with the higher order symmetries symmetries of r will be called higher dimensional symmetries of r for a broad class of pde systems we prove that every infinitesimal or finite symmetry of r comes from another one of r we show that r does not have internal infinitesimal symmetries modulo trivial symmetries this fact allows us in the infinitesimal case to compute the internal symmetries of r as external symmetries of r we also give an algorithmic method to obtain solutions of r invariant by a given internal symmetry

generalized symmetries in mechanics and field theories generalized symmetries are introduced in a geometrical and global formalism such a framework applies naturally to field theories and specializes to mechanics generalized symmetries are characterized in a lagrangian context by means of the transformation rules of the poincare cartan form and the generalized nother theorem is applied to obtain conserved quantities first integrals in mechanics in the particular case of mechanics it is shown how to use generalized symmetries to study the separation of variables of hamilton jacobi equations recovering standard results by means of this new method supersymmetries wess zumino model are considered as an intriguing example in field theory

contact transformations for difference schemes we define a class of transformations of the dependent and independent variables in an ordinary difference scheme the transformations leave the solution set of the system invariant and reduces to a group of contact transformations in the continuous limit we use a simple example to show that the class is not empty and that such contact transformations for discrete systems genuinely exist

tools for template dependencies template dependencies td s are a class of data dependencies that include multivalued and join dependencies and embedded versions of these a collection of techniques examples and results about td s are presented the principal results are 1 finite implication implication over relations with a finite number of tuples is distinct from unrestricted implication for td s 2 there are for td s over three or more attributes infinite chains of increasingly weaker and increasingly stronger full td s 3 however there are weakest nontrivial and strongest full td s over any given set of attributes 4 over two attributes there are only three distinct td s 5 there is no weakest not necessarily full td over any set of three or more attributes 6 there is a finite relation that obeys every strictly partial td but no full td 7 the conjunction of each finite set of full td s is equivalent to a single full td however the conjunction of a finite set of not necessarily full td s is not necessarily e

reasoning about functional and full hierarchical dependencies over partial relations we study the implication problem for the combined class of functional and full hierarchical dependencies in the presence of sql s not null constraints two different notions of implication are addressed one where a dependency is implied by the given set of dependencies plus the underlying schema and one where a dependency is implied by the given set of dependencies alone we establish axiomatizations for both notions of implication and reveal deep relationships between them

nonlocal symmetries and the kaup kupershmidt equation computational and geometric aspects of nonlocal infinitesimal symmetries of nonlinear partial differential equations are considered in particular the relation of nonlocal symmetries with classical generalized and internal symmetries is briefly discussed a nonlocal symmetry for the kaup kupershmidt equation is introduced and studied in some detail some explicit particular solutions are found with its help and a darboux like transformation is also obtained

on nonlocal symmetries of some shallow water equations a recent construction of nonlocal symmetries for the korteweg de vries camassa holm and hunter saxton equations is reviewed and it is pointed out that in the camassa holm and hunter saxton case these symmetries can be considered as nonlocal symmetries of integro differential equations

persistence of chaos in a time delayed feedback controlled duffing system this paper concerns global phase structures of a time delayed feedback controlled two well duffing system the remains of a global stretch and fold structure along an unstable manifold which develops from an unstable fixed point in function space reveals that the global chaotic dynamics is inherited from the original system by the controlled system the remains of the original chaotic dynamics causes a highly complicated domain of attraction for target orbits and a long chaotic transient before convergence

toward the classification of third order integrable evolution equations a non standard way of representing an evolution equation in the form of a system is proposed this representation allows us to investigate all the different classes of third order integrable evolution equations simultaneously using this approach a preliminary classification of these equations is made

deformation of lie derivative and μ symmetries we introduce in the spirit of witten s gauging of exterior differential a deformed lie derivative that allows a geometrical interpretation of and symmetries in complete analogy with standard symmetries the case of variational symmetries both for odes and for pdes is also considered in this approach leading to and conservation laws

membership problem for embedded multivalued dependencies under some restricted conditions abstract it is known that there is no finite set of inference rules that is complete for embedded multivalued dependencies this paper considers the problem called membership problem of deciding whether a given embedded multivalued dependency x v on u or functional dependency x v is implied by a given set d of functional and embedded multivalued dependencies a new inference rule for embedded multivalued dependencies is presented and the following results about membership problems are shown let u be a set of attributes and let w n w 0 u let d f e e 1 e n where 1 i f is a set of functional dependencies y z satisfying y w 0 or z w 0 2 ii e is a set of embedded multivalued dependencies y z on t satisfying at least one of y w 0 t z w 0 and t y z w 0 and 3 iii each e 1 i n is a set of embedded multivalued dependencies on w 1 1 if x v u w 0 then the membership problem is solaable that is it is decidable whether x v on u or x v is implied by d 2 2 if x v u w n then the membership problem cah be solved in o d v x time where d is the size of the description of d 3 3 if x w n and x v u w 0 then the membership problem can be solved in o d 2 w n x n t 1 w 1 w 1 l 1 time

symmetries and first integrals of ordinary difference equations this paper describes a new symmetry based approach to solving a given ordinary difference equation by studying the local structure of the set of solutions we derive a systematic method for determining one parameter lie groups of symmetries in closed form such groups can be used to achieve successive reductions of order if there are enough symmetries the difference equation can be completely solved several examples are used to illustrate the technique for transitive and intransitive symmetry groups it is also shown that every linear second order ordinary difference equation has a lie algebra of symmetry generators that is isomorphic to sl 3 the paper concludes with a systematic method for constructing first integrals directly which can be used even if no symmetries are known

characteristics and the geometry of hyperbolic equations in the plane abstract this paper focuses on the implementation and application of elie cartan s ideas on characteristics for second order non linear hyperbolic equations in the plane the topics include a discussion of both intrinsic and extrinsic contact equivalence a description of the theory of backlund and laplace transformations based on characteristics a geometric approach to the notion of riemann invariants and a study of the various possibilities for their existence resulting in a new simple proof of lie s description of the contact orbit of the wave equation the initial value problem is analyzed from the viewpoint of exterior differential systems and applied to establish a smooth existence theorem with an application to a shock wave problem

an equivalence between relational database dependencies and a fragment of propositional logic it is known that there is an eqmvalence between functional dependencies m a relatmonal database and a certain fragment of proposmonal logic thins eqmvalence is extended to include both functional and multivalued dependencmes thus for each dependency there is a corresponding statement m proposmonal logic it ms then shown that a dependency funcuonal or multivalued is a consequence of a set of dependencies ff and only ff the corresponding proposiuonal statement s a consequence of the corresponding set of proposmonal statements examples are given to show that these techniques are valuable mn provmdmg much shorter proofs of theorems about dependencies than have been obtained by more tradmonal means it is shown that this eqmvalence cannot be extended to include either join dependencies or embedded multmvalued dependencies

a proof procedure for data dependencies definition d une classe de dependances dependances generant l equalite et les triples et generalisation du processus de poursuite pour traiter ces dependances on montre quelques cas pour lesquels il y a une procedure de decision redondance de l egalite pour decider de l implication des dependances generant les triples et presque redondance pour decider de l implication des dependances generant l egalite

superposition formulas for exterior differential systems abstract in this article we solve an inverse problem in the theory of quotients for differential equations we characterize a family of exterior differential systems that can be written as a quotient of a direct sum of two associated systems that are constructed from the original the fact that a system can be written as a quotient can be used to find the general solution to these equations some examples are given to demonstrate the theory

control of unstable steady states by time delayed feedback methods we show that time delayed feedback methods which have successfully been used to control unstable periodic orbits provide a tool to stabilize unstable steady states we present an analytical investigation of the feedback scheme using the lambert function and discuss effects of both a low pass filter included in the control loop and nonzero latency times associated with the generation and injection of the feedback signal

sort sets in the relational model the notion of sort set is introduced here to formalize the fact that certain database relations can be sorted so that two or more columns are simultaneously listed in order this notion is shown to be applicable in several ways to enhance the efficiency of an implemented database a characterization of when order dependency implies the existence of sort sets in a database is presented along with several corollaries concerning complexity armstrong relations and cliques of certain graphs sort set dependencies are then introduced a finite sound and complete set of inference rules for sort set dependencies is presented as well as a proof that there is no such set for functional and sort set dependencies taken together deciding logical implication for sort set dependencies is proved to be polynomial but if functional dependencies are included the problem is co np complete each set of sort set and functional dependencies is shown to have an armstrong relation a natural generalization of armstrong relation here called separator is given and then used to study the relationship between order and sort set dependencies

internal external and generalized symmetries backlund s theorem which characterizes contact transformations is generalized to give an analogous characterization of internal symmetries of systems of differential equations for a wide class of systems of differential equations we prove that every internal symmetry comes from a first order generalized symmetry and conversely every first order generalized symmetry satisfying certain explicit contact conditions determines an internal symmetry we analyze the contact conditions in detail deducing powerful necessary conditions for a system of differential equations that admit genuine internal symmetries i e ones which do not come from classical external symmetries applications include a direct proof that both the internal symmetry group and the first order generalized symmetries of a remarkable differential equation due to hilbert and cartan are the noncompact real form of the exceptional simple lie group g2

rank 2 distributions of monge equations symmetries equivalences extensions abstract by developing the tanaka theory for rank 2 distributions we completely classify classical monge equations having maximal finite dimensional symmetry algebras with fixed albeit arbitrary orders investigation of the corresponding tanaka algebras leads to a new lie backlund theorem we prove that all flat monge equations are successive integrable extensions of the hilbert cartan equation many new examples are provided

functional dependencies and constraints on null values in database relations database relations with incomplete information are considered the no information interpretation of null values is adopted due to its characteristics of generality and naturalness coherently with the framework and its motivation two meaningful classes of integrity constraints are studied a functional dependencies which have been widely investigated in the classical relational theory and b constraints on null values which control the presence of nulls in the relations specifically three types of constraints on null values are taken into account nullfree subschemes existence constraints disjunctive existence constraints and the interaction of each of them with functional dependencies is studied in each of the three cases the inference problem is solved the complexity of the algorithms for its solution analyzed and the existence of a complete axiomatization discussed

on the undecidability of implications between embedded multivalued database dependencies the implication and finite implication problems for embedded multivalued database dependencies are both shown to be algorithmically undecidable the proof is by an interpretation of semigroup word problems via systems of permuting equivalence relations into database dependencies in contrast it is shown that for each fixed premise h one has a decision procedure for implications h f

inferences for numerical dependencies abstract we introduce and motivate the study of numerical dependencies which are a generalization of functional dependencies we prove that there does not exist a finite set of sound and complete inference rules for numerical dependencies in contrast to the case of functional dependencies we also prove that nontrivial numerical dependencies which are not functional dependencies cannot be expressed by horn formulas in first order logic and show some applications of numerical dependencies

axioms and algorithms for inferences involving probabilistic independence abstract this paper offers an axiomatic characterization of the probabilistic relation x is independent of y written x y where x and y are two disjoint sets of variables four axioms for x y are presented and shown to be complete based on these axioms a polynomial membership algorithm is developed to decide whether any given independence statement x y logically follows from a set of such statements i e whether x y holds in every probability distribution that satisfies the complexity of the algorithm is o k2 n where is the number of given statements n is the number of variables in x y and k is the number of variables in x y

local and nonlocal solvable structures in the reduction of odes solvable structures likewise solvable algebras of local symmetries can be used to integrate scalar ordinary differential equations odes by quadratures solvable structures however are particularly suitable for the integration of odes with a lack of local symmetries in fact under regularity assumptions any given ode always admits solvable structures even though finding them in general could be a very difficult task in practice a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra in this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order i e classical and higher in particular we introduce the notion of nonlocal solvable structure

stability domains for time delay feedback control with latency we generalize a known analytical method for determining the stability of periodic orbits controlled by time delay feedback methods when latencies associated with the generation and injection of the feedback signal cannot be ignored we discuss the case of extended time delay autosynchronization and show that nontrivial qualitative features of the domain of control observed in experiments can be explained by taking into account the effects of both the unstable eigenmode and a single stable eigenmode in the floquet theory