properties of two dimensional maximum entropy power spectrum estimates in this paper we present the results of a number of experiments that have been performed to study the properties of two dimensional maximum entropy spectral estimates the results presented include studies on the resolution differences for real and complex data resolution properties of the spectral estimates and the determination of the relative power of the sinusoids from the spectral estimates the results also include the effects of signal to noise ratio size and shape of the known autocorrelation region and data length and initial phase of a sinusoid on the spectral estimates in most cases studied the properties of two dimensional maximum entropy spectral estimates can be viewed as simple extensions of their one dimensional counterparts

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

group invariant classification of separable hamiltonian systems in the euclidean plane and the o 4 symmetric yang mills theories of yatsun we present a new and effective method of determining separable coordinate systems for natural hamiltonians with two degrees of freedom in flat riemannian space the method is based on intrinsic properties of the associated killing tensors and their invariants under the group of rigid motions e 2 applications to the hamiltonian systems derived by the late v a yatsun from o 4 symmetric yang mills theories are presented in addition an equivalence between separability of two dimensional hamiltonian systems and the existence of pfaffian quasi bi hamiltonian representations is specified

two dimensional spectral estimation in this paper effective methods for generating two dimensional quarter plane causal autoregressive ar and autoregressive moving average arma spectral estimation models are developed these procedures are found to provide super resolution capabilities when compared to other more classical methods such as the fourier transform the arma method involves manipulation of the model equation sum min k 0 max p 1 sum min k 0 max p 2 a km x n 1 k n 2 m sum min k 0 max q 1 sum min k 0 max q 2 b km epsilon n 1 k n 2 m and utilizes the given finite set of observations x n 1 n 2 for 1 leq n 1 leq n 1 1 leq n 2 leq n 2 in the above relationship the random excitation epsilon n 1 n 2 is taken to be white this arma model s autoregressive a km coefficients are selected to minimize a weighted least squares criterion composed of error elements while the moving average b km coefficients are obtained using an alternative approach the spectral estimation performance of the ar and arma methods will be empirically demonstrated by considering the problem of resolving two sinusoids embedded in noise

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

the geometrical framework for yang mills theories we construct a new geometrical framework for yang mills lagrangian field theories as an appropriate quotient space of the standard first jet bundle and investigate the geometrical properties of the resulting mathematical setting we deduce the field equations from a variational problem formulated through a regular poincare cartan form thus ensuring the kinematical admissibility of critical sections we state a generalized nother theorem and explicitly consider the case of the free yang mills field

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

second order sturm liouville problems with asymmetric superlinear nonlinearities abstract we consider the nonlinear sturm liouville problem p x u x q x u x f x u x h x in 0 c 00 u 0 c 01 u 0 0 c 10 u c 11 u 0 where p c 1 0 q c 0 0 with p x 0 for all x 0 ci02 ci12 0 i 0 1 h l2 0 we suppose that f 0 r r is continuous and there exist increasing functions l u 0 r and positive constants a b such that lim t l t and a l f x a u 0 f x a b 0 for all x 0 thus the nonlinearity is superlinear as u x but linearly bounded as u x existence and non existence results are obtained for the above problem similar results have been obtained before for problems in which f is linearly bounded as and these results have been expressed in terms of half eigenvalues of the problem the results obtained here for the superlinear case are expressed in terms of certain asymptotes of these half eigenvalues

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

semilinear elliptic problems with asymmetric nonlinearities abstract in this paper we are concerned on the semilinear elliptic problem u u q 2 u a u b u p 1 in u 0 on where r n is a bounded domain with regular boundary 1 q 2 p 2 if a is between two eigenvalues we get the existence of three nontrivial solutions for the problem above

on a robin problem with indefinite weight and asymmetric reaction superlinear at abstract the existence of at least three nontrivial smooth solutions to a semilinear robin problem with indefinite potential and asymmetric nonlinearity super linear at is established both crossing and resonance are allowed proofs exploit variational methods truncation techniques and morse theory

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

covariant differential identities and conservation laws in metric torsion theories of gravitation i general consideration arbitrary diffeomorphically invariant metric torsion theories of gravity are considered it is assumed that lagrangians of such theories contain derivatives of field variables tensor densities of arbitrary ranks and weights up to a second order only the generalized klein noether methods for constructing manifestly covariant identities and conserved quantities are developed manifestly covariant expressions are constructed without including auxiliary structures like a background metric in the riemann cartan space the following manifestly generally covariant results are presented a the complete generalized system of differential identities the klein noether identities is obtained b the generalized currents of three types depending on an arbitrary vector field displacements are constructed they are the canonical noether current symmetrized belinfante current and identically conserved hilbert bergmann current in particular it is stated that the symmetrized belinfante current does not depend

successively iterative method of nonlinear neumann boundary value problems abstract two successively iterative sequences are constructed for computing solutions of the nonlinear neumann boundary value problems with time singularity the sequences start off with some constants main tool is the fixed point theorem of increasing operator on the order interval by considering convergence of the sequences we prove the existence of nontrivial sign changing solutions

2 d spectral estimation combining parametric estimation of background and maximum entropy estimation a new algorithm for the estimation of the two dimensional 2 d power spectrum from finite correlation data is proposed this method is based on the combination of parametric estimation of a background power spectral component and maximum entropy estimation for point like spectral components for the discrimination of the background power spectrum we adopt a new measure which reflects the information of the point like spectral components a practical iterative algorithm is presented and the effectiveness of the method is demonstrated through several numerical examples

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

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

noether s second theorem for brst symmetries we present noether s second theorem for graded lagrangian systems of even and odd variables on an arbitrary body manifold x in a general case of brst symmetries depending on derivatives of dynamic variables and ghosts of any finite order as a preliminary step noether s second theorem for lagrangian systems on fiber bundles y x possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved

lagrangian supersymmetries depending on derivatives global analysis and cohomology lagrangian contact supersymmetries depending on derivatives of arbitrary order are treated in a very general setting the cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed in particular the first variational formula and conservation laws for lagrangian systems on graded manifolds using contact supersymmetries are obtained

variable separation for natural hamiltonians with scalar and vector potentials on riemannian manifolds the additive variable separation in the hamilton jacobi equation is studied for a natural hamiltonian with scalar and vector potentials on a riemannian manifold with positive definite metric the separation of this hamiltonian is related to the separation of a suitable geodesic hamiltonian over an extended riemannian manifold thus the geometrical theory of the geodesic separation is applied and the geometrical characterization of the separation is given in terms of killing webs killing tensors and killing vectors the results are applicable to the case of a nondegenarate separation on a manifold with indefinite metric where no null essential separable coordinates occur

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